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doi:10.1016/j.homp.2007.03.007
Copyright © 2007 Elsevier Ltd All rights reserved. Long term structural effects in water: autothixotropy of water and its hysteresis

Bohumil Vybíral^{, a,} and Pavel Voráček^a
aDepartment of Physics, Faculty of Pedagogy, University of Hradec Králové, Rokitanského 62, CZ-500 03 Hradec Králové, Czech Republic
Received 14 March 2007; accepted 27 March 2007. Available online 31 July 2007.

We discovered a previously unknown phenomenon in liquid water, which develops over time when water is left to stand undisturbed, and which made precise gravimetric measurement impossible. We term this property autothixotropy (weak gel-like behaviour developing spontaneously over time) and propose a possible explanation.

The results of quantitative measurements, performed by two different methods, are presented. We also report the newly discovered phenomenon of autothixotropy-hysteresis and describe the dependence of autothixotropy on the degree of molecular translative freedom. A very important conclusion is that the presence of very low concentration of salt ions, these phenomena do not occur in deionized water. Salt ions may be the determinative condition for the occurrence of the phenomena.

Keywords: water; autothixotropy; core-ions; deionization; hysteresis

Article Outline

‘Autothixotropy’ of water

Qualitative laboratory observations

Proposed explanation

Autothixotropy and molecular translative freedom

Salt ions

Quantitative experiments on autothixotropy and its hysteresis

Static torsion method

Principle

Experimental device

Quantitative experimental results

Measurements of the critical angle (φ_u)_crit.

Reproducibility

Hysteresis

Additional measurements

Experiments with deionized water

Method of torsion oscillation

Principle

Quantitative experimental results

Conclusions

References

‘Autothixotropy’ of water

Qualitative laboratory observations

From 1978 to 1986 we performed a series of measurements^{[1] and [2]} to verify the gravitational law in fluids as deduced by Horák.³ Originally, in 1978 we observed a peculiar phenomenon in the measurements which compelled us to use another method. A series of experiments focusing on this phenomenon were conducted. In the Department of Physics in University of Hradec Králové, an experimental apparatus was constructed (Figure 1) to observe the phenomenon.⁴

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Figure 1. Experimental setup for the static method of measurement.

After objects immersed in the water have been at rest for one or more days, seven qualitatively different phenomena are observed, using this method:

(1) When the hanger is rotated by a certain angle, the plate immersed in the water remains in practically the same position, in spite of the twisting tension arising in the thin filament. When a certain critical angle is reached, the plate will rotate, relatively quickly, to a new neutral position determined by the hanger, to the position where the filament is relaxed (ie with no torsion). If the rotation of the hanger is interrupted before the critical angle is reached, a ‘creep’ toward a new neutral position is observed over some days or weeks. When a smooth-surfaced cylinder, capable of rotating around its own axis, is used instead of the plate, these phenomena are not observed.

(2) Another, weaker phenomenon, is also observed: an immediate rotation of the plate in the direction of the rotation of the hanger; nevertheless, the angle of the immediate rotation is one or two orders of magnitude less than the angle in phenomenon (1).

(3) The critical angle of rotation in phenomenon (1) is dependent on the period of time the water has been at rest. This angle increases with time, starting from virtually zero. (The critical angle can reach values of several tens of degrees)

(4) If the plate is only partially immersed, the critical angle is significantly greater than when it is immersed completely.

(5) In the case of partial immersion, the phenomenon analogous to (2) is much more prominent. Phenomena (4) and (5) are time-dependent as described in (3) despite the time-invariance of the surface tension which we also tested.

(6) If the water is stirred after having been at rest for several days, then, when again at rest, the critical angle increases from zero more quickly than when new ‘fresh’ water is used.

(7) The critical angle is significantly increased and the phenomenon appears earlier if the (distilled) water is boiled (thus substantially deaerated) before the experiment is started.

Our first attempts to carry out quantitative experiments with any acceptable precision were not successful. This was due to a too large dispersion of the measured values; much more sophisticated laboratory equipment than we could acquire, as well as stricter measurement conditions than those we could guarantee, were necessary. In spite of many problems, such experiments have since been performed,⁵ and showed that the phenomena did not appear in deionized water. In accordance with the generally accepted terminology, we named this complex of phenomena autothixotropy of water.

Proposed explanation

In terms of explanation, a hypothesis based on ‘ephemeral polymerisation’ of water seems plausible. The existence of such a weak polymerisation was suspected decades ago, both defended and denied by experts. If ephemeral polymerisation of water is the cause of the observed phenomena, it suggests that water molecules are establishing chains or a network; first as minute complexes and thereafter combining successively with one another. The structure then becomes increasingly dense while oscillating at a certain amplitude on a scale of molecules. Such a structure will be relatively fragile, susceptible to differences in the concentration of materials dissolved in water, at different points inside the vessel. Brownian motion can be observed in the case of a conglomerate of molecules having a non-polar character, owing to collisions with molecules of water oscillating in the established network. Weak stirring of ‘old’ water seems to leave parts of the network intact, making the subsequent ‘dipole polymerisation’ quicker than it would be in the ‘fresh’ (ie well stirred) water. Further, the structure has some elasticity. If the water is boiled, no dissolved air (gases) disturb either on the developing process or integrity of the structures; consequently, the phenomenon appears earlier and is more pronounced.

One can expect that the described water structure can be important in biophysics for description and influence on cell characteristics (see eg Pollack⁶). Our observations are consistent with the recently published results of Wernet et al.⁷

Autothixotropy and molecular translative freedom

The autothixotropy of water depends, among other things, on the degree of freedom of the translative motion of its molecules. The freedom is limited close to the boundary between the water and some other environment, eg a solid body or the atmosphere over the surface of the water. The freedom of the molecular motion is then limited relatively very deep into the body of the water, perhaps on the scale of several hundred molecular layers or more. The limited degree of freedom, depending on the number of free space-dimensions being less than three, appears as follows:

(1) When the free motion is limited to two space-dimensions ie more or less to a plane, one can find its relevant manifestation in phenomena (4) and (5) described above.

(2) If a thin capillary tube were used, the free molecular transitive motion would be limited in practice to just one dimension. This explains the phenomenon of polywater, observed decades ago, and claimed to be a sensational discovery, but which soon proved to be false.

(3) When the transitive freedom is limited in all possible directions, ie in all three space-dimensions, the manifestation of the autothixotropy must logically become very prominent and influential. Such a situation occurs in small cellular spaces and possibly significantly influences, or even determines, the rigidity of the cytoskeleton. It is presumed, however, that the cells aresufficiently static in relevance to the autothixotropy.

Salt ions

Currently two diametrically sets different of results supported by serious observations exist concerning the duration of structures in liquid water. According to one⁸, molecular clusters in water have a duration of less than one hundred femtoseconds. According to ours, clusters grow to webs on a time scale of days. Since these webs do not arise in deionized water, we believe the purity of the water to be a decisive factor. The distilled water we used was not perfectly pure and could have been significantly contaminated by salt ions, even if only to a very minute degree. From a comparison of experiments with distilled water and deionized distilled water, it is possible to deduce that cores of macroscopic clusters of water molecules are salt ions contained in water.

Moral: If two different observations seem to be mutually incompatible within the frame of an established theory, the most probable explanation is not that one of the observations is wrong, but that the theory is wrong or at least incomplete, and that the observations merely discovered that it was not self-consisrent.

Quantitative experiments on autothixotropy and its hysteresis

Two different, independent strategies were used for quantitative experimental research on the autothixotropy of the water:

1. The static method of torsion.

2. Two dynamic methods: the method of torsion oscillations and the method of small balls falling in water under condition of laminar flow.

The results have been published by Vybíral,^{[5] and [9]} and are summarised below. Static torsion method

Principle

A stainless steel plate is suspended on an elastic filament of torsional rigidity k_τ, and immersed in the studied water (Figure 1). The water is in a steady state and the ideal fluid model is assumed. Thus, if we twist the upper end of the filament by angle φ_u, we expect that the plate will follow the rotation, so that φ_d=φ_u, φ_d being angle of rotation of the plate. According to our experiments, this equality was not achieved. In the static experiment, a series of increasing values of angle φ_d is observed, following a very slow, ‘step by step’, change of angle φ_u. One can specify the moment of force M_w, arising when the plate influences the water: M_w=k_τ (φ_u–φ_d). If angle φ_u reaches a critical value (φ_u)_crit., the rotation of the plate (ie ) becomes quick.

Experimental device

The equipment that was used for the experiment is illustrated in Figure 1. The phosphor–bronze filament had a length L=465 mm and a cross-section of 0.20×0.025 mm². The torsional rigidity of the filament was determined experimentally from torsion oscillations of the plate hung in non-perturbed air:⁵ k_τ=(1.01±0.02)×10⁻⁷ Nm/rad. After reduction to the unit length (1 m), we get k_τ1=(4.69±0.07)×10⁻⁸ Nm²/rad. The results shown here are related to an experiment with a flat stainless steel plate of width b=38.5 mm, height h=60.5 mm, thickness 0.50 mm and mass 8.50 g. Angles φ_u and φ_d were read with an accuracy of 0.5°. Water used for the experiment was distilled and then boiled for 3 min before the experiment began. In the course of the experiment, the temperature of the water was kept between 24 and 25 °C. Water with volume of approx. 350 ml was in a glass vessel with an inner diameter of 80 mm and a height of 110 mm. The vessel was closed with a paper lid with a small opening for the filament. The lid was removed only briefly to read the scale.

Quantitative experimental results

Measurements of the critical angle (φ_u)_crit.

The critical angle is the angle φ_u at which, when reached by the hanger the plate began to rotate (relatively quickly, in a time scale of tens of seconds) in the same direction. Some prominent results of repeated measurements⁵ are:

1. The plate immersed with 65% of its surface in water, which had been standing for seven days: (φ_u)_crit.=(398±3)°.

2. With the water boiled for a short time, but otherwise the same configuration of system (immersion 65%). After cooling (24 °C): (φ_u)_crit. ≈ 30°, after two days: (φ_u)_crit.≈115°.

3. With the water boiled, the plate entirely immersed (the upper edge 10 mm below water level), the critical angle measured on the second and third day was (φ_u)_crit.=(356±3)°.

4. The plate immersed only 50%: (φ_u)_crit.=(343±8)°.

5. The influence of plate immersion on the critical angle (φ_u)_crit. is small: for plate immersion in the range 100–23%, the difference is Δ(φ_u)_crit.≈ 14%.

6. The period of a water-standing influences the magnitude of the critical angle. For example, with immersion of 85% of the surface of the plate and a long period of standing (17 days), we observed (φ_u)_crit.=1800°. As a consequence of the ‘rupture’ which followed, the plate rotated through the angular interval Δφ_d=1430°. With total immersion such a great critical angle was never reached.

7. After stabilization of the position of the plate (ie, Δφ_d=1430°), a slow change of angle φ_d (‘creep’) was observed: 4° in 5 min and, another 32°, in the subsequent 70 hours.

Reproducibility

The results for a given configuration of the measurement system have good reproducibility. For example, if the water was boiled and stood for 24 h, with the plate totally immersed in water for 14 days, six measurements of angle φ_d were performed. For the same set of angles φ_u : 60°, 120°, and 180°, the measured respective average angles φ_d were: (19.6±0.7)°, (34.4±0.6)°, (52.3±1.3)°. When (φ_u)_crit.=(239±2)° was reached, the plate quickly rotated (tens of seconds) and reached a new equilibrium position (φ_d)₀=(198±2)°.

Hysteresis

Hysteresis means that a system does not instantly follow forces applied to it, but reacts slowly or does not return completely to its original state: its state depends on its history. Measurements for a cyclical change of angle φ_u were carried out. The results of three measurements are shown in Figure 2 and Figure 3. Figure 2 shows the results for the plate entirely immersed in the water which was thoroughly stirred 17 h before. While changing angle φ_u from the starting equilibrium position φ_u=φ_d=0°, the change of angle φ_d did not follow an ideal straight line φ_u=φ_d, but the curve O–A. At point A the critical value (φ_u)_crit.1 was reached and then the plate rotated to a new equilibrium position—point B. With decreasing angle φ_u, angle φ_d changed according to curve B–C, until it reached the second critical value, denoted (φ_u)_crit.2, then the plate rotated to another equilibrium position—point D. When angle φ_u was decreased again, the position of the plate went through the origin O to the third critical position—point E, with the third critical value, denoted (φ_u)_crit.3. Another equilibrium position corresponded to point F and the fourth critical position corresponded to point G, where (φ_u)_crit.4(φ_u)_crit.2. As the plate rotated further, a fourth equilibrium position point H, approximately identical with point D, was reached. From there, with decreasing angle φ_u, the position of the plate followed the previous section H–O and for φ_u=0° it returned to the original equilibrium position φ_d0°.

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Figure 2. Results of the experiment with the completely immersed plate: loop of the changes of angle φ_d=f (φ_u).

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Figure 3. Results of two experiments (loops of the changes of angle φ_d=f (φ_u)): with the completely immersed plate (loop a) and with half-immersed plate (loop b).

In Figure 3, the results of two other experiments with water standing for one week are presented: Loop a refers to experiment with the plate totally immersed, loop b to the experiment with the plate half-immersed; the effect is more pronounced for the half-immersed plate. The loops in Figure 3 are simpler than those in Figure 2 and the respective values (φ_u)_crit. are lower. This can be explained on the microscopic level: The plate probably deformed clusters of water molecules of various dimensions and rigidity.

These experiments suggest that the mechanical properties of clusters of water molecules display hysteresis. The hysteresis is however limited; in our experiment, for instance it does not appear in situations when the critical angle is not reached. For example, if a position of the plate corresponds to a point in the section O–A of the graph in Figure 2, before point A is reached, and if we begin to decrease angle φ_u, the character of the change of angle φ_d will follow the same curve O–A backwards. In these situations, the cluster seems to behave like an ideal elastic body. The dynamics of the phenomenon are similar to those of synovial fluid lubricating the joints of section, which is determined by the thixotropy of the hyaluronic acid present.

Additional measurements

During the experiment, some additional measurements were made to eliminate possible influences on the observed phenomena:

1. The pH of the sample of water was determined by potentiometric measurement. It did not change significantly over a long period; in the range of temperature from 24 to 25°C the pH moved in the range 7.1–6.9.

2. The electrical conductivity of entirely fresh water was 5.6 μS/cm, and after five weeks it increased to 30.5 μS/cm at 25 °C. A dependence of the observed water properties on this change was not noted.

3. Surface tension: Using a Du-Noüyho apparatus (with an accuracy of 1%), no measurable change of the surface tension was found.

Experiments with deionized water

In the second phase of these experiments, water, which was first distilled and then deionized, was used. These experiments showed that in deionized water the phenomenon of autothixotropy and its hysteresis was absent. The same equipment (Figure 1) was used for the experiment and the plate was immersed both to one half and entirely as well. The water stood for 10 days before the measurement. The rotation angle φ_d of the plate, which passed through the interval φ_d(0°, 360°, 0°), was equal to angle of torsion φ_u of the upper end of the filament, with accuracy of 1.5°, as evaluated from the repeated measurements. Neither the existence of critical angles (φ_u)_crit., nor the phenomenon of hysteresis, were found. From this experiment, we arrived at the important conclusion that the autothixotropy of water, characterized by a non-zero critical angle and hysteresis is caused by the presence of ions in the water.⁵

Method of torsion oscillation

Principle

A plate hangs on a filament (with torsional rigidity k_τ) with their axes of symmetry aligned. The moment of inertia of the plate, relative to its axis, is I. We immerse the plate in the water (Figure 1) and measured its torsion oscillations in two situations:⁵

• In ‘fresh’ water (ie with negligible autothixotropy), under assumption of a viscous damping of the water, the period of free damped oscillations is T₁.

• In ‘stood’ water (ie with autothixotropy and viscous damping of the water), we suppose that it is necessary to add, to the quantities related to the elasticity of the filament with torsional rigidity k_τ, the elasticity parameter of putative clusters of water molecules in the considered situation, represented by torsional rigidity k_w. Then period of free damped oscillations is T₂.

By measuring the periods of oscillation T₁ and T₂, we can determine the moment of inertia I (eg, from the plate dimensions and its mass), and calculate the equivalent torsional rigidity:

Quantitative experimental results

For the measurement, an aluminium plate with a thickness of 2.95 mm, width b=(47.59±0.03) mm, height h=(50.59±0.02) mm and mass 18.70 g, was used. Its moment of inertia was calculated from its dimensions and mass: I=(7.518±0.001)×10⁻⁶ kg m². The plate was hung along its longitudinal axis of symmetry on a phosphor–bronze filament of cross-section of 0.025×0.2 mm² and length of L=569 mm. The filament had a torsional rigidity k_τ=(8.25±0.12)×10⁻⁸ Nm/rad.⁵

The plate was immersed in distilled and boiled water so that the upper edge of the plate was 14 mm above the level of the water surface. The water with a volume of approximately 400 ml was in a glass vessel with an inner diameter 80 mm and height 110 mm; the experiment was carried out at a temperature of 23°C. The period of the damped torsion oscillations was measured three times.

First in fresh water. The period of oscillation was T₁=(101.7±1.2) s. Then the system was left at rest for seven days. Then plate was carefully rotated from this equilibrium position by 45°, and at that position it stayed. Then, the plate was given a torsional pulse, initiating damped torsion oscillations. The period of oscillation was measured ten times; resulting in T₂=(5.34±0.06) s. The torsional rigidity of this system with autothixotropy was determined to be k_w=(1.04±0.03)×10⁻⁵ Nm/rad. The degree of the level of autothixotropy of the system, is ascertainable by means of the measurement of critical angle (φ_u)_crit.. For our system this was ≈340°.

Conclusions

On this basis, it is possible to formulate some additional hypotheses about clusters of water molecules:

1. Clusters of water molecules may be of macroscopic dimensions, on scale of centimeters.

2. Clusters of water molecules may be destroyed by boiling or intense stirring or shaking.

3. Clusters of water molecules have certain mechanical properties analogous to the properties of solid substances, such as elasticity/rigidity and strength, but these properties are much smaller than for solid substances with a relative magnitude of 10⁻⁶ or less.

4. Mechanical properties of clusters of water molecules show a certain hysteresis.

5. Water slightly deviates from an ideal Newtonian viscous fluid, because autothixotropy also appears in the form of internal static friction, although very weak.

6. From comparison of experiments with natural distilled water and deionizated distilled water it is possible to deduce that the cause of macroscopic clusters of water molecules are the ions contained in water.

References

1 B. Vybíral, Experimental verification of gravitational interaction of bodies immersed in fluids, Astrophys Space Sci 138 (1987), pp. 87–98. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

2 Vybíral B. K experimentálnímu ověření gravitační interakce těles ponořených do tekutin. In: Sborník Pedagogické fakulty, 54 (Fyzika). Praha: SPN, 1989, pp 307–318 (in Czech).

3 Z. Horák, Gravitational interaction of bodies immersed in fluids, Astrophys Space Sci 100 (1984), pp. 1–11. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

4 Vybíral B, Voráček P. ‘Autothixotropy’ of Water—an Unknown Physical Phenomenon. Available via arxiv.org/abs/physics/0307046; 2003.

5 Vybíral B. The comprehensive experimental research on the autothixotropy of water. In: Pollack G, et al (eds). Water and the Cell. Dordrecht: Springer, 2006, Chap 15, pp 299–314.

6 G. Pollack, Cells, Gels and the Engines of Life, Exner and Sons Publisher, Seattle, WA (2001).

7 P.h. Wernet et al., The structure of the first coordination shell in liquid water, Science 304 (2004), pp. 995–999. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

8 M.L. Cowan et al., Ultrafast memory loss and energy redistribution in the hydrogen bond network of liquid H₂O, Nature 434 (2005), pp. 199–200.

9 Vybíral B. Experimental research of the autothixotropy of water. In: Proceedings of the Conference New Trends in Physics—NTF 2004, Brno: University of Technology, Czech Republic, pp 131–135.

Correspondence: Bohumil Vybíral, Department of Physics, Pedagogical Faculty, University of Hradec Králové, Rokitanského 62, CZ-500 03 Hradec Králové, Czech Republic.

Homeopathy
Volume 96, Issue 3, July 2007, Pages 183-188
The Memory of Water

This is part of the Homeopathy journal club project described here:

www.badscience.net/?p=490

doi:10.1016/j.homp.2007.03.005
Copyright © 2007 Elsevier Ltd All rights reserved. The silica hypothesis for homeopathy: physical chemistry

David J. Anick^{1, ,} and John A. Ives^2
1Harvard Medical School, McLean Hospital, Belmont, MA, USA
²Samueli Institute for Information Biology, 1700 Diagonal Road, Alexandria, VA, USA
Received 22 February 2007; accepted 27 July 2007. Available online 31 July 2007.

The ‘silica hypothesis’ is one of several frameworks that have been put forward to explain how homeopathic remedies, which often are diluted beyond the point where any of the original substance remains, might still be clinically effective. We describe here what the silica hypothesis says. From a physical chemistry viewpoint, we explore three challenges that the hypothesis would have to meet in order to explain homeopathy: thermodynamic stability of a large number of distinct structures, pattern initiation at low potencies, and pattern maintenance or gradual evolution at higher potencies. We juxtapose current knowledge about silicates with some of the conventional wisdom about homeopathic remedies, to see how well the latter might be a consequence of the former. We explore variants of the hypothesis including some speculations about mechanisms. We outline laboratory experiments that could help to decide it.

Keywords: homeopathy; mechanism; silica; silicate; physical chemistry

Article Outline

Introduction

Brief overview of silicates

Generation and perpetuation of remedy-specific silicates

Experiments to test the silica hypothesis

Conclusion

References

Introduction

Homeopathy has been called the third-most commonly used system of healing on the planet, and for that reason alone it deserves serious attention from the modern scientific community. As the reader of this article undoubtedly knows, many conventional scientists and doctors dismiss homeopathy as physically impossible because of the high dilutions that are commonly used. If a mother tincture (MT) contains a 1 M solution of starting substance (typically the concentration will be considerably smaller, eg sodium chloride in sea water is only 0.5 M), then a 20 ml bottle of its 12c potency has only a 1% chance of containing even a single solute molecule from that MT. For higher potencies like 30c, figures like 10⁻⁶⁰ have been given but it is meaningless to call the concentration anything other than ‘zero’. Within conventional chemistry, a solution at concentration zero must be identical with the unprepared solvent (water or ethanol-water). The challenge is to explain or justify how one sample of concentration zero can be different from another sample of concentration zero.

The challenge is greater than scientists working on the physics or chemistry of homeopathy usually admit. There are three physical chemistry puzzles that will have to be solved before homeopathy can be considered to be ‘explained’, and this does not even include explaining how remedies influence biological systems. Generally researchers have focused on finding some measurement or test according to which remedies and controls can be told apart. As significant as a consistent finding of this kind would be, it would not be enough for homeopathy. According to homeopathic theory, the ‘vibration’ of each living thing is different, and remedies of different potencies made from the same MT are subtly different too. Helios pharmacy [www.helios.co.uk] sells 2320 different remedies, each at three to eight (or more) different potencies. It would not be enough to demonstrate that liquid water can exist in a few distinct thermodynamically stable (or meta-stable) forms. Theoretically there should be a nearly infinite variety of ‘waters,’ each one constant over a time scale of at least several minutes. In one minute the H-bond network of liquid water will undergo literally trillions of rearrangements, yet something about the sample has to be recognizably the same at the end as at the start of that minute, and yet different from ‘other remedy’ and from ‘control.’ This is the first challenge: to describe thermodynamically stable parameter(s) that not only show how remedies might differ from controls, but also how thousands of remedies can all be different from each other.

Consider two vials of pure water (in practice doubly deionized distilled water is used) each containing 198 drops (about 4 ml). To the first, two drops of pure water (from the same source) are added, making 200 drops. To the second, two drops of Sepia 29c are added. Each vial is covered and succussed. At the end, one is Sepia 30c, and the other is succussed water. To a homeopath, Sepia 30c and shaken water are as different as night and day. From a scientist’s perspective, the only difference between these samples is the 2-drop ‘seed’ added just before succussion. Other than the seed representing 1% by volume, 99% of the two samples (before succussion) were identical. If Sepia 30c is different from succussed water, then something in that seed causes the whole sample, once succussed, to come out different from what we get if the seed is not first added. And the seed is Sepia 29c, which means it too contains nothing of the starting material, and its only difference from pure water is whatever arose from succussing a seed of Sepia 28c placed in 99 parts pure water.

So this is the second challenge: whatever pattern or information is in a remedy, it must somehow ‘survive’ being mixed into 99 parts of water, and then ‘convert’ the whole sample to that same pattern (or a slightly different pattern) when the whole is succussed. The 198 drops of unprocessed fresh water must never ‘convert’ the two added drops to its ‘ordinary’ pattern.

Finally let us describe the third challenge: generation of the pattern in the first place. The first few dilutions and succussions of the MT may consist principally of diluting and mixing, since these samples would still differ from controls (and each other) by virtue of their solutes. At some stage, however, the solute must act as a seed that initiates a ‘pattern’ in the diluent to which it has been added. Perhaps this starts just as the last molecules are disappearing, around 11c, or perhaps it starts much earlier in the sequence. If it starts earlier, then some low potencies will contain both low-concentration solute and ‘patterned solvent’. It is conceivable that low-concentration solute and ‘incipient pattern’ work together to establish the ‘mature pattern’ during succussion.

Hahnemann made his remedies using glass vials, and the practice of always using glass has continued. Small amounts of silicon dioxide and ions dissolve from the glass walls into aqueous solution, during succussion. The quantities dissolved are larger for soda glass, and smaller for borosilicate glass, but there is always some. The silicates and minerals have usually been ignored as unavoidable contaminants, as something to be minimized. However Milgrom¹ demonstrated that differences in T1 relaxation times between remedies and controls could be explained by different levels of dissolved silicates. Demangeat et al² found higher than expected silica content in remedies prepared in glass vials, and more silica in certain remedies than in succussed controls.

Could vial-derived silicates be the long-sought active ingredients in remedies?

This idea, the silica hypothesis, is the subject of this article. Others have noted a possible role for silica^{[3], [4] and [5]} in homeopathy, but it has not previously been examined at the level of detail given here. After a brief discussion of silicate structures, we will state the hypothesis and explore how well it can meet the three challenges listed above. Consideration of how biological systems might ‘read’ the information in structured silicates is beyond the scope of this article.

