Many thanks to everyone who took part in the Homeopathy Journal Club. The standard of commentary was very high and I think a fair amount of this stuff deserves the chance to be published in the journal itself. I know a couple of people have already submitted their work as letters, but Read the rest of this entry »
Peter Fisher and Elsevier have rather kindly given me permission to reproduce the experimental papers from the special issue of Homeopathy on the memory of water, so I’m posting them in full below. As you know I’m a strong believer in free access to academic journals, especially when they’ve been press-released and discussed in popular fora.
This is part of the Homeopathy journal club described here:
Copyright © 2007 Elsevier Ltd All rights reserved. Can water possibly have a memory? A sceptical view
José Teixeira, a,
aLaboratoire Léon Brillouin (CEA/CNRS), CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
Received 1 May 2007. Available online 31 July 2007.
Homeopathic medicines are currently used in medical practice, despite controversy about their effectiveness. The preparation method is based on extremely high dilutions of many substances in water, far beyond any detectable level. For this reason, it has been suggested that water could retain a ‘memory’ of substances that have been dissolved in it before the successive dilutions. The paper stresses the fact that this idea is not compatible with our knowledge of pure water. If an explanation on physical grounds is to be found, research must focus in other aspects of the preparation, such as the presence of other molecules and dissolved gases.
Keywords: water structure; water dynamics; aggregation; metastability
- Pure water and homeopathic drugs
- Properties of liquid water
- Aqueous solutions
Homeopathy and homeopathic medicines are widespread and well accepted by many doctors, pharmacists and patients. It is officially recognised by health authorities and agencies authorities and at a political level in many parts of the world. However, they are also criticized and attacked by others. It is not my purpose to participate actively in a complex debate that includes not only scientific aspects but also sociological and economic components. My contribution will address only the arguments relying on the properties of water and only from the physical view. Consequently, at best, it is a physicist’s view of the role played by water in homeopathic solutions.
To clarify this statement, I think that it is useful to remember that medicine is not only a science but also an art. A good doctor takes into account not only the sickness itself but also the patient, his environment and his psychological aspects. As a consequence, the prescription of a medicine fortunately includes a large part of empiricism. The goal is to restore a ‘normal’ state. One must admit that the complete knowledge of all the parameters intervening in a real situation is totally illusory and that this situation is unlikely to change in the foreseeable future. Anyway, even when the active principles and biological receptors are well known and identified, the reactions of different patients are not the same. To circumvent these inherent difficulties the performance of drugs is established via statistical analysis of large numbers of cases with a randomised double-blind methodology which implicitly recognizes the hidden role of components which escape to the normal scientific analysis of ‘exact sciences’.
Modern pharmacological research is based on a detailed knowledge of physical and chemical interactions between drugs and living cells. At the confluence of Biophysics and Chemistry, a more detailed and precise picture of those interactions is steadily emerging. Still, many traditional medications and frequently-prescribed drugs are currently used without such detailed knowledge of their action. For them, it is either difficult or useless to define the exact ‘paths’ from medicine to biology, then to chemistry and physics.
Pure water and homeopathic drugs
Many traditional drugs, as for example those extracted from plants, are extensively used in medicine. In some cases one or more active principles have been identified but even in such cases the exact action is usually not well understood at the level of chemical reactions or physical interactions taking place within living organisms. This situation is very common but has never been a limitation to prescribing drugs that have shown their effectiveness through many years of practical use. Certainly, in other cases, the interactions are known in great detail leading to the synthesis of well-defined drugs with specific and well controlled applications. But we remain far from a comprehensive and detailed knowledge of the action of drugs on living organisms.
Homeopathic drugs fall, at least partially, into the first category. Their use has been validated by real or supposed successes, the frontier of the two being probably irrelevant from the point of view of the patient. But there is an essential difference between traditional or ‘natural’ medicine and homeopathy. The latter is much more recent and based in a quasi philosophical concept (similia similibus curentur) stated by Hahnemann, perhaps by analogy with the contemporary first studies of immunization. With modern science, it should, in due course, be possible to understand the mechanisms of action of natural substances and of homeopathic drugs. For natural substances the search for the active principles has been successful in some cases; in others, it has been simply assumed that they are present but the level of interest of the drug or available resources has not justified further studies.
With homeopathic drugs the situation is very different. Their method of preparation is based essentially on two steps: sequential dilution with ‘succussion’ or ‘dynamisation’ (vigorous turbulent shaking). A molecular view of the matter and a trivial calculation demonstrates that, often it is extremely improbable that even one molecule of the compound present in the original solution persists in a vial of the final medicine. The role of succussion is not obvious, even less the diverse standards of methods of preparation.
Under the pressure of criticism, the natural evolution of researchers interested in finding acceptable scientific justifications of homeopathy has been to go from purely medical concepts of effective therapy to chemistry and finally to fundamental physics. Ultimately, schematically, the answer: if there is ‘only’ water in homeopathic medicines, then the explanation of the therapeutic action must be in pure water, itself!
This intellectual evolution is a paradox. While for many drugs, the action is known at a biological, sometimes at a chemical, but almost never at a physical level (that of the structure and energies defined with atomic resolution); for homeopathy, the discussion jumped directly into this microscopic sub-molecular physics world. The mixture of the precise methodology characterizing research in physics and procedures deriving from pharmacology in research in homeopathy is striking. For example, several measurements of physical properties of diluted solutions have been done double-blinded. An extreme and provocative hypothesis is that water can retain a ‘memory’ of substances previously dissolved in it.1
A critical analysis of several publications shows that several issues remain open to question. Schematically, one can distinguish the following:
- (1) How different from pure water are highly diluted solutions? In other words, is the simple calculation of the number of molecules of the ‘active principle’ per unit volume of the solution sufficient to account for the composition of homeopathic medicines?
- (2) If succussion is an essential step in the preparation of homeopathic medicines, what is exactly its role? How does it influence the dilution procedure?
- (3) What is the behaviour of complex molecules (eg biopolymers, organic compounds, surfactants, etc.) during the dilution process?
A clear answer to these (and perhaps other) questions is a necessary and essential precondition to any study of ‘pure’ water. Indeed, the conditions of preparation and conservation of homeopathic medicines are far from respecting the simplest procedures required in physical studies of pure water.
Some issues should be controlled more systematically:
- (1) Pure water is a very powerful solvent of many substances. For example, it dissolves and forms specific bonds with silica. In contact with the surface of quartz, water forms stable silanol groups (Si–O–H). With time, silica molecules and silicon atoms are solubilised and hydrated. The number of these ‘impurities’ is huge as compared with the calculated amount of molecules of the starting substance in most homeopathic medicines.
- It may be useful to recall that the interaction of water with solid surfaces is so strong that studies of nucleation must be done with minute amounts of water kept in levitation, without any contact with solid surfaces. The interaction with solid surfaces is so important that if a supercooled liquid freezes, it must be heated up to temperatures higher than the melting point in order to be supercooled again. Less important for water than for other liquids (eg gallium), this effect is due to more favourable nucleation of the solid form at the solid surface.
- Another point deserving investigation is the storage of homeopathic solutions over long periods of time. This procedure is totally incompatible with a chemical purity of water, even at a modest level.
- (2) The main consequence of succussion is the insertion of substantial amounts of air from the environment where the procedure takes place. In a laboratory that is not a cleanroom (such as those used for example in electronics), the procedure brings into the solution not only the gases present in the atmosphere (oxygen, nitrogen, argon,…) but also dust particles, micro-droplets of water, etc. Recent studies2 show that the properties of solutions are drastically modified when succussion is done under different atmospheres or at different pressures, a fact which should encourage further studies in this direction.
- (3) Many substances, which contain pharmacologically active principles, are not soluble in water. Some are previously diluted in alcohol suggesting the presence of surfactant molecules that go spontaneously to interfaces such as the free surface, the interface between the solution and micro-droplets of gases and the interface with the vial. Again, several very promising and striking studies performed by the analysis of the thermoluminescence of frozen solutions open new and exciting perspectives.3
To summarize, it is striking that in publications concerning highly diluted solutions, chemical ‘purity’ is assumed, solely on the basis of a calculation based on the dilution procedure itself. In fact most of the samples studied are far from being ‘pure water’. It would be interesting to perform to a real analysis of the composition of the solutions with physical methods such as mass spectroscopy.
Properties of liquid water
As stated above, many experiments with homeopathic medicines assume the purity of the highly diluted solutions and attribute its therapeutic action to modifications of the structure and dynamics of the pure liquid itself due to the past presence of a solute.1 Such a strong hypothesis would imply not only general or random changes but also a large variety of changes, specific to each solute. The main purpose of this paper is to recall that this hypothesis is totally incompatible with our present knowledge of liquid water.
Water, in all its forms (crystal, liquid, gas and amorphous forms) is certainly the most studied of all substances. All its properties have been measured with extremely high accuracy in very different conditions, including metastable states and ‘extreme’ conditions. This is due to the central role of water in many scientific domains in physics, chemistry, geophysics and, of course, biophysics. Essentially all known experimental techniques and computer simulations have been used to precise details of the behaviour of water at scales extending from hydrodynamics to the nuclear and electronic levels. In other words, water is not an unknown substance!
However, do we know ‘everything’ about water? Certainly not: several puzzling questions are open to discussion. In brief, the main open question about pure water concerns the supercooled (metastable) state (ie liquid water at temperatures below its freezing point) and its relation with different amorphous (glassy) states. The structure of liquid water, at atmospheric pressure, is not known in a large temperature range extending from the vicinity of the temperature of homogeneous nucleation of ice (−42 °C) down to the temperature of the glass transition (−140 °C). This problem is the object of debate and speculation mostly based in extrapolations of simulations of molecular dynamics performed by computer. and 
Another important domain of research is ‘confined water’, ie water occupying extremely small volumes, for example, in porous materials, in thin layers or in small pools formed at hydrophobic sites of bio-molecules. In this case, there is a large variety of situations that depend essentially on the nature of the substrate and on the relative importance of the number of molecules at the surface and in the bulk of the small volume. However, pure water at ambient conditions is well understood. Let us review some of its main properties that may be related to the subject of this paper.
Water is a simple molecule containing three atoms: one of oxygen and two of hydrogen strongly bound by covalent bonds. Because of the hybridisation of the molecular orbitals, the shape of the molecule is a V with the oxygen occupying the vertex of an angle of 104°; the O–H distance is almost exactly 0.1 nm. When two water molecules are sufficiently close, they orient one against the other to establish a chemical bond, called hydrogen bond. In this bond, one hydrogen atom is shared by two neighbouring molecules (Figure 1). The bonding energy is about 10 times larger than the kinetic energy but the bond is ‘fragile’ due the vibratory motions of the hydrogen atom particularly in the direction perpendicular to the line O–HO. It is possible to measure accurately the typical time for which the three atoms are aligned (the lifetime of hydrogen bonds): it is of the order of 0.9 ps (9×10−13 s) at room temperature.
