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arXiv:1605.00844

Relativistic locality and the action reaction principle predict de Broglie fields

Lopez, Carlos

Published May 3, 2016• 0 citations
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Abstract

The action reaction principle is violated in the standard formulation of Quantum Mechanics, so that its phase space is incomplete. Moreover, projection of state of a quantum system under indirect measurement, when there are alternative virtual paths and one of them is discarded by negative detection implies, according to the action reaction principle, a reaction on the detector, although its macroscopic state does not change. If all interactions are local, mediated by fields with relativistically causal evolution, some system, different from the particle which follows another path, must locally interact with the detector. Relativistic locality and the action reaction principle predict the existence of de Broglie fields. A formulation of Quantum Mechanics in extended Hilbert spaces is presented, in which kinematic and dynamical representations of physical magnitudes are distinguished.

DOI
10.48550/arxiv.1605.00844

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The action reaction principle is violated in the standard formulation of Quantum Mechanics, so that its phase space is incomplete. Moreover, projection of state of a quantum system under indirect measurement, when there are alternative virtual paths and one of them is discarded by negative detection implies, according to the action reaction principle, a reaction on the detector, although its macroscopic state does not change. If all interactions are local, mediated by fields with relativistically causal evolution, some system, different from the particle which follows another path, must locally interact with the detector. Relativistic locality and the action reaction principle predict the existence of de Broglie fields. A formulation of Quantum Mechanics in extended Hilbert spaces is presented, in which kinematic and dynamical representations of physical magnitudes are distinguished.
The standard formulation of Quantum Mechanics violates locality of interactions and the action reaction principle. An alternative formulation in an extended phase space could preserve both principles, but Bell's theorems show that a distribution of probability in a space of local variables can not reproduce the quantum correlations. An extended phase space is defined in an alternative formulation of Quantum Mechanics. Quantum states are represented by a complex va\-lued distribution of amplitude, so that Bell's theorems do not apply.
The action reaction principle (ARP), a fundamental ingredient of Physics, is taken for granted, because it is automatically fulfilled along the ordinary Hamiltonian, classical or quantum, time evolution law. But in quantum mechanics, there is an extraordinary evolution law, the projection of state rule along quantum measurements, which is not Hamiltonian. Consequently, the ARP is not automatically fulfilled along quantum measurements, and it must be checked case by case. Surprisingly, very simple quantum measurements, both theoretical processes and experiments, show an apparent violation of the ARP, so that the hidden reaction must be found. In the analyzed experiment, the ARP is restored if some new system, the quantum or de Broglie wave, exists and locally interacts with the detector. There cannot be interaction at a spatial distance between the particle (photon or electron) and the obstacle‐detector.
A local interpretation of quantum mechanics is presented. Its main ingredients are: first, a label attached to one of the virtual paths in the path integral formalism, determining the output for measurement of position or momentum; second, a mathematical model for spin states, equivalent to the path integral formalism for point particles in space time, with the corresponding label. The mathematical machinery of orthodox quantum mechanics is maintained, in particular amplitudes of probability and Born's rule; therefore, Bell's type inequalities theorems do not apply. It is shown that statistical correlations for pairs of particles with entangled spins have a description completely equivalent to the two slit experiment, that is, interference (wave like behaviour) instead of non locality gives account of the process. The interpretation is grounded in the experimental evidence of a point like character of electrons, and in the hypothetical existence of a wave like, the de Broglie, companion system. A correspondence between the extended Hilbert spaces of hidden physical states and the orthodox quantum mechanical Hilbert space shows the mathematical equivalence of both theories. Paradoxical behaviour with respect to the action reaction principle is analysed, and an experimental set up, modified two slit experiment, proposed to look for the companion system.
This paper follows on from a previous one in which it was shown that it is possible, within a de Broglie-Bohm style ontology for quantum mechanics, to incorporate action and reaction between the particle and its guiding field while remaining consistent with the usual experimental predictions. Whereas the previous paper focussed on the Dirac equation, the present work addresses the Schrodinger case and demonstrates that the same two-way interaction can be achieved. The aim in each case is to increase the physical plausibility of such models. The transition to include the reaction of the particle back on the field, and hence energy and momentum conservation, is attained by employing standard Lagrangian techniques. In formulating this description an interesting bonus emerges in that the hitherto unrelated concept of a gauge transformation is found to arise naturally as an essential part of the formalism. In particular, the phase S of the gauge transformation is seen to be the action function describing the hidden motion of the particle.
There are many evidences in Quantum Mechanics about the existence of de Broglie waves: the two-slit experiment, self interference when a particle can follow two or more paths that converge, etc.There is not direct evidence of its existence because we use exclusively particle detectors.This paper presents a new evidence of the existence of de Broglie waves grounded in the action reaction principle.The action reaction principle is a fundamental ingredient of Physics: when two systems interact both change of state (i.e., they depart from the free, isolated evolution path in the phase space).A simple experiment using a Mach-Zehnder interferometer is analysed.A representation of the evolution in the phase space for different cases (isolated system and interaction with a detector) is shown.By applying the action reaction principle we show that some subsystem, different from the corpuscular photon, must follow one arm of the interferometer when we can infer that the photon follows the other arm.There cannot be interaction between the photodetector in one arm and the photon following the other arm.This new subsystem would be a distributed de Broglie wave.