Alexandre V. Boukalov

e-mail: boukalov@gmail.com
The Centre of Physical and Space Researches, International Institute of Socionics
"Physics of Consciousness and Life, Cosmology and Astrophysics" journal, issue 2, 2001 .

The quantum-mechanical approach under the description of the small-concentration effect

The physic-chemical and medical effects of the ultra-small (1:10^20…10000) concentrations of the substances, that are used in homeopathy, can be explained by the interaction of the wave functions of the substance and the solvent. As a result a new wave function appears, bringing information about dissolved substance when it is physically absent, which interacts with the wave functions of the alive organism or the biochemical preparations.
Key words: quantum mechanics, wave function of the solution, homeopathy.

It is known that one of the homeopathy methods of the drug preparation and usage consists of the used substance solution in the distilled water by the relation 1:10^20…10000 [7]. These relations ate used from XIX century [8]. Despite such great dissolution the solutions act as if they contain the medicine substance. Meanwhile the calculations show that under such dissolutions with the concentrations less then 10^-24 molecules/mole the used dole can include no one molecule of the substance. Although the effectivity of the homeopathy action on organism is known long ago, the physical explanation of this effect is not obtained yet. Meanwhile, many researchers in the physical chemistry and biochemistry branches discovered independently that the different substances solutions in some solvents with concentrations 1:10^17…126 conserves their reaction ability [2, 5][1]. Thus we deal with the general physical effect of small concentrations in the homeopathy phenomena without the respect to the certain liquid structure.

Let us analyse from the physical point of view the process of the homeopathy preparation production. Firstly, the substance is soluted, for example, in water, it is desirable in the distillated one, in order to exclude any additional influence. Secondly, the initial solution is diluted and obligatory shaked up. It is very important condition, if the solution is not shaked the cure effect will not be observed or it will be rather small compared with the waited one.

Now let us consider the interaction between the solved substance molecule with the water ones. As the memory property does not depend on the certain liquid structure, thus it refers to the general, whole properties, described by the wave function , which is the superposition of the liquid molecules states. The matter molecule also is described by some wave function , which really has the limited set if own states. The system wave function, describing the pure state of the whole system before the solution process, has a standard form [3]:
    (1)

The solution and shaking after every dilution provide the interaction of the liquid and substance, which gives the following function on the whole system:
    (2)

The correspondent elementary statistical matrix has the following form:
    (3)
whereas the matrixes of liquid and matter have the following forms:

    (4)
where
.

Here p_k and p_&pho; are the combined states of the liquid and matter, correspondingly. For the liquid system its combined state is determined by the matter state and vice versa. It means also that in the phase space the liquid has the matter structure «image» whereas the matter has the liquid structure one.

The following dilution and shaking are the reproduction of the same structure, described by the wave function (2). Actually, from the point of view of the quantum mechanics measurement the situation is just the following: the soluted molecule acts as a gauge by the reduction of the water wave function into one of its states. After this the liquid wave function in the phase space includes the matter symmetry. On its turn the matter wave function is reduced into the one of water states which occurred to be the fixed one due to the state reduction according to the shaking. Thus the water, reduced into the soluted matter own state, is in whole the delocalized matter. But the one variable quantum delocalization causes, from the uncertainty principle, the localization by another variable. The wave phase and the particles quantity can serve as the possible unticommutating variables. For example, for the electromagnetic field there are the permutation relations between the phase operator  [1].
    (5)
or
,     (6)
where C and S are the phase cosine and sine operators, C±iS=e^±iφ.

As the photons quantity operators and the cosine and sine ones do not commutate between themselves the mentioned quantities ate connected by the following relations:
ΔN·ΔC~ΔS, ΔN·ΔS~ΔC.     (7)

Thus the electromagnetic wave cannot be characterized by the certain proton number and phase [1, 6].

By analogy in the solution we cannot consider the quantum wave, connected with chemical matter, for which the similar relations arise. If one adheres the quantum fields ideology the solution has to be considered as the «zero vacuum state» of the soluted chemical matter, i. e. the «chemical vacuum field with specific symmetry, describing the soluted matter structure and, possible, connected with the correspondent periodical phase operator[2]. This «chemical field» in solvent, which acts as a neutral vacuum, contains the information about the soluted matter[3].

According to the uncertainty relation the homeopathy preparation action is increases with the dilution rising[4] D10000 (10^-10000) and more [4]. Besides it is usually observed that the preparation action has the periodical character in dependence of the dilution number and reachs the maximum under the 10³⁰, 10⁵⁰, 10⁷⁰... of the dilution degrees. Basing in our analysis it is possible to suppose that the similar periodical dependence is connected with the delocalized drug, presented by the subsystem of the solution wave function (2) and organism. The selected dilution degree provides the very sharp resonance[5]. The total system wave function under the interaction of the diluted solution with organism or any other substance will have the following form:
    (8)
where w_f(z) is the whole set of the own orthonormalized functions of system-3 which is an organism or any substance, playing the role of observer. This one interacts with the solution subsystem , which yields the mixture of the diluted substance, liquid and organism. The solvent is able not to act on organism whereas the mixture arising, including the medicine substance states, is analogous of this substance action on organism. The quantum character of the ultrasmall concentrations mechanism is provided by the fact that the homeopathy liquid solutions break of their influence in the temperatures range T_C>50–60ºС. This property is rather comparable with the quantum effects of superfluidity or superconductivity when the united wave function is destroyed under the critical temperature exceeding, T>T_C.

Besides the solution in a liquid the homeopathy practice also uncludes the acting substance introducing into a neutral powder. In this case, it is possible to consider the solid solution, presented by the separate grains of the substance. In this case, all the quantum regularities, obtained for a liquid, are valid as well.

Till now we have considered the single substance solution. But if a set if substances is soluted, the solution has to possess the analogous properties. It is possible that the homeopathy solution includes two substances, which usually react and it yields the third substance production, under the dynamization and in certain conditions it can be produced the mentioned third substance solution etc. However, it is possible to produce the similar “solution” not only of the ferments but also of the cell organoids or namely the cell in order that the solution can possess their properties? Besides it is possible to produce the structurization of water or neutral powder as a solid state by the different methods, not obligatory by the substance solution but using the electromagnetic or other fields, for example the ones, generated by human organism. We propose to carry out a number of experiments in this direction and the unexpectable results can be obtained.

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