This is part of the Homeopathy journal club described here:

www.badscience.net/?p=490

doi:10.1016/j.homp.2007.05.004
Copyright © 2007 Elsevier Ltd All rights reserved. Can low-temperature thermoluminescence cast light on the nature of ultra-high dilutions?

Louis Rey^{, a,
a}Chemin de Verdonnet 2, CH-1010 Lausanne, Switzerland
Received 2 May 2007; revised 8 May 2007; accepted 16 May 2007. Available online 31 July 2007.

Abstract

Low-temperature thermoluminescence has been used in attempt to understand the particular structure of ultra high dilutions. Samples are activated by irradiation after freezing at the temperature of liquid nitrogen (77°K). Experimental results show that, in the course of rewarming, the thermoluminescent glow is susbtantially different between dilutions of different substances. It is suggested that the dispersed gas phase might play a role in this process.

Keywords: irradiation; frozen dilutions; nanobubbles; low-temperature glow

Article Outline

Introduction

Research objective

Method

Results

New prospects

Acknowledgements

References

Introduction

No chemical is more common on earth than water: it covers 75% of the earth’s surface with a total mass of 1.4 billion megatons. A very simple molecule, with one central, negatively charged, oxygen atom and two positively charged hydrogen atoms 0.1 nm apart at an angle of 104°¹ water is, nevertheless, a most atypical compound. In the liquid state, it is an abnormal fluid which should be a gas by comparison with other similar chemicals. Among other unusual properties, it increases in volume when crystallizing into solid ice at 0°C and boils at 100°C: both these temperatures are abnormally high for a substance which is neither a metal nor an ionic compound. Its dielectric constant as well as its increasing fluidity with rising pressure is equally odd.

In fact, liquid water is not a simple association of independent molecules; the molecules are actively interconnected by hydrogen bonds^{[2] and [3]}. Liquid water is, indeed, a structured fluid which behaves as a polymer. In an ever-moving universe, individual water molecules link to each other, most often in tetrahedral geometry, building evanescent clusters which are continuously formed and dissociated again at random in a pico-second timeframe. When an ionic compound is dissolved in H₂O, each ion is immediately surrounded by a spherical shell of water molecules so intensely that, should the concentration of the solute be high enough (over about 10%) all the shells come into contact and there is no more truly liquid water.

It can, thus, be understood that, in the preparation of an homeopathic medicine, any compound dispersed in water gives rise, from the outset, to a specific structure. When successive dilutions are made the violent turbulence created in the liquid by each succussion, helps to both maintain and possibly spread the original structure despite, progressively, the solute content of the dilution dropping by a factor of 100 with each centesimal step. However, Brownian motion is still very active and these ‘remnant structures’ fade away and reconstitute continuously. In other terms, we could say that homeopathic dilutions are ‘statistically structured’ and could remain so beyond the Avogadro number. Succussion appears to be an essential part of the overall process.

Research objective

It is easy to understand why, based upon this succession of dilutions–succussions, many scientists believe that eventually—and definitely beyond the Avogadro number—the resulting ‘solutions’ are no more than the dilution fluid itself. However, numerous physiological and clinical tests have demonstrated for decades, since Hahnemann himself, that this is not the case. Our research objective has been to try to demonstrate that the high dilutions are physically different from the diluent and have, indeed, an ‘individual personality’.

Method

Since any investigation is always difficult in an highly dynamic system we assumed that, should some specific ‘patterns’ exist in the liquid dilution they might be fixed when it is frozen giving rise to specific defects in the crystal lattice of ice, which could be investigated by appropriate means.

To perform this type of studies we selected low-temperature thermoluminescence. This technique, which is well known for archaeological and geological dating,⁴ has been adapted by us to low temperatures⁵ and described in detail in previous publications.^{[6] and [7]} I will here only summarize here its main features.

A 1 cc sample of the dilution under investigation is placed in an aluminum cup and frozen down to liquid nitrogen temperature (−196°C=77°K) following a well defined multi-step process. The frozen 1 mm thick ice disk is then ‘activated’ by radiation (Gamma rays, X-rays or electron beams) which displace electrons from their quantum ground states. The sample is then rewarmed at constant rate (3°C/min) from 77°K to melting point. During that process the electrons, powered by ‘thermal activation’ leave their respective traps and recombine with the empty quantum ‘holes’ releasing their ‘activation energy’ in the form of light as they do so. This light is the thermoluminescent glow that we record.

The analysis of the emitted light shows two main peaks around 120 and 166°K for deuterium oxide and 115 and 162°K for H₂O.⁵ Their relative intensity and shape vary both with the radiation dose and also with the nature of the radiant beam. In particular peak 2 displays a complex structure which can be resolved in a set of individual components by a deconvolution technique.^{[8] and [9]} It is assumed that the ‘defects’ present in the ice crystalline lattice are active luminescent centers, hence that thermoluminescence might be an appropriate tool to study the ‘image’ of the initial liquid samples.

Results

Thermoluminescence is known to be a very sensitive technique and has been used to identify trace compounds. For example see Figure 1, the thermoluminescence emissions of very dilute alumina colloidal sols which show major differences between the 10⁻⁸ g/ml, 10⁻⁹ and 10⁻¹⁰ g/ml solutions.

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Figure 1. Thermoluminescence glow of colloidal sols of alumina irradiated by gamma rays (10 kGy) at liquid nitrogen temperature (77°K).

For homeopathic high dilutions we use deuterium oxide (D₂O, heavy water) as the solute since the signal is 50 times more intense than that of H₂O, due to the more rigid nature of the two ‘arms’ of the molecule. As diluted substances we selected two ionic compounds: sodium chloride (NaCl) and lithium chloride (LiCl). The latter was selected because, like urea and ethanol, it is known to impact on and suppress the hydrogen bonds¹⁰ which are thought to be involved into the high temperature peak (ca 166°K) of the thermoluminescence glow.⁶ Figure 2 shows that the curves recorded for successive dilutions of LiCl (3c, 5c, 7c, 9c) prepared by the classical Hahnemannian method and following the French Homeopathic Pharmacopoeia (150 strokes of 2 cm amplitude in 7.5 s, delivered by mechanical succussion machine) are substantially different.

