Homeopathy’s claims of clinical efficacy and cost effectiveness1 are regarded with suspicion and contempt. Evidence other than that framed within the (sometimes biased)2-4 reductionism of Evidence-Based Medicine (EBM)5, 6 and the double-blind randomised-controlled trial (DBRCT),7, 8 is rejected.
EBM and the DBRCT, like much of biomedical science, are rooted in the reductionist philosophy of Logical Positivism combined with Local Realism. The latter states that, a), the universe is real and it exists whether we observe it or not; b), legitimate conclusions and predictions can be drawn from consistent experimental outcomes and observations; c), no signal can travel faster than light.9-11
In questioning a) and c) above, quantum theory transcends Local Realism10 and philosophically confounds the reductionism of biomedicine.11 Attempts at explaining homeopathy’s efficacy have made use of concepts generalised from the discourses of semiotics12, 13 and quantum theory.14-16 Thus, non-local entanglement17-19 between patient, practitioner, and remedy (PPR entanglement), could form a descriptive basis for the healing interaction.20-24 It combines from physics Greenberger- Horne-Zeilinger (GHZ) three-particle entanglement,25 and an algebraic generalisation of orthodox quantum theory called Weak Quantum Theory,18, 19 with semiotics12, 13 to generate a three-way PPR entangled state. ‘Cure’ results from the ‘reflection’ and ‘twisting’ of this state in a notional two-dimensional mirror-like ‘therapeutic state space’26 (an analogue of complex Hilbert space more familiar from orthodox quantum theory),10 depicted in ‘semiotic geometry’ as a hexagonal bipyramid.11, 23, 24
Though hypothetical, a post hoc explanation27, 28 of the observed ‘leakage’ between verum and placebo groups during recent double-blind provings of homeopathic remedies,29-31 is afforded by the PPR entanglement metaphor, pointing to its possible experimental verification. In addition, and when viewed semiotically, the PPR entangled state’s geometrical projection into a notional ‘therapeutic state space’ has been used to understand the concept of miasms in homeopathy,32 and the action of remedies and diseases on the Vital Force.33 The purpose of this paper is to further investigate the polyhedral geometry of the PPR entangled state,34 and to perhaps deepen insight into the complex therapeutic action and interaction of the patient, practitioner and the remedy on the way to cure.
ENTANGLEMENT IN THE THERAPEUTIC PROCESS
Entanglement is said to occur in a quantum system when its seemingly separate parts are so holistically matched or correlated, measurement of one part of the system instantaneously (i.e., not limited by the speed of light and without classical signal transmission) provides information about all its other parts, regardless of their separation in space and time, or their size.35 Quantum entanglement between photons was famously demonstrated by the French physicist Alain Aspect and his team in 1982.36
That there is no size limitation on quantum entangled systems is important as quantum theory is thought by many to apply only to sub-atomic particles, atoms and molecules. This is because the equations of quantum theory are dominated by an incredibly small number called Planck’s constant (6.626 x 10-34 J s), commensurate with events occurring on such a small scale.
In fact, under certain exceptional circumstances (especially around fluctuating instabilities at critical points when a material is on the verge of changing its physical state),37 correlated behaviour between the parts of a quantum system – a keynote of entanglement – can be ‘lifted’ into the macroscopic realm of bulk materials, which then exhibit properties similar to nanoscopic quantum systems, e.g., low-temperature superconductors and super-fluids.38
Such ‘quantum macro-entanglement’ is being used to develop a novel quantum model of energy medicine.39 Interestingly, as an explanation of the efficacy of homeopathic remedies, the Memory of Water also relies on macro-entangled coherence, albeit between large numbers of water molecules.41, 42
Non-local correlation is not the only pre-requisite for entanglement. A quantum system’s processes must also be describable in terms of a ‘non-commuting algebra of complementary observables’.10 Thus, when two separate operations of observation are performed sequentially the result depends on the sequence and what is being measured. This leads to another key quantum idea: complementarity.43, 44
So a single explanation or model might not adequately fit or explain all the different observations that can be made on a quantum system. In order to fully explain quantum phenomena therefore, it is necessary to have two different but complementary concepts. The answer one obtains performing two different sets of observations depends entirely on the order in which they are performed: yet both are necessary in order to acquire a complete picture of the system.