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Figure 1. Schematic representation of a hydrogen bond in water. The large circles represent two oxygen atoms of neighbouring molecules; the small circle is the hydrogen atom attached to the oxygen on the left hand side by a covalent bond. The length of the hydrogen bond is 0.18 nm.The hydrogen atom vibrates in all directions. Vibrations perpendicular to the bond are most likely to break the bond.
Because of its geometry, a water molecule can easily form four hydrogen bonds with four neighbouring molecules. This corresponds to the structural arrangement in common ice (Ih or hexagonal form). The angle of 104° is sufficiently close to the tetrahedral angle (109°) to impose this very open structure where each molecule is surrounded by four others at the apex of a tetrahedron (Figure 2). In liquid water this local geometry exists partly: on average a water molecule has 4.5 neighbours but this number decreases with decreasing temperature because the average number of ‘intact’ bonds increases. Incidentally, it is this decrease of the number of first neighbours that explains why the density of water decreases at low temperatures. At 4 °C, which is the temperature of maximum density, this effect compensates that of thermal expansion.
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Figure 2. Tetrahedral arrangement of five water molecules. The vibrational motion of a hydrogen atom is represented by an arc on the right-hand side of the figure (adapted from G Walrafen).
The average number of ‘intact’ bonds at a given moment is relatively high, although lower than in alcohols, for example. It is of the order of 60% which justifies seeing liquid water as a 3-dimensional network of hydrogen bonds, like a gel. But a gel with a life time of 1 picosecond (ps)! This means that in an ‘instantaneous picture’ of water structure (possible to obtain by computer simulations) one can identify local structures such as rings of 5, 6 or 7 molecules, regions with higher density of bonds than others, etc. All these structural properties can be identified by several techniques and correspond to thermodynamic properties. For example, the increase of isothermal compressibility observed at low temperatures is due to the enhancement of density fluctuations. It is very important to note that such fluctuations are not due to aggregation or formation of clusters. Hydrogen bonds form and break very rapidly generating short lived fluctuations of local density. In other words, even if at a given moment one can identify a region of higher density than the average, it will disappear after a very short time and will appear statistically in another place without any form of coherent motion such as would exist if a cluster was diffusing inside the liquid.
Historically, the first models of liquid water (due to WC Roentgen) represented liquid water as a mixture of an ideal liquid and small ice-like clusters. This model has been ruled out by many experiments. Among them, small angle X-ray scattering eliminates unambiguously any possibility of existence of clusters or aggregates in liquid water, even at very low temperatures. and 
Isolated or confined water molecules can have their mobility totally restricted. In such cases, the lifetime of a hydrogen bond can be infinite. This situation is frequent in proteins where hydrogen bonds with water can play a central role in protein structure. But, in these situations, water molecules don’t constitute a liquid. Consequently, it is worth emphasizing that to postulate the existence of stable structures in pure water is totally wrong. This is one of the limits imposed by the knowledge of the structure of water.
In aqueous solutions, the situation is more diverse. Water can dissolve and mix with many substances in different proportions (salts, acids, various alcohols, sugars, and gases, etc). Both local structure and dynamic properties may be drastically modified. Two well known examples give an idea of the diversity of situations. Trehalose is a sugar that promotes the formation of glassy water even when extremely dilute. It is present in animals and plants which, because of this property, can survive very low temperatures. Other examples are aerogels of silica with a huge content of water, which can contain more than 95% water while remaining macroscopically solid.
Generally speaking, the inclusion of molecules or ions destroys local tetrahedral geometry. Depending on the nature of the compound, the molecules of water arrange in a large variety of local structures. For example, when a salt is dissolved in water, it is dissociated into two ions each of which is surrounded by a layer of hydration where the strong electrostatic interactions between the charge of the ion and the dipoles of water generate a mini-cluster (Figure 3). The life time of this cluster is 10 to 100 times longer than the lifetime of hydrogen bonds but is not infinite, because of the exchange between molecules of water in the hydration shell and those of the bulk.
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Figure 3. Schematic representation of the arrangement around an anion (left) and a cation (right). In the first case the dipolar moment of the water molecules is directed towards the ion; in the opposite direction in the case of the anion. The screening of the electrical field of the ions is very efficient and the structure of water beyond the first hydration layer is almost not modified.
However, it is erroneous to believe that the electrical field generated by the ions extends over large distances. Actually, it is screened by the hydration layer. There is a large literature about the structure in hydration shells. The number of water molecules, distances and angles are known with great accuracy from neutron scattering experiments based on isotopic substitution.8
A very different situation concerns the solubility of hydrophobic atoms and molecules, such as methane or noble gases. In this case, water has tendency to form clathrate-like structures around the solute. A clathrate is a polyhedral structure; frequently a dodecahedron with pentagonal faces. This is a very stable structure, because the internal angle of the pentagon (104°) is equal to the internal angle, HOH, of the molecule. It forms a cage and the prisoner is the hydrophobic solute. The short lifetime of hydrogen bonds does not allow the formation of stable or long-lived clusters. Experiments simply detect, at best, a tendency to the formation of short lived planar pentagons.
Finally, it is interesting to consider situations in which stable aggregates are formed. The most interesting, including many industrial applications, are surfactants, which are molecules with a hydrophilic head (sometimes polar) and one or two hydrophobic tails. When dissolved in water in sufficiently large amount (above a critical micellar concentration, c.m.c.) they form structured clusters called micelles (Figure 4). The heads are at the external surface and the hydrophobic tails minimise the interaction energy with water inside the sphere. These structures are very stable. They persist essentially for ever, even if there are many exchanges of surfactant molecules between micelles, either by diffusion or as a result of collisions. Many structures of this type are known, of different sizes and shapes. Some are very important in biology or in pharmacy. For example, bi-layers of phospholipids mimic quite well some physical properties of biologic membranes, and vesicles are sometimes used as vectors or carriers of drugs.
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Figure 4. Spherical micellar aggregate showing the hydrophilic heads in contacts with the surrounding water or aqueous solvent. The hydrophobic tails fill the internal part of the spherical droplet.
In small quantities, surfactant molecules migrate to interfaces in geometries that minimise the interaction between the tails and water. Even at very low concentration they can modify substantially the surface tension of water. Whenever surfactant molecules are present in a substance, one must take into account their specific interactions with water.
To summarize this short overview, one can say that water is a ‘complex’ liquid with many fascinating, sometimes unique aspects. Except for some academic aspects concerning supercooled water, the structure of the liquid is well known. In particular, it is certain that:
- (a) There are no water clusters in pure liquid water, but only density fluctuations.
- (b) The longest life of any structure observed in liquid water is of the order of 1 ps (10−12 s).
This is why any interpretation calling for ‘memory’ effects in pure water must be totally excluded.
In contrast, there is great variety of behaviour of solutes depending on many parameters. Even in small quantities, some solutes can modify substantially some properties of pure water. Special attention should be given to surfactants, sugars and polymeric substances. Since homeopathic medicines are prepared in ‘extremely high dilutions’ but following a procedure that does not produce necessarily extremely pure water, experiments should address the problem of the presence of minute amounts of solutes as has recently been done recently, with striking results.2
Otherwise, as stressed at the beginning, the advantages of homeopathic treatments should be taken at a medical level, which, after all, is the case for other drugs recognized for their remarkable although not yet explained effectiveness.
1 E. Davenas, F. Beauvais and J. Amara et al., Human basophil degranulation triggered by very dilute antiserum against IgE, Nature 333 (1988), pp. 816–818. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus
3 L. Rey, Thermoluminescence of ultra-high dilutions of lithium chloride and sodium chloride, Physica A 323 (2003), pp. 67–74. SummaryPlus | Full Text + Links | PDF (306 K) | View Record in Scopus | Cited By in Scopus
5 J. Teixeira, A. Luzar and S. Longeville, Dynamics of hydrogen bonds: how to probe their role in the unusual properties of liquid water, J. Phys.: Cond. Matter 18 (2006), pp. S2353–S2362. Full Text via CrossRef
7 L. Bosio, J. Teixeira and H.E. Stanley, Enhanced density fluctuations in supercooled H2O, D2O and ethanol–water solutions: evidence from small-angle X-ray scattering, Phys Rev Lett 46 (1981), pp. 597–600. Full Text via CrossRef
8 L. Friedman H, A Course in Statistical Mechanics, Prentice Hall College Div. (1985).
Journal Club – “The ‘Memory of Water’: an almost deciphered enigma. Dissipative structures in extremely dilute aqueous solutions”
This is part of the Homeopathy journal club described here:
Copyright © 2007 Elsevier Ltd All rights reserved. The ‘Memory of Water’: an almost deciphered enigma. Dissipative structures in extremely dilute aqueous solutions
V. Elia1, , , E. Napoli1 and R. Germano2
1Dipto. di Chimica, Università ‘Federico II’ di Napoli, Complesso Universitario di Monte S.Angelo, via Cintia, 80126 Napoli, Italy;
2PROMETE Srl – INFM Spin off Company, Via Buongiovanni 49, San Giorgio a Cremano, 80046 Napoli, Italy
Received 2 April 2007; revised 22 May 2007; accepted 29 May 2007. Available online 31 July 2007.
In the last decade, we have investigated from the physicochemical point of view, whether water prepared by the procedures of homeopathic medicine (leading inexorably to systems without any molecule different from the solvent) results in water different from the initial water?
The answer, unexpectedly, but strongly supported by many experimental results is positive. We used well-established physicochemical techniques: flux calorimetry, conductometry, pHmetry and galvanic cell electrodes potential. Unexpectedly the physicochemical parameters evolve in time.
The water solvent exhibits large changes in measurable physicochemical properties as a function of its history, the solute previously dissolved, and time. In particular we found evidence of two new phenomena, both totally unpredicted, in homeopathic dilutions: the presence of a maximum in the measured physicochemical parameters vs sample age, and their dependence on the volume in which the dilution is stored. These new experimental results strongly suggest the presence of an extended and ‘ordered’ dynamics involving liquid water molecules.