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Figure 2. Thermoluminescence glow of successive dilutions (3c, 5c, 7c, 9c) of lithium chloride in D₂O irradiated by a 2.2 Mev electron beam (6 kGy) at 77°K.

Subsequently, since it appeared that we had a reliable tool for assessing the dilutions we applied the same method to ultra-high dilutions beyond Avogadro’s number.⁶ Figure 3 gives the results and shows evidence that the ‘signature’ peak of LiCl 15c is substantially lower than that of NaCl 15c and lower than succussed pure D₂O. This demonstrates that: ultra-high dilutions are different from their dilution fluid.

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Figure 3. Thermoluminescence glow of ultra-high dilutions (15c) in D₂O of LiCl, NaCl and of pure D₂O, diluted and succussed to 15c irradiated by gamma rays (19 kGy) at 77°K.

The high temperature components of the glow (ca 166°K) is linked to the hydrogen bond network. These results have been recently confirmed by another research group.¹¹

In recent and still unpublished experiments we found the same type of ‘scaling’ between increasing dilutions of other compounds, among which potassium dichromate looks particularly interesting.¹²

New prospects

As I said above, in the homeopathic preparation scheme, succussion is an important component of the preparation process of homeopathic medicines, releasing considerable energy in the fluid. In view of this I became interested in recent research on the role of ‘nanobubbles’ in water.¹³ Part of the ‘message’ transferred from one dilution step to the next one might be linked to the nanobubbles created into the liquid by the successive strong mechanical agitation which creates turbulence.

To investigate this, we built special equipment to perform dynamization in gas atmosphere or vacuum. We dynamize the dilution at room temperature (20°C) under a moderate vacuum (2337 Pa=24 mbar) which corresponds to the saturated water vapour pressure at 20°C. Time to reach vacuum is approximately 20 seconds. Dynamization is 150 strokes in 7.5 sec followed by stabilization under reduced pressure for 3 minute. The vacuum is broken reverting to atmospheric pressure in 20 seconds. Figure 4 gives preliminary results which show that the gas-phase seems to play a major role in the ‘personalization’ of the dilutions. Bearing in mind that the number of nanobubbles created into the fluid is of the order of billions (which represents a very large ‘contact’ surface with the surrounding liquid) and that, due to their size, they may remain stable and undisturbed in the dilution for months or even much longer, this might open some new perspectives on our understanding of the homeopathic preparation process.

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Figure 4. Thermoluminescence glow of LiCl 15c in D₂O dynamized in a vacuum and in a pure O₂ at 15 bars pressure and irradiated by a 2.2 Mev electron beam (6 kGy) at 77°K. We dynamize the dilution at room temperature (20°C) under moderate vacuum (2337 Pa=24 mbar) which corresponds to the saturated water vapour pressure at 20°C. The time to reach vacuum is approximately 20 seconds, we use our standard dynamization: 150 strokes of approximately 2 cm amplitude in 7.5 sec, followed by stabilization under reduced pressure for 3 minutes. The vacuum is then broken, reverting to atmospheric pressure in approximately 20 seconds.

Acknowledgments

The author thanks Laboratoires BOIRON and the AREVA Nuclear Center of Marcoule for their interest and support.

References

1 J. Teixeira, Can water possibly have a memory? A sceptical view, Homeopathy 96 (2007), pp. 158–162. SummaryPlus | Full Text + Links | PDF (366 K)

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

3 J. Teixeira, A. Luzar and S. Longeville, Dynamic of hydrogen bonds: how to probe their role in unusual properties of liquid water, J Phys Condens Matter 18 (2006), pp. S2353–S52362.

4 Gartia RK. Thermoluminescent materials: past, present and future. In: Sarma HNK, Sumitra P, Basantakumar Sharma H, (eds). Proceedings of Regional Conference on Materials and their Applications (RCMA), February 18–19, 2005, Manipur University, Imphal, India, 2005, p 33–40.

5 L. Rey, Thermoluminescence de la Glace, CR Physi I (2000), pp. 107–110.

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

7 L. Rey, Thermoluminescence of deuterated amorphous and crystalline ices, Rad Phys Chem 72 (2005), pp. 587–594. SummaryPlus | Full Text + Links | PDF (467 K) | View Record in Scopus | Cited By in Scopus

8 B.A. Sharma, Th. Basanta Sing and R.K. Gartia, Critical evaluation of goodness of fit of computerised glow curve deconvolution, Indian J Pure Appl Phys 42 (2004), pp. 492–497.

9 Rey L, Gartia RK, Belon P. Trap Spectroscopic Characterization of D₂O ice and its potentialities in homeopathy. In: Selvasekarapandian S, Murthy KVR, Natarajan V, Malathi J, Brahmanandhan GM, Khanna D, (eds). Macmillan Advanced Research Series. Proceedings of the National Conference on Luminescence and Its Applications (NCLA, 2007) January 18–20, Bharathiar University, India. New Delhi: Macmillan India Ltd., 2007, p 12–17.

10 Ourisson G. Personal communication, 2000.

11 R. van Wijk, S. Basman and E. van Wijk, Thermoluminescence in ultra-high dilution research, J Alternative Complementary Med 12 (2006), pp. 437–443. View Record in Scopus | Cited By in Scopus

12 Rey L, Muchitsch I. Recent unpublished results, 2007.

13 Ph. Vallée, J. Lafait, L. Legrand, P. Mentré, M-O. Monod and Y. Thomas, Effects of pulsed low-frequency electromagnetic fields on water characterized by light scattering techniques: role of bubbles, Langmuir 21 (6) (2005), pp. 2293–2299. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

Corresponding author. Louis Rey, Chemin de Verdonnet 2, CH-1010 Lausanne, Switzerland.

