On high dilution experiments.

"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. (1948). "Space-Time Approach to Non-Relativistic Quantum Mechanics" Reviews of Modern Physics 20(2).

Abstract:

The physical and methodological issues underlying Jacques Benveniste's experiments on high dilutions are considered. The inadequacies of the standard theoretical objections are investigated and a simple theoretical model based on recent ideas from quantum computing is proposed.

1. The issue

In 1988, a research group led by Jacques Benveniste published an article in Nature describing the results of an experiment, triggering what may be remembered as the "memory of water controversy". (1)

The experiment conducted may be schematically described as follows: An aqueous solution of an antibody was diluted with water in a container. Water was added, the solution was shaken and the excess thrown away. This process was repeated 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 the paper's authors, was positive.

A commission, led by Nature's editor John Maddox and including stage-magician James Randi and experimental critic Walter Stewart, visited Dr. Benveniste's laboratory and decided that the experiments were flawed and the results impossible in the light of accepted scientific knowledge. We propose here a simple theoretical model that may account for the effects observed. A passing knowledge of the content of is assumed. (1)

2. Experimental aspects.

Before tackling the theoretical issues underlying the experiments some remarks about the replicability of the results are in order. (1) It has been claimed that the results have never been independently replicated. (1,2) This claim is debatable. In particular it is worth examining the article by Hirst, et al., which appeared in Nature in 1993, where a replication of the experiments is attempted and whose conclusions vehemently reject the validity of it. (1,3)

Hirst, et al., is a very peculiar scientific paper. It is rare to find, in a journal of Nature's renown, a scientific article attributing all the results that are incompatible with its overall conclusions to unidentified systematic flaws in its own experiments. It is also rare to find a scientific article dismissing its own statistical data above the significance threshold as due to "chance". Indeed, despite its overall conclusions, if taken seriously the paper's content appears to provide independent confirmation to the main claims made in Benveniste's original article , except that no recursive degranulation waves are recognizable. The value p=0.0027 in Table 2 of Hirst, et &al, refers to the chance that experimental data are random, under the assumption that there is no difference between succussed high dilutions and control treatment. This may be reformulated as saying that the experimental data confirm within a 99.7% level of confidence that there is a difference between succussed high dilutions and control treatment. Such a claim is at the core of Jacques Benveniste's work and is rejected by his critics. Moreover the value p=0.086, again in Table 2, may suggest that degranulation is induced even by unsuccussed high dilutions, so that succussion appears only to strengthen the effect observed in1, not to cause it. We will touch upon this point again. (1)

As a matter of fact the authors of Hirst et al., explicitly acknowledge through the null-hypothesis that there is no difference between both succussed and unsuccussed highly dilutions solutions and placebo is incompatible with their data. Indeed they state (p.527) that "according to conventional scientific theory, there should be no differences within a session between the control treatment and the eight high-dilution treatments.... This is not the case". The authors, however, attribute this striking inconsistency to unknown causes.

Although no definitive independent confirmation of the results is available, it is difficult to see how the data may warrant their dismissal as pure artifacts. (1,2)

3. The theoretical objection

The main theoretical objection that has been raised against Benveniste's claims is simple. It is eloquently explained in Nature's editorial note: "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 there being a single molecule in any sample". (1)

In other words, the objection is that, in all likelihood, no molecule is left in the solution sample after dilution. If no molecule is left, then nothing is left and there can be no effect. The objection is based on the assumption that at any moment either there is at least one molecule left or there is none.

The starting point of the further considerations in this article is a critique of the above objection. According to quantum mechanics, a system subsists 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 this is the result of a series of measurements. Without 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 are testably false.

In the experiment described, the authors 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. It should be stressed that that these considerations arise from an absolutely standard interpretation of quantum systems. If the wave function in the Schrodinger equation encodes all the information about the system, then there is no way to define molecules' positions without measurement. (1)

The objection exposed in Nature's editorial note may be reformulated in terms of the support of the molecule's wave-packet. 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 container's 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.

It might also be argued that the wave-packets of relatively massive objects, such as antibody molecules, do not undergo any noticeable dispersion. This point of view is apparently widespread. It is also erroneous.

Macroscopic delocalization of relatively massive objects, such as rubidium atoms, has been experimentally verified. (4) The idea underlying the above objection is that the spread in an object's wave-packet is induced by Heisenberg's indeterminacy principle, so that the wavepacket of massive objects will barely spread. Heisenberg's principle provides indeed a lower bound for the spread of an object's wave-packet, but no upper bound. The actual spread of an object is wave-packet is determined by the relevant Schrodinger equation and it has in principle no a-priori upper bound. The insidious misunderstanding at the core of the objection has been definitively dispelled by the experimental results. (3) The inconsistency of the objection is also apparent once one analyzes the Schrodinger equations governing the maser. What is usually referred to as "the a molecules at different energy levels moving apart" is in reality a macroscopic spatial elongation of the molecules' wave-packet, where the upper energy states move in one direction, the lower energy states in the other, the molecules subsisting as superpositions of their upper and lower energy states.

Our conclusion is that, while it is true that there is a negligible chance of an appropriate measurement revealing a single molecule in any sample, the assumption that at any moment either there is at least one molecule left or there is none is basically meaningless.

4. A theoretical model: resonance, basophils and succussion.

Several theoretical models have been proposed to account for the results. (1,3) The model proposed here can, in principle, be experimentally tested against at least some of them.

We conjecture, based on our previous considerations, that the antibody's wave-packet will be spread across different samples. The antibody's amplitude in any sample being extremely thin, the problem is to clarify how a small perturbation of the null-state may trigger the basophils' response.

