"The logical error consisted in assuming that to get from a to c the system had to go through a condition such that B had to have some definite value b." R.P. Feynman "Space-Time Approach to Non-Relativistic Quantum Mechanics" Reviews of Modern Physics 20, 2 (1948).

1. The issue

In the 1997 September/October issue of the Skeptical Inquirer one can read an interesting article ( "Alternative Medicine and the Laws of Physics") by Robert L. Park. Reading this paper I have become interested in what may be remembered as the Memory Of Water Controversy. After perusing the relevant papers published in Nature in 1988 I have found that a significant point appears to have been neglected.

I will first give a brief sketch of the events to which I am referring. In 1988 a research group led by Jacques Benveniste published a paper in Nature (333, 816; Davenas et al. ,1988) describing an experiment that may be briefly described as follows. An antibody was diluted with water in a container. Water was added, the solution was shaken and the excess thrown away. And so on until the solution was so diluted that, according to Nature's editorial note to the article, the chance that a single molecule of antibody would be left was very small. Then the solution was tested for properties related to the presence of the antibody. The result, according to Benveniste and his team, was positive. A commission led by Nature's editor John Maddox visited Benveniste's laboratory and decided that the experiments were flawed. The ensuing controversy was not placated by a subsequent article by Hirst et al. (Nature, 366, 525).

There is an obviously relevant issue that appears not to have been raised during the debate, at least not to my knowledge. Both in Nature's editorial note to Davenas et al. and in later remarks in Nature (333, 787; 1988) (334, 367;1988),(335, 760; 1988) it is claimed that, in all likelihood, no molecule is left in the solution sample after dilution. The claim is based on the assumption that at any moment either there is at least one molecule left or there is none.

I believe that such an assumption is based on a misunderstanding. According to quantum mechanics a system may subsist as a superposition until its wave packet is reduced by a measurement. What is observed is the result of a measurement. An antibody molecule can be observed and localized. But again this is the result of a series of measurements. Without an appropriate measurement there is no way to localize distinct molecules in the solution. Actually the assumption that any object has a well-defined position at any time leads to predictions that in some cases are testably false. In the experiment described in Davenas et al. Benveniste and his team do not conduct any measurement counting antibody molecules in the solution. It appears therefore arbitrary to assume that the antibody molecules' wave-packet is reduced so as to localize the molecules during the experiment. These considerations arise from an absolutely standard interpretation of quantum systems. If the wave function in the Schrödinger equation encodes all the information about the system, then there is no way to define molecules' positions without a position measurement.

It might be argued that the support of an antibody molecule's wave-packet cannot straddle different solution samples, because of the potential barriers associated to the containers' walls . The container's walls do indeed prevent the diffusion of the wave-packet, but they are not in place when the wave-packet may be spreading, before the solution is poured into the samples or thrown away. There is no reason to believe that the insertion of potential barriers will force the wave-packet to choose on which side of the wall it wants to subsist. An objection may be raised in terms of decoherence .It is worth noting, however, that decoherence does not destroy long-range quantum superpositions, but only limits the ability of an observer subject to the second principle of thermodynamics to keep track of such superpositions. Moreover superpositions that are arguably macroscopic have been detected ([1]) and decoherence theory has come under substantial criticism as a red herring (e.g. by Anthony Leggett, see also [2]).

My main point can be summed up as follows. The editorial note to Davenas et al. states that " the essence of the result is that an aqueous solution of an antibody retains its abilty to evoke a biological response even when diluted to such an extent that there is a negligible chance of there being a single molecule in any sample". The above statement is meaningless. It may be meaningfully replaced by the following: " the essence of the result is that an aqueous solution of an antibody retains its ability to evoke a biological response even when diluted to such an extent that there is a negligible chance of an appropriate measurement revealing a single molecule in any sample".

Moreover, the way relevant experimental results have been dealt with provides some insight in the dialectics of mainstream orthodoxy vs. deviancy.

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