Homeopathy
Volume 96, Issue 3, July 2007, Pages 170-174
The Memory of Water

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

www.badscience.net/?p=490

doi:10.1016/j.homp.2007.03.009
Copyright © 2007 Elsevier Ltd All rights reserved. The defining role of structure (including epitaxy) in the plausibility of homeopathy

Manju Lata Rao^{1, ,} , Rustum Roy^{1, 5}, Iris R. Bell^{2, 3, 4, 5, 6} and Richard Hoover^1
1The Materials Research Institute, The Pennsylvania State University, University Park, PA, USA
²Department of Family and Community Medicine, The University of Arizona, College of Medicine, Tucson, AZ, USA
³Department of Psychiatry, The University of Arizona, College of Medicine, Tucson, AZ, USA
⁴Department of Psychology, The University of Arizona, Tucson, AZ, USA
⁵Department of Medicine (Program in Integrative Medicine), The University of Arizona, College of Medicine, Tucson, AZ, USA
⁶College of Public Health, The University of Arizona, Tucson, AZ, USA
Received 20 March 2007; accepted 27 March 2007. Available online 31 July 2007.

Abstract

The key stumbling block to serious consideration of homeopathy is the presumed “implausibility” of biological activity for homeopathic medicines in which the source material is diluted past Avogadro’s number of molecules. Such an argument relies heavily on the assumptions of elementary chemistry (and biochemistry), in which the material composition of a solution, (dilution factors and ligand–receptor interactions), is the essential consideration.

In contrast, materials science focuses on the three-dimensional complex network structure of the condensed phase of water itself, rather than the original solute molecules. The nanoheterogenous structure of water can be determined by interactive phenomena such as epitaxy (the transmission of structural information from the surface of one material to another without the transfer of any matter), temperature–pressure processes during succussion, and formation of colloidal nanobubbles containing gaseous inclusions of oxygen, nitrogen, carbon dioxide, and possibly the remedy source material.

Preliminary data obtained using Raman and Ultra-Violet–Visible (UV–VIS) spectroscopy illustrate the ability to distinguish two different homeopathic medicines (Nux vomica and Natrum muriaticum) from one another and to differentiate, within a given medicine, the 6c, 12c, and 30c potencies. Materials science concepts and experimental tools offer a new approach to contemporary science, for making significant advances in the basic science studies of homeopathic medicines.

Keywords: homeopathy; succussion; materials science; structure of water; epitaxy; nanobubbles

Article Outline

Introduction

Overview

Materials Science Models for homeopathic medicine

Implications of materials science models for basic science research methods in homeopathy

Preliminary studies of homeopathic medicines using Raman and infrared spectroscopy

Method

Results

Conclusions

Acknowledgements

References

Introduction

Overview

The key stumbling block to serious consideration of homeopathy is the alleged “implausibility” of biological activity for homeopathic medicines in which the source material is diluted past Avogadro’s number of molecules (6×10²³), because the remedy must be identical to the solvent. Negative studies of homeopathy are self-evidently correct from the skeptics’ perspective, because of this error.¹ The implausibility argument leads skeptics to ignore or reject positive evidence from numerous basic science, preclinical, and clinical studies showing effects of homeopathic medicines different from controls, in vitro and in living systems.² On the other hand, proponents predictably reject the negative and focus on positive studies, often uncertain how to address the black box nature of homeopathic medicines. Both skeptics and proponents of homeopathy have generally overlooked a large body of literature in the materials science field that could help resolve this impasse with systematic data.³

Thoroughly, established materials science concepts and research data render the implausibility hypothesis for homeopathy irrelevant. One example suffices. Diamond is the hardest material in nature and graphite among the softest. Yet they can be inter-converted with zero change of composition in microseconds.

The available studies enable significant hypothesis-driven advances in the rigorous study of the nature of homeopathic medicines. The purpose of this paper is to outline the key aspects of materials science considerations in developing experimental models for understanding homeopathic medicines and to summarize preliminary findings from hypothesis-driven studies in our laboratory on clinically known polychrests such as Nux vomica (Nux vom) and Natrum muriaticum (Nat mur).

Materials Science Models for homeopathic medicine

Chemists and medical scientists largely continue to focus reductionistically on the presence or absence of specific molecular species present in water vapor or liquid water without consideration of the ways in which these species are organized in space. From a chemical perspective, the dilution aspects of remedy preparation are the key issue, because of a lack of source molecules for potencies at or beyond 12c or 24c× (10⁻²⁴ dilution). Even when chemists focus on water itself, they emphasize the fleeting stability of hydrogen bonding between given water molecules,⁴ rather than the larger complex structural formations of water or the weaker forces that may favor formation of stable oligomeric and polymeric structures, involving the collective organization of many different water molecules within the condensed liquid phase.

In contrast, materials scientists focus on the organizational network arrangement of the water structures in three-dimensional (3-D) space. In a recent paper, Roy et al.³ presented the detailed technical aspects of the materials science argument concerning ultradilute sols including homeopathic medicines at length. For materials scientists, the succussion aspects of remedy preparation are the key consideration. Temperature and pressure can modify such water structures, leading to nanoheterogeneity of larger structures of water molecule “clusters” within liquid water. Succussion introduces intense turbulence and changes in pressure in any solution,⁵ as well as leading to the formation of nanobubbles in solution.

In brief, the plausibility argument for homeopathy is that liquid water, the primary solvent for source materials in which homeopathic medicines are made, is itself an anomalous substance and has many very different structures. As part of the natural nanoheterogeneity of water structure per se (as contrasted with its composition or the presence of solute molecules), processes such as epitaxy, pressure changes during succussion, formation of colloidal nanobubbles containing gaseous inclusions of oxygen, nitrogen, carbon dioxide, and possibly the remedy source material, and electromagnetic field effects play a role in altering water structure. Previous work by Elia and Niccoli⁶ and Rey,⁷ using different technical methods, respectively, to release heat or light from homeopathic medicines in potency, point to the ability to disrupt what appears to be order or structure in remedy solutions as compared with remedy-free control solvents.

In terms of nanoheterogeneity, water can take on many possible oligomeric and polymeric structures, ie, form complex networks of water molecules in 3-D space, held together by various forces that include not only hydrogen bonds (relatively strong), but also van der Waals forces (much weaker). Even if specific molecules or small molecular complexes leave their places in the network, other water structure complexes can take their places within the network structure itself, thereby maintaining the overall nanostructures within the solution, in part via configurational entropy or electromagnetic forces maintaining organizational stability of the network.⁸

Notably, research in the field of complex systems and network science has shown that, within a highly complex network, loss or disruption of a given member or node, which is a point of interconnection with other members of the network (eg. a water molecule or small complex of water molecules) does not destroy or significantly disrupt the overall network organization.^{[9] and [10]} With complexity in liquid water as a whole comes the capacity for overall stability that is not possible in the simpler organizational structures of water on which chemists usually focus.

