_{1}

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Theoretical and experimental evidences of a causal relation of the phase of the wave function and physical reality are presented. The Copenhagen interpretation of quantum mechanics, which gives physical meaning to the amplitude of the wave function only, cannot be considered complete on that ground. A new dynamics-statistical interpretation of quantum mechanics is proposed.

The quantum mechanics appears to be the most successful theory of physical reality at a microscopic level. Nevertheless, it is a subject of intensive debates mainly in the field of interpretation. The physical state in quantum mechanics is described not by a definite number of dynamical variables, coordinates, linear momenta, etc., as in the classical mechanics, but by an abstract quantity―the wave function. Although it describes the state of localized physical objects, i.e., particle or system of particles, the wave function (quantum state) is distributed in space as for the continuous objects, i.e., waves. Thus, particle-wave duality or locality versus non-locality is built in the foundations of quantum mechanics. The description of the state of a localized physical object by a substantially non-local quantity―the wave function, does not have an analog in the classical physics. That is why, the physical meaning of the wave function is not obvious and its relation to physical reality is a fundamental problem.

Since Einstein’s belief that “God does not play dice” was not adopted, the Copenhagen probabilistic interpretation has been widely accepted. It, however, still remains unsatisfactory for part of the physicists and a number of alternative interpretations have been proposed. The Copenhagen interpretation attributes probabilistic physical meaning to the amplitude of the wave function only, while its (dynamical) phase, hereafter referred to as material phase (MP), is considered, in principle, as unobservable. Occasionally, the phase difference is considered concerning mainly the interference phenomena but not the interpretation of quantum mechanics. Thus, the role of the MP is neglected or, at least, strongly underestimated in the standard quantum mechanics. Einstein, Podolsky, and Rosen (EPR) attempted to show in a gedanken experiment that the quantum mechanics is an incomplete theory and the quantum phenomena can be completely specified in terms of hidden variables [

The basic arguments in support of MP causality will be classified as: special theoretical arguments, general theoretical arguments, and experimental evidences.

The problem of MP causality is treated here within an analytic solution of the time dependent Schrödinger equation. To reveal the MP dynamics, the quantum system is involved in a definite physical process, in our case, interaction with electromagnetic field and environment (damping), described by the Hamiltonian

nonadiabatic dressed states (PSNADSs) [

excited

where Φ_{GR}, Φ_{GV}, Φ_{ER}, Φ_{EV} are the total MPs of the respective states, and

where

tial phases of the bare states,

The MP dynamics can be understood from a causal point of view based on the expressions for MP, Equations (1). Starting from

_{g} of _{GR} of_{GV} of the virtual component _{GR} of the real component _{F}. At the same time, physically, the virtual component of the ground state results from the real component of the ground state by a temporal association and reemission of one photon from the electromagnetic field. In the formation of _{ER} of the real component _{GV} of the virtual component _{NAD} acquired while the quantum system “overcomes” the frequency detuning_{EV} of the virtual component _{ER} of the real component _{F}. Physically, the virtual component of the excited state results from the real component of the excited state by a temporal emission and reabsorption of one photon from the quantum system. Similar behavior takes place at excited state initial condition or

The causal relation of the MP with the physical reality can be proved by general theoretical arguments. In polar representation, the wave function

Equations (2) and (3) constitute hydrodynamic representation of quantum mechanics. It is exploited by D. Bohm [

Such

Experimental confirmations of MP causality can be found in various fields of physics. Some of the most convincing results will be shortly summarized below, subject to a careful inspection, because the experiments were not particularly designed to study the MP causality. Interference of matter waves is a basic quantum mechanical phenomenon. The general outcome of mater wave experiments is that change of the MP affects the interference picture from matter waves and it can be observed experimentally. The phase sensitive experiments can be put into experiments with bound intraatomic/intramolecular wave-packets and experiments with free wave-packets.

The first case can be distinguished in an analog of Young’s double slit interferometer within an atom [

The interference of free particles (atoms, molecules, etc.) [

The special theoretical arguments reveal the MP behavior of a quantum system involved in an electromagnetic interaction. The general theoretical arguments and the experimental evidences have, to our opinion, a power of proof for the MP causality. Thus, the fundamental relation of the MP with the physical reality appears to be conclusively established on that ground. That relation is not consistent with the Copenhagen interpretation as well as with non-Copenhagen interpretations proposed so far. It suggests another interpretation of quantum mechanics.

The coupled Equations (2) and (3) play crucial role to understand what is actually founded in the quantum mechanics. The wave function is a complex construct from amplitude and phase. The action/phase

Theoretical and experimental evidences for existence of a fundamental relation of the phase of the wave function and the physical reality are presented. The wave function does not have a definite physical meaning but each of its elements, amplitude and phase, are causally related with the physical reality. The phase of the wave function is primarily related to the dynamics of the quantum system, influenced statistically by the amplitude. The amplitude of the wave function is primarily related to the statistical properties of the quantum system, influenced dynamically by the phase. A new dynamics-statistical interpretation of quantum mechanics is introduced on that ground.

Ivan GeorgievKoprinkov, (2016) Causality of Phase of Wave Function or Can Copenhagen Interpretation of Quantum Mechanics Be Considered Complete?. Journal of Modern Physics,07,390-394. doi: 10.4236/jmp.2016.74039