Brief overview of silicates

Silicon dioxide SiO₂, the principal ingredient in glass, dissolves in water by combining with two H₂O molecules to form a molecule of silicic acid, Si(OH)₄ (Figure 1a). The solubility of silica depends on many factors. Alexander et al. demonstrated a strong temperature dependence for solubility of amorphous silica and gave a figure of around 0.010% (or 47 ppm Si) at 20 °C.⁶ Quartz exhibits a much lower solubility than amorphous, and the addition of small amounts of Na₂O or other alkali can dramtically increase solubility.⁷ Two molecules of Si(OH)₄ can link up, forming the dimer H₆Si₂O₇ (Fig. 1b) by expelling a single H₂O and forming a Si–O–Si bond. The Si–O–Si bond is called a siloxane bond. This reaction is called condensation or polymerization, and its reverse reaction (the splitting of a siloxane bond by H₂O to make Si–OH and HO–Si) is called hydrolysis or depolymerization. The dimer can join another Si(OH)₄ unit to make a trimer, and so on. The minimum-energy configuration for the gas-phase dimer has the siloxane bond bent at about 140°, but the strain is not great for angles anywhere from 130° to 150°. As a result, chains of polymerized Si(OH)₄ can close, making rings, and can branch by allowing up to four siloxane bonds at each Si, creating a virtually infinite variety of polymeric species. Quartz and cristabolite are crystalline forms of (SiO₂)_x, and glass is an amorphous form that incorporates small quantities of other materials such as sodium or borate. ‘Silica’ is a general term for any bulk material consisting of polymerized, condensed, or crystallized SiO₂. Removing one H⁺ from Si(OH)₄ produces the H₃SiO₄⁻ anion; likewise the dimer can dissociate to H⁺ and H₅Si₂O₇⁻, and so on for the more complex forms. A ‘silicate’ is any of these anionic forms, generally combined with one or more cations, or a crystalline or amorphous material composed of cations and H_zSi_xO_y anions. (Obviously we cannot pretend to do justice in a few sentences to the complexity of silica and silicate chemistry, which accounts for most of the variety of minerals in Earth’s crust.) We will refer to any H_zSi_xO_y (charge would be 4x−2y+z) that is held together entirely by Si–O and O–H covalent bonds as a ‘silicate’, regardless of its dissociation state, charge, hydration, or extent of association with cations. Our interest is in the behavior of silicates in aqueous solution, or in ethanol-water solution.

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Fig. 1. (a) Si(OH)₄ monomer, optimized at B3LYP/6-311++G(3d,3p) level. (b) Si(OH)₃–O–Si(OH)₃ dimer, optimized at B3LYP/6-311++G(3d,3p) level.

A notation that has been used to characterize the connectivity of a Si in a silicate is Q^x, with the superscript indicating the number of siloxane bonds.⁸ Thus Q⁰ is the monomer, Q¹Q¹ is a notation for the dimer (since each of the Si atoms is involved in a single siloxane bond), and the linear trimer would be Q¹Q²Q¹. The cyclic trimer is Q²₃; branched polymers would contain Q³‘s or Q⁴‘s. Q⁰ through Q⁴ have distinct signatures when a sample is examined with 29Si-NMR. The cyclic trimer is also denoted 3R for ‘3-membered ring’, and the 4R, 5R, 6R, and 8R structures are also often seen. Commonly two rings combine into a prism (‘double ring’), for which the notation would be D3R, D4R, etc. The D4R motif or cube is shown in Figure 2a.

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Fig. 2. (a) D4R cube (H’s omitted). (b) Two representations of ACO zeolite showing how the cube of Fig. 2a occurs in a repeating 3-D structure. Siloxane bonds are shown as straight rods even though they actually include an angle. One O atom is implied on each siloxane bond.

Silicate patterns that occur in natural minerals include: monomer (nesocilicates), dimer (sorosilicates), single and double chains (inosilicates including rings of 3–8 SiO₂ units, the cyclosilicates), sheet (honeycomb pattern of hexagonal rings, or phyllosilicates), and framework silicate (complex 3D or tectosilicates). The last category includes the quartz group (minerals that are just (SiO₂)_x) and zeolites (crystals containing large pores that are typically occupied by cations). Figure 2b shows how the cube is a subunit in one zeolite structure called ACO.⁹

Condensation of aqueous silicic acid is slow under conditions of 20°C, 1 atm, and neutral pH. In a system with only silica and water, equilibrium of dissolved monomers with a condensed (amorphous) silica phase can take months to establish. A low-concentration system without a condensed phase produces few dimers,¹⁰ and the amount of dimer increases with pressure.^{[11] and [12]} In a concentrated potassium silicate solution, Harris et al found 11 distinct oligomers via 29Si-NMR analysis,⁸ and oligomers containing up to 12 Si atoms have been identified.¹³ Polymerization is favored by low temperatures, high Si concentration, and low alkalinity.^{[14] and [15]} Catalysis of polymerization by other solutes can be dramatic and will be addressed in the next section. Depolymerization and interconversion of silicate species occurs slowly at 20°C, so for practical purposes most silicate polymers can be considered to be ‘stable’ over a time frame of hours or longer.

When a sample is succussed, it is subjected to a series of brief intense shocks during which the pressure jumps for perhaps a millisecond to hundreds and probably thousands of atmospheres. Our premise is as follows. The first few succussion strokes agitate the glass walls by mechanical action and generate a saturated or supersaturated solution of silicic acid. During later succussion strokes, the momentary high-pressure shifts the equilibrium for silicic acid in favor of condensation, and polymers form. (Demangeat et al² reported a mean Si concentration of 6 ppm for their remedies, near the solubility limit for quartz,⁷ with certain remedies showing consistently higher concentrations than others. Our laboratory obtained Si concentrations of 1.3 to 4.0 ppm in succussed solutions [unpublished data]. These measurements are obtained after a remedy has had some time to “settle” in its glass vial so there could be higher concentrations during and immediately after the succussion strokes.) We will later discuss how, in remedies, specific condensation patterns might be catalyzed. As the high-pressure abates, the polymers remain as polymers.

(There is also some evidence that succussion may cause larger silica units as well as Si(OH)₄ to enter solution.¹⁶ We have unpublished light-microscopy and EM observations from our laboratory that indicate relatively large particles in succussed solutions. Although these are possibly due to condensation of silica units during the sample preparations, it is also likely that some large particles exist immediately after succussion.)

The ‘silica hypothesis’ for homeopathy states that remedies differ from succussed water controls and from each other, in the structure (not primarily in the quantity) of their dissolved silicates. At this point we lack experimental evidence to be more specific, but the differences could include the distribution of polymer sizes, the degree of arborization (Q³ and Q⁴ vs Q²), the frequency of specific motifs like 6R or D5R, or quite specific long-range patterns in larger units such as particular crystalline or zeolite forms. Characteristics such as these would be stable enough to last for at least a few minutes at ambient temperature and pressure while a remedy was being transferred to begin the next potency, or while being transferred onto lactose pellets (which would absorb the water and cease any further hydrolysis or condensation) for clinical use. In a glass bottle that would provide a baseline Si(OH)₄ concentration, these ‘identifying characteristics’ of a remedy could quite possibly last for days or months, though we would expect it eventually to degrade.

Interestingly, the fact that liquid remedies are normally kept for long-term storage in 87% ethanol rather than plain water might help their stability. Hydrolysis consumes H₂O, so hydrolysis incurs a higher free energy cost in hygroscopic ethanol than in water. Ethanol should slow the degradation of the ‘information’ in dissolved silicate structures, though the formation of some ethoxysilicates might be expected instead.¹⁷

Generation and perpetuation of remedy-specific silicates

Having seen how the silica hypothesis could address the first challenge, viz. the thermodynamic stability of a remedy’s ‘information’ encoded in its silicate structures, let us turn to the third challenge: generation of remedy-specific information. How feasible is it that components in the original MT could direct or catalyze remedy-specific silicate structures?

This turns out to be extremely feasible. An extensive literature already documents the capacity for both organic and inorganic solutes to direct the condensation of silicic acid into solute-specific patterns.¹⁸ Indeed, this capacity is the basis for numerous natural and commercial processes to generate specific silicate and organosilicate structures. We will review only a small part of this literature, emphasizing its relevance to pattern initiation in low-potency remedies.

For inorganic solutes, Kinradet and Pole ¹⁹ observed effects of metal cations on silicate condensation. Paired cations facilitated the approach of the negatively charged silicates so that condensation could occur. Alkali metals from Na⁺ to Cs⁺ stabilized different oligomers, with Li⁺–H₂O interactions further enhancing polymerization in the case of Li⁺. Tossell ²⁰ has explained the role of fluoride ion F⁻ in promoting the formation of D4R cubes. A comparative study of substituted ammonium, NA₄⁺, shows markedly different results depending on whether the alkyl group A is methyl, ethyl, or propyl.^{[13] and [21]} If A is methyl the preference is for D4R, whereas ethyl makes D3R and propyl guides the formation of the zeolite ZSM-5 ^{[22], [23] and [24]} but does not make double rings.

Organic solutes can choreograph the production of highly specific crystalline (repetitive) silicates. Diatoms, single-celled plants that live inside a silicate coat called a frustule, ‘produce an enormous variety of biosilica structures’.²⁵ The number of known species exceeds 20,000. The silica-condensing molecules are long-chain poly-amines (LCPAs) and modified proteins called silaffins, which generate the same species-specific structures from silicic acid solutions when used in vitro. ^{[25] and [26]} Working with LCPAs including spermine and spermidine, Belton et al²⁷ determined that ‘chain length, intramolecular N–N spacing and C:N ratio of the additives’ was responsible for ‘the combination of unique catalytic effects and aggregation behaviours’ that determined the materials’ properties. Working with amino acid silicate solutions, Belton and coworkers found that 11 of the 20 amino acid residues ‘affect the kinetics of small oligomer formation, the growth of aggregate structures and the morphology and surface properties of the silicas produced’.²⁸

Given this information, it is tempting to imagine that almost any inorganic or organic material could guide the formation of specific silicates. Focusing on plants, which are the source of the majority of remedies in clinical use, could the particular proteins or N-containing alkaloids in a plant account for plant-specific silicates appearing in remedies made from that plant? Obviously some compounds will be more effective than others at condensing silica, eg silaffins evolved specifically for that purpose. In a low-potency remedy like a diluted 3c being succussed to make a 4c, perhaps silicic acid ‘ignores’ most plant components while allowing particular ‘active ingredients’ to catalyze the relevant structures. It would be interesting if the silica-condensing ingredients were the same as the pharmacologically active ingredients. If so, it could explain why, say, the atropine in Belladonna plays the key role in determining the properties of potentized Bell, and it would suggest that remedy made from whole plant should be essentially identical to remedy made by starting with purified atropine. It is widely believed that the homeopathic remedies Bell and Atropinum have very similar clinical activity.

We should also express some notes of caution. While it is true that inorganic and organic solutes guide silicate formation, in many cases these solutes are incorporated into the final product, eg the cations occupy the pores in a zeolite, or organic matter remains embedded in the final silicate. Or, the concentration of ‘catalyst’ is comparable to that of silicate, eg, Belton et al²⁸ used a 2:1 molar ratio of Si to amino acid. This poses a problem for the silica hypotheses. As the remedy becomes progressively more dilute, there is less and less catalytic material available. To our knowledge, the question of how low the solute concentrations can get, and still generate significant quantities of solute-specific silica structures, has never been studied. Nor is it known how a pulse of high pressure, as in succussion, would affect the process. For the silica hypothesis to work, it would be essential that some components of the MT act as true catalysts, yielding many structured silicates per molecule, and not become trapped in individual silicate complexes. Questions can also be raised about how far the specificity of the catalysts can extend. For example atropine and hyoscyamine are enantiamers, differing solely in their orientation at a single C locus, yet Bell and Hyos are considered to be rather different remedies. Most silicates that have been studied are achiral, but some, like trigonal quartz, can be chiral.

Let us turn now to the second challenge: perpetuation of the pattern after all of the MT has been diluted away. Let us assume that a 12c remedy sample contains a measurable population of remedy-specific silicates. What happens when that remedy is diluted 1:100 and succussed? The process can begin the same way: the early succussion strokes release silicic acid from the vial walls. However there is no catalyst to condense the silicic acid—or is there? Clearly we would require that the remedy-specific silicate polymers from the prior potency serve as the catalyst. Suppose the relevant structure in the 12c were nanocrystals of a particular zeolite. We would be saying that diluting this zeolite solution 1:100, adding silicic acid, and succussing, should generate more zeolite. Indeed, we would need to have about 100 times as much zeolite nanocrystal at the end of the succussion cycle, as we had just after the 1:100 dilution. If we do not amplify the active ingredient by a factor of 100 each time, then with subsequent dilutions the amount of structured silicate will soon diminish to zero.

How feasible is it to generate particular silicates from silicic acid, by using only a seed containing already-structured silicate, and then succussing? We admit this is the weakest point of the silica hypothesis, but it is not impossible. We propose four ways it could happen. First, some silica motifs may be inherently amenable to self-replication. Perhaps a double ring like D5R has a tendency to split (hydrolyze) into two single 5R rings when vigorously shaken, and perhaps the two resulting single rings have a tendency to attract a second layer of condensation, re-creating the double ring. If so, a single succussion stroke could double the amount of D5R, and repeated succussion strokes could amplify the amount of D5R as much as 100 times. This hypothetical process would be comparable to the polymerase chain reaction for DNA. Building on the DNA analogy, in addition to double rings we could imagine a double form of any flat linear or branched silicate polymer. As noted above, single and double chains are among the naturally occurring forms of silicate in minerals. (Some cycles could be allowed too but joined rings and highly branched topologies cannot be ‘doubled’ without introducing a lot of bond angle strain.) If the double form were to ‘unzip’ like DNA, and if each half were then to act as a template to re-create the double form, we would have a mechanism for preserving the structure from one potency to the next.

This idea also permits us to see a way that remedies might change gradually with potency. For instance, if the ‘replication’ described above were not 100% perfect, but instead there was a tendency for small but predictable changes to occur, then the 13c might be subtly different from the 12c, the 14c might be slightly changed from the 13c, and so on. By ‘small but predictable changes’ we mean things like lengthening a chain by one or two units or adding a short side-branch. Small changes could function like point mutations in DNA: alterations that leave the structure mostly unchanged, and do not interfere with the capacity for replication, but which would be inherited and maintained by subsequent dilution/succussion cycles. Small changes might occur with low probability but might accumulate over many cycles, like DNA mutations, to result in a noticeably different structure with different clinical benefits. This would fit with the conventional wisdom of homeopaths that a 12c and a 13c and a 14c are not much different, but with passage of enough cycles, the 200c and the 12c can be quite different.

Second, we have alluded to silica nanocrystals as the information-carrying component. Crystals are well known for acting as seeds that can extend their pattern as other molecular units crystallize onto them. Once a particular silica crystal pattern got started, could it grow more of its own pattern when added to a silicic acid solution and succussed? We would be saying that of the 200+ known zeolite structures, if tiny nanocrystals of one zeolite are added to silicic acid and succussed, the result would be 100 times as much of that very same zeolite. This strikes us as a priori unlikely, yet it might work for at least some zeolite or other crystalline forms. We doubt the question has ever been studied.

Third, an intriguing mechanism could involve transfer of information from the silicates to structure the water during succussion, and transfer of information back from the structured water onto silicate particles, which then ‘hold’ the information when the succussion pressure abates. Zeng and coworkers²⁹ proposed such a mechanism when they studied the well known ‘memory effect’ of water. The ‘memory effect’ does not involve homeopathy: it says that a water sample that has been crystallized under pressure into a gas hydrate, and then melted, will more quickly re-form the clathrate hydrate structure when mixed with gas and re-pressurized, compared to a water sample that did not previously experience the hydrate state. Analysis of water samples with neutron scattering could not find any structural basis for a ‘memory effect’.³⁰ When Zeng and coworkers discovered that low concentrations of certain ice nucleation inhibitors could destroy the memory effect, they inferred that the effect was due to small impurity particles that received the ‘imprint’ of the clathrate state and, by holding that imprint long after melting and degassing, supplied a template for rapid nucleation back to the clathrate state.

Quoting Zeng et al, the memory effect ‘must be ascribed to an alteration of the surface states of the impurity particles that amplifies their nucleating action. This could occur because of an imprinting of the surface of the impurities by the growth of a hydrate crystal on the particle surfaces. For instance, if the impurities are hydrated or hydroxylated silicon or iron oxides, a hydrate crystal may well alter the surface geometry so that when the hydrate melts, the surface is now a better nucleator of hydrate than it was during the first nucleation cycle’ (emphasis added). They are explicitly postulating that silicate particles could be the information carriers that cause water, when pressurized, to form a particular pattern, and that the pattern could imprint other silicate particles. We are not proposing that water forms a momentary clathrate hydrate during succussion, but there could be other structural alterations. These alterations could start at (be nucleated by) silicate particles, could spread throughout the sample, and then imprint other silicate particles throughout the sample. The result would be an amplification, conceivably by the needed factor of 100, of the specific surface pattern on silica particles. Although the structural change in the water would be lost when the pressure returns to 1 atm, the information would persist in the silica surface changes. This explanation works best if silica is released into solution as nanoparticles, rather than as monomeric silicic acid, when agitated during succussion.

Fourth, if we postulate that silica surface carries the information, could the glass vial wall itself be that carrier? Some commercial remedies are prepared by the Korsakoff method. In this method, a single vial is used, and dilution is achieved by decanting most of the liquid and then refilling. Then the vial is succussed. A thin layer of water that wets the inside vial walls stays there when most of the liquid is decanted. This layer is estimated to be about 1% of the vial volume; so subsequent refilling accomplishes the 1:100 dilution. Asay and Kim³¹ found that water adsorbing onto glass at 20°C forms a three-molecule thick layer of ice. The pattern of the water adjacent to the glass will certainly be affected by alterations in the glass surface. Once a pattern is established on the vial walls, subsequent Korsakoff cycles might do nothing or might slowly alter the pattern. In order to transmit this information after the final potency is removed, however, it would have to contain some imprinted silica particles as well.

Experiments to test the silica hypothesis

The silica hypothesis and its variants are amenable to experiment and measurement to verify or negate them. Its challenges are the low concentrations at which silicates occur, and the difficulty of teasing apart chemically similar oligomers or surface features. A starting point will be to measure the amount of monomeric and polymeric silicates in remedies, in succussed water, and in diluted remedies after 0, 2, 8, 20, and 40 succussion strokes (or any similar sampling sequence). Alexander et al⁶ successfully used a molybdic acid assay to measure the amount of monomeric silicate, while mass spectroscopy can provide the total Si content of a sample. Obviously we would want to repeat these measurements for several different types of glass vials, and for ethanol-water vs water for the solvent.

Raman spectroscopy and ²⁹Si-NMR provide insight into the degree of polymerization of silicates. ²⁹Si-NMR will tell us ratios among Q^x loci. Assuming we see some consistent differences among remedies or between remedies and controls, we can use these methods to ask how well homeopathically relevant substances such as atropine can serve as silicate polymerizers, and whether their condensed silicate products have consistent and substance-specific properties. The protocol would be to add a known concentration of atropine to a silicic acid solution of known concentration (in plastic vial) and succuss. Electron microscopy of frozen and cracked samples or very thin frozen layers is one way to look for suspended silica nanoparticles and to examine their surface. If surface features seem to be the information-carrying aspect, we will ultimately need to develop assays that detect particular features. Such an assay might measure adsorption of particular molecules, or enhancement or stabilization of a particular enzyme.

If early experiments lead us to suspect that remedy-specific oligomers are the information-carrying ingredient, we will ultimately need to make remedies enriched in ²⁹Si in order to identify them via ²⁹Si-NMR. To make a vial out of ²⁹SiO would be prohibitively expensive, but here is an alternative. Remedies could be made by succussing them in polypropylene vials, and silica could be added in the form of small (1 mm diameter) recoverable beads. The total surface of the beads could be calculated to equal that of the vial (typically an 8-, 12-, or 20-ml vial). Beads would be strained away after the last succussion stroke. It would be an open question whether such beads can be immediately reused for another remedy or potency, or whether they would be ‘imprinted’ in some way that would carry information that could affect the next remedy made with them. If remedies made via ‘succuss with silica beads in plastic’ appear via ²⁹Si-NMR to yield similar results to ‘succuss in glass,’ the idea would be to replace the beads with ²⁹Si-enriched beads. Now, even that would get expensive when 95% ²⁹SiO₂ runs $3 to $5 per mg. But one could coat ceramic beads with melted ²⁹SiO₂ making a layer perhaps 10–30 μm thick. This would not require too much ²⁹SiO₂ and would allow us to simulate exposure to a ²⁹SiO₂ vial. All of the resulting silicate structures would then be ²⁹SiO₂-enriched. Note that only the potencies we intend to study would have to be made with the ²⁹SiO₂ beads.

Conclusion

The clichéd scientific objection to homeopathy is that it cannot work because ‘remedies have nothing in them chemically,’ besides water. The silica hypothesis turns this objection on its head. It declares that remedies made in glass do have something else in them chemically, namely silicates, and that the silicates are not irrelevant contaminants but meaningfully structured active ingredients. According to the hypothesis, succussion releases silicic acid monomers into the solution, which are then polymerized into remedy-specific patterns by catalytic action of MT components. For potencies above 12c, structured silicates themselves act as the catalysts or templates for perpetuation of the remedy-specific patterns. In a variant on the hypothesis, silica delaminates from the glass walls in the form of nanoparticles rather than Si(OH)₄ monomers, and the information is carried via silica surface alterations.

In this brief overview of the silica hypothesis we have begun to ask how the hypothesis might be able to meet three physical chemistry challenges that any explanation for homeopathy will have to overcome. Silicates can indeed form a huge variety of distinct and thermodynamically stable (for minutes or longer) structures in aqueous solution. Organic and inorganic MT components can guide selective silicate pattern formation. Structured silica seeds may be able to direct the formation of more copies of themselves, and may be capable of slowly changing or ‘evolving’ over the course of repeated dilution-succussion cycles. Gradual ‘evolution’ of silicate properties would explain the widely believed-in gradual change in clinical properties of remedies as the potency is increased.

Our overview contains many ideas that are speculations and extrapolations, and where this is the case we have admitted it. Rather than argue these points, it seems wisest to begin to collect experimental evidence that will support or negate various claims and versions of the hypothesis.

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Corresponding author. DJ Anick, Harvard Medical School, McLean Hospital, Centre Bldg 11, Belmont, MA 02478, USA.

Homeopathy
Volume 96, Issue 3, July 2007, Pages 189-195
The Memory of Water

This is part of the Homeopathy journal club described here:

www.badscience.net/?p=490

doi:10.1016/j.homp.2007.05.003    
Copyright © 2007 Elsevier Ltd All rights reserved. The possible role of active oxygen in the Memory of Water

Vladimir L. Voeikov^{, a,
a}Faculty of Biology, Lomonosov Moscow State University, Moscow 119234, Russia
Received 13 April 2007;  accepted 4 May 2007.  Available online 31 July 2007.

Abstract

Phenomena of long-term ‘memory of water’ imply that aqueous systems possessing it remain for a long period after the initial perturbation in an out-of equilibrium state without a constant supply of energy from the environment. It is argued here that various initial perturbations initiate development of a set of chain reactions of active oxygen species in water. Energy, in particular high grade energy of electronic excitation, released in such reactions can support non-equilibrium state of an aqueous system. In principle, such reactions can continue indefinitely due to specific local structuring of water with even minute ‘impurities’ that are always present in it and by continuous supply of oxygen amounts due to water splitting. Specific properties of several real aqueous systems, in particular, homeopathic potencies in which such processes could proceed, are discussed. The role of coherent domains in water in maintenance of active oxygen reactions and in emergence of oscillatory modes in their course is considered.

Keywords: active (reactive) oxygen species; water splitting; electronic excitation; homeopathy; nanoparticles; coherent domains

Article Outline

Introduction

Long-term effects of physical factors upon the properties of water

Water, a two-faced Janus: Pro- and anti-oxidant activity of water

Water participation in chain reactions

Oscillatory nature of reactions with active oxygen participation

Conclusion

References

Introduction

‘Memory of water’ is a popular idiom meaning long-term effects of various physical factors upon physical–chemical properties and biological activity of aqueous systems. The phenomenon of ‘water memory’ is on area of heated debate. The particular case of ‘water memory’ controversy is homeopathy. Its assertion that a homeopathic preparation can hardly contain a single molecule of an initial biologically active material but retain biological activity cannot be explained in the frame of the current biochemical and pharmacological paradigm. According to the latter a medicine exerts its action due to local interactions of active substantial principles present in a medication with appropriate biomolecules (enzymes, receptors, etc.). Specificity of these interactions is due to complementarities of electronic landscapes of interacting due to species. Specific binding of an appropriate ligand to the particular ‘receptor’ induces its conformational change, necessary for the development of a downstream chain of reactions.

It is generally considered that there is no problem in energy supply and transformation for performance of this chemical work. Conformational change in the receptor is supposed to be provided by energy released as a drug binds to it. Chemical work associated with all the downstream reactions of a cell is supported by energy supplied by metabolism. This reasoning tacitly implies the initial non-equilibrium state of the whole system: drug+a target cell.

From this perspective homeopathy seems improbable for several reasons. One of them is bewilderment about how a preparation not containing a single biologically active molecule from its original solution or tincture exerts any specific biological effect (the problem of specificity). Claims that the original molecular principle somehow leaves its imprint in water contradicts the textbook model of water, according to which water cannot retain any ‘memory’ after a perturbation due to fast relaxation to an equilibrium state for the given ambient conditions.

Thus, one of the key questions related to the problem of ‘water memory’ is the question whether water is a substance that after a perturbation does not easily relax to the original state and under special circumstances can even further move away from the equilibrium state? If so, what mechanisms provide for its stable non-equilibrium state? If one can answer these questions, the question of the specificity of homeopathic preparations may be solved more easily.

Here the hypothesis is presented that due to water’s capability to transform low grade energy (eg, mechanical) into high grade energy of electronic excitation and due to its dual oxidant–reductant nature, water may remain in a non-equilibrium (dissipative) state for a very long time.