Epitaxy is the transfer of information, not material, from the surface of one material, usually solid, to another, usually liquid¹¹. The substrate (eg. remedy source material) acts as a seed crystal for the formation of the structure in the recipient surface material (eg. network organization of water structures). Semi-conductor manufacturing often utilizes epitaxial growth to generate specific types of microtransistors and integrated circuitry. In addition to the original source material that uniquely contributes to remedy preparation, deliberate additives in homeopathic medicines, such as ethanol, and/or possible contaminants from succussion, such as silicates from glass container walls, may also stabilize the water molecule structures with their own epitaxial capabilities. Thus, epitaxy can interact with temperature–pressure factors to create unique patterns of information without the transfer of material.

In terms of “seeding” formation of informational structures within water, initial empirical observations on homeopathic medicines suggest that the passage of time between the original remedy preparation and the testing procedures can alter experimental findings. In calorimetric and thermoluminescence studies on homeopathic medicines, the time factor contributes to differences in the magnitude and even the direction of the divergence between remedy and control solutions.^{[4] and [12]} Overall, the behavior of homeopathic medicine liquids in terms of their structural properties in the basic science literature exhibits a somewhat unpredictable, self-organizing quality.

As additional data emerge, these lines of research may facilitate advances in understanding the nature and mechanisms of variability in clinical responsivity to homeopathic medicines.^{[13] and [14]} Water is an hub molecule (a highly interconnected and influential molecule) in most of the biochemical reactions in the body.¹⁵ In a more speculative but testable vein, seeding informational changes in body water at global and local levels¹⁶ of scale could be one way in which homeopathic medicines interface with patients to induce patterns of system-wide and local healing responses.¹³

Implications of materials science models for basic science research methods in homeopathy

Materials science models for the nature of homeopathic medicines leads to more rational selection of specific methodologies for basic science studies. For example, many earlier studies of homeopathic medicines relied on nuclear magnetic resonance (NMR) techniques.^{[17] and [18]} However, NMR spectroscopy provides information on structure of individual atoms in a pure molecule better than on complex networks of molecules. Technically, NMR also requires addition of substances to prepare a liquid for testing. The necessity of adding factors in the process of making observations can introduce unintended contaminants into the measurement process.

In contrast, the light scattering technologies of Raman spectroscopy and Fourier transform (FT) infra-red (IR) spectroscopy permit examination of remedy samples without fixatives or other potential contaminants. Furthermore, Raman and infra-red spectroscopic techniques allow the co-operative nature of structural differences to be detected. Recent studies¹⁹ of microscopic dynamics of hydrogen bonded liquids indicate the existence of highly directional H-bonds, whose energy value normally range between 8 and 25 kJ mol⁻¹ induces different chemical–physical properties and different local environments. As the mean lifetime of H-bonds is in the picosecond timescale, such structures are considered as transient species in dynamic equilibrium.

Our recent work has established the importance of the structure of water on its properties,³ we examined the structures of many water and alcohol-based homeopathic remedies. The results show that such materials can be easily distinguished from the pure solvent, and from each other, by the use of UV–VIS (ultraviolet–visual) and Raman spectroscopy, but Fourier transformed infra red (FTIR) spectroscopy proved insensitive to these differences. This opens up a whole new field of endeavor for inorganic materials scientists interested in developing a scientific basis for the efficacy of homeopathic remedies. The assumption of this study is that the joint employment of the two methodologies: optical spectroscopic tools and electronic microscopic tools can furnish a closer reference picture for the comprehension of the structural changes in the liquid phase besides providing an independent understanding on the role of the ‘active ingredient’ in a homeopathic medicine.

Also we believe that our very preliminary efforts in using cryo-scanning electron microscopy (cryo-SEM) and cryo-transmission electron microscopy (cryo-TEM) may eventually possibly provide definitive evidence of the presence, and the effects, of nanobubbles on homeopathic medicine studies.

Preliminary studies of homeopathic medicines using Raman and infrared spectroscopy

Method

A Food and Drug Administration-regulated homeopathic pharmacy (Hahnemann Laboratories, San Rafel, CA) prepared samples of two different test solutions in 16 ounce (450g), clear glass bottles [Type I borosilicate glass] previously annealed at temperatures between 600–700 °C for 15 minutes. One of the solutions, Nat mur (mineral: Sodium Chloride) and the other Nux vom (plant remedy, purchased as tincture from Boiron) were diluted by the standard Hahnemannian techniques in 95% ethanol and succussed: a 30c potency is diluted (1/100)³⁰ or 10⁻⁶⁰ from the original material. They were hand-succussed by trained experts [www.hahnemannlabs.com/preparation.html] 30×20=600 times during the manufacturing process. Each bottle was coded with an unique number, the bottles were shipped together by overnight courier in the same box, with temperature sensor.

We have used UV–VIS, IR, FTIR, and Raman spectroscopy for the bulk “liquid” which in most cases is either water or a mixture of water and ethanol (95% ethanol). UV–VIS spectroscopy and Raman spectroscopy proved to be useful tools to investigate the subtle but significant changes in the structural parameters in both water and alcohol based remedies. (For details refer to 20). While other techniques such as freezing point depression; acoustic loss spectroscopy, ellipsometry, viscosity, surface tension, have been explored and will eventually be used in depth to measure entirely different properties, we report here our experience with the major spectroscopic techniques which are widely available.

(a) UV–VIS spectrophotometer: VARIAN, Model CARY 100, run in dual beam mode,

(b) FTIR spectrophotometer: Thermo Nicolet, Model NEXUS 670, run in attenuated total reflection (ATR) mode, and

(c) Raman spectrophotometer: Inphotonics, Model RS2000-3b-785, using an InPhotonics fiber optic immersion probe.

