Journal Club – “Long term structural effects in water: autothixotropy of water and its hysteresis”

January 1st, 2000 by Ben Goldacre in journal club | 5 Comments »

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

www.badscience.net/?p=490

doi:10.1016/j.homp.2007.03.007 How to Cite or Link Using DOI (Opens New Window)
Copyright © 2007 Elsevier Ltd All rights reserved. Long term structural effects in water: autothixotropy of water and its hysteresis

Bohumil VybíralCorresponding Author Contact Information, a, E-mail The Corresponding Author and Pavel Voráčeka
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 (φu)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 kτ, 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 φu, we expect that the plate will follow the rotation, so that φdu, φd 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 φd is observed, following a very slow, ‘step by step’, change of angle φu. One can specify the moment of force Mw, arising when the plate influences the water: Mw=kτ (φuφd). If angle φu reaches a critical value (φu)crit., the rotation of the plate (ie Click to view the MathML source) 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 kτ=(1.01±0.02)×10−7 Nm/rad. After reduction to the unit length (1 m), we get kτ1=(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 φu and φd were read with an accuracy of not, vert, similar0.5°. 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 (φu)crit.

The critical angle is the angle φu 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: (φu)crit.=(398±3)°.
2. With the water boiled for a short time, but otherwise the same configuration of system (immersion 65%). After cooling (not, vert, similar24 °C): (φu)crit. ≈ 30°, after two days: (φu)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 (φu)crit.=(356±3)°.
4. The plate immersed only 50%: (φu)crit.=(343±8)°.
5. The influence of plate immersion on the critical angle (φu)crit. is small: for plate immersion in the range 100–23%, the difference is Δ(φu)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 (φu)crit.=1800°. As a consequence of the ‘rupture’ which followed, the plate rotated through the angular interval Δφd=1430°. With total immersion such a great critical angle was never reached.
7. After stabilization of the position of the plate (ie, Δφd=1430°), a slow change of angle φd (‘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 φd were performed. For the same set of angles φu : 60°, 120°, and 180°, the measured respective average angles φd were: (19.6±0.7)°, (34.4±0.6)°, (52.3±1.3)°. When (φu)crit.=(239±2)° was reached, the plate quickly rotated (tens of seconds) and reached a new equilibrium position (φd)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 φu 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 φu from the starting equilibrium position φu=φd=0°, the change of angle φd did not follow an ideal straight line φu=φd, but the curve OA. At point A the critical value (φu)crit.1 was reached and then the plate rotated to a new equilibrium position—point B. With decreasing angle φu, angle φd changed according to curve BC, until it reached the second critical value, denoted (φu)crit.2, then the plate rotated to another equilibrium position—point D. When angle φu 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 (φu)crit.3. Another equilibrium position corresponded to point F and the fourth critical position corresponded to point G, where (φu)crit.4congruent with(φu)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 φu, the position of the plate followed the previous section HO and for φu=0° it returned to the original equilibrium position φdcongruent with0°.


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


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Figure 3. Results of two experiments (loops of the changes of angle φd=f (φu)): 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 (φu)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 OA of the graph in Figure 2, before point A is reached, and if we begin to decrease angle φu, the character of the change of angle φd will follow the same curve OA 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 not, vert, similar1%), 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 φd of the plate, which passed through the interval φdset membership, variant(0°, 360°, 0°), was equal to angle of torsion φu of the upper end of the filament, with accuracy of not, vert, similar1.5°, as evaluated from the repeated measurements. Neither the existence of critical angles (φu)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 kτ) 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 kτ, the elasticity parameter of putative clusters of water molecules in the considered situation, represented by torsional rigidity kw. 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:

Click to view the MathML source

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 kτ=(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 not, vert, similar45°, 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 kw=(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 (φu)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. ‘Autothixotropyof Wateran Unknown Physical Phenomenon. Available via left angle bracketarxiv.org/abs/physics/0307046right-pointing angle bracket; 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.

Corresponding Author Contact InformationCorrespondence: 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

Journal Club – “The silica hypothesis for homeopathy: physical chemistry”

January 1st, 2000 by Ben Goldacre in journal club | 1 Comment »

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

www.badscience.net/?p=490

doi:10.1016/j.homp.2007.03.005 How to Cite or Link Using DOI (Opens New Window)
Copyright © 2007 Elsevier Ltd All rights reserved. The silica hypothesis for homeopathy: physical chemistry

David J. Anick1, Corresponding Author Contact Information, E-mail The Corresponding Author and John A. Ives2
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 HzSixOy 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 HzSixOy (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 Qx, 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 Qx 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 (not, vert, similar1 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.

References

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Corresponding Author Contact InformationCorresponding 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

Journal Club – “The possible role of active oxygen in the Memory of Water”

January 1st, 2000 by Ben Goldacre in journal club | 2 Comments »

This is part of the Homeopathy journal club described here:

www.badscience.net/?p=490

doi:10.1016/j.homp.2007.05.003    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2007 Elsevier Ltd All rights reserved. The possible role of active oxygen in the Memory of Water

Vladimir L. VoeikovCorresponding Author Contact Information, a, E-mail The Corresponding Author
aFaculty 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”:

Click to view the MathML source

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→HOradical dot+radical dotH, 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)

Hradical dot+O2→HO2radical dot, (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 (greater-or-equal, slanted1 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:

Rradical dot+RH→RH+Rradical dot;Rradical dot+RH→RH+Rradical dot;Rradical dot+Rtriple primeH→Rtriple primeradical dot+cdots, three dots, centered,

where Rn· is a free radical with an unpaired electron, and RmH 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

Corresponding Author Contact InformationCorrespondence: 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

Journal Club – “The nature of the active ingredient in ultramolecular dilutions”

October 20th, 2014 by Ben Goldacre in journal club | No Comments »

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

www.badscience.net/?p=490

doi:10.1016/j.homp.2007.05.005 How to Cite or Link Using DOI (Opens New Window)
Copyright © 2007 Elsevier Ltd All rights reserved. The nature of the active ingredient in ultramolecular dilutions Otto WeingärtnerCorresponding Author Contact Information, a, E-mail The Corresponding Author
aDepartment 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 zi 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:

Pring operatorQ-Qring operatorP≠0,

where ‘ring operator’ 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 Pring operatorQ of two observables is also an observable. P and Q are called compatible if they commute (ie Pring operatorQ-Qring operatorP=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 (iePring operatorQ-Qring operatorP≠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 {Ji1,…,im·σi1,…,im·σi1,…,im} of spin-like states, where indices i1,…,im vary over permutations, fit the axioms of WQT for an arbitrary big system BN in the SBM. The sets {Ji1,…,im·σi1,…,im·σi1,…,im} are a generalization of couplings (Jik·σi·σk) 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

Click to view the MathML source

where λx 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 BN of the SBM this suggests that the bigger the box BN 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 BN and it is clear that:

1. In every Box BN 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 BN. This means that in BN 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 phii (i=1,2,…), representations of states look like

Click to view the MathML source

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

Click to view the MathML source

Click to view the MathML source

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=H1circle times operatorH2 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 H1circle times operatorH2 is formed. This is a new Hilbert-space whose points have the form

Click to view the MathML source

where Φi,j denote basis elements in H=H1circle times operatorH2 and ci,j their multiples. Entangled states are those (ψ(1)ψ(2)) for which the multiples ci,j cannot be written as

ci,j=aibj,

with ai and bj 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=H1circle times operatorH2 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.


Corresponding Author Contact InformationCorrespondence: 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