Keywords: homeopathy; calorimetry; conductivity; pH; dissipative structures
The ‘Memory of Water’ is a journalistic expression, first used in the French newspaper Le Monde, after the publication in 1988 of Jacques Benveniste’s famous paper in the international scientific journal Nature.1 In this paper he claimed, with biological experimental data, that ‘homeopathic dilutions’ of substances (ie so much diluted as to not contain any molecules of the substance initially diluted in it) are able to induce biological effects typical of the substance initially dissolved in it. The ‘memory of water’ is a synthesis of a still unexplained phenomenon. Recent scientific publications suggest some possible ways to experimentally validate the reality of a whole new class of physicochemical new phenomena concerning liquid water.2
It seems that it really is possible to obtain physicochemical information depending on the recent or remote ‘history’ of a water sample (in Prigogine’s terminology: breaking of the temporal symmetry), almost as in the better known case of magnetic materials (Prigogine would say: breaking of the spatial symmetry).3 The so-called memory of water, is connected to the capacity of this kind of solvent, a multi-variable complex system, to be influenced by very tiny perturbations, such as mechanical or electromagnetic actions, in such a way to move away from the initial equilibrium conditions, and this is increasingly established. The ‘memory of water’, in this sense, is comprehensible in the framework of the theory of Irreversible Processes Thermodynamics due to the Nobel Laureate for Chemistry (1977), Ilya Prigogine.3
In the last 10 years,, , , , , , , ,  and  our research group has investigated this problem from the point of view of the physicochemical properties of water when prepared following the procedures of homeopathic medicine preparation: iterative dilutions (of specific solutes of medical interest) followed by agitation (succussion). This method leads inexorably to systems without any molecule different from the solvent, in our case pure water.
Can the ‘new water’ thus obtained really be ‘different’ from the initial one? Answering this question was our challenge. The answer, unexpected but strongly supported by the experimental results, is affirmative. In the meantime, other research groups came to similar conclusions using different experimental models and other methodologies., , , , ,  and  We also want to note here Giorgio Piccardi, the founder of the Italian physical-chemistry, and his pioneering work concerning fluctuating chemical reactions., ,  and  A critical mass of experimental data2 necessary to evidence a new class of physicochemical phenomena of the water has now been reached.
The experimental methodologies used for our investigations were chosen as the most efficient among the many tested. We list them, without entering into the technical details, but emphasising that they are well-established physicochemical methodologies: flux calorimetry, conductometry, pHmetry and galvanic cell electrode potential. The greatest difficulty of the preliminary work, which lasted for many years, was the selection of the most enlightening experimental methodologies and the establishment of optimal experimental conditions. It was also difficult to evaluate the contribution of the impurities released by the glassware, to the measured experimental values. In fact, the problem of impurities has been the principal objection probably due to the strong prejudice against the possibility that the procedures followed might really change the physicochemical nature of water.
Figure 1, Figure 2 and Figure 3 show that the presence of impurities released by the glassware makes a significant contribution to the physicochemical state of the dilutions, but it is not relevant in comparison with the unexpected contribution (much higher than the range of the experimental errors) of the auto-organisation process of the water molecules-the water is far from the thermodynamic equilibrium (see below) –and this auto-organization is triggered by external perturbations (such as iterative dilution and succussion).
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Figure 1. Heat of mixing, Qmix, vs concentration (determined by analytic methods) of impurities, Mtot, released by the glass vessels. Black symbols: heat of mixing of homeopathic solutions with sodium hydroxide, NaOH, 0.01 M (mol kg−1); red line: heat of mixing of aqueous solutions containing the same amount of impurities determined in the homeopathic solutions. The absolute values of the heat of mixing with sodium hydroxide using homeopathic solutions are always higher than the corresponding heat of mixing determined only by the ‘chemical’ contribution originating from the glassware.
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Figure 2. Specific conductivity, χ, vs concentration (determined by analytic methods) of impurities, MNa+, released by the glass vessels. Black symbols: specific conductivity of the homeopathic dilutions; red line: specific conductivity of aqueous solution containing only the same amount of impurities determined in the homeopathic solutions.
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Figure 3. pH values vs concentration of impurities MT (determined by analytic methods), released by the glassware. Circle symbols: pH of homeopathic dilutions; triangle symbols: pH of aqueous solution containing the same amount of impurities determined by analytic methods in the homeopathic solutions.
Figure 1, Figure 2 and Figure 3 show: (i) how the contributions of impurity were taken into account; (ii) the major contribution of ‘something’ different from any possible substance of chemical origin. This is a preliminary result but it cleared misunderstandings from the experimental methodologies and allowed us to proceed to collect further information and insights on the nature of the ‘homeopathic dilutions’., , , , , , , ,  and 
It is important to emphasise that, from the studies so far conducted, we cannot derive reproducible information concerning the influence of the different degrees of homeopathic dilution or the nature of the active principle (solute) on the measured physicochemical parameters. For this reason the experimental data reported in the figures are not given in terms of homeopathic dilutions or name of homeopathic medicine.
A stimulating, and somewhat serendipitous, result very important in understanding the complex system under study, was that the physicochemical properties of the homeopathic solutions depend on time. The fact that the numerous experiences were performed over many years, naturally introduced the time parameter. The analysis of the experimental results vs the ‘arrow of time’ was of unexpected relevance,, ,  and  and led to the idea that the system under observation (homeopathic solution) is a closed system (able to exchange only energy with the external environment), far from thermodynamic equilibrium, which allows structures with a local order higher than the water around them to emerge from chaos (‘dissipative structures’).
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Figure 4. Heat of mixing, Qmix, vs the samples age, t, for six homeopathic solutions.
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Figure 5. Excess specific conductivity, χE (μS cm−1) (defined as the experimental difference between the experimental χ value and the contribution to this parameter by the presence of impurities (χchem) vs the samples age, t, for six homeopathic solutions. Each studied sample has its own peculiar χE vs time evolution but with overall similar behaviour: an increment of χE in time.
What is the interpretation of this newly-observed characteristic of the homeopathic solutions? Are we simply observing a system seeking an energetic minimum and a new equilibrium in a slow kinetic process or this is something totally different? From the data in Figure 4 and Figure 5 we deduce that the temporal variations of the reported parameters are very slow, because it takes many months to evidence them unambiguously. However, this temporal behaviour does not match the idea of a simple slow kinetic. In fact, following the reductio ad absurdum, if there exists an energetic minimum towards which the system could move, it would be impossible that in the time that water has existed, it has not reached this hypothetical minimum. Moreover for both parameters (specific conductivity and heat of mixing with alkaline solutions) an increase with time is observed. The correlation between the specific conductivity and the heat of mixing with alkaline solutions, shown in Figure 6 is linear; in other words, these two parameters have the same underlying cause. This result provoked us to investigate the nature of the mechanism able to increase simultaneously the electrical conductivity and the heat of mixing with alkaline solutions, after repeated dilutions and succussions. The descriptive model proposed below, although simple, is in agreement with the experimentally observed ageing effect.
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Figure 6. Specific conductivity, χ, vs excess heat of mixing, QmixE (the difference between the experimental Qmix value and the contribution to this parameter due to the presence of impurities), for a given volume of homeopathic solution.
An explanation of the electrical conductivity increasing after the preparation procedure and ageing may be based on the so-called ‘hopping mechanism’, proposed by C.J.T. Grotthuss (1806)25 to explain the much higher mobility (about 5 times) of H+ and OH− ions (always present in liquid water) in comparison with other ions of comparable ionic radius. If H2O molecular clusters are present in the solution, bonded by hydrogen bonds, the hydrogen ions H+ colliding them experience the ‘hopping’ phenomenon (Figure 7): the water molecules catch an H+ ion at one end of the cluster (for the sake of simplicity considered linear) and release instantaneously another H+ ion at the other end of the cluster. The drift velocity under an electrical potential gradient (a measure of the conductivity) is much increased in comparison with that of ions which do not encounter H2O molecular clusters. The greater the number of the clusters and/or their length, the higher the conductivity value. The correlation between the electrical conductivity and the heat of mixing with alkaline solutions is a consequence of H2O clusters breaking, due to the pH variation (see Figure 8).
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Figure 7. Schematic representation of the Grotthuss hypothesis of the proton (H+) hopping mechanism to explain the much higher mobility (defined as the ionic drift velocity under a unitary gradient of electrical potential V cm−1) of H+ and OH− ions in water (H2O=H++OH−) in comparison with other ions of comparable ionic radius.
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Figure 8. Schematic representation of the phenomenon of molecular clusters breaking, due to pH variation during the experimental procedure of determining the heat of mixing with hydroxide solutions (NaOH) 0.01 M (mol kg−1 ) in a calorimetric cell. The experimental procedure consists of mixing a homeopathic dilution (that we suppose richer in H2O molecular clusters than the ‘standard’ water solvent) with an alkaline solution. The pH variation seems to reflect breaking of hydrogen-bonded H2O clusters, determining a transition order→disorder. This is experimentally evidenced by the increased heat of mixing compared to ‘normal’ water containing few molecular clusters.
The greater the number of the clusters and the larger their dimensions, the more is the measured thermal effect (Figure 8). These two experimental phenomena witness the same thing, both are sensitive to the number and/or dimensions of the clusters.
Let us return to the question: Are we measuring the presence of stable clusters seeking an energetic minimum? Or of unstable clusters consisting of dissipative auto-organised structures that are far from equilibrium and which remain or move away from equilibrium as a function of their ability to exchange energy with the external environment? We have already emphasised that the hypothesis of systems slowly evolving towards new equilibrium states is not compatible with our experimental findings. In particular, the hypothesis of systems evolving towards a minimum, even very slowly, contrasts with two new and very unexpected experimental phenomena characterising homeopathic dilutions:
- (a) the presence of a maximum in the physicochemical parameters with sample age (Figure 9);
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Figure 9. Specific excess conductivity, χE, vs the samples ageing, t. Each curve describes the temporal evolution of Arnica Montana (AM) samples in homeopathic dilutions prepared from the same mother tincture. There is no specific correlation between the χE behaviour and the degree of dilution (CH) of the samples.
- (b) the dependence of the physicochemical parameters (apart from age) also on the volume in which the homeopathic dilution is stored (Figure 10).
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Figure 10. Excess specific conductivity, χE, vs ageing volume, V. Each point represents the value of χE for each single dilution, experimentally determined at the same age. There is a very strong variation of the parameter, about one order of magnitude, for the systems aged in very small volumes. This volume dependence cannot be explained in the frame of the classical physico-chemistry.
Phenomenon (b) is absolutely anomalous and inexplicable in the current paradigm,13 it appears to be in sharp contradiction with the classical concept that an intensive physical quantity cannot depend on the volume.
The temporal evolution of the excess specific conductivity of four sample systems is shown in Figure 11. The samples were obtained as follows: a highly diluted aqueous system was divided into three smaller volumes at a certain ‘age’. As the figure shows, the excess specific conductivity (χE) behaviour across time of small volume samples is very different from that of larger volume samples. The larger volume sample does not display relevant modifications across time, while each new system of smaller volume evolves in a different way, with an overall common behaviour characterised by the presence of a maximum. This means that the evolution over time depends on the initial state (in this case: large or small volume), in a sense the systems have a ‘memory’ of the initial conditions.
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Figure 11. Excess specific conductivity, χE, vs sample age, t. In this experiment, a homeopathic dilution of Arnica Montana was left to age for about 250 days in a volume of about 200 ml. At this time point 18 ml were removed and divided into three different vessels of equal shape, containing 10, 5 and 3 ml. The four obtained samples, 182, 10, 5 and 3 ml, were studied vs time. Their temporal evolution was dramatically influenced by the perturbation induced by the repartition into smaller volumes. In particular the higher volume of 182 ml did not experience particular temporal variations, while in the case of the smaller volumes, a large temporal evolution was observed, depending strongly on the starting point.