Results

Nearly 200 runs were made to calibrate every step in the experimental configurations and procedures used for the different instruments. In the dual beam UV–VIS, the many experimental options are all tested separately to ensure that any differences within the data obtained on our samples are well above the instrument noise measured in the calibration run data. The data are obtained largely at different times scales by different individuals gave consistent results. We note that at very low signal levels, instrument noise coupled with artificial computer generated sensitivity can produce data that are not reliable. Hence, we operate the instruments in the sensitivity ranges in which we sacrifice some precision for reproducibility. In the Raman spectrometer, careful attention is paid to the positioning of the probe within the sample container, and stray light is eliminated by turning off all the room lights whenever data are being collected. Details of this work are published elsewhere.²¹

One of the objectives in undertaking this work is to examine evidence which would suggest reliability of physical properties, assuming structural changes in solvents, especially in ultradilute and dilute sols, an excellent example of the class of materials being homeopathic remedies. For our study, we chose to study Natrum muriaticum and Nux vomica, obtained from Hahnemann Laboratories. Both Nat mur and Nux vom are prepared in 95% ethanol. Three types of analyses are presented:

(a) Comparison of specific homeopathic remedies with different potencies [Nat mur 6c, 12c, 30c, and Nux vom 6c, 12c, 30c].

(b) Comparison between two different remedies of the same potency [Nat mur vs Nux vom 6c, 12c, and 30c].

(c) Comparison of the two homeopathic remedies with unsuccussed and succussed plain ethanol.

Figure 1 shows a comparison of Nux vom and Nat mur, 6c, 12c and 30c, showing representative UV-spectra demonstrating the differences between the remedies. In Figure 2 (a), and (b) we show the envelope of differences within a series of 10 preparations of each remedy of Nat mur and Nux vom. The spectra show clear differences in the same potency of an individual remedy for both Nat mur and Nux vom.

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Figure 1. Comparison of two different homeopathic medicines: Natrum muriaticum (NM) and Nux vomica (NV) showing representative UV-spectra demonstrating the differences between the remedies.

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Figure 2. Envelope of differences within a series of 10 preparations supplied of each Homeopathic medicine: Nat mur and Nux vom.

A comparison was also made between the unsuccussed ethanol and the Nat mur and Nux vom samples as shown in Figure 3. The Roy et al paper³, on “structure of water” clearly evidence the role of succussion besides epitaxy and other temperature effects, on the structure of liquids. Under the “normal” succussing procedures, it can be argued that very considerable pressures (of the order of 10 kbar) could be generated as a result of the shaking. Dachille and Roy²² showed that mere grinding in a mortar and pestle gives rise to high pressures up to 20 kbar, and the figures for force per unit area are strongly dependent on the size of the water particles and the velocity of the shaking. By analogy with similar liquids, such as ethanol, there will be many different structures of water formed both by the pressures generated in succussing in some combination with the epitaxy on any additives.

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Figure 3. UV–VIS spectra of: (a) succussed and unsuccussed ethanol, (b) comparative UV–VIS spectra of Nux vom (NV) 6c, 12c, 30c with unsuccussed ethanol, (c) comparative UV–VIS spectra of Nat mur (NM) 6c, 12c, 30c with unsuccussed ethanol.

It may be noted from Figure 3 that the absorption spectra for unsuccussed ethanol is significantly different from: (a) the succussed ethanol and (b) succussed homeopathic remedies, Nat mur and Nux vom. The difference may be attributed to the variation in intra and inter-molecular association of ethanol and water and the generation of both transient and stable nanobubbles. The work of Tyrrell and Attard at Australian National University has proved beyond any doubt that nanobubbles do exist and persist.²³ FTIR Spectra (not shown here) from all the samples of Nat mur and Nux vom overlap neatly, clearly signifying that FTIR is not the most sensitive technique for analyzing the subtle structural differences in these types of samples.

Comparison of homeopathic remedies with different potencies using Raman spectroscopy is done on the two sets of homeopathic remedies: Nat mur and Nux vom. From the spectra shown in Figure 4, a clear distinction in the Raman active modes is noted between the two different remedies as well as among the different potencies of the same remedy. A clear distinction is shown in the spectral peaks from the different potencies, peak positions identified as (a), (b), (c), (d) and (e) in the Raman spectra of Nat mur samples show significant structural changes. While the existence of distinct structural changes in Nat mur and Nux vom remedies is clear from the Raman spectra, significant structural changes are also noted in the spectra of Nux vom between the different potencies, 6, 12 and 30c, peak positions are identified as (a), (b), (c), and (d) in Figure 4b. Further, since all the homeopathic medicines were prepared in 95% ethanol, we analyzed the Raman spectra of unsuccussed and succussed ethanol shown in Figure 5. Note that 6c potency of the succussed ethanol show distinct structural variations.

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Figure 4. Comparison of the Raman spectra of the same potencies, 6c, 12c and 30c, for two different homeopathic medicines. The differences in the peaks identified as (a)–(e) is clearly visible in 30c samples of Nat mur and Nux vom, compared to other diluting of the same medicine.

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Figure 5. Raman spectra of plain ethanol and succussed 6c, 12c, 30c. Note that peak positions identified from (a)–(f) are prominent only in 6c sample. Also note that the intensity of peaks in the unsuccussed ethanol is significantly lower than the succussed samples.

Conclusions

Materials science provides a conceptual and empirical foundation for future research on the nature of all the dilute sols including homeopathic medicines in the physical plane. Processes such as epitaxy, temperature-pressure induced changes in water structure, and nanobubble formation offer testable hypotheses for understanding homeopathic medicines. Although hypotheses regarding seemingly unmeasurable “subtle energies”²⁴ and/or macro-entanglement phenomena^{[25] and [26]} may help explain the fuller nature of homeopathic medicines, the available evidence also suggests that homeopathic medicines can exhibit qualitatively and quantitatively different structural properties from those of unsuccussed or succussed solvents. Even in the case of subtle energies, initial findings indicate the possibility of measuring changes in liquid structure properties from the materials science perspective.^{[27] and [28]}

The convergence of data from different experimental models suggests that it is feasible to study the nature of homeopathic medicines using available basic science tools, notably here, Raman spectroscopy and ultraviolet–visual absorption (UV–VIS) spectroscopy. Reproducibility of findings is feasible within the same Raman equipment, but, not across different Raman spectrophotometers from the same manufacturer at different geographic locations, even for materials other than homeopathic medicines. Fourier transform infrared (FT-IR) spectroscopy cannot differentiate different homeopathic medicines or different potencies of the same remedy from one another. Transmission and structural electron microscopy are promising options for testing the nanobubble hypothesis.

