The statistical wave function

Pedro, Leonardo

One attractive interpretation of quantum mechanics is the ensemble interpretation, where Quantum Mechanics merely describes a statistical ensemble of objects and not individual objects. But this interpretation does not address why the wave-function plays a central role in the calculations of probabilities, unlike most other interpretations of quantum mechanics. On the other hand, Classical Statistical Field Theory suffers from severe mathematical inconsistencies (specially for Hamiltonians which are non-polynomial in the fields, e.g. General relativistic statistical field theory). We claim that both problems are related to each other and we propose a solution to both. We prove: 1) the wave-function is a parametrization of any probability distribution of a statistical ensemble: there is a surjective map from an hypersphere to the set of all probability distributions; 2) for a quantum system defined in a 2-dimensional real Hilbert space, the role of the (2-dimensional real) wave-function is identical to the role of the Euler's formula in engineering, while the collapse of the wave-function is identical to selecting the real part of a complex number; 3) the collapse of the wave-function of any quantum system is a recursion of collapses of 2-dimensional real wave-functions; 4) the wave-function parametrization is key in the mathematical definition of Classical Statistical Field Theory we propose here. The same formalism is applied to Quantum Yang-Mills theory and Quantum Gravity in another article.

Alberto Galindo, P. Pascual

Yuri A. Rylov

It is shown that the wave function describes the state of the statistical ensemble E[S] of individual particles, or the statistical average particle . This result follows from the fact that in the classical limit h=0 the Schroedinger equation turns to the dynamic equations for the statistical ensemble of classical particles. The statement that the wave function describes the state of an individual particle is incompatible with the quantum mechanics formalism. It is shown that the statistical interpretation of quantum mechanics is a corollary of the fact, that the QM formalism is the technique of the statistical ensemble description, restricted by constraints of the dynamic equation linearity.

Tower Chen

The solution (wave function) of Schrodinger’s equation is used to describe the motion of a quantum. Max Born treated the square of the absolute value of the wave function as the probability of a quantum appearing at any given point. With this statistical interpretation of a wave function, the physical meaning of the whole quantum theory becomes clearer and more understandable. The development of wave function is based on the De Broglie’s postulate: there is a matter wave related to an object. If wave functions can be explained with the statistical interpretation, then matter waves could simi-larly be explained with statiscal interpretation. This assump-tion is confirmed by deriving the Heisenburg uncertainty rela-tion through mutilplying the matter wavelength of an object Concepts of Physics, Vol. III (2006) 1 with the light wavelength of measuring medium. This new approach may offer another view to look at the reality of M. Born’s statistical interpretation of the wave function solution of Schrodinger’s equation.