However, before we go further clarity about the word ‘water’ should be introduced. ‘Water’ is never pure H₂O. Real water always contains impurities: products of its ionization (H⁺ and OH⁻), ions, dissolved gases, and traces of other substances. Even ultra-pure water is kept in a vessel. Water properties in the vicinity of its walls (interfacial water) may significantly differ from those in ‘bulk’ water and from those at a water/gas (air) interface. Unlike common belief that effects of solid surfaces with which water is in contact vanish on a nanometre scale, new evidence shows that they may propagate at distances of tens and hundreds of microns.¹

Long-term effects of physical factors upon the properties of water

Currently there is no shortage in evidence of long-term effects of physical factors, such as static and oscillating magnetic and electromagnetic fields, mechanical stirring and vibrations, sonication, etc. upon the properties of water. Here we will refer to only few of these studies that are seriously substantiated and relevant for further discussion of the role of active oxygen species in water memory.

In more than a decade of study of the effects of vigorous succussion and extreme serial dilutions in bi-distilled water or different aqueous solutions. Elia and co-workers found that already the third centesimal dilutions prepared with vigorous succussion demonstrated significant excess in heat release upon mixing with dilute alkali or acid and significant increase in electrical conductivity over unsuccussed solvent or dilutions.² Even more important was that these differences did not attenuate or vanish with time, but rather magnified in all the samples during several weeks of storage. Differences did not disappear even after several years of storage, and the smaller the volume of stored samples, the larger was the deviation.³ Elia et al establish that “these extremely diluted solutions (EDS), after strong agitation (succussion), enter a far from equilibrium state and remain there or get even farther by dissipating energy in the form and amount necessary to stay in a far from equilibrium state. What is the source of dissipating energy that does not exhaust for several years?

Elia et al acknowledge that in the process of vigorous succussion of aqueous samples traces of substances may be released by the glass of the containers, and these traces are able to ‘activate’ the EDS. Strong support for the suggestion that a long-term perturbation of aqueous systems treated by a physical factor depends on nano-‘impurities’ is provided by the recent seminal paper of Katsir and co-authors.⁴ They demonstrated that radio-frequency treatment (in the megahertz frequency range) of aqueous solutions can dramatically change their properties expressed, in particular, in peculiar patterns of electrochemical deposition of zinc sulphate solutions. Again, it takes some time after irradiation for the aqueous system to change its properties. The effects of radio-frequency treatment of solutions lasted for hours. If ultra-pure water used as a solvent was doped under radio-frequency treatment with barium titanate nanoparticles (diameter range 10–100 nm) special properties of zinc sulphate solutions prepared on such water were amplified and lasted for months. Saturation concentration for nanoparticles in irradiated water did not exceed 10⁻¹² M; at higher concentrations they clump and sediment. As it takes many hours for the emergence of special properties of nanoparticle-doped water (NPD) the authors assume that water goes through a self-organization process.

The findings of Katzir and co-authors have much in common with the research into physical–chemical properties and biological activity of aqueous dispersions of Fullerene C₆₀. Since the discovery of fullerenes a lot of surprising biomedical effects both in vivo and in vitro were reported. Those include antiviral (in particular, anti-HIV), anti-bacterial, anti-tumour, anti-oxidant, and anti-apoptosis effects among others.⁵ In most cases hydrophilic C₆₀ derivatives were used because pristine fullerenes C₆₀ are considered to be water-insoluble. Andrievsky et al developed a procedure for preparing molecular–colloidal solution of pristine C₆₀, with the help of ultrasonic treatment of fullerene water suspension. It contains both single fullerene molecules and small clusters.⁶ In such ‘fullerene–water-systems’ (FWS) single C₆₀ molecules and their clusters do not precipitate because they are covered with water shells in which water molecules are absorbed so strongly that water is not completely lost even in vacuum of 10⁻³ Pa. FWS do not have toxic effects and possess strong biological activity even in dilutions down to 10⁻⁹ M.⁷ Andrievsky ascribes the wide spectrum of beneficial biological effects of FWS to their strong ‘anti-oxidant’ activity that is also ascribed to aqueous solutions of hydrophilic fullerenes⁵ (we will discuss below what ‘antioxidant activity’ really means).

Water systems described above: ‘EDS’ of Elia et al, ‘NPD’ of Katzir et al, and ‘FWS’ of Andrievsky et al have much in common, though they are prepared using quite different procedures and have completely different chemical composition. On the one hand, in the course of their preparation basically the same procedure is used—physical treatment of water causing cavitation in it (‘cavitation’ is the emergence of gas-filled cavities and bubbles in a liquid and vigorous change of their volume and behaviour depending upon local pressure changes). Katzir et al, ascribe the “anomalous effects of radio-frequency treatments of water and aqueous solution to the formation of pliable network of gas nanobubbles that has special hierarchical organization effect”. They suggest that much more long-term changes in the properties of NPD than in irradiated water or simple aqueous solutions is explained by replacement of less stable nanobubbles with stable barium titanate nanoparticles. Succussion used for the preparation of EDS and ultrasound treatment of water used for the preparation of FWS also produce cavitation in water. In all three systems water becomes ‘doped’ with nanoparticles. In the case of EDS they are supposedly represented by silica oxide, in NPD—with barium titanate, and in the third case—with fullerenes. At least in the last two cases it has been demonstrated that nanoparticles serve ‘kernels’ around which water shells with properties very different from those characteristic for usual ‘bulk’ water originate. And for FWS so-called ‘anti-oxidant’ properties were demonstrated.

Water forming shells around nanoparticles is ‘gel-like’ and the shell may extend up to a micron in range (at least in the case of NPD). Thus, it is difficult to explain physical–chemical (‘anti-oxidant’) and biological activity of all these aqueous systems by chemical properties of ‘impurities’—nanoparticles that are so chemically different and rather inert. It is much more plausible that this activity is based on a specific structuring of interfacial water. But how can such ‘gel-like’ (or ‘ice-like’) water structures provide for stable non-equilibrium, energy dissipative properties of aqueous systems?

Water, a two-faced Janus: Pro- and anti-oxidant activity of water

Until recently water was considered just as a solvent in which biochemical processes go on and as a fluid used to transport different substances throughout the body. Though ‘anomalous’ properties of water, its role in base–acid equilibrium, its direct participation in the reactions of hydrolysis and photosynthesis is generally acknowledged, the much deeper fundamental role of water in practically all chemical reactions is neglected. Yet the discovery that water is the catalyst of at least oxidative reactions was made as long ago as in 18th century. In 1794 a British researcher, Elizabeth Fulhame published in London a book entitled ‘An Essay on Combustion’. Based on her own studies she stated that “hydrogen of water is the only substance, that restores oxygenated bodies to their combustible state; and that water is the only source of the oxygen, which oxygenates combustible bodies” (cited after [8]). For example, to explain the combustion of charcoal she suggested that “the carbon attracts the oxygen of the water, and forms carbonic acid, while the hydrogen of the water unites with oxygen of the vital air, and forms a new quantity of water equal to that decomposed”:

Thus, water according to Fulhame is both pro-oxidant (it oxidizes a fuel) and anti-oxidant (it reduces oxygen).

Though the discovery of Fulhame was soon forgotten, chemists of the 19th century acknowledged that water is necessary for oxidation (oxygenation) even of easily combustible bodies. They knew that metallic sodium and potassium do not lose their metallic luster in an atmosphere of dry oxygen, and that carbon, sulphur, and phosphorus burn under very dry conditions at much higher temperatures than in humid air.⁹ However, until the beginning of the 21st century, when it was rediscovered that water can ‘burn’—be oxidized by singlet oxygen¹⁰ this ‘mysterious’ property of water was neglected. It was also proved by quantum chemical modelling that water oxygenation is catalysed by water.¹¹

Water participation in chain reactions

How are catalytic and red/ox properties of water related to the phenomenon of water memory? Above it has been argued that water forming shells around nanoparticles is ‘gel-like’, so it has features of a polymeric substance. It is well known that polymers can undergo chemical transformations under the action of mechanical impacts, freezing–thawing and fast temperature variations, action of audible sound and ultrasound, and of other low density energy forces too weak to induce chemical reactions in monomers or short oligomers. Polymers may accumulate and concentrate mechanical energy to densities that comprise energy quanta sufficient to excite and break down their internal covalent bonds. Unpairing of electrons and appearance of a pair of free radicals results in the development of new reactions.¹²

Based on the presumption that liquid water contains quasi-polymeric structures Domrachev et al investigated the effect of low density energy physical factors on homolytic water dissociation (H—O—H→HO+H, cf. ionic water dissociation: H—O—H→H⁺+OH⁻). It was shown that water freezing–thawing, evaporation–condensation, sonication even with audible sound, filtration through narrow capillaries resulted in an increase of H₂O₂ even in ultra-pure and carefully degassed water. Efficiency of water splitting resulting from water filtration through narrow capillaries (where a significant part of it forms interfacial water) was more than 100 times greater than photodissociation with far UV-light.¹³ Yield of H₂O₂ in water containing ions and dissolved oxygen was much higher, and notably, H₂O₂ concentration continued to grow in water containing dissolved oxygen for some time after the completion of any treatment, as if it ‘remembered’ it.

In the case of a single water molecule in a mechanically excited polymeric entity being split:

(H2O)n(H–|–OH)(H2O)m→(H2O)n(H↓)+(↑OH)(H2O)m,

(1)

the initial products of water splitting are free radicals H↓ and ↑OH (here we symbolize a given electron as ↑ or ↓ to stress their alternative spin states). In most cases this singlet pair of radicals recombines back to water:

H↓+↑OH→H2O.

(2)

However, even in such a case this is not just a reverse, equilibrium reaction because water splitting has been achieved under the action of mechanical forces while back recombination of radicals gains an energy quantum of 5.2 eV. In condensed and organized media (such as water), long-range energy transfer of electronic and vibrational excitation has been demonstrated already in 1930s–1950s by J. Perrin, S. Vavilov, Th. Foerster, A. Szent-Giorgyi, and others. This phenomenon was recently confirmed with new techniques.¹⁴

The probability of radicals moving away from each other significantly increases when dissolved gases and other molecules and particles are present in water, especially in cases when multiple layers of water are organized by surfaces which it hydrates and when these layers move relative to each other at different rates (consider a vortex as an example). Here, a rich set of reactions may proceed, for example:

HO↑+HO↓→H2O2,

(3)

H↑+↓H→H2,

(4)

H+O2→HO2,

(5)

HO2↑+HO2↓→H2O2+O2,

(6)

2H2O2→2H2O+O2.

(7)

Besides these more or less stable products exotic metastable substances may appear, for example: HOOOH, H₂O₄, HOO–HOOO, HOOH–OOO, etc. Reactions 6 and 7 in which oxygen molecules are released are notable as they provide evidence that oxygen may abiogenically arise from water under very mild conditions. What is also important is that this ‘newborn’ oxygen arises in an activated, singlet state.

It should be reminded that O₂ is unique among molecules because in its ground state its two electrons are unpaired [O₂(↑↓)₂↑↑ or O₂(↑↓)₂↓↓] (besides, an oxygen atom also has two unpaired electrons). Thus, oxygen molecule is a bi-radical (in fact it is a tetra-radical) and it represents a vast store of energy. But the laws of quantum physics forbid direct reactions of bi-radicals (they are also called particles in a triplet state) with molecules in which all electrons are paired (singlet state particles). That is why oxygen needs to be activated to release its energy reserve.

There are a few ways for O₂ to be activated. It may be excited by an appropriate energy quantum (1 eV) and turn into a highly reactive singlet oxygen (O₂(↑↓), also denoted, ¹O₂). A peculiar feature of ¹O₂ is that this electronically excited species may relax only to triplet state because oxygen, unlike other substances does not have ground singlet state. Since singlet–triplet transition is ‘forbidden’ by quantum physics laws, the lifetime of excited singlet oxygen is usually much longer than that of any other molecule in an excited singlet state. Probably that is why the reaction of singlet oxygen with water goes with sufficiently high probability—¹O₂ is long-living enough to find an appropriate catalytic environment for water oxidation.

On the other hand, triplet oxygen easily reacts with free radicals—atoms and molecular particles with an odd number of electrons. In these reactions oxygen gains an electron, turns into a mono-radical which can easily take new electrons releasing large quanta of energy at each consecutive step of one-electron reduction.

The principal property of free radical reactions in which O₂ participates is that they may easily turn into a branching (or run-away) process.¹⁵ Several specific features distinguish branching chain reactions (BCRs) from ‘normal’ chemical reactions.¹⁶

First, the quantum yield (the ratio of the quantity of reaction events to the quantity of quanta that initiated the initial reaction events) is extremely high.

Second, BCR often start to develop after an induction period, long after the completion of the initiating stimulus impact. (Development of BCR is expressed in exponential growth of reaction centres represented usually by free radicals, until the rates of their production and annihilation equalize).

Third, the reaction proceeds at a very low rate below and above threshold values of critical parameters: temperature, volume of the reaction mixture or ratio of the reaction mixture volume to the surface of the reaction vessel, concentrations of reagents, etc.

The fourth specific feature of BCR is a very strong accelerating or rate-retarding effect of certain minute admixtures in the reaction mixture.

Fifth, large deviation of kinetics of BCR from classical laws of chemical kinetics—Arrhenius temperature law and the law of mass action—is observed at certain stages of BCR development.

Finally, as long as a BCR proceeds it serves as a source of high density energy—energy of electronic excitation, equivalent to quanta of visible or UV light, because free radical recombination events (recombination of unpaired electrons) are highly exergonic. That is why the reaction systems in which such reactions occur are often chemiluminescent.

In the gaseous phase BCRs usually develop as explosions. However, in condensed phases a lot of red/ox-reactions with O₂ participation meet many criteria of the BCRs though they develop and proceed without termination for an extremely long time. Semyonov¹⁶ suggested that these reactions go on as linear chain reactions in which chains do not branch:

R+R′H→RH+R′;R′+R″H→R′H+R″;R″+RH→R+,

where Rⁿ· is a free radical with an unpaired electron, and R^mH is a molecule which it oxidizes.But if a free radical is in turn oxidized with a bi-radical molecule oxygen, a peroxide radical, ROO·, is produced. When it oxidizes a certain molecule, a metastable and energy-rich peroxide (ROOH) is produced in addition to a new radical, which provides for chain propagation. Usually low energy of activation is needed for decomposition of peroxides at which two new active centres, RO· and ·OH emerge. Thus, even if a ‘parent’ chain is eliminated, the system in which peroxides appear stays ‘charged’ and new chains arise in it sometimes after a very slight perturbation. Such reactions are named “chain reactions with delayed branching” (CRDB). Systems in which CDRB go on are intrinsically non-equilibrium, though at a first sight may seem to be at rest.

Evidence is accumulating that very slow CRDB may under ‘appropriate conditions’ readily develop in water. As mentioned above, quantum chemical calculations show that if water is organized in a favourable way (water molecules are arranged in space, in particular, in relation to singlet oxygen and to each other), the energy of activation for oxidation of a water molecule with singlet oxygen diminishes to reasonable values. The immediate products of water oxidation are exotic and highly energy-rich peroxides such as HOOOH, HOOOOH, HOO–HOOO.¹¹ All these peroxides are typical active oxygen species. They easily decompose giving birth to new free radicals, initiating propagation of new chains, or to ozone, generating new singlet oxygen molecules. Stationary levels of all these active oxygen species are extremely low due to their instability, but since water is never devoid of molecular oxygen (recall that any perturbation of water gives birth to oxygen and hydrogen at a non-zero probability), high energy quanta-generating processes never completely fade out.

We observed that in the course of CRDB of slow oxidation of amino acids in aqueous solutions initiated with H₂O₂ addition or with low intensity UV-irradiation, concentration of H₂O₂ increases to levels that can be explained only by water oxidation with O₂.¹⁷ Recently, it has been shown that in water containing carbonates and phosphates¹⁸ or in water bubbled with noble gases, such as argon,¹⁹ concentration of H₂O₂ spontaneously increases and its augmentation goes on faster if water is stirred. Using chemiluminescent methods we also found that such processes spontaneously develop and proceed for an indefinitely long time in aerated mineral waters from natural sources.²⁰ Also is it was mentioned above H₂O₂ yield in pure water equilibrated with air under the conditions favourable for its splitting¹³ occurs faster, continues longer after initial perturbation, and reaches higher levels than in degassed water.

Oscillatory nature of reactions with active oxygen participation

At the beginning of this essay a question was asked: is water a special case of a substance that can stay after a perturbation for a sufficiently long time out of equilibrium with the environment required by the second law of thermodynamics, and if it can, what mechanisms provide its stable non-equilibrium state? According to the theory developed by Del Giudice et al based on the principles of quantum electro-dynamics coherent domains of sub-micron (‘nano’) dimensions spontaneously emerge in water and coexist in it together with non-coherent dense water ‘gas’.²¹ According to this theory water particles within a coherent domain oscillate coherently between two states belonging to individual spectrum of these states. Calculations show that two relevant levels involved in a coherent oscillation are separated by an energy of 12.06 eV whereas the ionization threshold of the water molecule is 12.6 eV, that is only 0.54 eV below ionization threshold.²² Del Guidice pointed my attention to the fact that, provided that this threshold is overcome, coherent domains (CD) may tunnel ‘hot’ electrons in the non-coherent surroundings where they stick to oxygen molecules thus initiating chain reactions described above.²³

Turning back to the three examples of stable non-equilibrium aqueous system mentioned earlier: ‘extremely diluted solutions’, ‘nanoparticle doped water’, and ‘FWS’, one may suggest that water shells surrounding nanoparticles present in these systems represent stable coherent domains that may supply electrons to oxygen. Energy of electronic excitation released due to oxygen reduction and free radical reactions may serve as activation energy for additional release of electrons from a CD. When too many electrons are extracted from a CD, it dissipates. Chain reactions terminate though metastable products of CDRB stay in a system. During this period water shells begin to build up around nanoparticles and as soon as they turn into CDs the latter again start to supply electrons to oxygen. This hypothetical scenario shows how complex oscillations of energy of electronic excitation generation, of red/ox potentials, and of other properties of aqueous systems may originate in systems where coherent water domains reduce oxygen, and its active species are present. The frequency range of oscillations varies from the optical region, characteristic for electronic excitation, to extremely low frequencies of oscillations of other parameters of the system. Thus, aqueous systems in which chain reactions with the participation of active oxygen proceed may serve as emitters and receivers of oscillatory signals in an extremely wide frequency range.²⁴ This to our mind is a necessary condition for homeopathic potencies to exert its action on living systems.

Conclusion

It is now evident that a substantial part of oxygen consumed by all aerobic organisms is one-electron reduced, and that all the processes in which active oxygen species participate described above in connection with inanimate aqueous systems in principle take place in living systems. The indispensable role of active oxygen species in regulation of practically all physiological processes is no longer disputed. According to our point of view their ubiquitous regulatory role is paradoxically provided by extremely fast elimination of active oxygen by multiple ‘anti-oxidant’ systems as soon as they emerge. As we reasoned elsewhere²⁵ evidence is accumulating that the energy of electronic excitation generated by unpaired electrons pairing may be utilized as energy of activation of particular biochemical reactions, as regulatory signals, and in special cases as the major source of energy for performing physiological functions. Since oscillatory patterns are characteristic for all processes in which active oxygen participate, both insufficient production of active oxygen and distortions in its use may result in derangement of oscillatory patterns of biochemical and physiological processes and their malfunction. External resonators such as homeopathic medicines may restore normal patterns of deranged processes. However, the problem of high specificity of particular homeopathic medicines needs further reflection.

References

1 J. Zheng and G.H. Pollack, Solute exclusion and potential distribution near hydrophilic surfaces. In: G.H. Pollack, I.L. Cameron and D.N. Wheatley, Editors, Water and the Cell, Springer, Dordrecht (2006), pp. 165–174.

2 V. Elia, S. Baiano and I. Duro et al., Permanent physico-chemical properties of extremely diluted aqueous solutions of homeopathic medicines, Homeopathy 93 (2004), pp. 144–150. SummaryPlus | Full Text + Links | PDF (154 K) | View Record in Scopus | Cited By in Scopus

3 V. Elia, L. Elia and E. Napoli et al., Conductometric and calorimetric studies of serially diluted and agitated solutions: the dependence of intensive parameters on volume, Int J Ecodyn 1 (2006), pp. 1–12.

4 Y. Katsir, L. Miller and Y. Aharonov et al., The effect of rf-irradiation on electrochemical deposition and its stabilization by nanoparticle doping, J Electrochem Soc 154 (2007), pp. D249–D259. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

5 Freitas Jr RA. Fullerene-based pharmaceuticals. Nanomedicine, Vol IIA: Biocompatibility. Georgetown, TX: Landes Bioscience, 2003 [chap 15.3.2.3].

6 G.V. Andrievsky, V.K. Klochkov and A. Bordyuh et al., Comparative analysis of two aqueous–colloidal solutions of C₆₀ fullerene with help of FTIR reflectance and UV–Vis spectroscopy, Chem Phys Lett 364 (2002), pp. 8–17. SummaryPlus | Full Text + Links | PDF (339 K) | View Record in Scopus | Cited By in Scopus

7 G.V. Andrievsky, V.K. Klochkov and L.I. Derevyanchenko, Is C₆₀ fullerene molecule toxic?!, Fuller Nanotub Car N 13 (2005), pp. 363–376. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

8 K.J. Laidler and A. Cornish-Bowden, Elizabeth Fulhame and the discovery of catalysis. In: A. Cornish-Bowden, Editor, New Beer in an Old Bottle: Eduard Buchner and the Growth of Biochemical Knowledge, Universitat de Valencia, Valencia (1997), pp. 123–126.

9 A.N. Bach, On the role of peroxides in the processes of slow oxidation, Zh Russ Phys-Chem Soc 29 (1897), pp. 373–395.

10 P. Wentworth Jr, L.H. Jones and A.D. Wentworth et al., Antibody catalysis of the oxidation of water, Science 293 (2001), pp. 1806–1811.

11 X. Xu, R.P. Muller and W.A. Goddard 3rd, The gas phase reaction of singlet dioxygen with water: a water-catalyzed mechanism, Proc Nat Acad Sci USA 99 (2002), pp. 3376–3381. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

12 N.K. Baramboim, Mechanochemistry of High Molecular Weight Compounds, Chimiya, Moscow (1971).

13 G.A. Domrachev, G.A. Roldigin and D.A. Selivanovsky, Mechano-chemically activated water dissociation in a liquid phase, Proc Russ Acad Sci 329 (1993), pp. 258–265. View Record in Scopus | Cited By in Scopus

14 S. Woutersen and H.J. Bakker, Resonant intermolecular transfer of vibrational energy in liquid water, Nature 402 (1999), pp. 507–509. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

15 V.L. Voeikov and V.I. Naleto, Weak photon emission of non-linear chemical reactions of amino acids and sugars in aqueous solutions. In: J.-J. Chang, J. Fisch and F.-A. Popp, Editors, Biophotons, Kluwer Academic Publishers, Dordrecht (1998), pp. 93–108.

16 N.N. Semyonov, Chemical Kinetics and Chain Reactions, Oxford University Press, Oxford (1935).

17 V.L. Voeikov, I.V. Baskakov and K. Kafkialias et al., Initiation of degenerate-branched chain reaction of glycin deamination with ultraweak UV irradiation or hydrogen peroxide, Russ J Bioorg Chem 22 (1996), pp. 35–42. View Record in Scopus | Cited By in Scopus

18 V.I. Bruskov, A.V. Chernikov and S.V. Gudkov et al., Activation of reducing properties of anions in sea water under the action of heat, Biofizika 48 (2003), pp. 1022–1029.

19 V.L. Voeikov and M.V. Khimich, Amplification by argon of luminol-dependent chemiluminescence in aqueous NaCl/H₂O₂ solutions, Biofizika 48 (2002), pp. 5–11. View Record in Scopus | Cited By in Scopus

20 V.L. Voeikov, R. Asfaramov and V. Koldunov et al., Chemiluminescent analysis reveals spontaneous oxygen-dependent accumulation of high density energy in natural waters, Clin Lab 49 (2003), p. 569.

21 E. Del Giudice, G. Preparata and G. Vitiello, Water as a free electric dipole laser, Phys Rev Lett 61 (1988), pp. 1085–1088. Full Text via CrossRef

22 R. Arani, I. Bono and E. Del Giudice et al., QED Coherence and the thermodynamics of water, Int J Mod Phys B 9 (1995), pp. 1813–1841. Full Text via CrossRef

23 E. Del Guidice, A. De Ninno and M. Fleischmann et al., Coherent quantum electrodynamics in living matter, Electromagn Boil Med 24 (2005), pp. 199–210.

24 V.L. Voeikov, Fundamental role of water in bioenergetics. In: L.V. Beloussov, V.L. Voeikov and V.S. Martynyuk, Editors, Biophotonics and Coherent. Systems in Biology, Springer, New York (2006), pp. 89–104.

25 V.L. Voeikov, Reactive oxygen species (ROS): pathogens or sources of vital energy? Part 1. ROS in normal and pathologic physiology of living systems, J Alt Compl Med 12 (2006), pp. 111–118. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus
V.L. Voeikov, Reactive oxygen species (ROS): pathogens or sources of vital energy? Part 2. Bioenergetic and bioinformational functions of ROS, J Alt Compl Med 12 (2006), pp. 265–270. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

Correspondence: Vladimir L. Voeikov, Faculty of Biology, Lomonosov Moscow State University, Moscow 119234, Russia.

Homeopathy
Volume 96, Issue 3, July 2007, Pages 196-201
The Memory of Water

This is part of the Homeopathy journal club described here:

www.badscience.net/?p=490

doi:10.1016/j.homp.2007.03.008    
Copyright © 2007 Elsevier Ltd All rights reserved. The octave potencies convention: a mathematical model of dilution and succussion

David J. Anick^{, a,
a}Harvard Medical School, McLean Hospital, Centre Bldg. 11, 115 Mill St., Belmont, MA 02478, USA
Received 22 February 2007;  accepted 27 March 2007.  Available online 31 July 2007.

Several hypothesized explanations for homeopathy posit that remedies contain a concentration of discrete information-carrying units, such as water clusters, nano-bubbles, or silicates. For any such explanation to be sustainable, dilution must reduce and succussion must restore the concentration of these units. Succussion can be modeled by a logistic equation, which leads to mathematical relationships involving the maximum concentration, the average growth of information-carrying units rate per succussion stroke, the number of succussion strokes, and the dilution factor (x, c, or LM). When multiple species of information-carrying units are present, the fastest-growing species will eventually come to dominate, as the potency is increased.

An analogy is explored between iterated cycles dilution and succussion, in making homeopathic remedies, and iterated cycles of reseeding and growth, in bacterial cultures. Drawing on this analogy, the active ingredients in low and medium potency remedies may be present at early dilutions but only gradually come to ‘dominate’, while high potencies may develop from the occurrence of low-probability but faster-growing ‘mutations.’ Conclusions from this model include: ‘x’ and ‘c’ potencies are best compared by the amount of dilution, not the amount of succussion; the minimum number of succussion strokes needed per cycle is proportional to the logarithm of the dilution factor; and a plausible interpretation of why potencies at approximately regular ratios are traditionally used (the octave potencies convention).