Finally, the materials science perspective provides a possible translational bridge from the emerging complex systems/network science models for clinical responses to homeopathic treatment^{[5], [12], [13], [29], [30], [31] and [32]} to another level of organizational scale, ie, the network structure of the homeopathic medicines themselves. Given the holistic quality of clinical diagnosis and remedy selection in homeopathy, the articulation of holistic (complex network) rather than reductionistic models for both the clinical healing process and the nature of homeopathic medicines is heuristically appealing.

Acknowledgments

The authors gratefully acknowledge financial support for their research from grants from The Council for Homeopathic Research and Education, Inc.; the Friends of Health Foundation; and NIH/NCCAM K24 AT000057.

Conflicts of interests

Dr Bell serves as a consultant to Standard Homeopathic Company/Hyland’s Inc., which did not provide any direct financial support for the research discussed in this paper.

References

1 Lancet, The end of homeopathy, Lancet 366 (2005), p. 690.

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

3 R. Roy, W. Tiller, I.R. Bell and M.R. Hoover, The structure of liquid water: novel insights from materials research and potential relevance to homeopathy, Mater Res Innovation 9 (4) (2005), pp. 557–608.

4 R. van Wijk, S. Bosman and E.P. van Wijk, Thermoluminescence in ultra-high dilution research, J Alternative Complementary Med 12 (5) (2006), pp. 437–443. View Record in Scopus | Cited By in Scopus

5 P. Bellavite and A. Signorini, The Emerging Science of Homeopathy. Complexity, Biodynamics, and Nanopharmacology (2nd ed), North Atlantic Books, Berkeley (2002).

6 V. Elia and M. Niccoli, Thermodynamics of extremely diluted aqueous solutions, Ann NY Acad Sci 879 (1999), pp. 241–248. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

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

8 Chaplin M. Water cluster structure. wwwmartinchaplinbtinternetcouk/abstrcthtml accessed 09/06/06.

9 Y. Bar-Yam, Dynamics of Complex Systems, Perseus Books, Reading, MA (1997).

10 Y. Bar-Yam, Introducing Complex Systems, New England Complex Systems Institute, Cambridge, MA (2001).

11 Jaeger, RC. “Film Deposition” Introduction to microelectronic fabrication. Upper saddle River. Prentice Hall 2002 p 141–148. Also West AR. Solid State Chemistry and its Applications, John Wiley & Sons (1998) p39.

12 V. Elia and M. Niccoli, New physico-chemical properties of extremely diluted aqueous solutions, J Thermal Anal Calorimetry 75 (2004), pp. 815–836. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

13 I.R. Bell and M. Koithan, Models for the study of whole systems, Integrative Cancer Therapies 5 (4) (2006), pp. 293–307. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

14 I.R. Bell, C.M. Baldwin and G.E. Schwartz, Translating a nonlinear systems theory model for homeopathy into empirical tests, Alternative Therapies Health Med 8 (3) (2002), pp. 58–66. View Record in Scopus | Cited By in Scopus

15 A.L. Barabasi and E. Bonabeau, Scale-free networks, Scientific Am 288 (5) (2003), pp. 60–69. View Record in Scopus | Cited By in Scopus

16 A. Vasquez, R. Dobrin, D. Sergi, J.P. Eckmann, Z.N. Oltvai and A.L. Barabasi, The topological relationship between the large-scale attributes and local interaction patterns of complex networks, Proc Nat Acad Sci USA 101 (52) (2004), pp. 17940–17945.

17 S. Aabel, S. Fossheim and F. Rise, Nuclear magnetic resonance (NMR) studies of homeopathic solutions, Br Homoeop J 90 (1) (2001), pp. 14–20. Abstract | PDF (130 K) | View Record in Scopus | Cited By in Scopus

18 D.J. Anick, High sensitivity 1H-NMR spectroscopy of homeopathic remedies made in water, BMC Complementary Alternative Med 4 (1) (2004), p. 1.

19 Angel CA. In: Frank F (Ed). Water: A Comprehensive Treatise Vol 7. New York: Plenum Press; 1981, p. 1–81.

20 M.L. Rao, R. Roy and I. Bell, Characterization of the structure of ultra dilute sols with remarkable biological properties, Mater Res Innovation 1 (1) (2007), pp. 3–18.

21 Roy R, Rao ML, Hoover MR, Bell I. UV–VIS spectra of ultradiluted aquasols and alcosols, containing different additions. Presented at Schwartzreport Conference, November, VA Beach, VA, 2006.

22 C.H. Bates, F. Dachille and R. Roy, High Pressure Transitions of Germanium and a New High Pressure Form of Germanium, Science 147 (1964), pp. 860–962.

23 J.W.G. Tyrrel and P. Attard, Images of nanobubbles on hydrophobic surfaces and their interactions, Phys Rev Lett 87 (2001), p. 176104.

24 Gerber R. Vibrational Medicine. Bear and Company; 2001.

25 H. Walach, Generalized entanglement: a new theoretical model for understanding the effects of complementary and alternative medicine, J Alternative Complementary Med 11 (3) (2005), pp. 549–559. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

26 L.R. Milgrom, Patient–practitioner-remedy (PPR) entanglement, Part 8: ‘Laser-like’ action of the homeopathic therapeutic encounter as predicted by a gyroscopic metaphor for the vital force, Forsch Komplementarmed Klassische Naturheilk 12 (4) (2005), pp. 206–213. View Record in Scopus | Cited By in Scopus

27 I.R. Bell, D. Lewis, A.J. Brooks, S. Lewis and G.E. Schwartz, Gas discharge visualization evaluation of ultramolecular doses of homeopathic medicines under blinded, controlled conditions, J Alternative Complementary Med 9 (1) (2003), pp. 25–38. View Record in Scopus | Cited By in Scopus

28 D.A. Lewis, S.E. Lewis, L. Mehl-Madrona, I.R. Bell and G.E. Schwartz, Gas discharge visualization measurements of the effect of intent on water, J Alternative Complementary Med 10 (4) (2004), p. 723.