Such notions of complementarity and entanglement can be broadened far beyond their specific meaning in the orthodox quantum theory of particles, atoms and molecules: they might be useful in describing the behaviour of what are also in essence macroscopic systems, i.e., the patient, practitioner, and remedy. Examples have been cited of complementarity and entanglement in engineering, information dynamics, philosophy and the cognitive sciences, especially psychology.18 On this basis, Atmanspacher et al formalised a more general version of quantum theory which relaxes several of its nanoscopically-limiting axioms, including dependence on Planck’s constant. Called Weak Quantum Theory (WQT),18 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 not ontological in origin.
As a result, WQT explicitly allows quantum theory’s application into the above-mentioned macroscopic areas and, by implication, into possible explanations of the dynamics of healing.19, 21, 23, 24
PPR entanglement and semiotics
Semiotics is the study of signs and symbols. A sign can be anything as long as it is interpreted as a sign, i.e., that it signifies something. Without signification by someone, a sign of itself has no intrinsic meaning. From this perspective, it is the meaningful use of signs that concerns semiotics.45 Its two dominant models are those of the French linguist Ferdinand de Saussure, and American pragmaticist philosopher, Charles Sanders Peirce.
De Saussure’s semiotics is dyadic, i.e., a sign is thought to consist of two parts: a signifier, which is the form of the sign; and that which is signified, or the concept the sign represents. Peirce introduced a third element, i.e., the sense made of the sign. Thus, Peirce’s semiotics is essentially triadic.
Modern semiotics impacts on our understanding of how and in what media we communicate, and among other things, influenced the development of post-Modern philosophies.46 Semiotics, however, has very ancient roots. The word itself derives from the ancient Greek shmeiwtikoz – semeiotikos, meaning an interpreter of signs; and both Plato and Aristotle are known to have considered the relationship between signs and the world of phenomena. Thus without calling it such, semiotics has long been associated with Western philosophical thought.
Henry Stubbes first used the word ‘semiotics’ to denote precisely the branch of medical science relating to the interpretation of signs and symptoms; an idea taken up by the late 17th century philosopher John Locke, 47 and still being examined today.48-50 Locke’s writings on the value of signs and symptoms seem to pre-date those of Hahnemann. Consider, for example Locke’s, “Nor is there any thing to be relied upon in Physick but an exact knowledge of medicinal physiology (founded on observation not principles), semeiotics, method of curing, and tried (not ex-cogitated, not commanding) medicines.“47 Then compare this with Hahnemann’s Organon of Medicine; article 6, written about one hundred years later:51 “The unprejudiced observer is well aware of the futility of transcendental speculations which can receive no confirmation from experience. Be his powers of perspicacity even very great, he can take note of nothing in every individual disease, except the changes in the health of the body and of the mind (morbid phenomena, accidents, symptoms) which can be perceived externally by means of the senses…. All these signs represent the disease in its whole extent, that is, together they form the true and only conceivable portrait of the disease.”
Walach specifically applies modern semiotics52, 53 to homeopathy by making some quite revolutionary assumptions.12, 13 Thus, the usual supposed local, causal (i.e., its pharmacological activity, regardless of the absence of molecules of the substance) effects of a potentised homeopathic remedy are dropped. Instead, Walach adopts the semiotic notion that the homeopathic remedy is a ‘sign’ working simultaneously in and for two different but connected meaningful contexts: 1) the symptoms of a sick person signify a certain disease state (first meaningful context), while simultaneously signifying, 2) a homeopathic remedy in the materia medica (second meaningful context), the two contexts of illness and remedies being connected by the Law of Similars (Figure 1).
Figure 1. Walach’s double entanglement model: two semiotic contexts (triangles) linked by the Law of Similars. Left, object = remedy substance, R?; sign = remedy, Rx; meaning = remedy picture, i.e., symptoms produced during provings, Sx. Right, object = patient’s ‘disease’, Dx; sign = patient’s symptoms, Sx; meaning = required remedy, Rx.12, 13
Walach then uses WQT to demonstrate how semiosis illustrates homeopathy as two instances of generalised entanglement: one between the potentised remedy (Rx) and the original unpotentised substance (R?); the other between the individual symptoms of a patient and the general symptoms of the substance produced during homeopathic provings. This generalised double entanglement is thought to be analogous to the cryptographic and teleportation applications of ordinary quantum entanglement.21 Walach goes on to derive what he considers are testable predictions of his double entanglement model.