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Homeopathy

Quasi-quantum model of potentization

Marcin Molski

Published Sep 29, 2011• 11 citations
Publisher

Abstract

Analytical time-dependent functions describing the change of the concentration of the solvent S(t) and the homeopathic active substance A(t) during decimal and centesimal dilution are derived. The function S(t) is a special case of the West-Brown-Enquist curve describing ontogenic growth, the increase in concentration of the solvent during potentization resembles the growth of biological systems. It is demonstrated that the macroscopic S(t) function is the ground state solution of the microscopic non-local Horodecki-Feinberg equation for the time-dependent Hulthèn potential at the critical screening. In consequence potentization belongs to the class of quasi-quantum phenomena playing an important role both in biological systems and homeopathy. A comparison of the results predicted by the model proposed with the results of experiments on delayed luminescence of a homeopathic medicine is made.

DOI
10.1016/j.homp.2011.06.002

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Analytical time-dependent functions describing the change of the concentration of the solvent S(t) and the homeopathic active substance A(t) during decimal and centesimal dilution are derived. The function S(t) is a special case of the West-Brown-Enquist curve describing ontogenic growth, the increase in concentration of the solvent during potentization resembles the growth of biological systems. It is demonstrated that the macroscopic S(t) function is the ground state solution of the microscopic non-local Horodecki-Feinberg equation for the time-dependent Hulthèn potential at the critical screening. In consequence potentization belongs to the class of quasi-quantum phenomena playing an important role both in biological systems and homeopathy. A comparison of the results predicted by the model proposed with the results of experiments on delayed luminescence of a homeopathic medicine is made.
Analytical time-dependent functions describing the change of the concentration of the solvent S(t) and the homeopathic active substance A(t) during the decimal and centesimal dilution are derived. The function S(t) is a special case of the West-Brown-Enquist curve describing the ontogenic growth, hence the increase in concentration of the solvent during potentization resembles the growth of biological systems. It is proven that the macroscopic S(t) function is the ground state solution of the microscopic non-local Horodecki-Feinberg equation for the time-dependent Hulthen potential at the critical screening. In consequence the potentization belongs to the class of quasi-quantum phenomena playing an important role both in the biological systems and homeopathy. A comparison of the model proposed with recently performed experiment on delayed luminescence of the homeopathic remedy will be also made.
Homeopathy is scientifically banned, both for lack of consistent empirical findings, but more so for lack of a sound theoretical model to explain its purported effects. This paper makes an attempt to introduce an explanatory idea based on a generalized version of quantum mechanics (QM), the weak quantum theory (WQT). WQT uses the algebraic formalism of QM proper, but drops some restrictions and definitions typical for QM. This results in a general axiomatic framework similar to QM, but more generalized and applicable to all possible systems. Most notably, WQT predicts entanglement, which in QM is known as Einstein-Podolsky-Rosen (EPR) correlatedness within quantum systems. According to WQT, this entanglement is not only tied to quantum systems, but is to be expected whenever a global and a local variable describing a system are complementary. This idea is used here to reconstruct homeopathy as an exemplification of generalized entanglement as predicted by WQT. It transpires that homeopathy uses two instances of generalized entanglement: one between the remedy and the original substance (potentiation principle) and one between the individual symptoms of a patient and the general symptoms of a remedy picture (similarity principle). By bringing these two elements together, double entanglement ensues, which is reminiscent of cryptographic and teleportation applications of entanglement in QM proper. Homeopathy could be a macroscopic analogue to quantum teleportation. This model is exemplified and some predictions are derived, which make it possible to test the model.
A model of living systems considered as coherent, time-dependent anharmonic oscillators is presented. It is based on the concept of space-like coherent states minimizing the time-energy uncertainty relation, adapted to the case of biological systems whose growth is described by the Gompertz or West-Brown-Enquist functions. The coherent states of biological growth evolve coherently in space being localized along the classical time trajectory; hence, the growth is predicted to be coherent in space. It is proven that the Gompertz function is a special solution of the space-like Horodecki-Feinberg equation for the time-dependent Morse oscillator in the dissociation state. Its eigenvalue represents the momentum of biological growth, associated with a space-like component whose properties resemble those attributed by vitalists to the life momentum or vital impulse. The physical characteristics of the life energy and momentum and their connection with the concept of zero-point momentum of vacuum are presented.