29 J.L. Torres, Homeopathic effect: a network perspective, Homeopathy 91 (2) (2002), pp. 89–94. Abstract | Abstract + References | PDF (137 K) | View Record in Scopus | Cited By in Scopus

30 M.E. Hyland and G.T. Lewith, Oscillatory effects in a homeopathic clinical trial: an explanation using complexity theory, and implications for clinical practice, Homeopathy 91 (3) (2002), pp. 145–149. Abstract | Abstract + References | PDF (133 K) | View Record in Scopus | Cited By in Scopus

31 L.R. Milgrom, Vitalism, complexity, and the concept of spin, Homeopathy 91 (1) (2002), pp. 26–31. Abstract | Abstract + References | PDF (295 K) | View Record in Scopus | Cited By in Scopus

32 P. Bellavite, Complexity science and homeopathy: a synthetic overview, Homeopathy 92 (4) (2003), pp. 203–212. SummaryPlus | Full Text + Links | PDF (182 K) | View Record in Scopus | Cited By in Scopus

Correspondence. Manju Lata Rao, Materials Science Research Laboratory, The Pennsylvania State University, University Park, PA 16802, USA.

Homeopathy
Volume 96, Issue 3, July 2007, Pages 175-182
The Memory of Water

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

www.badscience.net/?p=490

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

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

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

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

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

Article Outline

‘Autothixotropy’ of water

Qualitative laboratory observations

Proposed explanation

Autothixotropy and molecular translative freedom

Salt ions

Quantitative experiments on autothixotropy and its hysteresis

Static torsion method

Principle

Experimental device

Quantitative experimental results

Measurements of the critical angle (φ_u)_crit.

Reproducibility

Hysteresis

Additional measurements

Experiments with deionized water

Method of torsion oscillation

Principle

Quantitative experimental results

Conclusions

References

‘Autothixotropy’ of water

Qualitative laboratory observations

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

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

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

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

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

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

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

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

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

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

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

Proposed explanation

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

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

Autothixotropy and molecular translative freedom

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

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

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

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

Salt ions

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

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

Quantitative experiments on autothixotropy and its hysteresis

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

1. The static method of torsion.

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

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

Principle

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

Experimental device

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

Quantitative experimental results

Measurements of the critical angle (φ_u)_crit.

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

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

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

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

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

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

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

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

Reproducibility

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

Hysteresis

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

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

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

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

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

Additional measurements

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

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

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

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

Experiments with deionized water

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

Method of torsion oscillation

Principle

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

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

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

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

Quantitative experimental results

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

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

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

Conclusions

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

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

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

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

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

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

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

References

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

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

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

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

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

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

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

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

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

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

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

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

www.badscience.net/?p=490

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

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

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

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

Article Outline

Introduction

Brief overview of silicates

Generation and perpetuation of remedy-specific silicates

Experiments to test the silica hypothesis

Conclusion

References

Introduction

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

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

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

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

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

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

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

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

Brief overview of silicates

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

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

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

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

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

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

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

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

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

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

Generation and perpetuation of remedy-specific silicates

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

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

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

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

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

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

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

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

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

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

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

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

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

Experiments to test the silica hypothesis

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

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

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

Conclusion

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

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

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

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14 S.D. Kinradet and T.W. Swaddle, Silicon-29 NMR studies of aqueous silicate solutions. 1. Chemical shifts and equilibria, Inorg Chem 27 (1988), pp. 4253–4259.

15 X. Xue, J.F. Stebbins, M. Kanzaki, P.F. McMillan and B. Poe, Pressure-induced silicon coordination and tetrahedral structural changes in alkali oxide-silica melts up to 12 GPa: NMR, Raman, and infrared spectroscopy, Amer Mineral 76 (1991), pp. 8–26.

16 R.D. Ennis, R. Pritchard and C. Nakamura et al., Glass vials for small volume parenterals: influence of drug and manufacturing processes on glass delamination, Pharm Dev Technol 6 (3) (2001), pp. 393–405. View Record in Scopus | Cited By in Scopus

17 P.K. Jal, M. Sudarshan and A. Saha et al., Synthesis and characterization of nanosilica prepared by precipitation method, Colloids Surf A: Physicochem Eng Aspects 240 (2004), pp. 173–178. SummaryPlus | Full Text + Links | PDF (131 K) | View Record in Scopus | Cited By in Scopus

18 A. Corma and M.E. Davis, Issues in the synthesis of crystalline molecular sieves: towards the crystallization of low framework-density structures, Chemphyschem 5 (3) (2004), pp. 305–313.

19 S.D. Kinradet and D.L. Pole, Effect of alkali-metal cations on the chemistry of aqueous silicate solutions, Inorg Chem 31 (1992), pp. 4558–4563.

20 Tossell JA, Calculation of ¹⁹F and ²⁹Si NMR shifts and stabilities of F⁻ encapsulating silsesquioxanes, preprint.

21 R.F. Mortlock, A.T. Bell and C.J. Radke, Incorporation of aluminum into silicate anions in aqueous and methanoic solutions of TMA silicates, J Phys Chem 95 (1991), pp. 7847–7851. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

22 S.L. Burkett and M.E. Davis, Mechanism of structure direction in the synthesis of Si-ZSM-5: an investigation by intermolecular ¹H-²⁹Si CP MAS NMR, J Phys Chem B 98 (1994), p. 4647. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

23 Burkett SL, Davis ME, Mechanisms of structure direction in the synthesis of pure-silica zeolites. 1. Synthesis of TPNSJ-ZSM-5, 2. hydrophobic hydration and structural specificity. Chem Mater 1995; 7: 920-928, 1453-1463.

