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Physical Science International Journal

Fermi Problem and Superluminal Signals in Quantum Electrodynamics

B. A. Veklenko

Published Jan 10, 2016• 0 citations
Publisher

Abstract

Using as an example the Fermi problem dealing with nonstationary transformation of optical excitation from one atom to another the reason of superluminal signals appearance in quantum electrodynamics is clearing.It is shown that the calculation using the conventional methods in Heisenberg and Schrödinger representations in nonstationary problems lead to different results.The Schrödinger representation predicts the existents of specified quantum superluminal signals.In Heisenberg representation the superluminal signals are absent.The reason of non-identity of representations is close connected with using of the adiabatic hypothesis.

DOI
10.9734/psij/2016/26143

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Using as an example the Fermi problem dealing with nonstationary transformation of optical excitation from one atom to another the reason of superluminal signals appearance in quantum electrodynamics is clearing.It is shown that the calculation using the conventional methods in Heisenberg and Schrödinger representations in nonstationary problems lead to different results.The Schrödinger representation predicts the existents of specified quantum superluminal signals.In Heisenberg representation the superluminal signals are absent.The reason of non-identity of representations is close connected with using of the adiabatic hypothesis.
In quantum electrodynamics one can obtain a Hamiltonian which gives reasonable field equations in the Heisenberg picture, but which does not allow of solutions of the wave equation to represent physical states in the Schr\"odinger picture. The inference is that the Heisenberg picture is a good picture, the Schr\"odinger picture is a bad picture, and the two pictures are not equivalent. The usual proof of the equivalence of the two pictures fails because the state vector of the Schr\"odinger picture does not remain in Hilbert space. One can set up quantum electrodynamics entirely in the Heisenberg picture and thereby avoid the worst difficulties encountered in the Schr\"odinger picture. The theory takes a logical form and is not merely an assembly of working rules. It can be applied to the calculation of the anomalous magnetic moment and the Lamb shift, and is then similar to the usual calculations of these effects, with a good deal of dead wood cut away. There is a problem concerned with the general interpretation of quantum mechanics when one cannot use the Schr\"odinger picture and some postulates are proposed for dealing with it.
The field of scalar and vector potentials in electrodynamics is shown to represent an informational field capable of superluminally transmitting a signal (information) with no energy and momentum transfer. This conclusion strictly follows from Maxwell's equations for electromagnetic field interacting with electric charges and currents in vacuum, without resort to any additional hypotheses. That superluminal communication is possible is seen from the fact that the own field, generated by particles and inseparable from them, transforms the environment into a special physical medium which is capable to instantaneously transfer a signal (information) about any changes, happening to a particle in the region of its basic localization, to arbitrarily large distances. The phenomenon of superluminal communication is caused by the non-local connection of scalar and vector potentials with the electric and magnetic field strengths. The basis for the mechanism of superluminal communication considered in this work is the Aharonov-Bohm effect indicative of the field of electromagnetic potentials as a real physical field, which directly influences the behaviour of electron waves. The conclusion is made that in quantum systems superluminal signals occur constantly, in any quantum processes. The occurrence of superluminal signals is due to the space-time symmetry breaking of a special kind, consisting in that the equations for potentials do not possess relativistic invariance though Maxwell's equations for the field strengths are Lorentz-invariant. The results presented do not contradict the physical principles underlying special relativity and confirm the fundamental conclusion, made for the first time by de Broglie, that gauge invariance is not an absolute law in physics
Nonlinear modifications of quantum mechanics have a troubled history. They were initially studied for many promising reasons: resolving the measurement problem, testing the limits of standard quantum mechanics, and reconciling it with gravity. Two results substantially undermined the credibility of non-linear theories. Some have been experimentally refuted, and more importantly, all deterministic non-linear theories can be used for superluminal communication. However, these results are unconvincing because they overlook the fact that the distribution of measurement results predicted by non-linear quantum mechanics depends on the interpretation of quantum mechanics that one uses. For instance, although the Everett and Copenhagen interpretations agree on the expression of Born's rule for the outcomes of multiple measurements in linear quantum mechanics, they disagree in non-linear quantum mechanics. We present the range of expressions of Born's rule that can be obtained by applying different formulations of quantum mechanics to a class of non-linear quantum theories. We then determine that many do not allow for superluminal communication but only two seem to have a reasonable justification. The first is the Everett interpretation, and the second, which we name causal-conditional, states that a measurement broadcasts its outcome to degrees of freedom in its future light-cone, who update the wavefunction that their non-linear Hamiltonian depends on according to this new information.
The form of quantum theory of reaiation introdnced by Heiaonbarg is diarnaaed from the point of view of the transformation theory of quantum electrodynamics.A general investigation of the connection between Heisenberg's method and Dirac'smethod of variation of parameters is given.The exetension of Heisenberg's methodto eigenvalue problems.which was first carried out by Weissklpf for the self energyof the electron.is presented in such a way as to show more clearly its quantummechanical interpretation.Ageneral proof of the equivalence of We jsskopf's me-tbod and the method of the perturbation theory of stationary stntes in quantumicechanics is given.
Evanescent modes or the tunnelling process are characterized by an imaginary wave number. These special solutions of the Helmholtz and of the Schrödinger equations first noticed in connection with the total reflection were said to have no physical meaning about 200 years ago. Last century the tunnelling problem in quantum mechanics has been described by the phase time approach. The phase time approach yields the group velocity of a wave packet (see e.g. Hartman, 1962). Nowadays the phase time approach is used in network analyzers to determine the group velocity of an electromagnetic wave in devices. We have reported about superluminal signal velocities in photonic tunnelling. It was observed that the superluminal photonic tunnelling time data measured in the time domain are in agreement with the calculated phase time data. This result is also in agreement with the definition of the barrier transition time given in the Federal Standard 1037 C (NTIA, USA 2000). Thus we have added further credibility to the assumption that the photonic tunnelling results are representative for quantum mechanical tunnelling of particles.