Alexandre V. Boukalov
The quantum-mechanical approach under the description of the small-concentration effect
The physic-chemical and medical effects of the ultra-small (1:1020…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.
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
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 :
The solution and shaking after every dilution provide the interaction of the liquid and substance, which gives the following function on the whole system:
The correspondent elementary statistical matrix has the following form:
Here pk 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 .
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:
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. This «chemical field» in solvent, which acts as a neutral vacuum, contains the information about the soluted matter.
According to the uncertainty relation the homeopathy preparation action is increases with the dilution rising D10000 (10-10000) and more . 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. The total system wave function under the interaction of the diluted solution with organism or any other substance will have the following form:
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.
 The homeopathy solutions action on the nerve tissue was studied by I.M.Sechenov with the usage of the objective methods. According to the reports of different researchers the homeopathy solutions have the changed spectral characteristics compared to the pure water. For these solutions it is also observed the changes in the form and character of the glow under the Kirlian effect and microwave fields.
 Do not confuse with the phasing operator which does not exist .
 From this point of view it is possible to consider the relativity vacuum, including the zero states of the electroweak, quark-gluon, electron-positron and other fields such as the specific “relativity solution” in which these fields were “soluted” and dynamized under the Great Explosion with the following Universe expansion.
 The medicine effect realizes rather even under the dilution till D10000 (10-10000) and more .
 The single preparation usage with a high or superhigh (10-10000 and higher) dilution is considered as an ideal case .
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