24 C.J.Y. Houssin, C.E.A. Kirschhock and P.C.M.M. Magusin et al., Combined in situ ²⁹Si NMR and small-angle X-ray scattering study of precursors in MFI zeolite formation from silicic acid in TPAOH solutions, Phys Chem Chem Phys 5 (2003), pp. 3518–3524. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

25 N. Poulsen, M. Sumper and N. Kröger, Biosilica formation in diatoms: characterization of native silaffin-2 and its role in silica morphogenesis, Proc Nat Acad Sci 100 (2003), pp. 12075–12080. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

26 N. Poulsen and N. Kröger, Silica morphogenesis by alternative processing of silaffins in the diatom thalassiosira pseudonana, J. Biol Chem 279 (41) (2004), pp. 42993–42999. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

27 D.J. Belton, S.V. Patwardhan and C.C. Perry, Spermine, spermidine and their analogues generate tailored silicas, J Mater Chem 15 (2005), pp. 4629–4638. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

28 D.J. Belton, G. Paine, S.V. Patwardhan and C.C. Perry, Towards an understanding of (bio)silicification: the role of amino acids and lysine oligomers in silicification, J Mater Chem 14 (2004), pp. 2231–2241. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

29 H. Zeng, L.D. Wilson, V.K. Walker and J.A. Ripmeester, Effect of antifreeze proteins on the nucleation, growth, and the memory effect during tetrahydrofuran clathrate hydrate formation, J Am Chem Soc 128 (2006), pp. 2844–2850. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

30 P. Buchanan, A.K. Soper and J. Thompson et al., Search for memory effects in methane hydrate: Structure of water before hydrate formation and after hydrate decomposition, J Chem Phys 123 (2005), p. 164507. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus

31 D.B. Asay and S.H. Kim, Evolution of the adsorbed water layer structure on silicon oxide at room temperature, J Phys Chem B 109 (2005), pp. 16760–16763. View Record in Scopus | Cited By in Scopus

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

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

This is part of the Homeopathy journal club described here:

www.badscience.net/?p=490

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

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

Abstract

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

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

Article Outline

Introduction

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

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

Water participation in chain reactions

Oscillatory nature of reactions with active oxygen participation

Conclusion

References

Introduction

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Water participation in chain reactions

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

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

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

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

(1)

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

H↓+↑OH→H2O.

(2)

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

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

HO↑+HO↓→H2O2,

(3)

H↑+↓H→H2,

(4)

H+O2→HO2,

(5)

HO2↑+HO2↓→H2O2+O2,

(6)

2H2O2→2H2O+O2.

(7)

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

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

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

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

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

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

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

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

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

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

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

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

R+R′H→RH+R′;R′+R″H→R′H+R″;R″+RH→R+,

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

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

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

Oscillatory nature of reactions with active oxygen participation

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

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

Conclusion

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

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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.

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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.

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

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

This is part of the Homeopathy journal club described here:

www.badscience.net/?p=490

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

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

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

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

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

Article Outline

Introduction

Modeling succussion

Two active ingredients

Multiple active ingredients

High potencies

Conclusion

References

Introduction

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

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

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

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

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

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

Modeling succussion

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

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

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

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

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

Qm+1–Qm=(R-1)Qm(C–Qm)/C.

(1)

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

Qm+1–Qm=(R-1)Qm(C–Qm+1)/C

(2)

has the very nice exact solution

(3)

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

(4)

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

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

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

Two active ingredients

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

(5)

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

(6)

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

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

(7)

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

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

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

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

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

(8a)

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

(8b)

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

(9)

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

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

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

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

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

Multiple active ingredients

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

(10)

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

xi,P+1≈xi,P+h(rDOM–ri)/rDOM,

(11)

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

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

(12)

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

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

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

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

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

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

High potencies

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

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

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

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

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

Conclusion

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

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

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

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

References

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

www.badscience.net/?p=490

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

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

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

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

Article Outline

Introduction

Locality, non-locality, and philosophy

Local hypotheses and the memory of water

Non-local hypotheses and macro-entanglement

Quantum theory and homeopathy

Entanglement in the homeopathic process

Conclusion: a therapeutic Uncertainty Principle?

Acknowledgements

References

Introduction

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

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

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

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

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

Locality, non-locality, and philosophy

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

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

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

• No signal can travel faster than light.

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

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

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

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

(3) What is valid here is valid elsewhere.

(4) The universe is material and not spiritual.

(5) Everything that is physical is observable.

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

(7) Experiment validates theory.

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

• All swans are white.

• The creature in front of us is a swan.

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

• The creature is white.

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

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

• The next swan I see will be white.

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

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

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

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

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

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

Local hypotheses and the memory of water

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

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

Table 1.

Some physical constants for dihydrides of the Group 16 elements

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Non-local hypotheses and macro-entanglement

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

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

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

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

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

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

• WQT has no interpretation in terms of probabilities.

• Complementarity and indeterminacy are epistemological in origin not ontological.

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

Quantum theory and homeopathy

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

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

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

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

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

Entanglement in the homeopathic process

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

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

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

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

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

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

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

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

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

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

Conclusion: a therapeutic Uncertainty Principle?

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

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

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

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

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

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

Acknowledgements

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

References

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

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

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

www.badscience.net/?p=490

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

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

Abstract

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

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

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

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

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

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

Article Outline

Introduction

Necessity of a general principle

How non-locality arose

What is entanglement?

Weakening the axioms of quantum mechanics

WQT and homeopathy

Entanglement and information in quantum physics and beyond

Discussion

Acknowledgements

Appendix A. The sequential box model (SBM)

Appendix B. Entanglement

References

Introduction

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

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

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

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

Necessity of a general principle

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

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

2. A mother tincture is prepared from the substance.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

How non-locality arose

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

What is entanglement?

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

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

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

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

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

Weakening the axioms of quantum mechanics

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

PQ–QP≠0,

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

1. Systems are any part of reality.

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

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

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

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

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

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

WQT and homeopathy

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

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

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

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

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

Entanglement and information in quantum physics and beyond

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

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

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

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

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

Discussion

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

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

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

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

Acknowledgement

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

References

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

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

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

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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.

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

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

Appendix A. The sequential box model (SBM)

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

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

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

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

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

Appendix B. Entanglement

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

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

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

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

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

ci,j=aibj,

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

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

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

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

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

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

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

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