Among all the possible space-time paths of the aqueous solution there is a subset, a very small one, that leads to a state where at least one antibody molecule will be measured in the selected sample. This is the same as saying that there is a very small probability that an antibody molecule may actually be measured in a selected sample at the end of Benveniste's experiment. At least in principle for this subset, the results can be reconciled with the objections that have been raised. (1)

The subset is very small. This is the problem, which in Nature's editorial note is formulated as the solution being "diluted to such an extent that there is a negligible chance of there being a single molecule in any sample". The key question is whether the probability of the basophils reacting to the antibody's presence needs to be equally small. According to the model exposed here the answer is no. The impact of the very small amplitude may be amplified by an appropriate resonant device.

The system is governed by a Schrodinger equation whose Hamiltonian contains an interaction term between basophils and antibody, which we may assume to be null if there is no antibody amplitude in the sample. The interaction term induces a transition probability between the unperturbed states of the basophils and the state where they will degranulate. We can reasonably assume that the basophils rely on sensors, i.e. appropriate molecules, to detect the presence of the antibody.

The presence of the antibody amplitude will be detected by the sensors, which will switch on an activated state corresponding to the presence of the antibody. The amplitude of the activated state will be commensurate to the amplitude of the antibody in the sample, i.e., very small. In other words the presence of the antibody amplitude induces a switch in the sensor's state, from an unperturbed state |a> to superposition kA>+r|b>, where |b> is an excited state induced by the antibody, the module of r being very small, equal to the probability that antibody molecules may actually be measured in the sample.

The point now is that the amplitude of the excited states of the basophils' sensors may be boosted by an appropriate resonance mechanism. This means that once the excited amplitude is triggered by the antibody's amplitude, it may be pumped up by an appropriate resonant device. Resonance may boost the impact of a small amplitude.

An instance of such a device, the discrete Fourier transform, is at the core of Shor's algorithm, on which the most recent developments in quantum computing are based. (5) Actually the considerations exposed here were originally inspired by Shor's algorithm. The mechanism on which the basophils rely to detect the antibody's presence may be analogous to the device underlying Shor's algorithm or to the Grover algorithm for databank search, which is also based on Shor's ideas.

In this framework the need to shake the solution is clear, since the turbulent mixing induces spreading and filamentation of the antibody's amplitude through interaction with other molecules' amplitudes.

Without shaking the amplitude may remain confined in a small region of the solution and fail to affect the basophils' sensors or affect them in a barely perceptible way. This might account for the weaker but still perceptible effect observed in unsuccussed high dilutions. (1)

From a heuristic point of view it is convenient to visualize the antibody's amplitude as a continuum of weighted copies of the antibody's molecule, dispersing and interacting with the water molecules' amplitudes. The amplitude is then spread around by turbulent mixing. The basic assumption here is that the antibody molecule will undergo scattering induced by prolonged interaction with water molecules.

Since we are not able to write down the Hamiltonian for the aqueous solution, the above "explanation" is highly speculative, the basic idea being that the sensors pick up the small antibody amplitude and then act on it as quantum computers, implementing a procedure of the type

If an amplitude of type A is detected, THEN trigger macroscopic reaction R where "type A" may be characterized by a condition such as that in Grover's algorithm, i.e., F(A)=0 for an a appropriate functional F.

As speculative as this assumption may be, the role of basophils is precisely to detect the presence of antibodies and react accordingly. The idea that they may rely on a quantum mechanical device to implement their existential function seems fairly natural.

It is worth noting that, once one accepts that the effect described in Benveniste's paper is real, the model described here may be experimentally tested against the hypothesis of residual molecular order of the water molecules, based on the theory of "coherent domains", which has been proposed to explain the persistence of the antibody's action. (6)

The experiment would schematically go as follows: Asingle antibody molecule would be put in a bottle of water. After appropriately shaking the bottle, the water would be poured into two samples A and B.

According to the results, both samples A and B would induce basophils' degranulation, i.e., reveal the antibody's presence. (1) Sample A would then be physically or chemically tested for the presence of the molecule. This would amount to a quantum measurement of the antibody molecule's position and would therefore induce the reduction of the molecule's wave-packet. If the antibody molecule is localized in A, then according to the model described above no antibody amplitude would be left in B and therefore the basophils there would not degranulate. If the effect was due to molecular order, however, B would be unaffected and the basophils there would degranulate.

It may be appropriate to point out that some aspects of the results remain problematic for the model proposed here. According to the results, basophils will degranulate in a solution that has been filtered so as too sieve any antibody molecule out. It appears likely that such a filtering would eliminate the antibody amplitude from the sample, unless one assumes that tunneling takes place across the filter. Also the recursive degranulation waves reported remain unexplained by the model proposed here. (1)

Acknowledgements:

I would like to thank Dr. Ekaterina Gibiansky for some interesting exchanges about this topic and Prof. Brian Josephson for some critical remarks.

References

(1.) Davenas et al. (1988). Human basophil degranulation triggered by very dilute antiserum against IgE. Nature, 333, 816-818.

(2.) Park, R.L. (1997). Alternative medicine and the laws of physics. Skeptical Enquirer, September/October.

(3.) Hirst, S. J. et al. (1993). Human basophil degranulation is not triggrered by very dilute antiserum against IgE. Nature, 366, 525-527.

(4.), Durr S. et al. (1998). Origins of quantum-mechanical complementarity probed by a 'which way' experiment in an atom interferometer. Nature, 395, 33-37.

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

(6.) Preparta, G. (1995). QED Coherence in Matter, Chapter 10: Dynamics and Thermodinamics of Water. Singapore: World Scientific.ate

Italo Vecchi, Dr.rer.nat.

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