Another example of such ‘memory’ of the system is apparent in the experimental data displayed in Figure 12, which shows the temporal evolution of the excess specific conductivity for samples made from the same mother tincture diluted in double distilled water without succussion, in different dilution ratios.12 Again, the system’s evolution in time is strongly conditioned by the initial conditions, with temporal variations characterised by very different maximum and slope values: past history influences the evolution of the ‘pure water’ system.
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Figure 12. Excess specific conductivity, χE, vs age, t, of samples obtained by a simple dilution of the ‘mother tincture’ with double distilled water without succussion, in different dilution ratios (r). The volumes of the studied solutions were the same. The temporal evolution of the various systems, perturbed only by the simple dilution without succussion, is strongly dependent by the new starting state. In particular, the system with dilution 1:1, r=0.5 (final volume is twice the initial one) exhibits an initial χE value markedly lower than the solution from which it was obtained, then, in about 45 days, exhibiting χE values much higher with respect to the ‘mother tincture’, reaching a sharp maximum. In this case, the applied perturbation, determines a strongly different starting point, as well as different temporal evolution.
The apparent contradiction between the concept of intensive quantity, such as specific conductivity and heat of mixing, and the experimental evidence of dependence on volume may be solved by considering that, within the solutions there are molecular clusters consisting of water molecules connected by hydrogen-bonds, in far from equilibrium conditions. They can remain in, or move away, from their unstable equilibrium state, dissipating energy derived from the external environment: they are ‘dissipative structures’ as described by Prigogine.3
The spontaneous formation of molecular clusters in water is foreseen by the Coherent Quantum Electrodynamics (Coherent QED) without introducing the existence of hydrogen-bonds. This theoretical formulation, due to G. Preparata, E. Del Giudice, et al predicts the physicochemical properties of the water,, , ,  and  much better than other theories. The introduction of the ‘arrow of time’ into this theoretical framework should yield very interesting results.
We propose a simplified empirical model that in principle seems able to explain the unexpected dependence of the physicochemical parameters on the volumes used.
A first hypothesis to explain the experimental results is to suppose that the solutions, after strong agitation (succussion), enter a far from equilibrium state, remaining there or getting even farther by dissipating energy in the form and amount necessary to stay in the far from equilibrium state. Then, assuming that radiant energy is exchanged, we can further suppose that, for a given flux of dissipated energy (W cm−2), the same number of dissipative structures would be formed, even if contained in different volumes. In this frame, on average, at any given age, small volumes of water will contain a higher ‘concentration’ of dissipative structures in comparison with larger volumes (Figure 13). The physicochemical parameters electrical conductivity and heat of mixing are in fact functions of the number, size and shape of the dissipative structures.
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Figure 13. Schematic representation of a possible temporal evolution of a homeopathic solution, showing a variation of intensive quantities such as χE (μS cm−1) and QEmix (J kg−1) vs the storage volume. At the time zero, the two vessels, of equal shape and volume, contain two identical homeopathic dilutions (same age, same active principle, same CH dilution) with no experimentally measurable effects determined by dissipative structures, because of their small number (Figure 13a). Assuming the same formation efficiency (and/or increase in size) for the dissipative structures in the two systems (small volume and large volume), with the same conditions of energetic flux, the number and/or size of the dissipative structures is almost the same in the two containers, at any given time (Figure 13b and c). So, when dissipative structures are numerically increasing, their concentration is much higher in the small volume than in the large one. Consequently, intensive quantities such as those measured, χE (μS cm−1) and QEmix (J kg−1), sensitive to the structure concentration, will show a temporal behaviour dependent on the volume.
We conclude the following:
- • the parameters whose values results ‘in excess’ (in general: variable with the history of the solvent in time) are correlated with the dynamics of supermolecular (mesoscopic) structures in the water solvent;
- • the temporal evolution of the parameters is not connected to the tendency to seek an energetic minimum;
- • an empirical interpretation, consistent with all current experimental data, is based on the presence of dissipative structures.
Succussion may be the trigger for the spontaneous formation of dissipative structures, that is the emergence of new dynamics. The temporal evolution may be connected to the variation of the number, dimension or the shape of the dissipative structures. It is well known, in Thermodynamics of Irreversible Processes, that the temporal evolution of the systems depends on the initial conditions and on the way the systems evolve.Much new experimental data converge towards the validation of the statement that water, at least in the context of the procedure of the homeopathic medicine production, really has a ‘memory’. That is to say: the water solvent shows experimentally measurable physicochemical properties that vary as a function of the ‘lived path’, of the solute previously dissolved, and of elapsed time.
Without doubt liquid water has an extended and ‘ordered’ dynamics involving the whole body of the liquid. It is much more complex than the normal idea of a banal and chaotic cluster of ‘molecular balls’.
1 E. Davenas, F. Beauvais and J. Amara et al., Human basophil degranulation triggered by very dilute antiserum against IgE, Nature 333 (1988), pp. 816–818. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus
2 R. Germano, AQUA. L’acqua elettromagnetica e le sue mirabolanti avventure, Bibliopolis, Napoli (2007).
3 I. Prigogine, From Being to Becoming. Time and Complexity in the Physical Sciences, Freeman, San Francisco (1980).
5 V. Elia and M. Niccoli, New physico-chemical properties of water induced by mechanical treatments. A Calorimetric study at 25 °C, J Therm Anal Calorimetry 61 (2000), pp. 527–537. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus
6 V. Elia and M. Niccoli, New Physico-chemical properties of extremely diluted aqueous solutions, J Therm Anal Calorimetry 75 (2004), pp. 815–836. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus
7 V. Elia, S. Baiano and I. Duro et al., New and permanent physico-chemical properties of the extremely diluted aqueous solutions of the homeopathic medicine. A conductivity measurements study at 25 °C in function of the age of the potencies, Homeopathy 93 (2004), pp. 144–150. SummaryPlus | Full Text + Links | PDF (154 K) | View Record in Scopus | Cited By in Scopus
8 V. Elia, E. Napoli and M. Niccoli et al., New physico-chemical properties of extremely diluted aqueous solutions. A calorimetric and conductivity study at 25 °C, J Therm Anal Calorimetry 78 (2004), pp. 331–342. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus
9 V. Elia, M. Marchese and M. Montanino et al., Hydrohysteretic phenomena of ‘extremely diluted solutions’ induced by mechanical treatments. A calorimetric and conductometric study at 25 °C, J Solution Chem 34 (8) (2005), pp. 947–960. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus
10 V. Elia, L. Elia and P. Cacace et al., Extremely diluted solutions as multi-variable systems. A study of calorimetric and conductometric behaviour as function of the parameter time, J Therm Anal Calorimetry 84 (2) (2006), pp. 317–323. View Record in Scopus | Cited By in Scopus
11 V. Elia, L. Elia and M. Marchese et al., Interaction of ‘extremely diluted solutions’ with aqueous solutions of hydrochloric acid and sodium hydroxide. A calorimetric study at 298 K, J Mol Liq 130 (2007), pp. 15–20. SummaryPlus | Full Text + Links | PDF (189 K) | View Record in Scopus | Cited By in Scopus
12 V. Elia, L. Elia and M. Montanino et al., Conductometric studies of the serially diluted and agitated solutions. On an anomalous effect that depends on the dilution process, J Mol Liq 135 (2007), pp. 158–165. SummaryPlus | Full Text + Links | PDF (235 K)
13 V. Elia, L. Elia and E. Napoli et al., Conductometric and calorimetric studies of serially diluted and agitated solutions: the dependence of intensive parameters on volume, Int J Ecodyn 1 (4) (2006), pp. 1–12.
14 P. Belon, J. Cumps and P.F. Mannaioni et al., Inhibition of human basophil degranulation by successive histamine dilutions: results of a European multi-centre trial, Inflammation Research 48 (Suppl 1) (1999), pp. S17–S18. View Record in Scopus | Cited By in Scopus
15 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
16 L. Betti, M. Brizzi and D. Nani et al., A pilot statistical study with homoeopathic potencies of arsenicum album in wheat germination as a simple model, Br Hom J 83 (1994), pp. 195–201. Abstract | PDF (432 K)
17 L. Betti, M. Brizzi and D. Nani et al., Effect of high dilutions of arsenicum album on wheat seedlings from seed poisoned with the same substance, Br Hom J 86 (1997), pp. 86–89. Abstract | PDF (276 K)
18 M. Brizzi, D. Nani and M. Peruzzi et al., The problem of homoeopathy effectiveness: a comparative analysis of different statistical interpretations of a large data collection from a simple wheat germination model, Br Hom J 89 (2000), pp. 1–5.
19 P. Torrigiani, A.L. Rabiti and C. Bortolotti et al., Polyamine synthesis and accumulation in the hypersensitive response to TMV in Nicotiana tabacum, New Phytol 135 (1997), pp. 467–473. View Record in Scopus | Cited By in Scopus
20 A.L. Rabiti, L. Betti and C. Bortolotti et al., Short term polyamine response in TMV-inoculated hypersensitive and susceptible tobacco plants, New Phytol 139 (1998), pp. 549–553. View Record in Scopus | Cited By in Scopus
22 G. Piccardi, Chemical test made in Antarctic, Geofis Meteorol XII (1963), p. 55.
23 G. Piccardi, 22 year solar cycle and chemical test, Geofis Meteorol XX (1961), p. 104.
24 F. De Meyer and C. Capel-Boute, Statistical analysis of Piccardi chemical tests, Int J Biometeorol 31 (1987), pp. 301–322.
25 C.J.T. Grotthuss, Sur la décomposition de l’eau et des corps qu’elle tient en dissolution à l’aide de l’électricité galvanique, Ann Chim 58 (1806), pp. 54–73.
26 E. Del Giudice, R. Mele and G. Preparata, Dicke Hamiltonian and superradiant phase transitions, Mod Phys Lett B 7 (28) (1993), pp. 1851–1855.
27 G. Preparata, QED Coherence in Matter, World Scientific, Singapore (1995).
29 E. Del Giudice and G. Preparata, A new QED picture of water: understanding a few fascinating phenomena. In: E. Sassaroli et al., Editors, Macroscopic Quantum Coherence, World Scientific, Singapore (1998), pp. 49–64.
Journal Club – “Can low-temperature thermoluminescence cast light on the nature of ultra-high dilutions?”
This is part of the Homeopathy journal club described here:
Copyright © 2007 Elsevier Ltd All rights reserved. Can low-temperature thermoluminescence cast light on the nature of ultra-high dilutions?
Louis Rey, a,
aChemin de Verdonnet 2, CH-1010 Lausanne, Switzerland
Received 2 May 2007; revised 8 May 2007; accepted 16 May 2007. Available online 31 July 2007.