Keywords: dilution factor; succussion; mathematical model; logistic curve; competition

Article Outline

Introduction

Modeling succussion

Two active ingredients

Multiple active ingredients

High potencies

Conclusion

References

Introduction

Homeopathic remedies are made by iterated dilution (in water or ethanol–water) and succussion (vigorous repeated pounding of the closed vial against a firm surface), starting from a mother tincture (‘MT’), most often a plant or animal extract. Hahnemann experimented mainly with 1:9 (‘x’), 1:99 (‘c’), and 1:50 000 (‘LM’) dilutions. These have become, by convention, the dilution ratios that are used in commercially available remedies. We will call the volume increase during dilution the ‘dilution factor’ and denote it as H. Thus, H=10 for ‘x’ remedies, H=100 for ‘c’ remedies, and H=50 001 for ‘LM’ remedies.

The number of dilution–succussion cycles is the potency of the remedy, denoted P. Within homeopathic practice, while it is theoretically possible to give a patient any potency of a remedy, only certain potencies are normally available and stocked. For the ‘x’ series these are the ‘6’, ‘12’, ‘30’, and ‘200’ potencies, while for the ‘c’ series one can get ‘6’, ‘12’, ‘30’, ‘200’, ‘1000’, and ‘10 000’. Although in other homeopathic traditions different series may be used, there is a similar progression. LM’s start with LM1 and every potency is available (i.e. LM2, LM3, LM4, etc.) up to LM10 or so. The potencies most frequenty dispensed in practice (at least in the Anglo-American tradition), by far are the 6c and 12c (‘low potencies’), 30c and 200c (‘medium potencies’), and 1000c and 10 000c (‘high potencies’). Homeopaths generally believe that remedies gain strength with more dilution–succussion cycles, although there are believed to be qualitative differences: ‘stronger’ is not necessarily ‘better’. Posology, or how to decide what potency to give, is a complex subject about which there are many theories. In general, higher potency remedies are used when the remedy choice is more certain, when the patient’s vital force is stronger, and when the problem is chronic rather than acute.

Is there any rationale for the sequence: 6, 12, 30, 200, 1000, 10 000? The sequence bears some resemblance to a geometric progression, and the use of fixed potencies with (supposedly) approximately equal ratios is called the ‘Octave potencies convention’ (OPC). I wondered, could there possibly be a rationale for the OPC? The usual thinking about this is that the remedy’s qualities change gradually with potency, eg a 12c and a 13c are nearly the same, and 13c and 14c are nearly the same, but enough small changes accumulate in going from 12c to 30c, that 30c may bring different results in the clinic from 12c. While a 12c and a 13c are ‘nearly the same’, a 1000c and a 1001c would be considered to be clinically interchangeable.

Various hypotheses have been put forward to ‘explain’ homeopathy in terms of conventional physics and chemistry. ‘Local’ hypotheses posit that remedies differ from untreated water in that they contain a population or concentration of an active ingredient. For some explanations, the active ingredient is a (hypothetical) persistent structural feature in what is chemically pure water, such as a zwitterion,¹ a clathrate,² or nano-bubble.³ The ‘silica hypothesis’ posits that SiO₂ derived from the glass walls of the succussed vials is condensed into remedy-specific oligomers or nanocrystals, or else that silica nanoparticle surface is modified in patches to carry remedy-specific information.⁴

The mathematical model developed here is compatible with any of these explanations. Let Q denote the concentration of ‘active ingredient’. Depending on the hypothesis, Q could be the concentration of a particular zwitterion, of a particular species of nano-bubble, of a particular silica oligomer (or family of oligomers), or of a specific silica nanoparticle surface feature. Note that the concentration of active ingredient in ordinary solvent is zero or is assumed to be negligible. Right after dilution, the concentration will be Q_dil=Q/H.

The fundamental assumption underlying our mathematical model is the following. Since a 1000c and 1001c are (essentially) identical, we assume that the effect of diluting a remedy of concentration Q, followed by succussion, is to regenerate (approximately) the same concentration Q of the same active ingredient. The model will shortly be made more complex by postulating multiple species of active ingredients, but let us start with the assumption of a single active ingredient. Then succussion must raise the concentration from Q_dil back up to Q=HQ_dil. If succussion did not raise the concentration by a factor of (on average) H, then after repeated cycles the concentration would dwindle to zero.

Modeling succussion

How does succussion raise the concentration by a factor of H (typically H=100)? The answer depends on what the active ingredient is alleged to be. For the nano-bubble hypothesis, a nano-bubble might, during the pressure wave of succussion, organize the adjacent H₂O into another copy of the same nano-bubble, and both bubbles might survive as structural features after the pressure wave passes.

For the silica hypothesis, silica might be released into solution as Si(OH)₄ monomers by the mechanical agitation of succussion, and the specific silica nanocrystals might catalyze the formation of more copies of themselves out of the newly released monomers. It is beyond the scope of this article to assess or justify whether such notions are plausible.

Our starting point is to suppose that if any local hypothesis for homeopathy is valid, then there is some mechanism by which some structural feature replicates itself when succussed. We do not need to know what the feature is, or how it makes more copies, to develop the model.

Succussion consists of a series of ‘succussion strokes’. During each stroke several things happen: pressure rapidly surges then returns to 1 atm, the solution is turbulently mixed with air, Si(OH)₄ enters solution, and so on. Let S denote the number of strokes used in each cycle. We postulate that in the course of S strokes, the concentration climbs from Q_dil to HQ_dil. We cannot say what happens during a single stroke since we do not know the specific mechanism, but the hypothesized mechanisms suggest that each unit (ie each zwitterion, each nano-bubble, each silica nanocrystal, etc.) uses the added ‘raw material’ (ie the added water or newly dissolving air or Si(OH)₄ monomers) to create more copies of itself. Thus, we assume that succussion strokes induce replication of the active units.

To call it ‘replication’ suggests a 2-for-1 process, but the process may not be 100% efficient. Instead of 2-for-1 we postulate that one succussion stroke raises the concentration of active units by a factor we call R. If Q_m is the concentration after m strokes with Q₀=Q_dil, then Q₁=RQ₀, Q₂=RQ₁, and so on. This cannot continue forever, or Q_m would blow up exponentially. Replication ceases when the solution runs out of usable raw material. For instance, if the units are nano-bubbles, there will be some limit on how closely they can crowd together, and once the population reaches the crowding limit they will not be able to replicate further. This situation is a familiar one in population biology: growth starts exponentially but then is capped by a finite carrying capacity. Mathematically it is modeled by assuming the actual growth rate is proportional to the amount of raw material accessible for further growth, which in turn is proportional to the difference between Q and a maximum concentration C. We obtain the discrete logistic equation,

Qm+1–Qm=(R-1)Qm(C–Qm)/C.

(1)

This equation does not have a simple solution in its discrete form, but the very similar equation

Qm+1–Qm=(R-1)Qm(C–Qm+1)/C

(2)

has the very nice exact solution

(3)

which exhibits the expected S-shaped curve asymptotic to C as m→∞. After S succussion strokes the concentration is HQ₀, ie Q_S=HQ₀, and putting this into Eq. (3) shows that the concentration at the end of each cycle is given by

(4)

According to Eq. (4), if R^SH, then Q_S will be close to the maximum allowable concentration C, but if R^S<H, there is no (positive) solution, and the concentration will die out to zero with repeated dilution–succussion cycles.

This already tells us something interesting about the number of succussion strokes needed. If our growth rate reflects ‘perfect’ replication when very dilute, ie R=2, then to get R^S>H we require a minimun of 7 succussion strokes per cycle for H=100 (since 2⁷>100 but 2⁶<100), and a minimum of 16 strokes for the LM series. For a slower growth rate like R=1.2, we need at least 38 strokes per cycle to bring the concentration u to 90% of the maximum when H=100, and 72 strokes per cycle for LM’s. (These stroke counts are obtained by setting Q_S/C=0.9 in Eq. (4) and solving for S).

Although we have no experimental evidence to give us a range for R, Eq. (4) suggests that we should not skimp on succussion, with 40 strokes as a reasonable minimum when making ‘c’ potencies. Hahnemann himself held changing views about the optimum value for S. In the 5th edition of the Organon he recommended S=2 but revised the figure upward to S=100 in the 6th edition [5, p. 270].

Two active ingredients

If there were just a single active ingredient, dilution would reduce and succussion would restore the concentration each cycle. Nothing would change with dilution–succussion cycles and there would be no point in repeating dilution and succussion. But suppose there are two active ingredients, each of which would, if it were alone, increase according to Eq. (1). Approximate Eq. (1) by a continuous version, with the stroke count parameter ‘m’ being replaced by a ‘time’ parameter t. The difference equation (1) becomes the familiar logistic differential equation,⁶

(5)

where we have scaled the concentration so that X=Q/C, and instead of R we encounter r =ln(R). The solution is X(t)=(1+(X(0)^-1-1)e^–rt)^-1, which is the continuous form of Eq. (3).Let us add a second species of active ingredient, eg a different nano-bubble type or a different form of silica crystal. Let us assume that when some of each is present, the two species ignore each other. Each species replicates at its own rate as if the other were not present. There is still interaction, however, since both species draw upon the same raw material, of which there is a fixed amount. This sets up a competition scenario. The differential equations are

(6)

where without losing generality we assume s>r. There is no elementary solution but the trajectories can be found by dividing the two equations, giving dY/dX=(s/r)(Y/X), hence

Y/Y(0)=(X/X(0))s/r.

(7)

Let us further assume that the number of succussion strokes is large enough that the limiting concentrations are nearly attained; this is modeled by letting t→∞. Then the final concentrations are given by the intersection of trajectory (7) with the line 1–X–Y=0.

Suppose we conduct a series of dilution–succussion cycles for this two-component model. Let (X_P,Y_P) describe the concentrations at the end of the Pth cycle, P denoting the potency. The relationship between (X_P+1,Y_P+1) and (X_P,Y_P) is as follows. Starting with (X_P,Y_P), after dilution the concentrations are (X_P/H,Y_P/H). Putting X(0)=X_P/H and Y(0)=Y_P/H into Eq. (7), we see that (X_P+1,Y_P+1) is found by intersecting the line X+Y=1 with the curve HY/Y_P=(HX/X_P)^s/r.

To proceed it is easier to work with the ‘pH’ values, x=−log(X) and y=−log(Y) (‘log’ is log₁₀). Set h=log(H) (so h=2 for ‘c’ potencies). Referring to Figure 1, dilution takes us on a line of slope 1 from (x_P,y_P) to (x_P+h,y_P+h), and succussion takes us in a straight line of slope s/r from there back to the curve 10^−x+10^−y=1. (x_P+1,y_P+1) is the intersection of that curve and line.

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Figure 1. Log concentrations in alternating succussed and diluted stages of a two-ingredient remedy undergoing a transition from ‘X’-dominated to ‘Y’-dominated, for s/r=1.2. Succussed remedies lie on the blue curve, 10^–x+10^–y=1 (X+Y=1). Dilution raises both x and y by h=2.

Iterating the process, we ‘walk’ along the curve, at some point transitioning from values where y>x (meaning that X>Y and ‘X’ is the dominant species present) to values where x>y (ie ‘Y’ dominates). After the transition x_P→∞ while y_P→0, ie ‘X’ continues fade to zero while ‘Y’ converges to the maximum concentration. Before the transition, ie where y>x, the curve 10^−x+10^−y=1 is nearly vertical and a good approximate formula relating (x_P+1,y_P+1) to (x_P,y_P) is

(8a)

while after the transition (where x>y) it is nearly horizontal and

(8b)

Using only the fact that the curve 10^−x+10^−y =1 has a negative slope, we obtain the inequalities

(9)

Clearly, what happens with increasing potency is that the slower-growing species ‘X’ is gradually replaced by the faster-growing species ‘Y’. Exponentiating Eq. (9) we see that the concentration ratio Y_P/X_P increases by a factor of between 10^h(s−r)/s and 10^h(s−r)/r, or between H^(s−r)/s and H^(s−r)/r, with each dilution–succussion cycle. Pre-transition the ratio increase is very close to H^(s−r)/r, while post-transition it is very close to H^(s−r)/s. Thus, the transition potency can be predicted fairly easily if one knows the growth rates and the initial concentration ratio at a low potency. If s/r is only slightly bigger than 1, it takes more cycles to reach the transition and the transition occurs gradually over several cycles. If s/r is substantially bigger than 1, the transition is reached quickly and occurs abruptly. Of course, there is no transition at all if the initial concentration of ‘Y’ exceeds that of ‘X’: in this case the slower growing ‘X’ just declines, out-competed by ‘Y’.

Translating this to the clinical context, the implication is that, remedies where the two-component model applies will feature one species below the transition potency, and a different species above it. For example, if the transition occurs at P=20, then potencies below 20c should all have approximately the same clinical action, since the are all dominated by the same pre-transition active species, whereas those above 20c will be similar to each other but different from the pre-transition potencies. Because of this, having any one pre-transition remedy and any one post-transition remedy should suffice in the clinic. Having a ‘12c’ and a ‘30c’ would cover it.

The number of cycles needed to get from a potency whose concentration ratio is W_P=Y_P/X_P to the transition potency, is about −log(W_P)/(h(s−r)/r). Without needing to know any values for s, r, or W_P, this formula tells us that the number of cycles needed is inversely proportional to h=log(H). Starting from the same point, ‘c’ potencies attain the transition twice as fast as ‘X’ potencies, and ‘LM’ progress faster than ‘c’ by a factor of log(50 001)/log(1 0 0)=2.35. More generally, our formulas show that each ‘c’ dilution–succussion cycle has almost exactly the same effect as two ‘X’ cycles. To the extent that this type of model turns out to be valid, it appears to answer the long-standing argument in homeopathy as to whether dilution or succussion matters more in ‘potentizing’ remedies. This model predicts that it is the total amount of dilution that determines a remedy’s properties. Succussion at each stage must exceed a minimum threshold, but succussing significantly beyond that threshold will not make much difference.

Our mathematical model of two structural ‘species’ with different growth rates competing for raw material and limited by a maximum concentration has a perfect analogy in population biology. The analogy would be two living species that compete for a resource base but one reproduces faster than the other. A series of cycles occur, driven by periodic natural disasters that decimate each species’ numbers by the same factor of H each time. As they recover between disasters, the faster-growing species gains some ground each cycle and eventually replaces the slower-growing one.

Bacteriologists use this model deliberately to select for variants with desired traits. Bacteria with resistance to a toxin T will be ‘faster-growing’ in the presence of T. A baseline low mutation rate means that some low initial concentration of the bacteria is of the T-resistant ‘species’ (not necessarily a distinct species in the biological meaning). After culturing it to maximum growth with T, a small amount (eg 1%, corresponding to H=100) is re-seeded onto a new dish and then recultured. After many cycles the T-resistant species comes to dominate. ‘Dilution’ is like seeding a sterile culture dish while ‘succussion’ is like growth and selection.

Multiple active ingredients

The model can be extended to n species of active ingredient, n>2. The concentration of the ith species is denoted X_i, or if we also include the potency in the notation, as X_i,P. The growth rate of X_i is in (R_i), and −log(X_i) is denoted x_i. The system of equations governing succussion is

(10)

We omit details of its solution. The effect of one dilution–succussion cycle is described by

xi,P+1≈xi,P+h(rDOM–ri)/rDOM,

(11)

where r_DOM denotes the growth rate of whatever species happens to have the greatest concentration at potency P. Note that Eq. (11) reduces to Eqs. (8a) and (8b) when n=2. The effect of one dilution–succussion cycle on the concentration ratio for any two of the species, say for X_i,P/X_j,P, is to change the ratio by a factor of H^{(r_i–r_j)/r_DOM}, ie

(Xi,P+1/Xj,P+1)/(Xi,P/Xj,P)≈H(ri–rj)/rDOM.

(12)

Depending on their initial concentrations, several of the n species may dominate in turn, but as P→∞, eventually only the fastest-growing species remains.Figure 2 illustrates the model with n=4 species and H=100. We suppose that the four species are present at the 4c potency, having been generated by some process that utilizes components from the MT. Perhaps compounds in the MT might catalyze the formation of specific silicates through directed polymerization of Si(OH)₄ monomers. Again, how the MT and early potencies would do this is not relevant to our model. Initial (ie in the 4c potency) concentrations and growth rates (R_i) are taken to be: X₁=0.99, R₁=1.2; X₂=0.01, R₂=1.3; X₃=10^–8, R₃=1.35; X₄=10^–12, R₄=1.36. These are entirely made-up numbers but they are not implausible. Note that initial concentrations correlate inversely with growth rates. As a result we can expect that each species may lead the ‘race’ for an interval of several potencies, but ultimately X₄ will ‘win.’

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Figure 2. Log (conc) vs potency, for four-component model.

Figure 2 displays log(X_i,P) as a function of P. Figure 2 was generated by a computer program that used the four-species analog of Eq. (1) to compute exact predictions of concentrations using S=40 succussion strokes per cycle. Each of the first three concentrations dominates for a while but then at a transition gives way to the next faster-growing species. Transitions correspond to points where the top two curves cross: at P=6.5, 23.5, and 79. With a log scale for the ordinate, each curve consists of a succession of nearly straight line segments. This behavior is explained by Eq. (11), which predicts that the slope should change at transition points (where r_DOM changes) but should remain nearly constant between transition points.

Figure 3 shows the same information but displays X_i,P as a function of log(P). Note that for each of ‘6c’, ‘12c’, ‘30c’, and ‘200c’, a different species is dominant. Vertical lines have been added at these positions. Potency intervals are defined by which species dominates, and the potencies falling within any interval would be expected to be clinically equivalent. Interval boundaries occur at transition points: in this example the intervals are 4c to 6c, 7c to 23c, 24c to 79c, and 80c and up. Thus, there are just four essentially different remedies derivable from this MT.

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Figure 3. Conc vs log(potency), for four-component model.

Figure 3 illustrates the ‘best case scenario’ for the octave potencies convention: there are four species, each of which dominates one interval of potencies, and the potencies efficiently make available one potency from each interval. (For this MT, all potencies beyond 200c would be virtually identical to the 200c potency and would be unnecessary.) This illustrates what one would ideally want from a prescribing convention: one example of each dominant species is included, without redundancy. Given that the number of species and their growth rates must vary from MT to MT, it would be inconceivable that one number sequence (ie 6, 12, 30, 200, 1000, 10 000) would work in this ideal manner for every MT. Still, it may do a good enough job of balancing the need for simplification against comprehensive coverage, for the majority of MT’s.

High potencies

Dr JT Kent, developer of the octave potencies concept, ^{[7] and [8]} actually continued the sequence beyond 10 000: the continuation was 50 000, 10⁵, 5×10⁵, 10⁶. These ‘very high’ potencies are not often used today. Does our model support a role for high (1000 and 10 000) and very high potencies? As we have noted, use of a potency above 200c only makes sense if there is a transition that occurs at a potency higher than 200, and likewise a potency above 1000c adds something new only if there is a species whose transition to dominance occurs above P=1000.

In Figure 2, the last transition (at 79c) resulted from two growth rates that are very close (R₃=1.35 and R₄=1.36), along with a very small initial concentration of X₄ (10^–12). For the model to yield a transition beyond 200c, there would have to be an even smaller difference in growth rates or a much smaller initial concentration (of the species whose transition to dominance occurs beyond 200c).

Tiny differences in rates are certainly a mathematical possibility, but this strikes me as unlikely to be the explanation for the majority of high potency remedies. Tiny initial concentrations likewise work in the model, but if we go below 10^–17 or so we run into the Avogadro limit. (Concentrations have been scaled so that the maximum concentration C of a structural component is set to ‘1’. Measurements of silica^{[9] and [10]} and other considerations place C in the micromolar range. If C is 10 μM then X_P=10^–17 means 10^–22 M, and in a 10 mL sample there would be 10^–24 mol, ie probably none, of this active ingredient.)

There is a way around this, and that is to suppose that the species with the late (ie >200) transition is not present in the initial low-potency mix at all: it only appears later in the potentizing process, presumably as a result of imperfect replication of one of the other species during a succussion step. Drawing on the biological analogy, the late-transitioning species would arise as a mutation of an earlier-transitioning species. If the mutation rate is low, it could take many cycles of dilution and succussion until the mutation first appears. To survive, the mutation would need to have a selective advantage (which in our model means a faster growth rate).

If this is correct, the high potency remedies (and possibly some 30c’s or 200c’s as well) feature an active ingredient that arises out of a lower-potency active ingredient and eventually replaces it. Ballpark numbers might be that the mutation has only a 0.5% chance of arising in any given succussion–dilution cycle, and once it arises it takes 50 cycles to become dominant. Many of the cycles between 200c and 1000c may be doing nothing except ‘waiting’ until the chance event of this particular mutation occurs. However, with enough repetitions even a 0.5% event is almost sure to occur eventually. It has a 1–(0.995)⁷⁵⁰=97.6% chance of occurring somewhere between the 200th and 950th cycle, and of achieving dominance between the 250th and 1000th cycle. According to this explanation, high potency remedies contain their intended active ingredient only with a certain probability, though the probability may be quite high (over 95%). The explanation for the need for a 10 000c would be that it depends upon the emergence of an even lower likelihood mutation (around 0.05% occurrence rate per cycle), and so on for the very high potencies.

Conclusion

Kent’s octave potency sequence is widely accepted in homeopathic practice. In the clinic, when homeopaths refer to ‘the next higher potency after 30c’, they mean 200c, not 31c. Our model suggests a reason this may be literally correct: the 31c is essentially identical to 30c, but somewhere between 30c and 200c a transition occurs to the ‘next’ active ingredient. One cannot derive Kent’s specific potency list from the model, but it does support Kent’s principle of stocking discrete potencies that occur at approximately geometric (‘octave’) intervals.

We started with a single assumption, namely that each succussion stroke amplifies the structural active ingredient by drawing upon finite resources (space, H₂O, Si(OH)₄, or silica surface). This assumption led to a relationship (Eq. (4)) among the growth rate, dilution factor, and stroke count. Based on Eq. (4) we recommended a minimum of 40 succussion strokes per cycle, for ‘c’ potencies.

When there are multiple species of active ingredients with different growth rates, we assumed there was no interaction other than competition for the finite resources. The choice of language was intentional, to draw attention to a parallel in mathematical biology. This assumption can be questioned or altered. For example, there could be other interactions including cooperative ones between the species. Also, instead of a small number of distinct species there could be a continuum or near-continuum of species (eg nano-bubble or nanocrystal size might be a continuous parameter) that is better handled with a diffusion–selection model.¹¹ A ‘gradual evolution’ derived from selection among a near-continuum of homeopathically active silicates has been hypothesized.⁴ Our assumption of a small number of distinct active ingredients leads to a picture that in general is like Figure 2 and Figure 3: most potencies contain a single ‘dominant’ species with the other species occurring at levels one or more orders of magnitude lower. Each species remains dominant for an interval of potencies, until it is replaced by a different species that grows faster but starts at a lower level. The transitions can be predicted well using Eqs. (11) and (12). The locations of the transitions are proportional to log(dilution factor), meaning that a 60x will be equivalent to a 30c, a 200x like a 100c, and so on.

The strengths of this model are its generality—it works the same regardless of what the actual structural ingredient turns out to be—and its power to explain a complex clinical practice from simple starting assumptions. The model may not apply if the mechanism turns out to be ‘non-local,’ ie does not involve discrete information-carrying units (eg coherence or quantum entanglement^{[2], [10] and [12]}) or, obviously, if remedies are ultimately proved to be mere placebos or markers that support the ritual of healer–client interaction. The great weakness of the model is that it is inspired solely by clinical conventions with no direct experimental support. Still, we have provided a new way to think about the dilution–succussion cycle, which could some day suggests experiments to test the model.

References

1 D.J. Anick, Stable Zwitterionic water clusters: the active ingredient in homeopathy?, J Am Inst Homeop. 93 (1999), pp. 129–135.

2 In: J. Schulte and P.C. Endler, Editors, Ultra High Dilution, Kluwer Academic Publishers, Dordrecht (1994).

3 R. Roy, W.A. Tiller, I. Bell and M.R. Hoover, The structure of liquid water; novel insights from materials research; potential relevance to homeopathy, Mater Res Innovation (9–4) (2005), pp. 93–124.

[4] D.J. Anick and J.A. Ives, The silica hypothesis for homeopathy: physical chemistry, Homeopathy 96 (2007), pp. 189–195. SummaryPlus | Full Text + Links | PDF (242 K)

5 Hahnemann S. Organon of Medicine. Fifth and sixth editions. New Delhi: Jain Publ. Pvt. Ltd.; reprinted 1995 (transl: Dudgeon RE and Boericke W).

6 L. Edelstein-Keshet, Mathematical models in biology, SIAM Classics Appl Math 46 (2004).

[7] Bhatia M. Homeopathic Potency Selection. Hpathy Ezine, April 2004: www.hpathy.com/philosophy/bhatia-potency-selection2.asp.

[8] Thomas AL, Homeopathic Posology. Similima 18: www.similima.com/org18.html.

9 J.-L. Demangeat, P. Gries, B. Poitevin and J.-J. Droesbeke et al., Low-field NMR water proton longitudinal relaxation in ultrahighly diluted aqueous solutions of silica-lactose prepared in glass material for pharmaceutical use, Appl Magn Reson 26 (2004), pp. 465–481. View Record in Scopus | Cited By in Scopus

10 H. Walach, W.B. Jonas and J. Ives et al., Research on homeopathy: state of the art, J Alternative Complementary Med 11 (2005), pp. 813–829. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

11 G.F. Webb and M.J. Blaser, Dynamics of bacterial phenotype selection in a colonized host, Proc Natl Acad Sci USA 99 (2002), pp. 3135–3140. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

12 L.R. Milgrom, Are randomized controlled trials (RCTs) redundant for testing the efficacy of homeopathy? A critique of RCT methodology based on entanglement theory, J Alternative Complementary Med 11 (2005), pp. 831–838. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

Corresponding author. DJ Anick, Harvard Medical School, McLean Hospital, Centre Bldg. 11, 115 Mill St., Belmont, MA 02478, USA.

