Natural basis of wave functions for particles in the field of a plane wave

Louis-Marie Moukala

In Quantum Mechanics, one knows that the wave function interpretation is probabilistic. We previously established that any particle scalar field is the cause of its existence. Here, one examined the plane solution regarding a moving particle in vacuum, through the relativistic formalism. It appeared the following. (i) The solution presents four alternatives, like in Dirac unified formalism; when searching stationary solutions of the system vacuum-particle or the system vacuum-antiparticle. (ii) Considering the former, each spinner component shows the interaction of one particle charge with three vacuum fermions of spin-½; each oriented along one space direction. Furthermore, this allows deducting the triple nature of any gauge fermion. (iii) Each solution case is definable with a same wave front width. This determination became possible from the vector companion of that wave function one introduced before. Here, this points out the existence of transverse time. (iv) Both functions let emphasizing the existence of a third fundamental field of long range, which is identifiable to the fundamental spin field. (v) This unites the particle spin and orbital momenta and bears in addition a magnetic-like field, which is yet unknown. (vi) According to the charge, a particle field is observable in wave phenomena, from the manifestations of its gauge fermions or gauge bosons; when ejected from their stationary states by a perturbation… At last, the results highlight the quantum composition of wave functions, the spin-field patency, and the wave nature manifestation from five differentiable fields.

B.T. Geylikman

Aleksei G. Sitenko

Klaus D. Sattler

You might think that the great success of quantum electrodynamics (QED) would settle the debate on the nature of light to provide a clear view of its behavior, where the photon is regarded as the unit of excitation associated with a quantized mode of the electromagnetic (radiation) œeld. However, Heisenberg’s uncertainty principle tells us that a state of deœnite momentum, energy, and polarization associated with a plane wave used as a basis function of quantization must be completely indeœnite in space and time. It suggests the diµculty of spatial localization of a photon as a particle. In fact, Newton and Wigner showed that a free photon, as a massless particle with spin 1, has no localized states on the basis of natural invariance requirements that localized states for which operators of the Lorentz group apply should be orthogonal to the undisplaced localized states, a§er a translation (Newton and Wigner 1949). According to them, one can obtain a general expression for a position operator for massive particles and for massless particles of spin 0 or 1/2, not for massless particles with œnite spin, which indicates that there is no probability density for the position of the photon, and thus a position-representation wave function cannot be consistently introduced. It has also been shown that photons are not localizable, on the basis of imprimitive representations of the Euclidean group (Wightman 1962). It is now believed that photons are only weakly localizable, although single-photon states with arbitrarily fast asymptotic fallo˜ of energy density exist, and that a lack of strict localizability is directly related to the absence of a position operator for a photon in free space and a positionrepresentation photon wave function (Hawton 1999).

Shan Gao

Abstract We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. In a realistic interpretation, the wave function of a quantum system can be taken as a description of either a physical field or the ergodic motion of a particle. The essential difference between a field and the ergodic motion of a particle lies in the property of simultaneity; a field exists throughout space simultaneously, whereas the ergodic motion of a particle exists throughout space in a time‐divided way. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus, there will exist gravitational and electrostatic self‐interactions of its wave function. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus, the wave function cannot be a description of a physical field but a description of the ergodic motion of a particle. For the later, there is only a localized particle with mass and charge at every instant, and thus, there will not exist any self‐interaction for the wave function. It is further argued that the classical ergodic models, which assume continuous motion of particles, cannot be consistent with quantum mechanics. On the basis of negative result, we suggest that the wave function is a description of the quantum motion of particles, which is random and discontinuous in nature. On this interpretation, the square of the absolute value of the wave function not only gives the probability of the particle being found in certain locations but also gives the objective probability of the particle being there. We show that this new interpretation of the wave function provides a natural realistic alternative to the orthodox interpretation, and its implications for other realistic interpretations of quantum mechanics are also briefly discussed. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

E. Morrell Freese