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
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 and . 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.
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’.
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. and  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. and  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.
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
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.
The author thanks Laboratoires BOIRON and the AREVA Nuclear Center of Marcoule for their interest and support.
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.
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
Journal Club – “The defining role of structure (including epitaxy) in the plausibility of homeopathy”
Copyright © 2007 Elsevier Ltd All rights reserved. The defining role of structure (including epitaxy) in the plausibility of homeopathy
Manju Lata Rao1, , , Rustum Roy1, 5, Iris R. Bell2, 3, 4, 5, 6 and Richard Hoover1
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.
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
- 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 Conclusions Acknowledgements References
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. and  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. and  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. and  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. and  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.
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.
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.
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 and  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. and 
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, , , , ,  and  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.
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.
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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.
5 P. Bellavite and A. Signorini, The Emerging Science of Homeopathy. Complexity, Biodynamics, and Nanopharmacology (2nd ed), North Atlantic Books, Berkeley (2002).
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
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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
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.
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
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
Copyright © 2007 Elsevier Ltd All rights reserved. Long term structural effects in water: autothixotropy of water and its hysteresis
Bohumil Vybíral, a, and Pavel Voráčeka
aDepartment of Physics, Faculty of Pedagogy, University of Hradec Králové, Rokitanského 62, CZ-500 03 Hradec Králové, Czech Republic
Received 14 March 2007; accepted 27 March 2007. Available online 31 July 2007.
We discovered a previously unknown phenomenon in liquid water, which develops over time when water is left to stand undisturbed, and which made precise gravimetric measurement impossible. We term this property autothixotropy (weak gel-like behaviour developing spontaneously over time) and propose a possible explanation.
The results of quantitative measurements, performed by two different methods, are presented. We also report the newly discovered phenomenon of autothixotropy-hysteresis and describe the dependence of autothixotropy on the degree of molecular translative freedom. A very important conclusion is that the presence of very low concentration of salt ions, these phenomena do not occur in deionized water. Salt ions may be the determinative condition for the occurrence of the phenomena.
Keywords: water; autothixotropy; core-ions; deionization; hysteresis
- Qualitative laboratory observations
- Proposed explanation
- Autothixotropy and molecular translative freedom
- Salt ions
Quantitative experiments on autothixotropy and its hysteresis
- Measurements of the critical angle (φu)crit.
- Additional measurements
- Experiments with deionized water
Method of torsion oscillation Conclusions References
Qualitative laboratory observations
From 1978 to 1986 we performed a series of measurements and  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.
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.
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.
A stainless steel plate is suspended on an elastic filament of torsional rigidity kτ, and immersed in the studied water (Figure 1). The water is in a steady state and the ideal fluid model is assumed. Thus, if we twist the upper end of the filament by angle φu, we expect that the plate will follow the rotation, so that φd=φu, φd being angle of rotation of the plate. According to our experiments, this equality was not achieved. In the static experiment, a series of increasing values of angle φd is observed, following a very slow, ‘step by step’, change of angle φu. One can specify the moment of force Mw, arising when the plate influences the water: Mw=kτ (φu–φd). If angle φu reaches a critical value (φu)crit., the rotation of the plate (ie ) becomes quick.
The equipment that was used for the experiment is illustrated in Figure 1. The phosphor–bronze filament had a length L=465 mm and a cross-section of 0.20×0.025 mm2. The torsional rigidity of the filament was determined experimentally from torsion oscillations of the plate hung in non-perturbed air:5 kτ=(1.01±0.02)×10−7 Nm/rad. After reduction to the unit length (1 m), we get kτ1=(4.69±0.07)×10−8 Nm2/rad. The results shown here are related to an experiment with a flat stainless steel plate of width b=38.5 mm, height h=60.5 mm, thickness 0.50 mm and mass 8.50 g. Angles φu and φd were read with an accuracy of 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.
Measurements of the critical angle (φu)crit.
The critical angle is the angle φu at which, when reached by the hanger the plate began to rotate (relatively quickly, in a time scale of tens of seconds) in the same direction. Some prominent results of repeated measurements5 are:
- 1. The plate immersed with 65% of its surface in water, which had been standing for seven days: (φu)crit.=(398±3)°.
- 2. With the water boiled for a short time, but otherwise the same configuration of system (immersion 65%). After cooling (24 °C): (φu)crit. ≈ 30°, after two days: (φu)crit.≈115°.
- 3. With the water boiled, the plate entirely immersed (the upper edge 10 mm below water level), the critical angle measured on the second and third day was (φu)crit.=(356±3)°.
- 4. The plate immersed only 50%: (φu)crit.=(343±8)°.
- 5. The influence of plate immersion on the critical angle (φu)crit. is small: for plate immersion in the range 100–23%, the difference is Δ(φu)crit.≈ 14%.
- 6. The period of a water-standing influences the magnitude of the critical angle. For example, with immersion of 85% of the surface of the plate and a long period of standing (17 days), we observed (φu)crit.=1800°. As a consequence of the ‘rupture’ which followed, the plate rotated through the angular interval Δφd=1430°. With total immersion such a great critical angle was never reached.
- 7. After stabilization of the position of the plate (ie, Δφd=1430°), a slow change of angle φd (‘creep’) was observed: 4° in 5 min and, another 32°, in the subsequent 70 hours.
The results for a given configuration of the measurement system have good reproducibility. For example, if the water was boiled and stood for 24 h, with the plate totally immersed in water for 14 days, six measurements of angle φd were performed. For the same set of angles φu : 60°, 120°, and 180°, the measured respective average angles φd were: (19.6±0.7)°, (34.4±0.6)°, (52.3±1.3)°. When (φu)crit.=(239±2)° was reached, the plate quickly rotated (tens of seconds) and reached a new equilibrium position (φd)0=(198±2)°.
Hysteresis means that a system does not instantly follow forces applied to it, but reacts slowly or does not return completely to its original state: its state depends on its history. Measurements for a cyclical change of angle φu were carried out. The results of three measurements are shown in Figure 2 and Figure 3. Figure 2 shows the results for the plate entirely immersed in the water which was thoroughly stirred 17 h before. While changing angle φu from the starting equilibrium position φu=φd=0°, the change of angle φd did not follow an ideal straight line φu=φd, but the curve O–A. At point A the critical value (φu)crit.1 was reached and then the plate rotated to a new equilibrium position—point B. With decreasing angle φu, angle φd changed according to curve B–C, until it reached the second critical value, denoted (φu)crit.2, then the plate rotated to another equilibrium position—point D. When angle φu was decreased again, the position of the plate went through the origin O to the third critical position—point E, with the third critical value, denoted (φu)crit.3. Another equilibrium position corresponded to point F and the fourth critical position corresponded to point G, where (φu)crit.4(φu)crit.2. As the plate rotated further, a fourth equilibrium position point H, approximately identical with point D, was reached. From there, with decreasing angle φu, the position of the plate followed the previous section H–O and for φu=0° it returned to the original equilibrium position φd0°.
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Figure 2. Results of the experiment with the completely immersed plate: loop of the changes of angle φd=f (φu).
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Figure 3. Results of two experiments (loops of the changes of angle φd=f (φu)): with the completely immersed plate (loop a) and with half-immersed plate (loop b).
In Figure 3, the results of two other experiments with water standing for one week are presented: Loop a refers to experiment with the plate totally immersed, loop b to the experiment with the plate half-immersed; the effect is more pronounced for the half-immersed plate. The loops in Figure 3 are simpler than those in Figure 2 and the respective values (φu)crit. are lower. This can be explained on the microscopic level: The plate probably deformed clusters of water molecules of various dimensions and rigidity.
These experiments suggest that the mechanical properties of clusters of water molecules display hysteresis. The hysteresis is however limited; in our experiment, for instance it does not appear in situations when the critical angle is not reached. For example, if a position of the plate corresponds to a point in the section O–A of the graph in Figure 2, before point A is reached, and if we begin to decrease angle φu, the character of the change of angle φd will follow the same curve 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.
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.
In the second phase of these experiments, water, which was first distilled and then deionized, was used. These experiments showed that in deionized water the phenomenon of autothixotropy and its hysteresis was absent. The same equipment (Figure 1) was used for the experiment and the plate was immersed both to one half and entirely as well. The water stood for 10 days before the measurement. The rotation angle φd of the plate, which passed through the interval φd(0°, 360°, 0°), was equal to angle of torsion φu of the upper end of the filament, with accuracy of 1.5°, as evaluated from the repeated measurements. Neither the existence of critical angles (φu)crit., nor the phenomenon of hysteresis, were found. From this experiment, we arrived at the important conclusion that the autothixotropy of water, characterized by a non-zero critical angle and hysteresis is caused by the presence of ions in the water.5
A plate hangs on a filament (with torsional rigidity kτ) with their axes of symmetry aligned. The moment of inertia of the plate, relative to its axis, is I. We immerse the plate in the water (Figure 1) and measured its torsion oscillations in two situations:5
- • In ‘fresh’ water (ie with negligible autothixotropy), under assumption of a viscous damping of the water, the period of free damped oscillations is T1.
- • In ‘stood’ water (ie with autothixotropy and viscous damping of the water), we suppose that it is necessary to add, to the quantities related to the elasticity of the filament with torsional rigidity kτ, the elasticity parameter of putative clusters of water molecules in the considered situation, represented by torsional rigidity kw. Then period of free damped oscillations is T2.
By measuring the periods of oscillation T1 and T2, we can determine the moment of inertia I (eg, from the plate dimensions and its mass), and calculate the equivalent torsional rigidity:
For the measurement, an aluminium plate with a thickness of 2.95 mm, width b=(47.59±0.03) mm, height h=(50.59±0.02) mm and mass 18.70 g, was used. Its moment of inertia was calculated from its dimensions and mass: I=(7.518±0.001)×10−6 kg m2. The plate was hung along its longitudinal axis of symmetry on a phosphor–bronze filament of cross-section of 0.025×0.2 mm2 and length of L=569 mm. The filament had a torsional rigidity kτ=(8.25±0.12)×10−8 Nm/rad.5
The plate was immersed in distilled and boiled water so that the upper edge of the plate was 14 mm above the level of the water surface. The water with a volume of approximately 400 ml was in a glass vessel with an inner diameter 80 mm and height 110 mm; the experiment was carried out at a temperature of 23°C. The period of the damped torsion oscillations was measured three times.
First in fresh water. The period of oscillation was T1=(101.7±1.2) s. Then the system was left at rest for seven days. Then plate was carefully rotated from this equilibrium position by 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 kw=(1.04±0.03)×10−5 Nm/rad. The degree of the level of autothixotropy of the system, is ascertainable by means of the measurement of critical angle (φu)crit.. For our system this was ≈340°.
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.
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).
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).
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.