Homeopathy
Volume 96, Issue 3, July 2007, Pages 202-208
The Memory of Water

This is part of the Homeopathy journal club project described here:

www.badscience.net/?p=490

doi:10.1016/j.homp.2007.05.002
Copyright © 2007 Elsevier Ltd All rights reserved. Conspicuous by its absence: the Memory of Water, macro-entanglement, and the possibility of homeopathy

L.R. Milgrom^{1, ,
1}Department of Chemistry, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, UK
Received 23 February 2007; revised 8 May 2007; accepted 14 May 2007. Available online 31 July 2007.

In order to fully comprehend its therapeutic mode of action, homeopathy might require both ‘local’ bio-molecular mechanisms, such as memory of water and ‘non-local’ macro-entanglement, such as patient–practitioner–remedy (PPR) descriptions.

Keywords: homeopathy; locality; non-locality; memory of water; macro-entanglement

Article Outline

Introduction

Locality, non-locality, and philosophy

Local hypotheses and the memory of water

Non-local hypotheses and macro-entanglement

Quantum theory and homeopathy

Entanglement in the homeopathic process

Conclusion: a therapeutic Uncertainty Principle?

Acknowledgements

References

Introduction

Despite increasingly sterile debates over ‘whether’ homeopathy works,¹ the ‘how’ and ‘why’ have yet to be seriously addressed by science. One need not look far to see why.

Formerly a successful allergy researcher,² Jacques Benveniste spent the last 20 years of his life out of the scientific mainstream because of his fascination with the ‘Memory of Water’.³ Despite democratic appearances, when it comes to dealing with what it considers ‘heretical’ (eg, homeopathy), science can be as narrow-minded, unforgiving, and vicious as any inquisition. Disregarding the burning stakes of peer opprobrium however, some are seeking answers to the question of how homeopathy might be possible.

Two types of hypothetical ‘mechanism’ are under consideration. Labelled ‘local’ and ‘non-local’, they depend, respectively, on conventional scientific positivism,⁴ or appeal to generalised quantum theoretical concepts of complementarity and entanglement.⁵ Local hypotheses envisage homeopathic remedies behaving in a way similar to any other medicine, ie, ‘pharmacologically’. The problem is that most homeopathic remedies are diluted out of molecular existence. In order therefore to comply with the causal principles of positivist science, a mechanism has to be envisaged by which some kind of information transfer (usually thought of as electromagnetic) can occur to a molecular substrate (eg, water), via homeopathy’s unique method of remedy production.⁶ Involving successive iterations of dilution followed by violent agitation collectively known as succussion, it is this information transfer to the solvent which has been called the Memory of Water (MoW).

Non-local hypotheses,⁷ are concerned less with the remedy per se, proposing generalised forms of quantum entanglement as the basis for homeopathy’s efficacy. They suggest instantaneous, acausal correlations are somehow established between various combinations of patient, practitioner, and remedy, ultimately leading to an observed change in the patient’s state of health. These ideas are in their infancy and even more controversial than MoW: indeed, to many the idea that quantum theory might be applicable in our macroscopic domain is anathema. The received conventional wisdom is that non-deterministic quantum theory describes the world of sub-atomic particles, atoms and molecules, while deterministic Newtonian (classical) and Einsteinian (relativistic) theories are sufficient for the macroscopic world of material objects. Non-local hypotheses however, have the advantage of being generalisable outside homeopathy to other healing disciplines.

The purpose of this paper is to review the two types of descriptions of homeopathy’s effects. Then, viewing these different approaches as complementary, not contradictory, and realising that some local explanations are also ‘tarred’ with the brush of entanglement (albeit at the molecular level), to consider how a more complete picture of the homeopathic process might be possible, ultimately leading to new experimental tests.

Locality, non-locality, and philosophy

Most, but by no means all, of science is based on a set of assumptions about the universe collectively known as Local Reality.⁸ This may be summed up as follows:

• The universe is real and things in it exist whether we observe them or not.

• It is legitimate to draw general conclusions and predictions from the outcome of consistent experiments and observations.

• No signal can travel faster than light.

This is very much a ‘common sense’ view of the universe as (a) it defines ‘reality’ as something obviously ‘out there’ separate and independent of us and (b) it is ‘local’ because parts of the universe out of speed of light contact cannot possibly be in communication. For most of the time, this assumption of Local Reality ‘works’: it is an accurate descriptive model of how most things in the universe interact. However, recent quantum physics experiments on photons, electrons, atoms, and even molecules demonstrate beyond doubt that particle interactions result in non-local correlations.⁸ This means that although there is no signal transfer in the classical sense between these particles, nevertheless, they can be instantaneously ‘connected’ over vast distances and across time itself, a phenomenon known as quantum entanglement.⁹ It is as if at a deep level, everything in the universe is instantaneously linked together in a vast holistic matter-energy network of interacting fields which transcends ordinary concepts of space and time. And we, composed of trillions of particles are an inseparable part of it: far from what reason seems to tell us.

The three Local Reality points above have been expanded into seven propositions, which are essentially ‘articles of faith’,¹⁰:

(1) The universe is consistent over all space and all time.

(2) The universe is understandable, ie, predictable.

(3) What is valid here is valid elsewhere.

(4) The universe is material and not spiritual.

(5) Everything that is physical is observable.

(6) The universe can be described and ascertained mathematically.

(7) Experiment validates theory.

This ‘catechism’ arises out of science’s primarily inductive logical structure. Philosophers have described two types of reasoning called deductive and inductive logic. In the former, one can draw true conclusions from true starting premises. For example, consider the following statements:

• All swans are white.

• The creature in front of us is a swan.

Ergo, from these two premises, we can conclude (especially if we choose not to look) that:

• The creature is white.

With inductive logic however, we move from the particular to the general from premises about objects we have examined, towards conclusions about objects that we have not yet examined. Thus:

• Every swan I have ever seen has been white; Ergo….

• The next swan I see will be white.

What this simple example demonstrates is that many of our beliefs are based on extrapolations from observed (past or present) events to situations which are unknown, unobserved, or in the future. It was the 18th century philosopher Hume who pointed out that inductive reasoning is based on custom or habit, and in so far as it predicts the future will resemble the past, cannot actually ‘prove’ anything, for instance the impossibility of a swan being black. Hume also pointed out that the principle of induction cannot itself be proven by induction. The word ‘proof’, in fact, should be applied strictly only when reasoning deductively, as in mathematics. As most science is rooted in inductive logic, if follows that it too is predictive and actually incapable of proving or disproving anything.

In addition, Peirce drew attention to abduction which refers to the creative process prior to induction and deduction, by which scientists arrive at their initial hypotheses in the first place.¹¹ It involves ordering disparate pieces of information into a first hypothetical structure and may be likened to pattern recognition: something humans seem particularly good at. Reductionist scientific theories generally overlook or are incapable of considering the process of abduction.

So what tends to happen in practice is that the more often a premise’s predictions turn out to are fulfilled, the more it is taken as ‘proof’ that the premise must be true. Eventually, the ‘truth’ of the premise becomes ingrained: it changes from ‘Every swan I have ever seen has been white’ to ‘All swans are white.’ From that moment, black swans are ‘impossible’.

Most people assume that science starts from secure reproducible observations out of which ‘facts’ about the world are distilled, an ideal enshrined in logical positivism. Its core beliefs are that scientific questions can be answered completely objectively; that experiments allow scientists to compare theory directly with facts; and that science is a sure route to ‘truth’. In this respect, it is scientifically established ‘evidence’ that is now supposed to provide the only basis for the ‘facts’ on which medical decisions are to be based, regardless of practitioners’ empirical ‘hands on’ experience and intuition.^{[12] and [13]}

However, since the second half of the 20th century, logical positivism has been under sustained attack as being too simplistic from Post-Modernist philosophies of science.¹⁴ There is no such thing as unbiased observation free of any sociological or cultural conditioning, even in science and even under the most stringent experimental circumstances. Therefore, our acceptance or rejection of ‘evidence’ is also open to serious question. Our tendency is to reject evidence which does not fit with currently-held theory. Consequently, positive results from even the highest standard scientific trials are rejected by those who will not accept homeopathy’s claim that remedies diluted out of molecular existence might have any effect. For black swans, read homeopathy.

Kant, in the 18th century, pointed out that observation depends on our individual senses, assumptions, and background beliefs.¹⁵ He suggested that our picture of the world is structured by a combination of sensory data (‘phenomena’) and fundamental concepts of reason, eg, ‘causation’, that are culturally ‘hardwired’ into our minds. Consequently, we cannot know anything about how the world ‘really is’. Recent interpretations of quantum theory¹⁶ take this idea further by suggesting there is no world ‘out there’ separate from and independent of our observation of it. Or even more starkly, information is all there is.

Local hypotheses and the memory of water

Benveniste did not coin the phrase ‘Memory of Water’ (MoW), as research into solvent effects dates back to the 1960s. However, his research was highlighted by Nature in 1988,³ and subsequent failed attempts to repeat it.¹⁷ A multi-centre European trial involved modifications to Benveniste’s original method (eg, the use potentised histamine instead of anti-IgE), and was statistically significant only on pooling the results from all the laboratories involved.¹⁸ Though still controversial, MoW is based on the same conventional scientific notions of atoms and molecules that inform chemistry, biochemistry and molecular biology. I shall deal with this on a general basis only as excellent and more detailed contributions will be found in this issue from Anick, Chaplin, Elia, Rey, Rao and others.

As Albert Szent-Gyorgyi pointed out, ‘Water is the mater and the matrix, the mother and the medium of life.’⁴ Without water, life as we know it would be impossible. Yet, water is more complex than the simple chemical formula H₂O suggests. Oxygen, at the top of Group 16 in the Periodic Table, is a gas while the other members of this column (sulphur, selenium, and tellurium) are solids. With the di-hydrides of these elements we notice another major difference. H₂S, H₂Se, and H₂Te, are highly toxic, inflammable, evil-smelling gases, while H₂O is a clear, tasteless, odourless, life-giving and sustaining liquid (see Table 1). This is due to electrical forces originating within the oxygen atom. Apart from establishing the main chemical bonds between each oxygen and two hydrogen atoms, they also give rise to extra more complex forms of weak bonding (hydrogen bonds and even weaker van de Waal’s interactions). At room temperature these loosely bind individual water molecules into large rapidly-changing (in the order of pico-seconds) dynamic ‘structures’ (Fig. 1).⁴ These, in turn influence interactions between chemical and biochemical entities.

Table 1.

Some physical constants for dihydrides of the Group 16 elements

Compound	Molar mass (g/mol)	Melting point (°C)	Boiling point (°C)	H2O	18	0	100
H2S	34	−85.5	−59.55
H2Se	81	−65.73	−41.25
H2Te	130	−49	−2

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Fig. 1. Molecular models of water: (a) shows a so-called ‘space-filling’ model and a representation of the electronic charge distribution over the water molecule. The green-to-pink envelope represents the distribution of electrical charge within the molecule, biased towards the oxygen atom. In (b), we see the more classical ‘ball and stick’ model. The red ball represents the oxygen atom while the white balls represent hydrogen atoms, the white spheres without inscribed ‘H’s’ are hydrogen-bonded hydrogen atoms from a neighbouring (unseen) water molecule: the short white ‘sticks’ between the balls represent static chemical bonds between hydrogen and oxygen atoms. In (c), we see a representation of how water molecules might loosely bind to each other via hydrogen bonding (the longer white sticks) to form a coherent but short-term structure.²⁰

Adopting a theatrical metaphor, if nucleic acids, proteins, carbohydrates, lipids and hormones, etc are the principal ‘actors’ in the unfolding biochemical ‘drama’ that is life at the molecular level, then water provides the stage, set, theatre, and direction. From this perspective, it could be that conventional bio-medicine places too much emphasis on bio-molecules at the expense of the solvent in which they perform. Because of individual patterns of electrically charged and neutral atomic constituents, each type of bio-molecule will have associated with it an ever-changing ‘halo’ of loosely bound and interconnected water molecules.¹⁹ At the charged sites on each bio-molecule, water molecules will congregate, while few water molecules gather at the neutral sites. Thus, electric fields generated by bio-molecules will be modified and modulated by their surrounding ever-changing but coherent ‘halo’ of water molecules, and this could be transmitted extremely rapidly partly via water’s rapidly switching network of interconnecting hydrogen bonds, throughout the whole solvent and received by other bio-molecules.

There is much about water yet to be discovered, so that even if scientific attention were to shift away from bio-molecules to their aqueous medium, the experimental and theoretical problems would be enormous. For example, within a single cell, there are huge differences in the water content and properties of its various parts, from the jelly-like consistency of the cytoplasm, to the more fluid content of vacuoles. Modelling such diversity is likely to be a computational nightmare.¹⁹ However, modelling water itself shows that its molecules can form short-term coherent ‘structures’, whose life is of the order of pico-seconds (10⁻¹² s) similar to icosahedra (Fig. 2) around central cavities that may contain, or may have once contained solute species.²⁰ From here, it is not hard to imagine that such dynamic aqueous ‘structures’ could be the bearers of a ‘memory’ of things once dissolved but now dissolved out.

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Fig. 2. Two coherent icosahedral water ‘structures’ formed from dynamic hydrogen bonding between water molecules. These diagrams represent ‘snapshots’ and are not meant to depict long-term chemical structures.²⁰

Using chemical terminology, MoW might be considered a supra-molecular phenomenon involving many water molecules. This means that MoW would be an emergent dynamic property of bulk liquid water (ie, involving many trillions of water molecules: in other words, the whole is more than the sum of its individual molecular parts). This would defy explanation in terms of the usual ideas of static chemical bonds and purely additive behaviour between individual water molecules alone. Certainly water molecules’ ability to dynamically switch hydrogen bonding to each other would be of crucial importance here, as are other weak intermolecular interactions (eg, van de Waal’s forces). Chaplin gives a compelling description of this behaviour on his website.²⁰

Sceptics often quote the laws of thermodynamics as grounds for the impossibility of MoW. They are correct if one attempts to understand MoW effects in terms of a system at thermodynamic equilibrium. However, the principles of equilibrium thermodynamics cannot explain what happens to a system far from equilibrium, especially at what are called critical points. These are temperatures and pressures where, for example, a gas is just about to liquefy. In this critical state, a gas is much denser than under normal equilibrium conditions. It remains as a single phase system but is exquisitely sensitive to even the slightest externally-induced fluctuations, which can cause separation into gaseous and liquid phases.

Now, highly metastable far-from-equilibrium critical states develop patterns of chaos and self-similarity better described by Prigogine’s seminal work on non-equilibrium thermodynamics than by classical thermodynamics. Such states occur during the chemical reactions within living cells.²¹ Hankey has presented a plausible hypothesis that might help explain MoW effects in terms of such critical points acting as local dynamic attractors of a system. This led him to a novel model of the life force, capable of predicting the correct relationship between it and cure in several systems of complementary medicine, including homeopathy.²²

The key to such models is the recognition that fluctuating instabilities at critical points necessarily exist in quantum form, and require quantum descriptions to predict their effects. It turns out these quantised instability fluctuations can serve the highly unusual function of ‘lifting’ quantum properties out of their confinement within the microscopic domain of atoms and molecules, and into our macroscopic world of bulk material properties. Under these exceptional circumstances, macroscopic systems may exhibit similar properties to microscopic quantum systems, such as coherence, and this has been observed and recognised with low-temperature superconductors and super-fluids.²³

Interestingly, support for the MoW concept has come recently from the field of materials science.²⁴ Using a large interdisciplinary research base, Roy et al examined the structures of many non-crystalline, inorganic, covalently-bonded condensed liquid phases, including liquid water. They predicted that at ambient conditions, typical samples of water likely contain many dynamic water structures. These consist of a statistical mixture of single water molecules (monomers) and different-sized water molecule clusters (oligomers), the largest consisting of several hundred H₂O units. From this, they arrived at the important conclusion that it is solution structure not solution composition which is important in determining the plausibility of MoW effects. From the materials science perspective, although an ultra-diluted solution (where the solution is diluted out of existence) up having the same composition as the original solvent water, their structures could be entirely different.

In quantum physics there is also support for the MoW concept. For example, Smith has for many years argued for electromagnetic coherence and memory effects in water.²⁵ While Del Guidici et al predicted that given a large enough number of water molecules (of the order of 10¹⁵–10¹⁷, an amount visible to the naked eye), the sum total of all the hydrogen-bonded interactions between the water molecules could, under the right circumstances, lead to a dynamic, rapidly fluctuating yet correlated state where they all resonate together, spontaneously organising themselves into so-called ‘coherent domains’.²⁶ Del Guidice et al went on to show that such dynamic and correlated ‘coherent domains’ could not only be triggered by homeopathy’s potentisation process (ie, serial dilution and strong agitation), but that they would survive removal of all trace of the original dissolved substance. In other words, a possible theoretical mechanism for MoW effects exists and fits neatly with Roy et al‘s conclusions on the importance of solution structure over composition.

Critics of MoW incorrectly assume that that the physical and chemical properties of a solution are not dependent on its history. Samal and Geckler have reported such historical dependence in a series of experiments, using solutions of a wide variety of substances including common salt, starch and DNA at different non-homeopathic dilutions.²⁷ This work demonstrated that molecules of a substance aggregate on dilution rather than getting further apart as common sense might suggest. Also, the size of these molecular aggregates relates to the starting concentrations of the original solute: in other words, they show an historical dependence.

In a completely different field, Rey obtained thermoluminescence data from highly agitated ultra-high dilutions of lithium and sodium chloride, suggesting reproducible differences from pure water diluted with itself.^28a However, replication of this study by van Wijk though to some extent reproducing Rey’s original findings, failed to show statistical significance until the solutions had been standing for several weeks prior to obtaining thermoluminescence data.^28b This could suggest the possibility of the data being artefactual as a result of the D₂O used in the experiments leaching traces of silica from the glassware. Such silica leaching artefacts have previously been noted in high-dilution experiments.²⁹ However, Elia has obtained thermodynamic and conductivity data which strongly suggest that the process of sequential dilution and succussion is capable of permanently modifying many of the structural features of water. Elia concludes that, thermodynamically speaking, such systems are far from equilibrium and capable of self-organising themselves as a result of only small perturbations, confirming Roy et al‘s conclusions.³⁰

It is perhaps sufficient to say that an explanation for the efficacy of highly diluted homeopathic remedies within the ‘local’ paradigm of the molecular sciences, though difficult is not as improbable as homeopathy’s critics claim.

Non-local hypotheses and macro-entanglement

In which case, why bother with quantum theoretical non-local hypotheses? Simply because deterministic local hypotheses could have the effect of confining attention to the medicine as the sole therapeutic agent, at the expense of the perhaps equally important contextual dynamics of the patient–practitioner relationship. Having said that, it is worth pointing out that some local explanations of homeopathy’s effects, eg Del Guidice et al and their concept of ‘coherent domains’ of water molecules moving in some correlated fashion, are strongly suggestive of entanglement at the molecular level.²⁶ Consequently, it is worth remembering that the sections in this paper headed ‘local hypotheses’ and ‘non-local hypotheses’ are not intended to suggest that they are mutually contradictory. On the contrary, it is far more likely that both will be required in order to fully explain homeopathy’s effectiveness: a prediction consistent with the complementary nature of quantum theory.

Biomedicine takes little account of patient individuality or therapeutic context. From this point of view, perhaps the time has come for the discussion of homeopathy (indeed of all therapeutic modalities) to move out of the narrow confines of deterministic biomedicine. Theoretical models need to be developed that more fully encompass and make sense of its experiences, while at the same time not losing sight of the ‘local’ importance of the medicine. But why invoke non-local explanations based in something as seemingly exotic as quantum theory? How could it possibly apply to ‘macroscopic’ objects, especially people? And does not that play right into the hands of sceptics who accuse homeopaths of clutching at ill-understood scientific straws so that they can justify the patently unjustifiable? It is probably worth noting that homeopathy’s sceptics do not have a monopoly on the understanding or indeed misunderstanding of quantum theory. As the Nobel-pzrize winning physicist Richard Feynman once famously remarked, ‘Anyone who thinks they have understood quantum theory has probably got it wrong!’³¹ For example, a common assumption is that quantum theory and its implications apply only within the confines of particle physics, not in our macroscopic world.

It is true quantum theory’s algebraic language is dominated by an incredibly small number called Planck’s constant (6.626×10⁻³⁴ J s), commensurate with observations and measurements of events occurring at the sub-atomic through to the molecular domains. However, it turns out that one of the strangest outcomes of quantum theory—the notion of entanglement—need not be size-limited.³² Entanglement is said to occur when the parts of a system are so holistically matched, measurement of one part of the system instantaneously (ie, not limited by the speed of light) provides information about its other parts, regardless of their separation in space and time.⁹ What is important is whether the elements of the system are correlated (ie, act as one coherent indivisible whole), and whether such a system’s processes can be described using a ‘non-commuting algebra of complementary observables’.³³ This means when two separate operations of observation are performed sequentially, the overall result depends on the sequence and what is being measured. This is readily understood when considering a set of operations involved in, say, cooking. Here the operational sequence is paramount, for in a different order, instead of a tasty meal, one is likely to end up with any number of disagreeable and inedible offerings. Expanding on this concept leads to another key idea from quantum theory: complementarity.³¹

Thus, a single explanation or model might not adequately explain all the different observations that can be made on a quantum system. For example, in order to explain how electrons are diffracted when they strike the atoms in a crystal lattice, it is necessary to assume that each electron behaves as a wave. However, when considering the photoelectric effect and electrons being expelled from a solid when struck by photons of the right energy, it is necessary to assume that the electrons and the photons are behaving as particles. This results in the well-known apparent contradiction of particle-wave duality. The point is, in order to fully explain quantum phenomena it is necessary to have two different but complementary concepts. It is almost as if the answer one obtains on performing the two observations depends entirely on how the (experimental) question is asked; and both are necessary in order to acquire a complete picture of a quantum process or system.

But notions of complementarity and entanglement have implications far beyond the specific meaning ascribed to them in the orthodox quantum theory of particles, atoms and molecules. Using less formal approaches, examples have been cited from engineering, the cognitive sciences, especially psychology, and philosophy.⁵ Atmanspacher et al took the radical approach of developing a more generalised version of quantum theory which relaxes several of orthodox quantum theory’s axioms, including dependence on Planck’s constant. Called Weak Quantum Theory (WQT),⁵ it differs from orthodox quantum theory in that:

• Complementarity and entanglement are not restricted by a constant like Planck’s constant.

• WQT has no interpretation in terms of probabilities.

• Complementarity and indeterminacy are epistemological in origin not ontological.

As a result, WQT explicitly allows quantum theory’s application into such macroscopic areas as philosophy, psychology and information dynamics and into possible explanations of the dynamics of healing.

Quantum theory and homeopathy

Classical physics and quantum physics differ in an important respect. The former enshrines common sense, for everything considered physical is observable and therefore measurable: this is the leitmotif for all reductionist science and underpins the whole of biomedicine. However, in quantum physics this is not always be the case: not everything considered physical is observable or measurable.³³ So, in quantum physics, there is the concept of the wave function which is not a directly observable entity as such: only its effects are. A wave function is considered to be a multi-dimensional descriptor of a system’s state, whose existence may only be inferred from the observable effects it produces in our ‘reality’.

The reason for this is not because of any fault in measurement; it depends on the mathematical language we use to describe those measurements. Thus, measurement of a quantum state, as with any experiment, provides data in the form of what are called real numbers, eg, the numbers we use everyday like 1, 2, −6, π e, 1/2, √2, etc. But because mathematicians and physicists think in many more than four dimensions, they need a much more versatile number system. And in mathematics, the real numbers are seen as a special case of much larger number sets. One of these is called the complex numbers,³⁴ used to fully describe the multi-dimensionality of quantum states in a way that the real numbers cannot. Complex numbers are irreducible aggregates of real numbers and ‘imaginary’ numbers, based on √-1, which cannot be understood in terms of real numbers.

Real numbers are part of the larger set of complex numbers but not vice versa. Trying to fit a state or a system whose full description requires complex numbers into the real number set is like trying to squeeze a three-dimensional cube into a two-dimensional plane: it does not fit and some information invariably gets lost, notably in this case, the cube’s three dimensionality. It is a similar loss of information in trying to make sense of a quantum state’s complex number description by translating it into the real numbers of hard data, that leads to much of what is considered to be ‘quantum weirdness’.³³

The consequences of the quantum description of reality for our view of the universe are profound. Ultimately it means relinquishing any notion of knowledge of things ‘out there’, ‘in themselves’, separate from our observation of them. We have to come to terms with the unsettling fact that in quantum theory, like the parts of a complex number, the observer and the observed are intimately and irreducibly connected. But what is it about quantum theory that could resonate with homeopathy and other forms of complementary and alternative medicine (CAMs)?

In homeopathy and other CAMs there is a notion of an all-pervading vital force (Vf) which strives to hold the whole organism in balance.³⁵ However, this Vf is not a directly observable entity: like the wave function in quantum theory, it is observed only indirectly through the effects it produces, in this case the patient’s state of health. Thus, through this descriptive similarity of wave function and Vf, there is a similarity in discourse between quantum physics and homeopathy and other CAMs which include a concept of Vf. Perhaps quantum theory’s language of non-commuting operations, non-locality and entanglement could be used to describe the homeopathic process.³⁶

Entanglement in the homeopathic process

There are several ways ideas derived from quantum theory can be used to describe the homeopathic process which may be ordered nominally in terms of the complexity of entanglement between different types of entities.^7c Space limitations do not allow for their detailed consideration here, but see Weingaertner’s contribution in this issue on possible non-local correlations between the different particles of solvent and solute.³⁷ Weingaertner’s model attempts to understand the homeopathic process solely in terms of the potentised medicine as a pharmacologically-active substance, so only one type of entity is considered (Fig. 3).

