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

www.badscience.net/?p=490

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

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

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

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

Article Outline

Introduction

Locality, non-locality, and philosophy

Local hypotheses and the memory of water

Non-local hypotheses and macro-entanglement

Quantum theory and homeopathy

Entanglement in the homeopathic process

Conclusion: a therapeutic Uncertainty Principle?

Acknowledgements

References

Introduction

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

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

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

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

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

Locality, non-locality, and philosophy

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

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

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

• No signal can travel faster than light.

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

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

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

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

(3) What is valid here is valid elsewhere.

(4) The universe is material and not spiritual.

(5) Everything that is physical is observable.

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

(7) Experiment validates theory.

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

• All swans are white.

• The creature in front of us is a swan.

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

• The creature is white.

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

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

• The next swan I see will be white.

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

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

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

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

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

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

Local hypotheses and the memory of water

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

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

Table 1.

Some physical constants for dihydrides of the Group 16 elements

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Non-local hypotheses and macro-entanglement

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

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

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

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

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

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

• WQT has no interpretation in terms of probabilities.

• Complementarity and indeterminacy are epistemological in origin not ontological.

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

Quantum theory and homeopathy

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

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

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

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

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

Entanglement in the homeopathic process

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

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

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

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

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

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

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

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

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

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

Conclusion: a therapeutic Uncertainty Principle?

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

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

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

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

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

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

Acknowledgements

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

References

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

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

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

www.badscience.net/?p=490

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

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

Abstract

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

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

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

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

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

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

Article Outline

Introduction

Necessity of a general principle

How non-locality arose

What is entanglement?

Weakening the axioms of quantum mechanics

WQT and homeopathy

Entanglement and information in quantum physics and beyond

Discussion

Acknowledgements

Appendix A. The sequential box model (SBM)

Appendix B. Entanglement

References

Introduction

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

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

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

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

Necessity of a general principle

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

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

2. A mother tincture is prepared from the substance.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

How non-locality arose

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

What is entanglement?

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

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

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

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

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

Weakening the axioms of quantum mechanics

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

PQ–QP≠0,

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

1. Systems are any part of reality.

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

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

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

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

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

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

WQT and homeopathy

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

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

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

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

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

Entanglement and information in quantum physics and beyond

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

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

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

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

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

Discussion

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

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

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

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

Acknowledgement

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

References

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Appendix A. The sequential box model (SBM)

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

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

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

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

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

Appendix B. Entanglement

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

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

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

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

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

ci,j=aibj,

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

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

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

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

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

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

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

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

This is part of the Homeopathy journal club described here:

www.badscience.net/?p=490

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

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

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

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

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

Article Outline

Historical overview: the early history of high dilution experiments

Exploring the physical nature of the biological signal

From high dilution to digital biology

The present situation

Acknowledgements

References

Historical overview: the early history of high dilution experiments

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

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Figure 1. Jacques Benveniste 1935–2004.

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

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

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

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

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

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

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

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

Exploring the physical nature of the biological signal

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

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

From high dilution to digital biology

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The present situation

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

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

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

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

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

Acknowledgments

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

References

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

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

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

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

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

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

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

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

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

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

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

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

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

www.badscience.net/?p=490

doi:10.1016/j.homp.2007.05.005
Copyright © 2007 Elsevier Ltd All rights reserved. The nature of the active ingredient in ultramolecular dilutions Otto Weingärtner^{, a,
a}Department of Basic Research, Dr. Reckeweg & Co. GmbH, Berliner Ring 32, D 64625 Bensheim, Germany
Received 8 March 2007; revised 14 May 2007. Available online 31 July 2007.

Abstract

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

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

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

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

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

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

Article Outline

Introduction

Necessity of a general principle

How non-locality arose

What is entanglement?

Weakening the axioms of quantum mechanics

WQT and homeopathy

Entanglement and information in quantum physics and beyond

Discussion

Acknowledgements

Appendix A. The sequential box model (SBM)

Appendix B. Entanglement

References

Introduction

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

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

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

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

Necessity of a general principle

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

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

2. A mother tincture is prepared from the substance.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

How non-locality arose

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

What is entanglement?

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

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

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

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

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

Weakening the axioms of quantum mechanics

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

PQ–QP≠0,

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

1. Systems are any part of reality.

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

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

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

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

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

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

WQT and homeopathy

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

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

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

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

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

Entanglement and information in quantum physics and beyond

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

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

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

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

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

Discussion

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

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

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

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

Acknowledgement

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

References

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Appendix A. The sequential box model (SBM)

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

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

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

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

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

Appendix B. Entanglement

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

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

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

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

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

ci,j=aibj,

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

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

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

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

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

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

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

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