This is part of the Homeopathy journal club project described here:
Copyright © 2007 Elsevier Ltd All rights reserved. The silica hypothesis for homeopathy: physical chemistry
David J. Anick1, , and John A. Ives2
1Harvard Medical School, McLean Hospital, Belmont, MA, USA
2Samueli Institute for Information Biology, 1700 Diagonal Road, Alexandria, VA, USA
Received 22 February 2007; accepted 27 July 2007. Available online 31 July 2007.
The ‘silica hypothesis’ is one of several frameworks that have been put forward to explain how homeopathic remedies, which often are diluted beyond the point where any of the original substance remains, might still be clinically effective. We describe here what the silica hypothesis says. From a physical chemistry viewpoint, we explore three challenges that the hypothesis would have to meet in order to explain homeopathy: thermodynamic stability of a large number of distinct structures, pattern initiation at low potencies, and pattern maintenance or gradual evolution at higher potencies. We juxtapose current knowledge about silicates with some of the conventional wisdom about homeopathic remedies, to see how well the latter might be a consequence of the former. We explore variants of the hypothesis including some speculations about mechanisms. We outline laboratory experiments that could help to decide it.
Keywords: homeopathy; mechanism; silica; silicate; physical chemistry
- Brief overview of silicates
- Generation and perpetuation of remedy-specific silicates
- Experiments to test the silica hypothesis
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,  and  in homeopathy, but it has not previously been examined at the level of detail given here. After a brief discussion of silicate structures, we will state the hypothesis and explore how well it can meet the three challenges listed above. Consideration of how biological systems might ‘read’ the information in structured silicates is beyond the scope of this article.
Brief overview of silicates
Silicon dioxide SiO2, the principal ingredient in glass, dissolves in water by combining with two H2O molecules to form a molecule of silicic acid, Si(OH)4 (Figure 1a). The solubility of silica depends on many factors. Alexander et al. demonstrated a strong temperature dependence for solubility of amorphous silica and gave a figure of around 0.010% (or 47 ppm Si) at 20 °C.6 Quartz exhibits a much lower solubility than amorphous, and the addition of small amounts of Na2O or other alkali can dramtically increase solubility.7 Two molecules of Si(OH)4 can link up, forming the dimer H6Si2O7 (Fig. 1b) by expelling a single H2O and forming a Si–O–Si bond. The Si–O–Si bond is called a siloxane bond. This reaction is called condensation or polymerization, and its reverse reaction (the splitting of a siloxane bond by H2O to make Si–OH and HO–Si) is called hydrolysis or depolymerization. The dimer can join another Si(OH)4 unit to make a trimer, and so on. The minimum-energy configuration for the gas-phase dimer has the siloxane bond bent at about 140°, but the strain is not great for angles anywhere from 130° to 150°. As a result, chains of polymerized Si(OH)4 can close, making rings, and can branch by allowing up to four siloxane bonds at each Si, creating a virtually infinite variety of polymeric species. Quartz and cristabolite are crystalline forms of (SiO2)x, and glass is an amorphous form that incorporates small quantities of other materials such as sodium or borate. ‘Silica’ is a general term for any bulk material consisting of polymerized, condensed, or crystallized SiO2. Removing one H+ from Si(OH)4 produces the H3SiO4− anion; likewise the dimer can dissociate to H+ and H5Si2O7−, and so on for the more complex forms. A ‘silicate’ is any of these anionic forms, generally combined with one or more cations, or a crystalline or amorphous material composed of cations and HzSixOy anions. (Obviously we cannot pretend to do justice in a few sentences to the complexity of silica and silicate chemistry, which accounts for most of the variety of minerals in Earth’s crust.) We will refer to any HzSixOy (charge would be 4x−2y+z) that is held together entirely by Si–O and O–H covalent bonds as a ‘silicate’, regardless of its dissociation state, charge, hydration, or extent of association with cations. Our interest is in the behavior of silicates in aqueous solution, or in ethanol-water solution.
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Fig. 1. (a) Si(OH)4 monomer, optimized at B3LYP/6-311++G(3d,3p) level. (b) Si(OH)3–O–Si(OH)3 dimer, optimized at B3LYP/6-311++G(3d,3p) level.
A notation that has been used to characterize the connectivity of a Si in a silicate is Qx, with the superscript indicating the number of siloxane bonds.8 Thus Q0 is the monomer, Q1Q1 is a notation for the dimer (since each of the Si atoms is involved in a single siloxane bond), and the linear trimer would be Q1Q2Q1. The cyclic trimer is Q23; branched polymers would contain Q3‘s or Q4‘s. Q0 through Q4 have distinct signatures when a sample is examined with 29Si-NMR. The cyclic trimer is also denoted 3R for ‘3-membered ring’, and the 4R, 5R, 6R, and 8R structures are also often seen. Commonly two rings combine into a prism (‘double ring’), for which the notation would be D3R, D4R, etc. The D4R motif or cube is shown in Figure 2a.
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Fig. 2. (a) D4R cube (H’s omitted). (b) Two representations of ACO zeolite showing how the cube of Fig. 2a occurs in a repeating 3-D structure. Siloxane bonds are shown as straight rods even though they actually include an angle. One O atom is implied on each siloxane bond.
Silicate patterns that occur in natural minerals include: monomer (nesocilicates), dimer (sorosilicates), single and double chains (inosilicates including rings of 3–8 SiO2 units, the cyclosilicates), sheet (honeycomb pattern of hexagonal rings, or phyllosilicates), and framework silicate (complex 3D or tectosilicates). The last category includes the quartz group (minerals that are just (SiO2)x) and zeolites (crystals containing large pores that are typically occupied by cations). Figure 2b shows how the cube is a subunit in one zeolite structure called ACO.9
Condensation of aqueous silicic acid is slow under conditions of 20°C, 1 atm, and neutral pH. In a system with only silica and water, equilibrium of dissolved monomers with a condensed (amorphous) silica phase can take months to establish. A low-concentration system without a condensed phase produces few dimers,10 and the amount of dimer increases with pressure. and  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. and  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. and  If A is methyl the preference is for D4R, whereas ethyl makes D3R and propyl guides the formation of the zeolite ZSM-5 ,  and  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.  and  Working with LCPAs including spermine and spermidine, Belton et al27 determined that ‘chain length, intramolecular N–N spacing and C:N ratio of the additives’ was responsible for ‘the combination of unique catalytic effects and aggregation behaviours’ that determined the materials’ properties. Working with amino acid silicate solutions, Belton and coworkers found that 11 of the 20 amino acid residues ‘affect the kinetics of small oligomer formation, the growth of aggregate structures and the morphology and surface properties of the silicas produced’.28
Given this information, it is tempting to imagine that almost any inorganic or organic material could guide the formation of specific silicates. Focusing on plants, which are the source of the majority of remedies in clinical use, could the particular proteins or N-containing alkaloids in a plant account for plant-specific silicates appearing in remedies made from that plant? Obviously some compounds will be more effective than others at condensing silica, eg silaffins evolved specifically for that purpose. In a low-potency remedy like a diluted 3c being succussed to make a 4c, perhaps silicic acid ‘ignores’ most plant components while allowing particular ‘active ingredients’ to catalyze the relevant structures. It would be interesting if the silica-condensing ingredients were the same as the pharmacologically active ingredients. If so, it could explain why, say, the atropine in Belladonna plays the key role in determining the properties of potentized Bell, and it would suggest that remedy made from whole plant should be essentially identical to remedy made by starting with purified atropine. It is widely believed that the homeopathic remedies Bell and Atropinum have very similar clinical activity.
We should also express some notes of caution. While it is true that inorganic and organic solutes guide silicate formation, in many cases these solutes are incorporated into the final product, eg the cations occupy the pores in a zeolite, or organic matter remains embedded in the final silicate. Or, the concentration of ‘catalyst’ is comparable to that of silicate, eg, Belton et al28 used a 2:1 molar ratio of Si to amino acid. This poses a problem for the silica hypotheses. As the remedy becomes progressively more dilute, there is less and less catalytic material available. To our knowledge, the question of how low the solute concentrations can get, and still generate significant quantities of solute-specific silica structures, has never been studied. Nor is it known how a pulse of high pressure, as in succussion, would affect the process. For the silica hypothesis to work, it would be essential that some components of the MT act as true catalysts, yielding many structured silicates per molecule, and not become trapped in individual silicate complexes. Questions can also be raised about how far the specificity of the catalysts can extend. For example atropine and hyoscyamine are enantiamers, differing solely in their orientation at a single C locus, yet Bell and Hyos are considered to be rather different remedies. Most silicates that have been studied are achiral, but some, like trigonal quartz, can be chiral.
Let us turn now to the second challenge: perpetuation of the pattern after all of the MT has been diluted away. Let us assume that a 12c remedy sample contains a measurable population of remedy-specific silicates. What happens when that remedy is diluted 1:100 and succussed? The process can begin the same way: the early succussion strokes release silicic acid from the vial walls. However there is no catalyst to condense the silicic acid—or is there? Clearly we would require that the remedy-specific silicate polymers from the prior potency serve as the catalyst. Suppose the relevant structure in the 12c were nanocrystals of a particular zeolite. We would be saying that diluting this zeolite solution 1:100, adding silicic acid, and succussing, should generate more zeolite. Indeed, we would need to have about 100 times as much zeolite nanocrystal at the end of the succussion cycle, as we had just after the 1:100 dilution. If we do not amplify the active ingredient by a factor of 100 each time, then with subsequent dilutions the amount of structured silicate will soon diminish to zero.
How feasible is it to generate particular silicates from silicic acid, by using only a seed containing already-structured silicate, and then succussing? We admit this is the weakest point of the silica hypothesis, but it is not impossible. We propose four ways it could happen. First, some silica motifs may be inherently amenable to self-replication. Perhaps a double ring like D5R has a tendency to split (hydrolyze) into two single 5R rings when vigorously shaken, and perhaps the two resulting single rings have a tendency to attract a second layer of condensation, re-creating the double ring. If so, a single succussion stroke could double the amount of D5R, and repeated succussion strokes could amplify the amount of D5R as much as 100 times. This hypothetical process would be comparable to the polymerase chain reaction for DNA. Building on the DNA analogy, in addition to double rings we could imagine a double form of any flat linear or branched silicate polymer. As noted above, single and double chains are among the naturally occurring forms of silicate in minerals. (Some cycles could be allowed too but joined rings and highly branched topologies cannot be ‘doubled’ without introducing a lot of bond angle strain.) If the double form were to ‘unzip’ like DNA, and if each half were then to act as a template to re-create the double form, we would have a mechanism for preserving the structure from one potency to the next.