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Fig. 3. Diagrammatic representation of ‘sequential box’ model. It proposes the theoretical possibility of keeping a constant volume of mother tincture physically present in every potency. MT=mother tincture; 1×=ten times bigger box 9/10ths full of solvent into which MT is poured and succussed, and so on into 2X….NX.³⁷

Walach’s semiotic model combines WQT with two-way entanglement (Fig. 4) between the patient and the remedy,^{[7b] and [38]} while Hyland has developed a two-way patient–practitioner entanglement model called Extended Network Entanglement Theory.³⁹ In the entanglement metaphors I am developing (Fig. 5), three-way patient, practitioner, remedy (PPR) entanglement is considered.⁷ These are based on ideas derived from Greenberger–Horne–Zeilinger three-way entanglement of particles,⁴⁰ and quantum field theory.⁴¹

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Fig. 4. Walach’s double entanglement model. Two semiotic processes linked by the Law of Similars. On the left, object=the remedy substance, R; sign=remedy, Rx; meaning=remedy picture, Sx. On the right, object=the patient’s ‘disease’, Dx; sign=the patient’s symptoms, Sx; meaning=the required remedy, Rx.^{[7b] and [38]}

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Fig. 5. PPR entanglement represented geometrically. In (a), Walach’s two semiotic triangles for remedy and patient (also wave functions, ψ_Rx and ψ_Px) are joined by a third for the practitioner ψ_Pr, which are entangled into the PPR ‘state’ represented by ψ_PPR in (b). The multi-dimensional geometry of this state is represented in (c)–(e) and shows the action of the homeopathic operator Πr in ‘reflecting’ this state (d). But the reflection is not passive: by opening out the polyhedra in (d) and superimposing them, it is seen that the reflecting plane also twists the reflection through 60° (e). The ‘space’ in which these wave functions and ‘operations’ take place is a therapeutic state space created by the homeopathic operator Πr, which also functions within it.^{[7] and [42]}

Here, the homeopathic process is regarded as a set of non-commuting complementary observations made by the practitioner. These are local (observations of the patient) and global (observations of the practitioner’s own inner state, how that fluctuates during the consultation, and the state of the patient–practitioner relationship), resulting in the prescription of an homeopathic medicine. Patient, practitioner, and remedy comprise therefore a three-way entangled therapeutic entity, so that attempting to isolate any of them ‘collapses’ the entangled state,⁴² represented geometrically in Fig. 5.

In addition, the Vf may be envisaged as observable only from the amount and severity of the observed signs and symptoms it produces. From this, it is possible to construct a mathematical metaphor for the Vf as a multi-dimensional quantised gyroscope (Fig. 6).⁴³ The slower the Vf gyroscope ‘spins’, the less upright it stands against the braking effects of disease: it begins to ‘wobble’, or, in this metaphor, to express symptoms. Conversely, the therapeutic remedy increases the Vf’s spin rate, throwing off the disease. Thus remedies and diseases may be understood as accelerating and braking ‘torques’ acting on the Vf gyroscope.⁴³

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Fig. 6. Schematic of the Vf gyroscope: a real gyroscope in 3-D space precesses around the z-axis sweeping out gradually increasing ‘orbits’ in the x–y plane. The metaphorical Vf gyroscope precesses in fixed quantised ‘orbits’ as shown and the y and z axes are complex. Symptoms are observed along the real x-axis. Thus, the Vf only ‘appears’ when it expresses symptoms in real space and time, represented by the x-axis in the figure.⁴³

Mathematically, Vf, diseases, and remedies can be represented as ‘wave functions’ (without yet specifying the ‘particles’ involved or ‘interactions’ between them), leading to the prediction that the more potent a remedy, the greater its effect on the Vf. At very low potencies, when a homeopathic medicine is used in a material dose as in conventional medicine, the gyroscopic metaphor approximates in such a way as to deliver predictions about the lack of therapeutic efficacy of highly-diluted homeopathic remedies in line with those of conventional medicine.⁴⁴

In other words, the Vf gyroscope metaphor may be pointing towards a more inclusive paradigm about the effects of remedies that contains both homeopathy and conventional medicine and explains their apparent contradictions. In this sense, the metaphor could be said to parallel theoretical developments in conventional science, where new theories supersede older ones, yet generally include them. Perhaps it suggests that conventional medicine is a smaller subset of a much broader holistic paradigm that includes homeopathy.

Conclusion: a therapeutic Uncertainty Principle?

One application of the PPR entanglement metaphor I have described is to provide a rationale for why RCTs of homeopathy often return equivocal results.⁴⁵ It suggests the double blind RCT ‘collapses’ the three-way patient–practitioner–remedy entangled state in a way analogous to that by which observation collapses a particle’s wave function in the Copenhagen Interpretation of orthodox quantum theory.⁴⁶ Thus, while unobserved, a particle exists in an indeterminate state; its evolution in time expressed as a wave function. Observation causes the wave function to ‘collapse’ to a particle whose complementary position and momentum are related via Heisenberg’s Uncertainty Principle. The profound meaning of this is that the act of observation in part creates that which is observed. Or, even more starkly, “The price of knowledge is the loss of an underlying ontological physical reality”.⁴⁷ In a similar way, the observational procedure of the RCT may ‘collapse’ the three-way entangled state, leading to the loss of the underlying homeopathic effect, a therapeutic equivalent of Heisenberg’s Uncertainty Principle.

But some trials of non-individualised homeopathic remedies have generated positive results.⁴⁵ This could be due to some surviving relic of entanglement from the production process, ironically as a result of a water memory effect. The work of del Guidice et al mentioned earlier, suggested the formation of ‘coherent domains’ within water’s dynamic hydrogen-bonded ‘structure’.²⁶ Such mass correlation over huge numbers of water molecules suggests a form of molecular entanglement.

The tantalising prospect emerges that there could be several levels of entanglement operating during the homeopathic process: the molecular (created during production of the homeopathic medicine), contextually integrated into that occurring between patient, practitioner, and remedy.⁴⁸ Consequently, although double-blind RCTs on non-individualised homeopathic remedies rule out the possibility of over-arching three-way PPR entanglement, the residual molecular entanglement built into the remedy via water memory effects could survive, explaining the positive effects observed in many homeopathic clinical trials.

Ultimately, it will be necessary to find experimental protocols that demonstrate entanglement in the therapeutic process. This is not easy, but clues have been uncovered in double-blind homeopathic pathogenetic trials (HPTs, provings). Many HPTs have not been conducted in a double-blind placebo-controlled manner. After symptoms have been gathered, collation of the data allows a remedy picture to emerge, traditionally one of the central ‘pillars’ of homeopathy.⁴⁹ In two recent double blind placebo-controlled provings, although there were differences in proving symptoms between remedy and placebo groups, there was also overlap or ‘leakage’ of symptoms between them.^{[49] and [50]} Walach et al concluded that as a result of blinding, remedy and placebo groups had become entangled, another demonstration of a possible therapeutic Uncertainty Principle, perhaps? Interestingly, there has been some independent confirmation of this result recently by another research group,⁵¹ and an explanation couched in terms of the PPR entanglement metaphor.^{[45a] and [52]}

Another approach might be to set up a therapeutic analogue of the famous Aspect experiments of the 1980s that demonstrated entanglement between photons.⁸ These experiments depended on the violation of Bell’s Inequalities (our ‘intuition’ based on local realism, makes predictions which differ markedly from those made by quantum mechanics: these predictions are enshrined in Bell’s Inequalities: if they are violated, then the predictions of quantum mechanics, e.g., entanglement, must be true and our intuition wrong). A way forward might be to use the much more general Information Theoretic Bell’s Inequalities—if local realism does not hold, then two systems must carry information inconsistent with the inequalities. The design of suitable experiments is currently being explored.⁵³

In conclusion, what this all seems to be pointing to is that, far from being competing, contradictory explanations, ‘local’ MoW and ‘non-local’ contextually ‘entangled’ effects (like wave-particle duality in orthodox quantum theory) could be complementary and both are necessary in order to make sense of homeopathy’s effects.

Acknowledgements

I thank Bill Scott, Kate Chatfield and Professor Harald Walach for introducing me to the consolations of philosophy.

References

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Corresponding to: Department of Chemistry, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, UK.

Homeopathy
Volume 96, Issue 3, July 2007, Pages 209-219
The Memory of Water

This is part of the Homeopathy Journal Club, more info here:

www.badscience.net/?p=490

doi:10.1016/j.homp.2007.05.005    
Copyright © 2007 Elsevier Ltd All rights reserved. The nature of the active ingredient in ultramolecular dilutions

Otto Weingärtner^{, a,
a}Department of Basic Research, Dr. Reckeweg & Co. GmbH, Berliner Ring 32, D 64625 Bensheim, Germany
Received 8 March 2007;  revised 14 May 2007.  Available online 31 July 2007.

Abstract

This paper discusses the nature of the active ingredient of homeopathic ultramolecular dilutions in terms of quantitative physics.

First, the problem of the nature of an active ingredient in ultramolecular dilutions is analysed leading to the recognition of the necessity of characterizing the active ingredient as a non-local quality.

Second, non-locality in quantum mechanics, which is used as a paradigm, is formally presented.

Third, a generalization of quantum mechanics is considered, focussing on the consequences of weakening of the axioms.

The formal treatment leads to the possible extension of the validity of quantum theory to macroscopic or even non-physical systems under certain circumstances with a while maintaining non-local behaviour. With respect to the survival of entanglement in such non-quantum systems a strong relationship between homeopathy and non-local behaviour can be envisaged. I describe how several authors apply this relationship. In conclusion, the paper reviews how quantum mechanics is closely related to information theory but why weak quantum theory and homeopathy have not hitherto been related in the same way.

Keywords: potencies; non-locality; entanglement; weak quantum-theory; information

Article Outline

Introduction

Necessity of a general principle

How non-locality arose

What is entanglement?

Weakening the axioms of quantum mechanics

WQT and homeopathy

Entanglement and information in quantum physics and beyond

Discussion

Acknowledgements

Appendix A. The sequential box model (SBM)

Appendix B. Entanglement

References

Introduction

When I started basic research on homeopathy more than 20 years ago I endeavoured to describe homeopathic potencies according to the laws of physics as far as possible. This soon led me to the hypothesis of a field being responsible for the homeopathic phenomenon. In investigating this hypothesis I learned from biophysics that such a field has to be closely related to electromagnetism, because of the ability of living organisms to react in a specific way on electromagnetic signals.¹ I concluded that the mechanism of homeopathic effects must be similar to resonances between electromagnetic waves and started to search for stored patterns of electromagnetic origin or, more generally, of physically measurable properties which differ between potencies and their solvent.

The results of the series of experiments that were carried out with a variety of standard physical–chemical methods² were disappointing. Almost none of the experiments could reproduce results reported in specialist literature, and for no experimental arrangement could the results be forecast. However, the totality of experiments with nuclear magnetic resonance (NMR) showed a clear tendency in favour of a difference between potencies and their solvent in the water- and OH-portions of the ethanol–water-molecule.³ I was quite pleased with this tendency, which is now being investigated by other researchers,⁴ but I realized that looking for effects without having any clue of their significance is hazardous. Therefore, I started building models for the ‘Therapeutically Active Ingredient’ (TAI) and it soon became clear that models for the TAI have to have holistic character.⁵

While playing with models, I developed a construct which I called the ‘Sequential Box Model’ (SBM, see Appendix A). SBM is a thought experiment illustrating that the homeopathic phenomenon can be treated within physics with no consideration of the degree of dilution. Furthermore, the SBM explicitly underlines the long-standing presumption that for a TAI to emerge during the potentization procedure a quality beyond ordinary correlation between particles has to occur or be in existence already.

About this time the idea of the so-called ‘quantum computing’ was proposed in computer science.^{[6] and [7]} This involves the idea of non-local correlations between states of entities. For my work, such non-local behaviour was the missing link between the SBM and a possible TAI, particularly as it was already known that non-local behaviour can occur in non-quantum systems under certain circumstances. The relationship between non-local behaviour of events in nature and the homeopathic phenomenon may give a clue to the ‘nature of the active ingredient in ultramolecular dilutions’ (NAIUD). It is the aim of this paper to analyse this relationship without going too far into technical details.

Necessity of a general principle

When we talk about the active ingredient of ultramolecular dilutions as used in homeopathy, we mean a non-material quality which—according to the principles of homeopathy—can be traced back to a substance. Moreover, this quality is understood to be able to make the symptoms of a patient disappear when administered via a vehicle. Many people call this quality ‘information’. Let us first look at the set of events that are required for a therapeutic active ingredient to develop out of a substance. In this context, the existence of a TAI is temporarily assumed as being proven by successful treatment (Figure 1).

1. First of all, a proving (homeopathic pathogenetic trial) must have been conducted resulting in a drug picture with specific symptoms.

2. A mother tincture is prepared from the substance.

3. Apart from some specific procedures for the preparation of low potencies that depend on the nature of the substance itself, the mother tincture is potentized stepwise with no consideration of the degree of dilution. Dilutions far beyond Avogadro’s number are used in daily practice.

4. When a homeopathic potency is prescribed, this is done according to the law of similars without consideration of the occurrence or not, of any molecule of the original substance in the medicine administered.

5. An artificial disease is triggered off resulting in healing.

These points demonstrate that the active ingredient of homeopathic potencies might have a variety of possible originators, especially when we only look at the squares and arrows in Figure 1 separately. There is no reason as to why two or more of these originators should complement one another. But if we look at Figure 1 as a whole, the necessity of a general principle becomes obvious. For such a principle, the symptoms of the homeopathic drug picture, the principle of releasing hidden energies of the substances by potentizing, the law of similars and the triggering of an artificial disease are specific projections. The problem is, how to specify this principle, especially with respect to the following questions:

1. Could such a general principle possibly be derived from the presence of a physical field?

2. For ultramolecular dilutions, interactions between molecules of the solute and those of the solvent do not make sense in terms of current scientific understanding. How can this be resolved?

3. Are there any reliable arguments for a concept of a global influence being responsible for an active ingredient in homeopathic potencies? Rupert Sheldrake’s morphogenetic field⁸ might serve as an example of such a concept.

In physics, fields are inevitably linked to interaction between material partners via interaction-particles. Photons, for instance, are the interaction-particles of the electromagnetic field.⁹ Thus, potentization as well as treatment with potencies—procedures that implicitly do not depend on matter–matter-interaction—are not primarily based on physical fields.

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Figure 1. Schema of events which are required for a TAI to: (a) develop out of a substance, and (b) proved to be existent by successful treatment. Arrows represent procedures, they map states onto states.

Both procedures, however, suggest mind–matter and matter–mind correlations.

1. Neither a specific chemical nor a specific physical property of the original substance is known to be transferred during the preparation of potencies although mother tinctures, which of course contain many molecules of the original substance, are mandatory for a starting point of this procedure. Potentization here appears to embody a procedure that relates matter to mind.

2. No common donor–acceptor-mechanism is known to be responsible for the effects of potencies. Treatment appears to embody a procedure that relates the ‘mind of matter’ to the ‘mind of illness’. The latter of course itself is strongly related to biological matter and is often looked upon as a relationship belonging to psychosomatics.

Are these correlations better described by interaction mechanisms that are not linked to particles? A possible alternative is non-local correlations, known from specific effects in quantum physics. Roughly speaking these correlations have the following characteristic:

1. Non-local correlations between systems or entities represent a real simultaneous behaviour of the correlation partners because no interacting particles (which have a finite speed and therefore cause a time delay) are necessary for interaction.

2. Non-local correlations are not able to interchange matter but only non-material information.

3. Non-local correlations are, in principle, independent of spatial distances.

How non-locality arose

Although Einstein was one of the founders of quantum physics, he did not accept quantum mechanics as to be a complete description of the phenomena of the micro world. He explained the reason for this attitude in a paper which he published with Podolsky and Rosen in 1935. In this famous paper, the three physicists described a thought experiment in which two physical quantities have simultaneous reality.¹⁰ For Einstein, this was a counter example for the completeness of quantum mechanics as a description of nature and for the rest of his life he did not change this attitude. He was not willing to accept counter-intuitive features in the description of nature. Schrödinger later on called this counter-intuitive property of quantum systems ‘entanglement’. Only three decades later, John Bell¹¹ gave a theory-based criterion by which it was possible to decide whether a system is a quantum system or not. This criterion was applied in 1982 by Aspect and co-workers to an experimental arrangement in which they showed, for the first time, that entangled states can occur in quantum systems.¹² Since then many properties of systems in micro-physics have been demonstrated in experimental arrangements based on entanglement.^{[5], [6] and [7]} All have one thing in common: ‘Entanglement in quantum systems’.

What is entanglement?

Entanglement is a highly counter-intuitive quality of quantum systems. The fact that entanglement is irrelevant to Newtonian physics does not justify the assumption that quantum physics is the only field where entanglement occurs. At least theoretically, entanglement can occur in any system that fulfils a certain set of axioms. Entanglement comes in various guises and it is not easy for non-specialists to see whether a phenomenon belongs to the category of entangled systems or not. For our purposes, it should suffice to get a clue what entanglement is, without too much technical fuss. Readers who are interested in a more precise explanation are referred to Appendix B.

As an example let us imagine a secluded island exclusively inhabited by females. Being asked what human beings are, the inhabitants of this island would most probably point their fingers at themselves. Similarly, the inhabitants of another island exclusively inhabited by males would identify human beings with males. For the rest of the world, human beings are females as well as males. This is a description of a factual connection, where a generic quality in a system has a different meaning in its subsystems. Furthermore, if we look at pairs of human beings there might be couples among them in the rest of the world, in total contradiction to the local meaning in the two islands.

A generalization of this example leads to the following. Let p₁ be a particle in a system A and let p₂ be another particle in a system B. System A and system B are assumed to be disjoined, ie have no common points/particles. System A rules the behaviour of particle p₁ and system B does the same for particle p₂ (see Figure 2).

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Figure 2. Schema of two entangled systems A and B. p₁ and p₂ are assumed to be correlated. Seen from (A+B) correlation can be observed. Seen from A or B only local observations are possible.

It might be that states of the totality of the two systems occur which cannot be recognized in system A or in system B alone, but are exclusively linked to the recognition of (A+B) as a third generic system. In the above example as well as in the following generalization constellations, in which global observations are not compatible with local ones, are possible. This is the idea behind entanglement.

Weakening the axioms of quantum mechanics

Quantum mechanics deals with states z_i and observables P, Q of quantum systems. Examples of observables are momentum, angular momentum, etc. Observables are thought to act as maps on the set of states. So, an observable P maps a state z₁ into another state z₂. Onto z₂ a second observable Q may be applied resulting in a state z₃. Unlike in classical mechanics in quantum mechanics one does not always have P(W(z))=Q(P(z)) or equivalently:

PQ–QP≠0,

where ‘’ is to be interpreted as ‘apply to’, where ‘0’ on the right-hand side of this inequality denotes the ‘zero-operator’ and where states ‘z’ have been omitted. Such a relation is known as a ‘commutation-relation’ of the two observables. Using states and observables as well as their relation to each other, quantum mechanics can be described as an algebraic system whose behaviour is ruled by a set of axioms that reflect the physical properties.In 2002, Atmanspacher et al. published¹³ the idea that weakening the axioms of quantum theory (weak quantum theory, WQT) could lead to theories that are no longer quantum systems or even physical systems at all, but which still have the property of possible entanglement. To be more precise, Atmanspacher et al. considered systems that comply with the following conditions (see also¹⁴):

1. Systems are any part of reality.

2. Systems are assumed to have the capacity to reside in different states. The set of states is not assumed to have the structure of the above-mentioned abstract space.

3. Observables are features of a system which can be investigated. They map states into states.

4. The composition PQ of two observables is also an observable. P and Q are called compatible if they commute (ie PQ–QP=0).

5. To every observable P there is a set of different (possible) outcomes.

6. There are special observables (propositions) whose possible outcomes are either ‘yes’ or ‘no’. They follow the laws of ordinary proposition logic and have specific spectral properties (omitted here).

Within these conditions entanglement arises if global observables P pertaining to all of a system are not compatible to local observables Q pertaining to parts of the system (iePQ–QP≠0).

WQT and homeopathy

Since WQT systems are not necessarily quantum systems, WQT could be a tool to develop models for phenomena which are not quantum but have features which resemble entanglement, for instance, homeopathy. Several authors therefore have applied WQT to the homeopathic phenomenon. Walach, one of the co-authors of the original WQT paper,¹⁵ presented a model in which the two semiotic processes ‘substance and potency’ as well as ‘drug picture and symptoms of the patient’ are assumed to be entangled by the law of similars. Milgrom has sketched a model for the homeopathic phenomenon in which the three pairs ‘Patient and practitioner’, ‘patient and remedy’ as well as ‘practitioner and remedy’ are assumed to be entangled in pairs.¹⁶ In a metaphorical way he derives, in succeeding papers, from this entanglement triangle an astonishing variety of principles of homeopathy.

Both models presuppose the validity of WQT for the specific situation in homeopathy and Milgrom, at least, deduces implications which reflect the way homeopaths think. In terms of logic, the approach of these two models is called the sufficiency part of a proof. The necessity part would be the proof that the assumptions which underlie homeopathy such as the potentization, the law of similars, etc., fit the preconditions of WQT.

I have tackled the TAI problem in a previous paper.¹⁷ This is where the SBM (see Appendix A) becomes relevant as a thought model, because it characterizes homeopathic potencies as a real physical system in which an unknown inner correlation is sought. In essence, paper¹⁷ showed that sets {J_i1,…,i_m·σ_i1,…,i_m·σ_i1,…,i_m} of spin-like states, where indices i₁,…,i_m vary over permutations, fit the axioms of WQT for an arbitrary big system B_N in the SBM. The sets {J_i1,…,i_m·σ_i1,…,i_m·σ_i1,…,i_m} are a generalization of couplings (J_ik·σ_i·σ_k) of two spins, in NMR-theory, for instance. The generalization strongly suggests to investigate the possibility of global couplings instead of pair-to-pair couplings.

In summary, a number of arguments exist for non-locality being the general principle underlying the NAIUD. Quantum mechanics, however, cannot be considered, without further investigations, the theoretical frame for the NAIUD. The paradigm is rather non-locality. Quantum physics is merely the scientific discipline where non-locality has proven to occur in reality. Figure 3 gives a schematic classification of phenomena which can be treated within quantum mechanics, and those which have less structure in the set of their states and therefore need another theoretical environment, WQT. Questions concerning the NAIUD might even go beyond WQT.

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Figure 3. (I) The set of phenomena understood by quantum mechanics (essentially quantum physics); (II) the set of phenomena possibly understood by weak quantum theory (ie quantum physics and beyond); and (III) the set of phenomena belonging to homeopathy, possibly not a proper subset of II. Although quantum mechanics is an excellent paradigm for entanglement occurring in nature, quantum mechanics itself is not the frame in which NAIUD can be described.

Entanglement and information in quantum physics and beyond

It is the purpose of this section to explain the considerable difficulties one should be aware of when applying WQT instead of normal quantum mechanics to systems in nature.

This will be exemplified by the difficulties which arise when the attempt is made to translate ‘informational content’ (=entropy) in a quantum system to a system which is not quantum but which can be investigated by WQT. For formally correct representations of the factual connections given here, the reader is referred, for instance, to.⁶

The key concept of classical information theory is that of Shannon entropy. According to this concept, the entropy of a random variable A quantifies how much information we gain, on average, when we learn the value of A. Conversely, the entropy of A measures the amount of uncertainty about A before we learn its value. Thus, on the one hand, entropy measures the uncertainty associated with a classical probability distribution. On the other hand, in quantum ensembles density operators ρ, which represent the statistics of ensembles of different molecules in different states, formally replace probability distributions.

It was John von Neumann’s brilliant insight that in quantum mechanics the entropy S(ρ) of ρ can be expressed by the formula

where λ_x are the eigenvalues of the density operator ρ. If entanglement between two subsystems of a quantum system occurs and if one considers the density operators of these subsystems separately it can be shown that the von Neumann entropy of one of these reduced density operators is a measure of the degree of entanglement. This measure has an upper bound log(s), where s (the Schmidt-number) is the dimensionality of an abstract space in which these states ‘live’. Clearly, the bigger the s, the more the particles or states entangled. Applied to an arbitrary box B_N of the SBM this suggests that the bigger the box B_N is, the larger s has to be chosen and therefore the larger the measure of the amount of information.These considerations, however, presuppose entanglement of those particles being directly concerned. If we turn to a situation where WQT has to be applied instead of quantum mechanics, many of the basic constituents are no longer present or at least no longer adequately defined. For instance, if the set of states is structured so poorly then the above formula for von Neumann entropy makes no sense.

Discussion

The principle of non-local behaviour of systems in nature, first investigated in the context of the counter-intuitive phenomena of quantum physics, is not necessarily restricted to physics at the micro scale. This is the essence of WQT. Roughly speaking WQT shows that in every system where local and global observables do not commute with each other non-local behaviour is possible. For some authors, WQT was the reason for using non-locality to characterize the nature of the active ingredient of ultramolecular dilutions. Some models have simply drawn consequences from such a possible generalized non-locality, another looks at the real potentization procedure, asking what non-locality might contribute to an active ingredient. But WQT is not known to be powerful enough to describe the NAIUD entirely.

So the question arises, why considered WQT in such detail in connection with homeopathy? The answer is simple. With WQT, for the first time, special emphasis is placed quantitatively on entanglement as an idea. Moreover, WQT has shown to be a powerful tool for the characterization of the physics of the class of mathematical problems which arise when the NAIUD is to be described.

It is a great temptation to use WQT as a special way of describing the laws of quantum physics. People who do so tend to ignore the restraints given of WQT and use it as a theory applicable to everything, including the NAIUD. This is certainly not the right way to describe the NAIUD. An attempt to characterize the informational content of a system to be investigated by WQT, shows that it is not easy to generalize the concept in quantum mechanics to WQT or beyond.

Of course, all these considerations do concern the NAIUD in modelling situations. The question is, why do such work instead of looking for the TAI in experiments? The answer is that model building is a method of finding a way of thinking which allows us to understand a set of phenomena in a wider context. In contrast, experimental work tends to reductionism. I hope that both tendencies will ultimately meet.

Acknowledgement

This paper was partially done within the project ‘Modelling and simulating the therapeutically active ingredient of homeopathic potencies’ which was supported by the Carstens-Foundation.

