Comment on: “Conspicuous by its absence: the Memory of Water, macro-entanglement, and the possibility of homeopathy” and “The nature of the active ingredient in ultramolecular dilutions”

Sir,

The two central problems of homeopathy are the absence of studies that clearly demonstrate the superiority of homeopathic remedies over placebos in randomized, controlled double-blind trials (RCT) and the implausibility of the claim that dilutions beyond Avogadro's limit can have any specific effect linked to the properties of the original substance. While the first problem is located within the domain of the medical sciences, the second is much more fundamental and, if solved to the satisfaction of the adherents of homeopathy, probably will revolutionize physics. With this in mind, the decision of the editor of “Homeopathy” to focus on the key issue of the Memory of Water and to invite contributions from proponents and critics of this idea has to be applauded.

Since it has been well established that neither classical nor quantum mechanics (QM) offer a plausible explanation for the alleged specific effects of high dilutions, it seems logical enough to look for alternative physical theories to explain this effect. Most prominent in this line of thought is “Weak Quantum Theory” (WQT).[ ¹ ] Based on WQT, both Walach,[ ² ] Weingärtner[ ³ ] and Milgrom[ ⁴ ] have developed models of homeopathy. I have criticized Walach's model previously[ ⁵ ]; Weingärtner's and Milgrom's models essentially have the same flaws as Walach's.

First and foremost, it is not at all clear whether there is something to explain. Walach, Weingärtner and Milgrom take the “fact” that high potencies have specific effects for granted. Thus, the real test of these models is not whether they explain previously known features of homeopathy, but whether they can be used to improve the design of experimental tests of homeopathy's core hypothesis that high dilutions are different from appropriately prepared placebos. Unfortunately, all three models fail this test. Walach argues that due to entanglement, “clinical trials […] are a bad investment of time, money and effort”[ ⁶ ]; Milgrom asserts that “[…] 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”.[ ⁴ ] However, if the gold-standard of evidence-based medicine (randomized, double-blind trials) is rejected, another way to account for the (surprisingly powerful!) placebo effect needs to be proposed. None of the suggested methods—essentially, trials with lower standards of placebo control,[ ^2,6 ]—would impress critics in the event of a positive outcome.

Second, while WQT itself is a legitimate mathematical framework for scientific theories, its application to homeopathy relies on leaps of faith and unconvincing analogies to proper quantum mechanics. The basic idea of WQT is to use mathematical models similar to algebraic quantum theory to describe a wide range of phenomena (not restricted to physics; see Ref.[ ⁷ ] for an interesting example from the realm of psychology). But, as even one of the authors of the original WQT article concedes, “it has yet to be determined whether homeopathy is a good application of generalized quantum theory”.[ ⁸ ] The most striking difference between the WQT models of homeopathy and proper QM concerns the use of mathematics. While QM has always relied heavily on mathematics and impressed even its most prominent critics by its ability to predict the results of experiments with unmatched precision, and while WQT is defined as a set of mathematical axioms, mathematics are conspicuous by their absence in the WQT models of homeopathy!

The crucial feature of quantum mechanics that needs to be generalized for the WQT models of homeopathy is entanglement. As there are no clear and unambiguous (mathematical) definitions of the relevant systems, states and operators, the proponents of these models speculate freely about the properties of their entangled states. The fact that entanglement is easily destroyed in proper quantum mechanics is used to explain the failure of homeopathy in RCTs, as the blinding procedure is thought to “[…] ‘collapse’ the three-way patient-practitioner-remedy entangled state in a way analogous to that by which observation collapses a particle's wave function […]”.[ ⁴ ] The fragility of entangled states would seem to indicate that great care needs to be taken in the preparation, storage and administration of the homeopathic remedies, but this concern is only discussed in the case of the “homeopathic ritual”[ ² ] (preparation). Finally, what is typically referred to as an entangled state in quantum mechanics is a maximally entangled state. If the homeopathic remedy and the set of symptoms are entangled, how is it that there are no limits on the potencies of homeopathic remedies? And how is it that two so fundamentally different concepts as a remedy (a material object) and a collection of symptoms (an abstract idea generalized from individual observations) can be entangled at all? Proper quantum entanglement is only possible if all parts of the system have common properties that can be described within the same mathematical framework.