This idea also permits us to see a way that remedies might change gradually with potency. For instance, if the ‘replication’ described above were not 100% perfect, but instead there was a tendency for small but predictable changes to occur, then the 13c might be subtly different from the 12c, the 14c might be slightly changed from the 13c, and so on. By ‘small but predictable changes’ we mean things like lengthening a chain by one or two units or adding a short side-branch. Small changes could function like point mutations in DNA: alterations that leave the structure mostly unchanged, and do not interfere with the capacity for replication, but which would be inherited and maintained by subsequent dilution/succussion cycles. Small changes might occur with low probability but might accumulate over many cycles, like DNA mutations, to result in a noticeably different structure with different clinical benefits. This would fit with the conventional wisdom of homeopaths that a 12c and a 13c and a 14c are not much different, but with passage of enough cycles, the 200c and the 12c can be quite different.
Second, we have alluded to silica nanocrystals as the information-carrying component. Crystals are well known for acting as seeds that can extend their pattern as other molecular units crystallize onto them. Once a particular silica crystal pattern got started, could it grow more of its own pattern when added to a silicic acid solution and succussed? We would be saying that of the 200+ known zeolite structures, if tiny nanocrystals of one zeolite are added to silicic acid and succussed, the result would be 100 times as much of that very same zeolite. This strikes us as a priori unlikely, yet it might work for at least some zeolite or other crystalline forms. We doubt the question has ever been studied.
Third, an intriguing mechanism could involve transfer of information from the silicates to structure the water during succussion, and transfer of information back from the structured water onto silicate particles, which then ‘hold’ the information when the succussion pressure abates. Zeng and coworkers29 proposed such a mechanism when they studied the well known ‘memory effect’ of water. The ‘memory effect’ does not involve homeopathy: it says that a water sample that has been crystallized under pressure into a gas hydrate, and then melted, will more quickly re-form the clathrate hydrate structure when mixed with gas and re-pressurized, compared to a water sample that did not previously experience the hydrate state. Analysis of water samples with neutron scattering could not find any structural basis for a ‘memory effect’.30 When Zeng and coworkers discovered that low concentrations of certain ice nucleation inhibitors could destroy the memory effect, they inferred that the effect was due to small impurity particles that received the ‘imprint’ of the clathrate state and, by holding that imprint long after melting and degassing, supplied a template for rapid nucleation back to the clathrate state.
Quoting Zeng et al, the memory effect ‘must be ascribed to an alteration of the surface states of the impurity particles that amplifies their nucleating action. This could occur because of an imprinting of the surface of the impurities by the growth of a hydrate crystal on the particle surfaces. For instance, if the impurities are hydrated or hydroxylated silicon or iron oxides, a hydrate crystal may well alter the surface geometry so that when the hydrate melts, the surface is now a better nucleator of hydrate than it was during the first nucleation cycle’ (emphasis added). They are explicitly postulating that silicate particles could be the information carriers that cause water, when pressurized, to form a particular pattern, and that the pattern could imprint other silicate particles. We are not proposing that water forms a momentary clathrate hydrate during succussion, but there could be other structural alterations. These alterations could start at (be nucleated by) silicate particles, could spread throughout the sample, and then imprint other silicate particles throughout the sample. The result would be an amplification, conceivably by the needed factor of 100, of the specific surface pattern on silica particles. Although the structural change in the water would be lost when the pressure returns to 1 atm, the information would persist in the silica surface changes. This explanation works best if silica is released into solution as nanoparticles, rather than as monomeric silicic acid, when agitated during succussion.
Fourth, if we postulate that silica surface carries the information, could the glass vial wall itself be that carrier? Some commercial remedies are prepared by the Korsakoff method. In this method, a single vial is used, and dilution is achieved by decanting most of the liquid and then refilling. Then the vial is succussed. A thin layer of water that wets the inside vial walls stays there when most of the liquid is decanted. This layer is estimated to be about 1% of the vial volume; so subsequent refilling accomplishes the 1:100 dilution. Asay and Kim31 found that water adsorbing onto glass at 20°C forms a three-molecule thick layer of ice. The pattern of the water adjacent to the glass will certainly be affected by alterations in the glass surface. Once a pattern is established on the vial walls, subsequent Korsakoff cycles might do nothing or might slowly alter the pattern. In order to transmit this information after the final potency is removed, however, it would have to contain some imprinted silica particles as well.
Experiments to test the silica hypothesis
The silica hypothesis and its variants are amenable to experiment and measurement to verify or negate them. Its challenges are the low concentrations at which silicates occur, and the difficulty of teasing apart chemically similar oligomers or surface features. A starting point will be to measure the amount of monomeric and polymeric silicates in remedies, in succussed water, and in diluted remedies after 0, 2, 8, 20, and 40 succussion strokes (or any similar sampling sequence). Alexander et al6 successfully used a molybdic acid assay to measure the amount of monomeric silicate, while mass spectroscopy can provide the total Si content of a sample. Obviously we would want to repeat these measurements for several different types of glass vials, and for ethanol-water vs water for the solvent.
Raman spectroscopy and 29Si-NMR provide insight into the degree of polymerization of silicates. 29Si-NMR will tell us ratios among Qx loci. Assuming we see some consistent differences among remedies or between remedies and controls, we can use these methods to ask how well homeopathically relevant substances such as atropine can serve as silicate polymerizers, and whether their condensed silicate products have consistent and substance-specific properties. The protocol would be to add a known concentration of atropine to a silicic acid solution of known concentration (in plastic vial) and succuss. Electron microscopy of frozen and cracked samples or very thin frozen layers is one way to look for suspended silica nanoparticles and to examine their surface. If surface features seem to be the information-carrying aspect, we will ultimately need to develop assays that detect particular features. Such an assay might measure adsorption of particular molecules, or enhancement or stabilization of a particular enzyme.
If early experiments lead us to suspect that remedy-specific oligomers are the information-carrying ingredient, we will ultimately need to make remedies enriched in 29Si in order to identify them via 29Si-NMR. To make a vial out of 29SiO would be prohibitively expensive, but here is an alternative. Remedies could be made by succussing them in polypropylene vials, and silica could be added in the form of small (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.
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.
1 L.R. Milgrom, K.R. King, J. Lee and A.S. Pinkus, On the investigation of homeopathic potencies using low resolution NMR T2 relaxation times: an experimental and critical survey of the work of Roland Conte et al, Br Hom J 90 (1) (2001), pp. 5–13. Abstract | PDF (150 K) | View Record in Scopus | Cited By in Scopus
2 J.-L. Demangeat, P. Gries and B. Poitevin et al., Low-field NMR water proton longitudinal relaxation in ultrahighly diluted aqueous solutions of silica-lactose prepared in glass material for pharmaceutical use, Appl Magn Reson 26 (2004), pp. 465–481. View Record in Scopus | Cited By in Scopus
3 H. Walach, W.B. Jonas and J. Ives et al., Research on homeopathy: state of the art, J. Altern. Compl. Med. 11 (5) (2005), pp. 813–829. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus
4 C.M. Witt, R. Ludtke and T.E. Weisshuhn et al., The role of trace elements in homeopathic preparations and the influence of container material, storage duration, and potentisation, Forsch Komplementarmed 13 (2006), pp. 15–21. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus
5 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, Mat Res Innovat, 9–4 (2005), pp. 93–124.
7 Iler RK, ed., The Chemistry of Silica, ch. 1 & 2 (pp. 3–171), Wiley, New York (1979).
8 R.K. Harris, C.T.G. Knight and W.E. Hull, Nature of species present in an aqueous solution of potassium silicate, J Amer Chem Soc 103 (1981), pp. 1577–1578. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus
10 R.H. Busey and R.E. Mesmer, Ionization equilibria of silicic acid and polysilicate formation in aqueous sodium chloride solutions to 300 °C, Inorg Chem 16 (10) (1977), p. 2444. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus
11 Manning CE. Polymeric silicate complexing in aqueous fluids at high pressure and temperature. In: Wanty RB, (ed.). Water–Rock Interaction I, Taylor & Francis, 2004; pp. 45–52.
12 N. Zotov and H. Keppler, Silica speciation in aqueous fluids at high pressures and high temperatures, Chem Geol 184 (2002), pp. 71–82. SummaryPlus | Full Text + Links | PDF (249 K) | View Record in Scopus | Cited By in Scopus
13 W.M. Hendricks, A.T. Bell and C.J. Radke, Effects of organic and alkali metal cations on the distribution of silicate anions in aqueous solutions, J Phys Chem 95 (1991), pp. 9513–9518. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus
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
This is part of the Homeopathy journal club described here:
Copyright © 2007 Elsevier Ltd All rights reserved. The possible role of active oxygen in the Memory of Water
Vladimir L. Voeikov, a,
aFaculty of Biology, Lomonosov Moscow State University, Moscow 119234, Russia
Received 13 April 2007; accepted 4 May 2007. Available online 31 July 2007.
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
- 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
‘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 ). 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:
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:
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:
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:
where Rn· is a free radical with an unpaired electron, and RmH is a molecule which it oxidizes.But if a free radical is in turn oxidized with a bi-radical molecule oxygen, a peroxide radical, ROO·, is produced. When it oxidizes a certain molecule, a metastable and energy-rich peroxide (ROOH) is produced in addition to a new radical, which provides for chain propagation. Usually low energy of activation is needed for decomposition of peroxides at which two new active centres, RO· and ·OH emerge. Thus, even if a ‘parent’ chain is eliminated, the system in which peroxides appear stays ‘charged’ and new chains arise in it sometimes after a very slight perturbation. Such reactions are named “chain reactions with delayed branching” (CRDB). Systems in which CDRB go on are intrinsically non-equilibrium, though at a first sight may seem to be at rest.
Evidence is accumulating that very slow CRDB may under ‘appropriate conditions’ readily develop in water. As mentioned above, quantum chemical calculations show that if water is organized in a favourable way (water molecules are arranged in space, in particular, in relation to singlet oxygen and to each other), the energy of activation for oxidation of a water molecule with singlet oxygen diminishes to reasonable values. The immediate products of water oxidation are exotic and highly energy-rich peroxides such as HOOOH, HOOOOH, HOO–HOOO.11 All these peroxides are typical active oxygen species. They easily decompose giving birth to new free radicals, initiating propagation of new chains, or to ozone, generating new singlet oxygen molecules. Stationary levels of all these active oxygen species are extremely low due to their instability, but since water is never devoid of molecular oxygen (recall that any perturbation of water gives birth to oxygen and hydrogen at a non-zero probability), high energy quanta-generating processes never completely fade out.
We observed that in the course of CRDB of slow oxidation of amino acids in aqueous solutions initiated with H2O2 addition or with low intensity UV-irradiation, concentration of H2O2 increases to levels that can be explained only by water oxidation with O2.17 Recently, it has been shown that in water containing carbonates and phosphates18 or in water bubbled with noble gases, such as argon,19 concentration of H2O2 spontaneously increases and its augmentation goes on faster if water is stirred. Using chemiluminescent methods we also found that such processes spontaneously develop and proceed for an indefinitely long time in aerated mineral waters from natural sources.20 Also is it was mentioned above H2O2 yield in pure water equilibrated with air under the conditions favourable for its splitting13 occurs faster, continues longer after initial perturbation, and reaches higher levels than in degassed water.