References

1 Fröhlich H, Kremer F (eds). Coherent Excitations in Biological Systems. Berlin, Heidelberg, New York: Springer, 1983.

2 O. Weingärtner, Homöopathische Potenzen, Springer, Berlin, Heidelberg, New York (1992).

3 O. Weingärtner, Kernresonanz-Spektroskopie in der Homöopathieforschung, KVC-Verlag, Essen (2002).

4 J.L. Demangeat, P. Gries and B. Poitevin et al., Low-field NMR water proton longitudinal relaxation in ultrahighly diluted aqueous solutions of silica–lactose prepared in glass material for pharmaceutical use, Appl Magn Reson 26 (2004), pp. 465–481. View Record in Scopus | Cited By in Scopus

5 O. Weingärtner, Über die wissenschaftliche Bearbeitbarkeit der Identifikation eines ‘arzneilichen Gehalts’ von Hochpotenzen, Forsch Komplementärmed Klass Naturheilk 9 (2002), pp. 229–233. View Record in Scopus | Cited By in Scopus

6 M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge (2000).

7 C.P. Williams and S.H. Clearwater, Explorations in Quantum Computing, Springer, New York (1998).

8 R. Sheldrake, The Presence of the Past, Times Book, New York (1988).

9 J.D. Bjorken and S.D. Drell, Relativistic Quantum Fields, McGraw-Hill Book Company, New York (1965).

10 A. Einstein, B. Podolsky and N. Rosen, Can quantum–mechanical description of physical reality be considered complete?, Phys Rev 47 (1935), pp. 777–780. Full Text via CrossRef

11 J.S. Bell, On the Einstein Podolsky Rosen paradox, Physics 1 (1964), pp. 195–200.

12 A. Aspect, P. Grangier and G. Roger, Experimental realization of Einstein–Podolsky–Rosen–Bohm–Gedanken experiment: a new violation of Bell’s inequalities, Phys Rev Lett 48 (1982), pp. 91–94. Full Text via CrossRef

13 H. Atmanspacher, H. Römer and H. Walach, Weak quantum theory: complementarity and entanglement in physics and beyond, Found Phys 32 (2002), pp. 379–406. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

14 Römer H. Weak Quantum Theory and the Emergence of Time, 2004, arXiv:quant-ph/0402011 v1, 2 February 2004.

15 H. Walach, Entanglement model of homeopathy as an example of generalized entanglement predicted by weak quantum theory, Forsch Komplementärmed Klass Naturheilk 10 (2003), pp. 192–200. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

16 L. Milgrom, Patient-practitioner-remedy (PPR) entanglement. Part 1: a qualitative, non-local metaphor for homeopathy based on quantum theory, Homeopathy 91 (2002), pp. 239–248. Abstract | Abstract + References | PDF (240 K) | View Record in Scopus | Cited By in Scopus

17 O. Weingärtner, What is the therapeutically active ingredient of homeopathic potencies?, Homeopathy 92 (2003), pp. 145–151. SummaryPlus | Full Text + Links | PDF (156 K) | View Record in Scopus | Cited By in Scopus

Appendix A. The sequential box model (SBM)

Imagine a certain volume of mother tincture is present in a box B₀. Then imagine the contents of B₀ are poured into another box B₁, 10 times bigger than B₀ and already 9/10th full of solvent. Imagine then B₁ being vigorously shaken as in the preparation procedure of homeopathic potencies. Imagine then the whole content of B₁ being poured into another box B₂, 10 times bigger than B₁ and again 9/10th full of solvent.

This procedure can be continued to an arbitrary box B_N and it is clear that:

1. In every Box B_N the whole volume of mother tincture is present, ie the problem of high potencies can be, at least in a thought experiment, treated physically.

2. If one attempted to conduct this experiment in reality the procedure would come to an end very soon because of the unrealizable dimensions of the boxes.

3. The higher N grows the less probable is the occurrence of a molecule in a random sample taken out of B_N. This means that in B_N an additional property has to be present which carries the information of B₀. This property has to be non-local.

Appendix B. Entanglement

Mathematicians represent every point in the three-dimensional space of our experience as a sum of multiples of vectors of unit lengths in the x-, y– and z-axes. In the same way, they often represent objects in abstract spaces as sums of multiples of basic elements of these spaces. A direct application of this to quantum physics leads to the following.^{[6] and [7]}

The states of quantum systems are mathematically represented by elements (points in) of an abstract Hilbert-space H. If points in this space are denoted by ψ and if the basic elements of H are denoted by _i (i=1,2,…), representations of states look like

This is commonly known as the principle of superposition in quantum mechanics, ie a wave function ψ is the superposition of multiples a_i of basis ‘waves’ _i. In case of two particles forming two different systems we have the two representations:

where the numberings (1) and (2) are used to distinguish between the two. For the sake of clarity, we also index the Hilbert-spaces belonging to each of these representations (and get H₁ and H₂, respectively) although they are usually identical.The crucial point now is the consideration of a system consisting of the two particles as a whole. In this case, it is necessary to construct another Hilbert-space H=H₁H₂ out of H₁ and H₂ in such a way that this new system ‘lives’ in H₁ and in H₂ at the same time. In order to achieve this, a so-called tensor-product H₁H₂ is formed. This is a new Hilbert-space whose points have the form

where Φ_i,j denote basis elements in H=H₁H₂ and c_i,j their multiples. Entangled states are those (ψ⁽¹⁾ψ⁽²⁾) for which the multiples c_i,j cannot be written as

ci,j=aibj,

with a_i and b_j being the multiples from above and independent from each other.Remarks

1. The above relation between states can be interpreted as the possible arising of additional qualities when two single systems are looked upon as a whole.

2. The set of entangled states in most of quantum systems is not empty. For many systems, the subset of possibly entangled states is much bigger than the non-entangled.

3. The above characterization is not restricted to pairs of particles.

4. States (ψ⁽¹⁾ψ⁽²⁾) in H=H₁H₂ which cannot be split into products of pure states in H₁ and H₂, respectively, might be imagined as the pure states of the composite system.

5. The description of entanglement in quantum mechanics, which is a counter-intuitive, strongly depends on a mathematical apparatus with a rich structure.

Correspondence: Otto Weingärtner, Department of Basic Research, Dr. Reckeweg & Co. GmbH, Berliner Ring 32, D 64625 Bensheim, Germany.

Homeopathy
Volume 96, Issue 3, July 2007, Pages 220-226
The Memory of Water

This is part of the Homeopathy journal club described here:

www.badscience.net/?p=490

doi:10.1016/j.homp.2007.03.006    
Copyright © 2007 Elsevier Ltd All rights reserved. The history of the Memory of Water

Yolène Thomas^{, a,
a}Institut Andre Lwoff IFR89, 7, rue Guy Moquet-BP8, 94 801 Villejuif Cedex, France
Received 26 March 2007;  accepted 27 March 2007.  Available online 31 July 2007.

‘Homeopathic dilutions’ and ‘Memory of Water’ are two expressions capable of turning a peaceful and intelligent person into a violently irrational one,’ as Michel Schiff points out in the introduction of his book ‘The Memory of Water’. The idea of the memory of water arose in the laboratory of Jacques Benveniste in the late 1980s and 20 years later the debate is still ongoing even though an increasing number of scientists report they have confirmed the basic results.

This paper, first provides a brief historical overview of the context of the high dilution experiments then moves on to digital biology. One working hypothesis was that molecules can communicate with each other, exchanging information without being in physical contact and that at least some biological functions can be mimicked by certain energetic modes characteristics of a given molecule. These considerations informed exploratory research which led to the speculation that biological signaling might be transmissible by electromagnetic means. Around 1991, the transfer of specific molecular signals to sensitive biological systems was achieved using an amplifier and electromagnetic coils. In 1995, a more sophisticated procedure was established to record, digitize and replay these signals using a multimedia computer. From a physical and chemical perspective, these experiments pose a riddle, since it is not clear what mechanism can sustain such ‘water memory’ of the exposure to molecular signals. From a biological perspective, the puzzle is what nature of imprinted effect (water structure) can impact biological function. Also, the far-reaching implications of these observations require numerous and repeated experimental tests to rule out overlooked artifacts. Perhaps more important is to have the experiments repeated by other groups and with other models to explore the generality of the effect. In conclusion, we will present some of this emerging independent experimental work.

Keywords: high dilution; memory; water; molecular signal; audio-frequency oscillator; computer-recorded signals

Article Outline

Historical overview: the early history of high dilution experiments

Exploring the physical nature of the biological signal

From high dilution to digital biology

The present situation

Acknowledgements

References

Historical overview: the early history of high dilution experiments

Presenting a brief history of what is known as the ‘Memory of Water’ is not an easy task mainly because one of the main actors, Jacques Benveniste, is no longer with us (Figure 1). There are always many controversies around cutting edge science, and especially with those whose lives have been spent pursuing unorthodox trails.

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Figure 1. Jacques Benveniste 1935–2004.

I first met Benveniste during a FASEB meeting in Atlanta in 1981 and joined his laboratory a few years later to set up my own Immunology team. I had the good fortune of being able to collaborate with him for over 16 years. At that time, he was at the top of his fame and gained an international reputation as a specialist on the mechanisms of allergies and inflammation with his discovery of the ‘Platelet Activating Factor’ (paf-acether) in 1970.^{[1] and [2]} Throughout his long career, working both in the US and in France, he was responsible for the development of new ways of approaching inflammation including the patenting by the French National Institute of Health and Medical Research (INSERM) of his innovative allergy test using blood cells called basophils (FR-patent-7,520,273). Jacques’ research into allergies took him deep into the mechanisms which create such responses: understanding how the smallest amount of a substance affects the organism. The life and work of Jacques Benveniste was not only written in water.

In the early 1980s, while heading up the unit INSERM 200, Jacques took a new member onto his staff, a young medical doctor, Bernard Poitevin, whose side-interest was homeopathy. ‘He asked me if he could try my basophil degranulation test on some homeopathic preparations’, Jacques recalled, ‘and I remember distinctly saying “OK, but all you will be testing is water”.’ Thus, Jacques expressed his skepticism but accepted the proposal.

After 5 years of research they empirically observed that highly dilute (i.e., in the absence of any physical molecule) biological agents nevertheless triggered the relevant biological systems. Intrigued but cautious, Jacques was a man who adhered to the facts. He ordered a two-year long series of retests, but the same results kept recurring. Finally, Poitevin and Benveniste submitted two papers which were published in peer review journals.^{[3] and [4]} Here, the work was treated as conventional research like many other manuscripts from peer-reviewed journals which can be found in the scientific literature on the effect of high dilutions (HD) (review in^{[5] and [6]}).

Following accepted scientific practice, Jacques then asked other laboratories to try to replicate the findings. In 1988, scientists from six laboratories in four countries (France, Canada, Israel and Italy) co-authored an article showing that highly diluted antibodies could cause basophil degranulation. This was established under stringent experimental conditions such as blind double-coded procedures. Further, the experimental dilution (anti-IgE) and the control one (anti-IgG) were prepared in exactly the same manner, with the same number of dilution and agitation sequences. The article was submitted to Nature.⁷ Nature‘s referees could not fault Benveniste’s experimental procedures but could not comprehend his results. How can a biological system respond to an antigen when no molecules of it can be detected in the solution? It goes against the accepted ‘lock-and-key’ principle, which states that molecules must be in contact and structurally match before information can be exchanged. In the paper, Jacques suggested that specific information must have been transmitted during the dilution/shaking process via some molecular organization occurring in the water.

Finally, the editor of the journal, John Maddox agreed to publication, on condition that a ‘committee’ could verify Benveniste’s laboratory procedures. In July 1988, after two weeks after publication, instead of sending a committee of scientific experts, Maddox recruited—James Randi, a magician, and Walter Stewart, a fraud investigator. The three of them spent 5 days in the laboratory. Well, you all know what followed. Nature‘s attempted debunking exercise failed to find any evidence of fraud. Nevertheless, they concluded that Benveniste had failed to replicate his original study.⁸ This marked the beginning of the ‘Water Memory’ war, which placed him in a realm of ‘scientific heresy’. As Michel Schiff later remarked in his book: ‘INSERM scientists had performed 200 experiments (including some fifty blind experiments) before being challenged by the fraud squad. The failure to reproduce⁸ only concerned two negative experiments’.⁹ Benveniste replied to Nature¹⁰ and reacted with anger, ‘not to the fact that an inquiry had been carried out, for I had been willing that this be done… but to the way in which it had been conducted and to the implication that my team’s honesty and scientific competence were questioned. The only way definitely to establish conflicting results is to reproduce them. It may be that we are all wrong in good faith. This is not crime but science…’.

As a consequence of the controversy that ensued, Jacques became increasingly isolated. Nonetheless the team repeated the work on a larger scale, entirely designed and run under the close scrutiny of independent statistical experts, and confirmed the initial findings in Nature.¹¹ These further experiments have been coolly received or ignored by most scientists at least partly because, given Jacques’ now-acrimonious relationship with Nature, they were published in a less renowned journal.

To date, since the Nature publication in 1988, several laboratories have attempted to repeat Benveniste’s original basophil experiments. Most importantly, a consortium of four independent research laboratories in France, Italy, Belgium, and Holland, led by M. Roberfroid at Belgium’s Catholic University of Louvain in Brussels, confirmed that HD of histamine modulate basophil activity. An independent statistician analyzed the resulting data. Histamine solutions and controls were prepared independently in three different laboratories. Basophil activation was assessed by flow-cytometric measurement of CD63 expression (expressed on cytoplasmic granules and on the external membrane after activation). All experiments were randomized and carried out under blind conditions. Not much room, therefore, for fraud or wishful thinking. Three of the four labs involved in the trial reported statistically significant inhibition of the basophil degranulation reaction by HD of histamine as compared to the controls. The fourth lab gave a result that was almost significant. Thus, the total result over all four labs was positive for histamine HD solutions.^{[12] and [13]} ‘We are,’ the authors say in their paper, ‘unable to explain our findings and are reporting them to encourage others to investigate this phenomenon’.

Different attempts have been made to substantiate the claim that serial dilution procedures are associated with changes in the water’s physical properties (^{[14] and [15]}and see Louis Rey contribution in this issue pages 170–174). Yet, the challenge of understanding the mechanisms of how HDs work, and the role of water in them, is a difficult one to say the least. Several possible scenarios have been suggested. One proposed by Giuliano Preparata and Emilio Del Giudice, is that long range coherent domains between water molecules (quantum electrodynamics, QED) gives high dilution laser-like properties.^{[16] and [17]} When the field matches the kinetic of the reaction, the latter becomes functional as the optimal field strength as for a radio receiver. It was to a scientific meeting in Bermuda that took place a few months before the Nature ‘affair’ erupted that these two physicists working at Milan University brought the theoretical basis for the memory of water. Another scenario predicts changes in the water structure by forming more or less permanent clusters.¹⁸ Other hypotheses will be discussed in this issue. High dilution experiments and memory water theory may be related, and may provide an explanation for the observed phenomena. As M. Schiff points out, only time and further research will tell, provided that one gives the phenomena a chance.⁹

Exploring the physical nature of the biological signal

Despite the difficulties after the Nature fracas, Jacques and his now-depleted research team continued to investigate the nature of the biological activity in high dilutions and aimed at understanding the physical nature of the biological signal. In his Nature paper, Jacques reasoned that the effect of dilution and agitation pointed to transmission of biological information via some molecular organization going on in the water. The importance of agitation in the transmission of information was explored by pipetting dilutions up and down ten times and comparing with the usual 10-s vortexing. Although the two processes resulted in the same dilution, basophil degranulation did not occur at HD after pipetting. So transmission of the information depended on vigorous agitation, possibly inducing a submolecular organization of water or closely related liquids (ethanol and propanol could also support the phenomenon). In contrast, dilutions in dimethylsulphoxide did not transmit the information from one dilution to the other. In addition, heating, freeze-thawing or ultrasonication suppressed the activity of highly diluted solutions, but not the activity of several active compounds at high concentrations. A striking feature was that molecules reacted to heat according to their distinctive heat sensitivity, whereas all highly diluted solutions ceased to be active between 70 and 80 °C. This result suggested a common mechanism operating in HDs, independent of the nature of the original molecule. In addition, in 1991 and in collaboration with an external team of physicists (Lab. Magnetisme C.N.R.S.-Meudon Bellevue, France), it was shown in twenty four blind experiments that the activity of highly dilute agonists was abolished by exposure to a magnetic field (50 Hz, 15×10⁻³ T, 15 min) which had no comparable effect on the genuine molecules. Moreover, it is worth pointing out that a growing number of observations suggest the susceptibility of biological systems or water to electric and low-frequency electromagnetic fields.^{[19], [20] and [21]} In addition, what is suggested from the literature is a possible role of electromagnetic fields regarding informational process in cell communication.^{[22], [23] and [24]}

At this stage, Jacques hypothesized that transmission of this ordering principle was electromagnetic in nature and move on to the idea that molecules could communicate via specific electromagnetic waves. If so, what molecule vibration modes are efficient and how can these signals be used to mimic some of the biological functions of a molecule without its physical presence?

From high dilution to digital biology

It was at the beginning of the nineties that a homeopathic physician, E. Attias convinced Jacques to try out an electrical device that he claimed transmitted chemical information. After a few positive trials with this machine, Jacques had another one built, which was used for later experiments. This second device was essentially a standard audio amplifier that, when connected to another coil, behaves as an audio-frequency oscillator. Between 1992 and 1996, we performed a number of experiments showing that we could transfer, in real time, molecular signals indirectly to water or directly to cells. Briefly, cells were placed in a 37 °C humidified incubator on one coil attached to the oscillator, while an agonist (or vehicle as control) was placed on another coil at room temperature. Here, the transfer was not a two step-process, as when water acts as an intermediary recipient of the molecular signal. In one such exploration, we showed that molecular signals associated with a common phorbol ester (phorbol-myristate-acetate) could be transmitted by physical means directly to human neutrophils to modulate reactive oxygen metabolite production. In 1996, I submitted an article about these experiments to several prestigious journals. The article was flatly rejected each time, on the grounds that we could not explain the underlying mechanism, in spite of the referees’ general opinions that our work was ‘state-of-the-art’ and was ‘provocative and intriguing and we have gone to great lengths to try to eliminate any biological variables that could bias our results.’ It was finally published in 2000.²⁵ Appended to this article were two affidavits, one from a French laboratory (F. Russo Marie, INSERM U332, Paris, France) testifying that they supervised and blinded the experiments we did in this laboratory; the other from an US laboratory (W. Hsueh, Department of Pathology, Northwestern University, Chicago) testifying that they did some preliminary experiments similar to ours, without any physical participation on our part, and detected the same effect.

Because of the material properties of the oscillator and the limitations of the equipment used, it is most likely that the signal is carried by frequencies in the low kilohertz range.²⁶ These considerations led to the establishment in 1995 of a more sophisticated procedure for the recording and retransmission of the molecular signals. DigiBio, a company that Jacques had set up in 1997 to finance his research, obtained in 2003 an approval for one of his French patents by the US Patent Office (6,541,978: method, system and device for producing signals from a substance biological and/or chemical activity). The characteristics of the equipment are described in Figure 2 and in.²⁶ Briefly, the process is to first capture the electromagnetic signal from a biologically active solution using a transducer and a computer with a sound card. The digital signals are stored (Microsoft sound files *.wav). The signal is then amplified and ‘played back’, usually for 10 min, from the computer sound card to cells or organs placed within a conventional solenoid coil. The digitally recorded signals can also be played back into untreated water, which thereafter will act as if the actual substance was physically present.

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Figure 2. Schematic drawing of the computer-recorded signals: capture, storage and replay:

• Shielded cylindrical chamber: Composed of three superposed layers: copper, soft iron, permalloy, made from sheets 1 mm thick. The chamber has an internal diameter of 65 mm, and a height of 100 mm. A shielded lid closes the chamber.

• Transducers: Coil of copper wire, impedance 300 Ω, internal diameter 6 mm, external diameter 16 mm, length 6 mm, usually used for telephone receivers.

• Multimedia computer (Windows OS) equipped with a sound card (5–44 KHz in linear steps), (Sound Blaster AWE 64, CREATIVE LABS).

• HiFi amplifier 2×100 watts with an ‘in’ socket, an ‘out’ socket to the speakers, a power switch and a potentiometer. Pass band from 10 Hz to 20 kHz, gain 1–10, input sensitivity +/− V.

• Solenoid coil: Conventionally wound copper wire coil with the following characteristics: internal diameter 50 mm, length 80 mm, R=3.6 Ω, three layers of 112 tums of copper wire, field on the axis to the centre 44×10⁻⁴ T/A, and on the edge 25×10⁻⁴ T/A.

All links consist of shielded cable. All the apparatus is earthed.

From 1995 to the present, several biologically active molecules (eg histamine, acetylcholine, caffeine, PMA, Melagatran… even homeopathic medicines such as Arnica montana) have been recorded, digitized and replayed to biological systems sensitive to the original molecular substance. Several biological models were used. The first one was a commonly used system by pharmacologists, called the Langendorff preparation. By injecting different vasoactive substances into the coronary artery of an isolated, perfused guinea pig heart and measuring the coronary flow, you can quantify the vasoconstricting or vasodilating effect of the agent. In typical experiments, the signal of acetylcholine (or water as control), a classical vasodilating molecule was recorded and digitized. The signal was then amplified and ‘played’ back onto water. The signal-carrying water is then injected into the isolated heart, and consequently the coronary flow increased. Interestingly, atropine, an acetylcholine inhibitor, inhibited both the effects of the molecular acetylcholine as well as the digital signal of acetylcholine. Of note, the order of the conditions and their repetitions was always randomized and blinded. Other models include: human neutrophil activation; detection of the recorded signal of bacteria (E. Coli and Streptococcus) by playing them to a biological system specific to the bacterial signal and; the inhibition of fibrinogen coagulation by a Direct Thrombin Inhibitor. Further details of three of these salient biological models have been previously described.²⁶ Together, these results suggested that at least some biologically active molecules emit signals in the form of electromagnetic radiation at a frequency of less than 44 kHz that can be recorded, digitized and replayed directly to cells or to water, in a manner that seems specific to the source molecules.²⁶

Assuming that we give credence to the phenomena described, one question naturally springs to mind: what do molecule vibration modes sound like? Can measurable signals been identified in the form of low frequency spectral components? Didier Guillonnet, an engineer in computer science, and at the time, a close collaborator of Jacques Benveniste admitted, ‘When we record a molecule such as caffeine, for example, we should get a spectrum, but it seems more like noise. We are only recording and replaying; at the moment we cannot recognize a pattern although the biological systems do.’ Jacques called this matching of broadcast with reception ‘co-resonance,’ and said it works like a radio set.

Among the various theoretical problems associated with such a signal, two appear particularly relevant. First, how is such information using water as an intermediary detected amongst much electromagnetic noise? In fact, it has been suggested that stochastic resonance is an important mechanism by which very weak signals can be amplified and emerge from random noise.²⁷ Second, the limitations of the equipment used here, suggest that the signal is carried by frequencies in the low kilohertz range, many orders of magnitude below those generally associated with molecular spectra (located in the infrared range). However, molecules may also produce much lower ‘beat’ frequencies (Hz to kHz) specific for every different molecule. The ‘beat frequency’ phenomenon may explain this discrepancy, since a detector, for instance a receptor, will ‘see’ the sum of the components of a given complex wave.²⁸ Clearly, more experimental and theoretical work is needed in order to unveil the physical basis of the transfer (and storage?) of specific biological information either between interacting molecules or via an electronic device.

Replicability: Although since the very beginning we have placed a great deal of emphasis on carrying out our work under the highest standards of methodology and that great effort has been made to isolate it from environmental artifacts, attempts to replicate these data in other laboratories yielded mixed results. For instance, in 1999, Brian Josephson, Nobel Laureate for Physics in 1973 invited Benveniste to the Cavendish Laboratory in Cambridge. He said, ‘We invited him to learn more about the research which seems both scientifically interesting and potentially of considerable practical importance. Jacques definitely recognized there was a problem with reproducing the effect. The situation seemed to be that in some circumstances you had reproduction and in others you didn’t; but the overall results were highly significant.’ We then realized the difficulty in ‘exporting’ a method, which is very far from conventional biology. There are many key variables that might be involved like, water purification, the container shape and material being used, the purity of chemicals, atmospheric conditions…. Only if these underlying variables are known could the experiments be reproducible. When the transfer is a two-step process using water as an intermediary support for transmitted molecular signals, it takes even more stringent conditions for the experiments to be repeatable. The digital signal is replayed onto the water, which may take or not take the signal depending, for instance, upon the local electromagnetic conditions. In this regard, it is interesting to note that the ‘informed water’ as in the HD experiments, loses its activity after heating or being exposed to magnetic fields.

More surprising and mysterious was the fact that in some cases certain individuals (not claiming special talents) consistently get digital effects and other individuals get no effects or perhaps block those effects (particularly when handling a tube containing informed water). The inhibition of fibrinogen–thrombin coagulation by a digitized thrombin inhibitor is a model particularly sensitive to experimenter effects and therefore may account for the difficulty in consistently replicating this experimental system. Despite the precautions taken to shield the information transfer equipment from magnetic or electromagnetic pollution, very little concern has been given to possible subtle human operator effects.²⁹ We dealt with this problem in some of our own studies and also in the course of one independent replication.³⁰

The present situation

Now that Jacques Benveniste is no longer with us, the future of the ‘digital biology’ is in the hands of those who have been convinced of the reality of the basic phenomena. It is up to them to explore with other models the generality of the effect. Most likely they will succeed if they combine full biological and physical skills to understand the nature of the biological signals.

In this regard, since June 2005, Luc Montagnier, the co-discoverer of HIV, is conducting experiments (detection of the recorded signals of various micro-organisms derived from human pathologies) which, confirm and extend the original finding. In 2006, he set up a company called Nanectis. Perhaps the most impressive emerging data is from a US group located in La Jolla, CA.

In barely four years, they have conducted novel research programs and expanded the original technology into a series of potential industrial applications. Since 2004, they have obtained several US patents (6,724,188; 6,952,652; 6,995,558; 7,081,747) and applied for International Patents (WO 06/015038: system and method for collecting, storing, processing, transmitting and presenting very low amplitude signals; WO 06/073491: system and method for producing chemical or biochemical signals). They can improve the molecular signal recording in particular by using both magnetic and electromagnetic shielding coupled to a superconducting quantum interference device (SQUID). The system records a time-series signal for a compound; the wave form is processed and optimized (selected noise amplitude, power setting…) to identify low-frequency peaks that are characteristic of the molecule being interrogated (Molecular Data Interrogation System, MIDS). The optimized signal is played back for various periods of time to sensitive biological systems. For instance, they describe one interesting model particularly relevant to the specificity of the molecular signal transmission effect. The arabinose-inducible bacterial system with a lac operon is inducible by signals from the L (+) arabinose form but not from the D (−) arabinose inactive isomer or the white noise control. Other systems include digital herbicides and plant growth regulator as well as pharmaceutical compounds such as Taxol ^®, a prototype for a class of anticancer drugs. For instance, in a classic in vivo mouse xenograft model, the digital Taxol was assessed by the growth inhibitory potential of a human breast tumor. The results revealed that tumor growth, by day 36, was as statistically significantly inhibited in the group treated with the Taxol signal, as it was in the control group treated with actual molecular Taxol. If these new experimental observations can be validated, we will have added yet another valuable piece to the puzzle.

Although a theoretical explanation of how the memory of water might work must still be explored, the fact that the effective transmission of molecular signals has now been observed by independent teams using different biological systems, provides a strong additional basis to suggest that the phenomena observed by Jacques were not due simply to laboratory artefacts.