Surprisingly, positive outcomes of RCTs can also be used to confirm the WQT models, as “[…] some trials of non-individualised homeopathic remedies have generated positive results [which] could be due to some surviving relic of entanglement from the production process […]”.[ ⁴ ]

As a side note, the apparent understanding of quantum physics of Walach, Weingärtner or particularly Milgrom does not inspire much confidence. From various papers, Daniel Chrastina has compiled a list of errors and inaccuracies on his blog,[ ⁹ ] some of which may be trivial, some of which would shame a second year physics student (such as the claim that quantum mechanics is non-deterministic or giving the units of Planck's constant as [J/s] in Ref.[ ¹⁰ ]). Continuing in this vein, it should not go unnoticed that regarding WQT, Milgrom writes “Complementarity and indeterminacy are epistemological in origin not ontological”,[ ⁴ ] which is a serious misquote of the original paper, where it says that “[…] there is no way to argue that complementarity and indeterminacy in weak quantum theory are of ontic rather than epistemic nature.[…] one would expect them to be of rather innocent epistemic origin in many cases.”[ ¹ ] The difference between the two versions cannot be emphasized enough, as quantum effects such as entanglement are due to the ontic nature (ie not simply to our incomplete knowledge) of complementarity and indeterminacy! In classical physics or in daily life, there are trivial—epistemological—examples of “entanglement”. For example, two identical candles being lit at the same time and then separated will still burn at the same rate. Thus, an observation of one candle also reveals the state of the other one. But this epistemological kind of entanglement is too trivial for Walach's or Milgrom's models of homeopathy, as it lacks many of the required features.

To summarize the above criticisms, it can be concluded that in their present states, the proposed applications of Weak Quantum Theory to the problem of ultra-molecular dilutions in homeopathy are not science, but rhetoric. There is simply no compelling evidence suggesting that a generalized form of quantum entanglement might be a useful concept in the discussion of the mode of action of homeopathic remedies. Unfortunately, with vocabulary borrowed from physics, referenced journal articles and scholarly discussions, journalists and lay readers may get the impression that there is a controversy about or even a cutting-edge-physics explanation of the mechanisms behind the action of ultra-high dilutions.

• References

• 1 Atmanspacher H., Römer H., Walach H. Weak quantum theory: complementarity and entanglement in physics and beyond . Found Phys 2002; 32 (03)  
• 2 Walach H. Entanglement model of homeopathy as an example of generalized entanglement predicted by weak quantum theory. Forsch Komplementärmedizin Klassische Nat 2003; 10:  
• 3 Weingärtner O. The nature of the active ingredient in ultramolecular dilutions. Homeopathy 2007; 96: 220-226.
• 4 Milgrom L.R. Conspicuous by its absence: the memory of water, macro-entanglement, and the possibility of homeopathy. Homeopathy 2007; 96: 209-219.
• 5 Leick P. Die “schwache Quantentheorie” und die Homöopathie, Skeptiker 3/06 (in German).
• 6 Walach H. Reinventing the wheel will not make it rounder: controlled trials of homeopathy reconsidered. J Altern Complem Med 2003; 9 (01) 7-13.
• 7 Atmanspacher H., Filk T., Römer H. Quantum zeno features of bistable perception. Biol Cybern 2004; 90: 33-40.
• 8 Römer H, Leick P. Letters to the editor, Skeptiker 4/06 (in German).
• 9 Chrastina D. ⟨ http://shpalman.livejournal.com/tag/lionel+milgrom⟩, accessed 30.09.2007.
• 10 Milgrom L.R. Journeys in the country of the blind: entanglement theory and the effects of blinding on trials of homeopathy and homeopathic provings. Evidence-Based Complem Altern Med 2007; 4 (01) 7-16.