Oscillatory nature of reactions with active oxygen participation
At the beginning of this essay a question was asked: is water a special case of a substance that can stay after a perturbation for a sufficiently long time out of equilibrium with the environment required by the second law of thermodynamics, and if it can, what mechanisms provide its stable non-equilibrium state? According to the theory developed by Del Giudice et al based on the principles of quantum electro-dynamics coherent domains of sub-micron (‘nano’) dimensions spontaneously emerge in water and coexist in it together with non-coherent dense water ‘gas’.21 According to this theory water particles within a coherent domain oscillate coherently between two states belonging to individual spectrum of these states. Calculations show that two relevant levels involved in a coherent oscillation are separated by an energy of 12.06 eV whereas the ionization threshold of the water molecule is 12.6 eV, that is only 0.54 eV below ionization threshold.22 Del Guidice pointed my attention to the fact that, provided that this threshold is overcome, coherent domains (CD) may tunnel ‘hot’ electrons in the non-coherent surroundings where they stick to oxygen molecules thus initiating chain reactions described above.23
Turning back to the three examples of stable non-equilibrium aqueous system mentioned earlier: ‘extremely diluted solutions’, ‘nanoparticle doped water’, and ‘FWS’, one may suggest that water shells surrounding nanoparticles present in these systems represent stable coherent domains that may supply electrons to oxygen. Energy of electronic excitation released due to oxygen reduction and free radical reactions may serve as activation energy for additional release of electrons from a CD. When too many electrons are extracted from a CD, it dissipates. Chain reactions terminate though metastable products of CDRB stay in a system. During this period water shells begin to build up around nanoparticles and as soon as they turn into CDs the latter again start to supply electrons to oxygen. This hypothetical scenario shows how complex oscillations of energy of electronic excitation generation, of red/ox potentials, and of other properties of aqueous systems may originate in systems where coherent water domains reduce oxygen, and its active species are present. The frequency range of oscillations varies from the optical region, characteristic for electronic excitation, to extremely low frequencies of oscillations of other parameters of the system. Thus, aqueous systems in which chain reactions with the participation of active oxygen proceed may serve as emitters and receivers of oscillatory signals in an extremely wide frequency range.24 This to our mind is a necessary condition for homeopathic potencies to exert its action on living systems.
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.
1 J. Zheng and G.H. Pollack, Solute exclusion and potential distribution near hydrophilic surfaces. In: G.H. Pollack, I.L. Cameron and D.N. Wheatley, Editors, Water and the Cell, Springer, Dordrecht (2006), pp. 165–174.
2 V. Elia, S. Baiano and I. Duro et al., Permanent physico-chemical properties of extremely diluted aqueous solutions of homeopathic medicines, Homeopathy 93 (2004), pp. 144–150. SummaryPlus | Full Text + Links | PDF (154 K) | View Record in Scopus | Cited By in Scopus
3 V. Elia, L. Elia and E. Napoli et al., Conductometric and calorimetric studies of serially diluted and agitated solutions: the dependence of intensive parameters on volume, Int J Ecodyn 1 (2006), pp. 1–12.
4 Y. Katsir, L. Miller and Y. Aharonov et al., The effect of rf-irradiation on electrochemical deposition and its stabilization by nanoparticle doping, J Electrochem Soc 154 (2007), pp. D249–D259. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus
5 Freitas Jr RA. Fullerene-based pharmaceuticals. Nanomedicine, Vol IIA: Biocompatibility. Georgetown, TX: Landes Bioscience, 2003 [chap 18.104.22.168].
6 G.V. Andrievsky, V.K. Klochkov and A. Bordyuh et al., Comparative analysis of two aqueous–colloidal solutions of C60 fullerene with help of FTIR reflectance and UV–Vis spectroscopy, Chem Phys Lett 364 (2002), pp. 8–17. SummaryPlus | Full Text + Links | PDF (339 K) | View Record in Scopus | Cited By in Scopus
7 G.V. Andrievsky, V.K. Klochkov and L.I. Derevyanchenko, Is C60 fullerene molecule toxic?!, Fuller Nanotub Car N 13 (2005), pp. 363–376. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus
8 K.J. Laidler and A. Cornish-Bowden, Elizabeth Fulhame and the discovery of catalysis. In: A. Cornish-Bowden, Editor, New Beer in an Old Bottle: Eduard Buchner and the Growth of Biochemical Knowledge, Universitat de Valencia, Valencia (1997), pp. 123–126.
9 A.N. Bach, On the role of peroxides in the processes of slow oxidation, Zh Russ Phys-Chem Soc 29 (1897), pp. 373–395.
10 P. Wentworth Jr, L.H. Jones and A.D. Wentworth et al., Antibody catalysis of the oxidation of water, Science 293 (2001), pp. 1806–1811.
11 X. Xu, R.P. Muller and W.A. Goddard 3rd, The gas phase reaction of singlet dioxygen with water: a water-catalyzed mechanism, Proc Nat Acad Sci USA 99 (2002), pp. 3376–3381. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus
12 N.K. Baramboim, Mechanochemistry of High Molecular Weight Compounds, Chimiya, Moscow (1971).
13 G.A. Domrachev, G.A. Roldigin and D.A. Selivanovsky, Mechano-chemically activated water dissociation in a liquid phase, Proc Russ Acad Sci 329 (1993), pp. 258–265. View Record in Scopus | Cited By in Scopus
14 S. Woutersen and H.J. Bakker, Resonant intermolecular transfer of vibrational energy in liquid water, Nature 402 (1999), pp. 507–509. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus
15 V.L. Voeikov and V.I. Naleto, Weak photon emission of non-linear chemical reactions of amino acids and sugars in aqueous solutions. In: J.-J. Chang, J. Fisch and F.-A. Popp, Editors, Biophotons, Kluwer Academic Publishers, Dordrecht (1998), pp. 93–108.
16 N.N. Semyonov, Chemical Kinetics and Chain Reactions, Oxford University Press, Oxford (1935).
17 V.L. Voeikov, I.V. Baskakov and K. Kafkialias et al., Initiation of degenerate-branched chain reaction of glycin deamination with ultraweak UV irradiation or hydrogen peroxide, Russ J Bioorg Chem 22 (1996), pp. 35–42. View Record in Scopus | Cited By in Scopus
18 V.I. Bruskov, A.V. Chernikov and S.V. Gudkov et al., Activation of reducing properties of anions in sea water under the action of heat, Biofizika 48 (2003), pp. 1022–1029.
19 V.L. Voeikov and M.V. Khimich, Amplification by argon of luminol-dependent chemiluminescence in aqueous NaCl/H2O2 solutions, Biofizika 48 (2002), pp. 5–11. View Record in Scopus | Cited By in Scopus
20 V.L. Voeikov, R. Asfaramov and V. Koldunov et al., Chemiluminescent analysis reveals spontaneous oxygen-dependent accumulation of high density energy in natural waters, Clin Lab 49 (2003), p. 569.
23 E. Del Guidice, A. De Ninno and M. Fleischmann et al., Coherent quantum electrodynamics in living matter, Electromagn Boil Med 24 (2005), pp. 199–210.
24 V.L. Voeikov, Fundamental role of water in bioenergetics. In: L.V. Beloussov, V.L. Voeikov and V.S. Martynyuk, Editors, Biophotonics and Coherent. Systems in Biology, Springer, New York (2006), pp. 89–104.
25 V.L. Voeikov, Reactive oxygen species (ROS): pathogens or sources of vital energy? Part 1. ROS in normal and pathologic physiology of living systems, J Alt Compl Med 12 (2006), pp. 111–118. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus
V.L. Voeikov, Reactive oxygen species (ROS): pathogens or sources of vital energy? Part 2. Bioenergetic and bioinformational functions of ROS, J Alt Compl Med 12 (2006), pp. 265–270. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus
This is part of the Homeopathy journal club described here:
Copyright © 2007 Elsevier Ltd All rights reserved. The octave potencies convention: a mathematical model of dilution and succussion
David J. Anick, a,
aHarvard 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
- Modeling succussion
- Two active ingredients
- Multiple active ingredients
- High potencies
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 Qdil=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 Qdil back up to Q=HQdil. If succussion did not raise the concentration by a factor of (on average) H, then after repeated cycles the concentration would dwindle to zero.
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 Qdil to HQdil. 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 Qm is the concentration after m strokes with Q0=Qdil, then Q1=RQ0, Q2=RQ1, and so on. This cannot continue forever, or Qm 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,
This equation does not have a simple solution in its discrete form, but the very similar equation
has the very nice exact solution
which exhibits the expected S-shaped curve asymptotic to C as m→∞. After S succussion strokes the concentration is HQ0, ie QS=HQ0, and putting this into Eq. (3) shows that the concentration at the end of each cycle is given by
According to Eq. (4), if RSH, then QS will be close to the maximum allowable concentration C, but if RS<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 RS>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 QS/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
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
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
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 (XP,YP) describe the concentrations at the end of the Pth cycle, P denoting the potency. The relationship between (XP+1,YP+1) and (XP,YP) is as follows. Starting with (XP,YP), after dilution the concentrations are (XP/H,YP/H). Putting X(0)=XP/H and Y(0)=YP/H into Eq. (7), we see that (XP+1,YP+1) is found by intersecting the line X+Y=1 with the curve HY/YP=(HX/XP)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 (xP,yP) to (xP+h,yP+h), and succussion takes us in a straight line of slope s/r from there back to the curve 10−x+10−y=1. (xP+1,yP+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 xP→∞ while yP→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 (xP+1,yP+1) to (xP,yP) is
while after the transition (where x>y) it is nearly horizontal and
Using only the fact that the curve 10−x+10−y =1 has a negative slope, we obtain the inequalities
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 YP/XP increases by a factor of between 10h(s−r)/s and 10h(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 WP=YP/XP to the transition potency, is about −log(WP)/(h(s−r)/r). Without needing to know any values for s, r, or WP, 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 Xi, or if we also include the potency in the notation, as Xi,P. The growth rate of Xi is in (Ri), and −log(Xi) is denoted xi. The system of equations governing succussion is
We omit details of its solution. The effect of one dilution–succussion cycle is described by
where rDOM 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 Xi,P/Xj,P, is to change the ratio by a factor of H(ri-rj)/rDOM, ie
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 (Ri) 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(Xi,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 rDOM changes) but should remain nearly constant between transition points.
Figure 3 shows the same information but displays Xi,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.
Dr JT Kent, developer of the octave potencies concept,  and  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 and  and other considerations place C in the micromolar range. If C is 10 μM then XP=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.
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,  and ) 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.
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.
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).
 Bhatia M. Homeopathic Potency Selection. Hpathy Ezine, April 2004: www.hpathy.com/philosophy/bhatia-potency-selection2.asp.
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