Whatever knowledge ongoing and future investigation may bring, the difficult road that Jacques travelled by opposing the automatic acceptance of received ideas, will have contributed to sustaining freedom in scientific research and putting the emphasis back where it belongs, on observable fact.

Acknowledgments

I am grateful to Drs. Isaac Behar and Anita K. Gold for critical comments on the manuscript.

References

1 J. Benveniste, P.M. Henson and C.G. Cochrane, Leukocyte-dependent histamine release from rabbit platelets. The role of IgE, basophils, and a platelet-activating factor, J Exp Med 136 (1972), pp. 1356–1377. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

2 J. Benveniste, Platelet-activating factor, a new mediator of anaphylaxis and immune complex deposition from rabbit and human basophils, Nature 249 (1974), pp. 581–582. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

3 E. Davenas, B. Poitevin and J. Benveniste, Effect of mouse peritoneal macrophages of orally administered very high dilutions of silica, Eur J Pharmacol 135 (1987), pp. 313–319. Abstract | Abstract + References | PDF (543 K) | View Record in Scopus | Cited By in Scopus

4 B. Poitevin, E. Davenas and J. Benveniste, In vitro immunological degranulation of human basophils is modulated by lung histamine and Apis mellifica, Br J Clin Pharmacol 25 (1988), pp. 439–444. View Record in Scopus | Cited By in Scopus

5 H. Walach, W.B. Jonas, J. Ives, R. van Wijk and O. Weingartner, Research on homeopathy: state of the art, J Altern Complement Med 11 (2005), pp. 813–829. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

6 P. Bellavite, R. Ortolani, F. Pontarollo, V. Piasere, G. Benato and A. Conforti, Immunology and Homeopathy, Evidence-based Complementary Alternative Med 2 (2005), pp. 441–452. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

7 E. Davenas, F. Beauvais and J. Amara et al., Human basophil degranulation triggered by very dilute antiserum against IgE, Nature 333 (1988), pp. 816–818. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

8 J. Maddox, J. Randi and W.W. Stewart, High-dilution’experiments a delusion, Nature 334 (1988), pp. 287–290.

9 Schiff M. The Memory of Water. UK: Ed. Thorsons, 1995.

10 J. Benveniste, Dr Jacques Benveniste replies, Nature 334 (1988), p. 291. Full Text via CrossRef

11 J. Benveniste, E. Davenas, B. Ducot, B. Cornillet, B. Poitevin and A. Spira, L’agitation de solutions hautement diluées n’induit pas d’activité biologique spécifique, CR Acad Sci Paris 312 (1991), pp. 461–466.

12 P. Belon, J. Cumps and M. Ennis et al., Inhibition of human basophil degranulation by successive histamine dilutions: results of a European multi-centre trial, Inflamm Res (Suppl 1) 48 (1999), pp. S17–S18. View Record in Scopus | Cited By in Scopus

13 P. Belon, J. Cumps and M. Ennis et al., Histamine dilutions modulate basophil activation, Inflamm Res 53 (2004), pp. 181–188. View Record in Scopus | Cited By in Scopus

14 Lobyshev VI, Tomkevitch MS. Luminescence study of homeopathic remedies. In: Priezzhev AV, Cote GL (eds). Optical Diagnostics and Sensing of Biological Fluids and Glucose and Cholesterol Monitoring, Proceedings of the SPIE, Vol 4263. MAIK “Navka/Interperiodica” (Russia), 2001, pp 1605–7422.

15 V. Elia, S. Baiano, I. Duro, E. Napoli, M. Niccoli and L. Nonatelli, Permanent physico-chemical properties of extremely diluted aqueous solutions of homeopathic medicines, Homeopathy 93 (2004), pp. 144–150. SummaryPlus | Full Text + Links | PDF (154 K) | View Record in Scopus | Cited By in Scopus

16 E. Del Giudice, G. Preparata and G. Vitiello, Water as a free electric dipole laser, Phys Rev Lett 61 (1988), pp. 1085–1088. Full Text via CrossRef

17 G. Preparata, QED Coherence in Matter, World Scientific, Singapore (1995).

18 E.E. Fesenko and A.Y. Gluvstein, Changes in the state of water, induced by radiofrequency electromagnetic fields, FEBS Lett 367 (1995), pp. 53–55. Abstract | Abstract + References | PDF (294 K) | View Record in Scopus | Cited By in Scopus

19 R. Goodman and M. Blank, Initial interactions in electromagnetic field-induced biosynthesis, J Cell Physiol 199 (2004), pp. 359–363.

20 E. Ben Jacob, Y. Aharonov and Y. Shapira, Bacteria harnessing complexity, Biofilms (2004), pp. 239–263.

21 P.h. Vallée, J. Lafait, P. Mentré, M.O. Monod and Y. Thomas, Effects of pulsed low frequency electromagnetic fields on water using photoluminescence spectroscopy: role of bubble/water interface?, J Chem Phys 122 (2005), pp. 114513–114521. Full Text via CrossRef

22 G. Albrecht-Buehler, Rudimentary form of cellular ‘vision’, Proc Natl Acad Sci USA 89 (1992), pp. 8288–8292. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

23 M.W. Trushin, Studies on distant regulation of bacterial growth and light emission, Microbiology 149 (2003), pp. 363–368. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

24 B.W. Ninham and M. Boström, Building bridges between the physical and biological sciences, Cell Mol Biol 51 (2005), pp. 803–813. View Record in Scopus | Cited By in Scopus

25 Y. Thomas, M. Schiff, L. Belkadi, P. Jurgens, L. Kahhak and J. Benveniste, Activation of human neutrophils by electronically transmitted phorbol-myristate acetate, Med Hypotheses 54 (2000), pp. 33–39. Abstract | Abstract + References | PDF (188 K) | View Record in Scopus | Cited By in Scopus

26 Y. Thomas, L. Kahhak and J. Aissa, The physical nature of the biological signal, a puzzling phenomenon: the critical role of Jacques Benveniste. In: G.H. Pollack, I.L. Cameron and D.N. Wheatley, Editors, Water and the Cell, Springer, Dordrecht (2006), pp. 325–340.

27 K. Wiesenfeld and F. Moss, Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDS, Nature 373 (1995), pp. 33–36. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

28 C.N. Banwellk, Fundamentals of Molecular Spectroscopy, McGraw-Hill Publ., UK (1983) pp 26–28.

29 B.J. Dunne and R.G. Jahn, Consciousness, information, and living systems, Cell Mol Biol 51 (2005), pp. 703–714. View Record in Scopus | Cited By in Scopus

30 W.B. Jonas, J.A. Ives and F. Rollwagen et al., Can specific biological signals be digitized?, FASEB J 20 (2006), pp. 23–28. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

Correspondence: Yolène Thomas, Institut Andre Lwoff IFR89, 7, rue Guy Moquet-BP8, 94 801 Villejuif Cedex, France. Tel.: +33(0) 1 49 58 34 81.

Homeopathy
Volume 96, Issue 3, July 2007, Pages 151-157
The Memory of Water

This is part of the Homeopathy journal club described here:

www.badscience.net/?p=490

doi:10.1016/j.homp.2007.05.001    
Copyright © 2007 Elsevier Ltd All rights reserved. Can water possibly have a memory? A sceptical view

José Teixeira^{, a,
a}Laboratoire Léon Brillouin (CEA/CNRS), CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
Received 1 May 2007.  Available online 31 July 2007.

Homeopathic medicines are currently used in medical practice, despite controversy about their effectiveness. The preparation method is based on extremely high dilutions of many substances in water, far beyond any detectable level. For this reason, it has been suggested that water could retain a ‘memory’ of substances that have been dissolved in it before the successive dilutions. The paper stresses the fact that this idea is not compatible with our knowledge of pure water. If an explanation on physical grounds is to be found, research must focus in other aspects of the preparation, such as the presence of other molecules and dissolved gases.

Keywords: water structure; water dynamics; aggregation; metastability

Article Outline

Introduction

Pure water and homeopathic drugs

Properties of liquid water

Aqueous solutions

Conclusion

References

Introduction

Homeopathy and homeopathic medicines are widespread and well accepted by many doctors, pharmacists and patients. It is officially recognised by health authorities and agencies authorities and at a political level in many parts of the world. However, they are also criticized and attacked by others. It is not my purpose to participate actively in a complex debate that includes not only scientific aspects but also sociological and economic components. My contribution will address only the arguments relying on the properties of water and only from the physical view. Consequently, at best, it is a physicist’s view of the role played by water in homeopathic solutions.

To clarify this statement, I think that it is useful to remember that medicine is not only a science but also an art. A good doctor takes into account not only the sickness itself but also the patient, his environment and his psychological aspects. As a consequence, the prescription of a medicine fortunately includes a large part of empiricism. The goal is to restore a ‘normal’ state. One must admit that the complete knowledge of all the parameters intervening in a real situation is totally illusory and that this situation is unlikely to change in the foreseeable future. Anyway, even when the active principles and biological receptors are well known and identified, the reactions of different patients are not the same. To circumvent these inherent difficulties the performance of drugs is established via statistical analysis of large numbers of cases with a randomised double-blind methodology which implicitly recognizes the hidden role of components which escape to the normal scientific analysis of ‘exact sciences’.

Modern pharmacological research is based on a detailed knowledge of physical and chemical interactions between drugs and living cells. At the confluence of Biophysics and Chemistry, a more detailed and precise picture of those interactions is steadily emerging. Still, many traditional medications and frequently-prescribed drugs are currently used without such detailed knowledge of their action. For them, it is either difficult or useless to define the exact ‘paths’ from medicine to biology, then to chemistry and physics.

Pure water and homeopathic drugs

Many traditional drugs, as for example those extracted from plants, are extensively used in medicine. In some cases one or more active principles have been identified but even in such cases the exact action is usually not well understood at the level of chemical reactions or physical interactions taking place within living organisms. This situation is very common but has never been a limitation to prescribing drugs that have shown their effectiveness through many years of practical use. Certainly, in other cases, the interactions are known in great detail leading to the synthesis of well-defined drugs with specific and well controlled applications. But we remain far from a comprehensive and detailed knowledge of the action of drugs on living organisms.

Homeopathic drugs fall, at least partially, into the first category. Their use has been validated by real or supposed successes, the frontier of the two being probably irrelevant from the point of view of the patient. But there is an essential difference between traditional or ‘natural’ medicine and homeopathy. The latter is much more recent and based in a quasi philosophical concept (similia similibus curentur) stated by Hahnemann, perhaps by analogy with the contemporary first studies of immunization. With modern science, it should, in due course, be possible to understand the mechanisms of action of natural substances and of homeopathic drugs. For natural substances the search for the active principles has been successful in some cases; in others, it has been simply assumed that they are present but the level of interest of the drug or available resources has not justified further studies.

With homeopathic drugs the situation is very different. Their method of preparation is based essentially on two steps: sequential dilution with ‘succussion’ or ‘dynamisation’ (vigorous turbulent shaking). A molecular view of the matter and a trivial calculation demonstrates that, often it is extremely improbable that even one molecule of the compound present in the original solution persists in a vial of the final medicine. The role of succussion is not obvious, even less the diverse standards of methods of preparation.

Under the pressure of criticism, the natural evolution of researchers interested in finding acceptable scientific justifications of homeopathy has been to go from purely medical concepts of effective therapy to chemistry and finally to fundamental physics. Ultimately, schematically, the answer: if there is ‘only’ water in homeopathic medicines, then the explanation of the therapeutic action must be in pure water, itself!

This intellectual evolution is a paradox. While for many drugs, the action is known at a biological, sometimes at a chemical, but almost never at a physical level (that of the structure and energies defined with atomic resolution); for homeopathy, the discussion jumped directly into this microscopic sub-molecular physics world. The mixture of the precise methodology characterizing research in physics and procedures deriving from pharmacology in research in homeopathy is striking. For example, several measurements of physical properties of diluted solutions have been done double-blinded. An extreme and provocative hypothesis is that water can retain a ‘memory’ of substances previously dissolved in it.¹

A critical analysis of several publications shows that several issues remain open to question. Schematically, one can distinguish the following:

(1) How different from pure water are highly diluted solutions? In other words, is the simple calculation of the number of molecules of the ‘active principle’ per unit volume of the solution sufficient to account for the composition of homeopathic medicines?

(2) If succussion is an essential step in the preparation of homeopathic medicines, what is exactly its role? How does it influence the dilution procedure?

(3) What is the behaviour of complex molecules (eg biopolymers, organic compounds, surfactants, etc.) during the dilution process?

A clear answer to these (and perhaps other) questions is a necessary and essential precondition to any study of ‘pure’ water. Indeed, the conditions of preparation and conservation of homeopathic medicines are far from respecting the simplest procedures required in physical studies of pure water.

Some issues should be controlled more systematically:

(1) Pure water is a very powerful solvent of many substances. For example, it dissolves and forms specific bonds with silica. In contact with the surface of quartz, water forms stable silanol groups (Si–O–H). With time, silica molecules and silicon atoms are solubilised and hydrated. The number of these ‘impurities’ is huge as compared with the calculated amount of molecules of the starting substance in most homeopathic medicines.

It may be useful to recall that the interaction of water with solid surfaces is so strong that studies of nucleation must be done with minute amounts of water kept in levitation, without any contact with solid surfaces. The interaction with solid surfaces is so important that if a supercooled liquid freezes, it must be heated up to temperatures higher than the melting point in order to be supercooled again. Less important for water than for other liquids (eg gallium), this effect is due to more favourable nucleation of the solid form at the solid surface.

Another point deserving investigation is the storage of homeopathic solutions over long periods of time. This procedure is totally incompatible with a chemical purity of water, even at a modest level.

(2) The main consequence of succussion is the insertion of substantial amounts of air from the environment where the procedure takes place. In a laboratory that is not a cleanroom (such as those used for example in electronics), the procedure brings into the solution not only the gases present in the atmosphere (oxygen, nitrogen, argon,…) but also dust particles, micro-droplets of water, etc. Recent studies² show that the properties of solutions are drastically modified when succussion is done under different atmospheres or at different pressures, a fact which should encourage further studies in this direction.

(3) Many substances, which contain pharmacologically active principles, are not soluble in water. Some are previously diluted in alcohol suggesting the presence of surfactant molecules that go spontaneously to interfaces such as the free surface, the interface between the solution and micro-droplets of gases and the interface with the vial. Again, several very promising and striking studies performed by the analysis of the thermoluminescence of frozen solutions open new and exciting perspectives.³

To summarize, it is striking that in publications concerning highly diluted solutions, chemical ‘purity’ is assumed, solely on the basis of a calculation based on the dilution procedure itself. In fact most of the samples studied are far from being ‘pure water’. It would be interesting to perform to a real analysis of the composition of the solutions with physical methods such as mass spectroscopy.

Properties of liquid water

As stated above, many experiments with homeopathic medicines assume the purity of the highly diluted solutions and attribute its therapeutic action to modifications of the structure and dynamics of the pure liquid itself due to the past presence of a solute.¹ Such a strong hypothesis would imply not only general or random changes but also a large variety of changes, specific to each solute. The main purpose of this paper is to recall that this hypothesis is totally incompatible with our present knowledge of liquid water.

Water, in all its forms (crystal, liquid, gas and amorphous forms) is certainly the most studied of all substances. All its properties have been measured with extremely high accuracy in very different conditions, including metastable states and ‘extreme’ conditions. This is due to the central role of water in many scientific domains in physics, chemistry, geophysics and, of course, biophysics. Essentially all known experimental techniques and computer simulations have been used to precise details of the behaviour of water at scales extending from hydrodynamics to the nuclear and electronic levels. In other words, water is not an unknown substance!

However, do we know ‘everything’ about water? Certainly not: several puzzling questions are open to discussion. In brief, the main open question about pure water concerns the supercooled (metastable) state (ie liquid water at temperatures below its freezing point) and its relation with different amorphous (glassy) states. The structure of liquid water, at atmospheric pressure, is not known in a large temperature range extending from the vicinity of the temperature of homogeneous nucleation of ice (−42 °C) down to the temperature of the glass transition (−140 °C). This problem is the object of debate and speculation mostly based in extrapolations of simulations of molecular dynamics performed by computer.^{[4] and [5]}

Another important domain of research is ‘confined water’, ie water occupying extremely small volumes, for example, in porous materials, in thin layers or in small pools formed at hydrophobic sites of bio-molecules. In this case, there is a large variety of situations that depend essentially on the nature of the substrate and on the relative importance of the number of molecules at the surface and in the bulk of the small volume. However, pure water at ambient conditions is well understood. Let us review some of its main properties that may be related to the subject of this paper.

Water is a simple molecule containing three atoms: one of oxygen and two of hydrogen strongly bound by covalent bonds. Because of the hybridisation of the molecular orbitals, the shape of the molecule is a V with the oxygen occupying the vertex of an angle of 104°; the O–H distance is almost exactly 0.1 nm. When two water molecules are sufficiently close, they orient one against the other to establish a chemical bond, called hydrogen bond. In this bond, one hydrogen atom is shared by two neighbouring molecules (Figure 1). The bonding energy is about 10 times larger than the kinetic energy but the bond is ‘fragile’ due the vibratory motions of the hydrogen atom particularly in the direction perpendicular to the line O–HO. It is possible to measure accurately the typical time for which the three atoms are aligned (the lifetime of hydrogen bonds): it is of the order of 0.9 ps (9×10⁻¹³ s) at room temperature.

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Figure 1. Schematic representation of a hydrogen bond in water. The large circles represent two oxygen atoms of neighbouring molecules; the small circle is the hydrogen atom attached to the oxygen on the left hand side by a covalent bond. The length of the hydrogen bond is 0.18 nm.The hydrogen atom vibrates in all directions. Vibrations perpendicular to the bond are most likely to break the bond.

Because of its geometry, a water molecule can easily form four hydrogen bonds with four neighbouring molecules. This corresponds to the structural arrangement in common ice (I_h or hexagonal form). The angle of 104° is sufficiently close to the tetrahedral angle (109°) to impose this very open structure where each molecule is surrounded by four others at the apex of a tetrahedron (Figure 2). In liquid water this local geometry exists partly: on average a water molecule has 4.5 neighbours but this number decreases with decreasing temperature because the average number of ‘intact’ bonds increases. Incidentally, it is this decrease of the number of first neighbours that explains why the density of water decreases at low temperatures. At 4 °C, which is the temperature of maximum density, this effect compensates that of thermal expansion.

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Figure 2. Tetrahedral arrangement of five water molecules. The vibrational motion of a hydrogen atom is represented by an arc on the right-hand side of the figure (adapted from G Walrafen).

The average number of ‘intact’ bonds at a given moment is relatively high, although lower than in alcohols, for example. It is of the order of 60% which justifies seeing liquid water as a 3-dimensional network of hydrogen bonds, like a gel. But a gel with a life time of 1 picosecond (ps)! This means that in an ‘instantaneous picture’ of water structure (possible to obtain by computer simulations) one can identify local structures such as rings of 5, 6 or 7 molecules, regions with higher density of bonds than others, etc. All these structural properties can be identified by several techniques and correspond to thermodynamic properties. For example, the increase of isothermal compressibility observed at low temperatures is due to the enhancement of density fluctuations. It is very important to note that such fluctuations are not due to aggregation or formation of clusters. Hydrogen bonds form and break very rapidly generating short lived fluctuations of local density. In other words, even if at a given moment one can identify a region of higher density than the average, it will disappear after a very short time and will appear statistically in another place without any form of coherent motion such as would exist if a cluster was diffusing inside the liquid.

Historically, the first models of liquid water (due to WC Roentgen) represented liquid water as a mixture of an ideal liquid and small ice-like clusters. This model has been ruled out by many experiments. Among them, small angle X-ray scattering eliminates unambiguously any possibility of existence of clusters or aggregates in liquid water, even at very low temperatures.^{[6] and [7]}

Isolated or confined water molecules can have their mobility totally restricted. In such cases, the lifetime of a hydrogen bond can be infinite. This situation is frequent in proteins where hydrogen bonds with water can play a central role in protein structure. But, in these situations, water molecules don’t constitute a liquid. Consequently, it is worth emphasizing that to postulate the existence of stable structures in pure water is totally wrong. This is one of the limits imposed by the knowledge of the structure of water.

Aqueous solutions

In aqueous solutions, the situation is more diverse. Water can dissolve and mix with many substances in different proportions (salts, acids, various alcohols, sugars, and gases, etc). Both local structure and dynamic properties may be drastically modified. Two well known examples give an idea of the diversity of situations. Trehalose is a sugar that promotes the formation of glassy water even when extremely dilute. It is present in animals and plants which, because of this property, can survive very low temperatures. Other examples are aerogels of silica with a huge content of water, which can contain more than 95% water while remaining macroscopically solid.

Generally speaking, the inclusion of molecules or ions destroys local tetrahedral geometry. Depending on the nature of the compound, the molecules of water arrange in a large variety of local structures. For example, when a salt is dissolved in water, it is dissociated into two ions each of which is surrounded by a layer of hydration where the strong electrostatic interactions between the charge of the ion and the dipoles of water generate a mini-cluster (Figure 3). The life time of this cluster is 10 to 100 times longer than the lifetime of hydrogen bonds but is not infinite, because of the exchange between molecules of water in the hydration shell and those of the bulk.

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Figure 3. Schematic representation of the arrangement around an anion (left) and a cation (right). In the first case the dipolar moment of the water molecules is directed towards the ion; in the opposite direction in the case of the anion. The screening of the electrical field of the ions is very efficient and the structure of water beyond the first hydration layer is almost not modified.

However, it is erroneous to believe that the electrical field generated by the ions extends over large distances. Actually, it is screened by the hydration layer. There is a large literature about the structure in hydration shells. The number of water molecules, distances and angles are known with great accuracy from neutron scattering experiments based on isotopic substitution.⁸

A very different situation concerns the solubility of hydrophobic atoms and molecules, such as methane or noble gases. In this case, water has tendency to form clathrate-like structures around the solute. A clathrate is a polyhedral structure; frequently a dodecahedron with pentagonal faces. This is a very stable structure, because the internal angle of the pentagon (104°) is equal to the internal angle, HOH, of the molecule. It forms a cage and the prisoner is the hydrophobic solute. The short lifetime of hydrogen bonds does not allow the formation of stable or long-lived clusters. Experiments simply detect, at best, a tendency to the formation of short lived planar pentagons.

Finally, it is interesting to consider situations in which stable aggregates are formed. The most interesting, including many industrial applications, are surfactants, which are molecules with a hydrophilic head (sometimes polar) and one or two hydrophobic tails. When dissolved in water in sufficiently large amount (above a critical micellar concentration, c.m.c.) they form structured clusters called micelles (Figure 4). The heads are at the external surface and the hydrophobic tails minimise the interaction energy with water inside the sphere. These structures are very stable. They persist essentially for ever, even if there are many exchanges of surfactant molecules between micelles, either by diffusion or as a result of collisions. Many structures of this type are known, of different sizes and shapes. Some are very important in biology or in pharmacy. For example, bi-layers of phospholipids mimic quite well some physical properties of biologic membranes, and vesicles are sometimes used as vectors or carriers of drugs.

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Figure 4. Spherical micellar aggregate showing the hydrophilic heads in contacts with the surrounding water or aqueous solvent. The hydrophobic tails fill the internal part of the spherical droplet.

In small quantities, surfactant molecules migrate to interfaces in geometries that minimise the interaction between the tails and water. Even at very low concentration they can modify substantially the surface tension of water. Whenever surfactant molecules are present in a substance, one must take into account their specific interactions with water.

Conclusion

To summarize this short overview, one can say that water is a ‘complex’ liquid with many fascinating, sometimes unique aspects. Except for some academic aspects concerning supercooled water, the structure of the liquid is well known. In particular, it is certain that:

(a) There are no water clusters in pure liquid water, but only density fluctuations.

(b) The longest life of any structure observed in liquid water is of the order of 1 ps (10⁻¹² s).

This is why any interpretation calling for ‘memory’ effects in pure water must be totally excluded.

In contrast, there is great variety of behaviour of solutes depending on many parameters. Even in small quantities, some solutes can modify substantially some properties of pure water. Special attention should be given to surfactants, sugars and polymeric substances. Since homeopathic medicines are prepared in ‘extremely high dilutions’ but following a procedure that does not produce necessarily extremely pure water, experiments should address the problem of the presence of minute amounts of solutes as has recently been done recently, with striking results.²

Otherwise, as stressed at the beginning, the advantages of homeopathic treatments should be taken at a medical level, which, after all, is the case for other drugs recognized for their remarkable although not yet explained effectiveness.

References

1 E. Davenas, F. Beauvais and J. Amara et al., Human basophil degranulation triggered by very dilute antiserum against IgE, Nature 333 (1988), pp. 816–818. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

[2] L. Rey, Can low temperature Thermoluminescence cast light on the nature of ultra-high dilutions?, Homp 96 (2007), pp. 170–174. SummaryPlus | Full Text + Links | PDF (267 K)

3 L. Rey, Thermoluminescence of ultra-high dilutions of lithium chloride and sodium chloride, Physica A 323 (2003), pp. 67–74. SummaryPlus | Full Text + Links | PDF (306 K) | View Record in Scopus | Cited By in Scopus

4 O. Mishima and H.E. Stanley, The relationship between liquid, supercooled and glassy water, Nature 396 (1998), pp. 329–335. View Record in Scopus | Cited By in Scopus

5 J. Teixeira, A. Luzar and S. Longeville, Dynamics of hydrogen bonds: how to probe their role in the unusual properties of liquid water, J. Phys.: Cond. Matter 18 (2006), pp. S2353–S2362. Full Text via CrossRef

6 R.W. Hendricks, P.G. Mardon and L.B. Schaffer, X-ray zero-angle scattering cross section of water, J. Chem. Phys. 61 (1974), pp. 319–322. Full Text via CrossRef

7 L. Bosio, J. Teixeira and H.E. Stanley, Enhanced density fluctuations in supercooled H₂O, D₂O and ethanol–water solutions: evidence from small-angle X-ray scattering, Phys Rev Lett 46 (1981), pp. 597–600. Full Text via CrossRef

8 L. Friedman H, A Course in Statistical Mechanics, Prentice Hall College Div. (1985).

Correspondence: Laboratoire Léon Brillouin (CEA/CNRS), CEA Saclay, 91191 Gif-sur-Yvette Cedex, France.

Homeopathy
Volume 96, Issue 3, July 2007, Pages 158-162
The Memory of Water