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arXiv:2209.05343 · Communications in Theoretical Physics

Consequences of a two-time relativistic Bohmian model

Giuseppe Raguní

Published May 9, 2024• 0 citations
arXivHTMLPDF

Abstract

Abstract Effects of a Bohmian type quantum-relativistic theory are explored. The model is obtained by introducing a new and independent time parameter whose relative motions are not directly observable and cause quantum uncertainties of the physical observables. Unlike the usual de Broglie–Bohm theories, the Quantum Potential does not directly affect the observable motion, but determines the one that is relative to the new time variable. It turns out that the Zitterbewegung of a free particle, of which a more general law is obtained, is the key example of these hidden motions and, through it, it seems possible to give physical reality to the Feynman’s paths. A relativistic revision of the uncertainty principle is also derived from the theory.

DOI
10.1088/1572-9494/ad48fe

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Abstract Effects of a Bohmian type quantum-relativistic theory are explored. The model is obtained by introducing a new and independent time parameter whose relative motions are not directly observable and cause quantum uncertainties of the physical observables. Unlike the usual de Broglie–Bohm theories, the Quantum Potential does not directly affect the observable motion, but determines the one that is relative to the new time variable. It turns out that the Zitterbewegung of a free particle, of which a more general law is obtained, is the key example of these hidden motions and, through it, it seems possible to give physical reality to the Feynman’s paths. A relativistic revision of the uncertainty principle is also derived from the theory.
A new Bohmian quantum-relativistic model, in which from the Klein-Gordon equation a generalization of the standard Zitterbewegung arises, is explored. It is obtained by introducing a new independent time parameter, whose relative motions are not directly observable but cause the quantum uncertainties of the observables. Unlike Bohm's original theory, the quantum potential does not affect the observable motion, as for a normal external potential, but it only determines that one relative to the new time variable, of which the Zitterbewegung of a free particle is an example. The model also involves a relativistic revision of the uncertainty principle.
We present a novel covariant relativistic guidance formula à la de Broglie-Bohm derived from conserved quantities associated with the Lagrangian of the Dirac equation in a 1+1-dimensional spacetime. In line with the standard guidance formula of Bohmian mechanics, this generalized guidance formula incorporates space-time derivatives of the Dirac spinor phases and consistently reproduces relativistic features such as mass-dependent trajectories and zitterbewegung. We formally show that this formulation explicitly reveals how the relativistic quantum potential affects the trajectories. Using numerical simulations, we compare these trajectories with those presented in the usual approaches. Finally, we show how the guidance formula naturally transitions to the standard de Broglie-Bohm theory in the non-relativistic limit and gives additional contributions in the expansions giving new insight into the zitterbewegung in pilot-wave theories.
Bohmian mechanics, also known as pilot-wave theory or de Broglie–Bohm theory, is a formulation of quantum mechanics whose fundamental axioms are not about what observers will see if they perform an experiment but about what happens in reality. It is therefore called a “quantum theory without observers,” alongside with collapse theories and many-worlds theories and in contrast to orthodox quantum mechanics. It follows from these axioms that in a universe governed by Bohmian mechanics, observers will see outcomes with exactly the probabilities specified by the usual rules of quantum mechanics for empirical predictions. Specifically, Bohmian mechanics asserts that electrons and other elementary particles have a definite position at every time and move according to an equation of motion that is one of the fundamental laws of the theory and involves a wavefunction that evolves according to the usual Schr\\"odinger equation. Bohmian mechanics is named after David Bohm (1917–1992), who was, although not the first to consider this theory, the first to realize (in 1952) that it actually makes correct predictions.
Bohmian mechanics, also known as pilot-wave theory or de Broglie-Bohm theory, is a formulation of mechanics whose fundamental axioms are not about what observers will see if they perform an experiment but about what happens in reality. It is therefore called a quantum theory without observers, alongside with collapse theories and many-worlds theories and in contrast to orthodox mechanics. It follows from these axioms that in a universe governed by Bohmian mechanics, observers will see outcomes with exactly the probabilities specified by the usual rules of mechanics for empirical predictions. Specifically, Bohmian mechanics asserts that electrons and other elementary particles have a definite position at every time and move according to an equation of motion that is one of the fundamental laws of the theory and involves a wave function that evolves according to the usual Schr\odinger equation. Bohmian mechanics is named after David Bohm (1917-1992), who was, although not the first to consider this theory, the first to realize (in 1952) that it actually makes correct predictions.
Bohmian mechanics, also known as pilot-wave theory or de Broglie-Bohm theory, is a formulation of quantum mechanics whose fundamental axioms are not about what observers will see if they perform an experiment but about what happens in reality. It is therefore called a "quantum theory without observers," alongside with collapse theories and many-worlds theories and in contrast to orthodox quantum mechanics. It follows from these axioms that in a universe governed by Bohmian mechanics, observers will see outcomes with exactly the probabilities specified by the usual rules of quantum mechanics for empirical predictions. Specifically, Bohmian mechanics asserts that electrons and other elementary particles have a definite position at every time and move according to an equation of motion that is one of the fundamental laws of the theory and involves a wave function that evolves according to the usual Schrödinger equation. Bohmian mechanics is named after David Bohm (1917-1992), who was, although not the first to consider this theory, the first to realize (in 1952) that it actually makes correct predictions.
Bohmian mechanics, also referred to as the de Broglie-Bohm pilot-wave theory, represents a deterministic and nonlocal interpretation of quantum mechanics. Central to this framework is a description of quantum motion in terms of particle trajectories, whose reconciliation with relativity remains a fundamental challenge. Although relativistic guidance laws have been proposed, their predicted dynamics has remained experimentally untested. Here we use weak measurements in a single-photon interferometer to jointly reconstruct the photon energy and momentum weak values and the associated relativistic velocity field. The reconstructed average trajectories agree with theoretical predictions. Near destructive interference, the flow exhibits local reconstructed velocities exceeding the speed of light and negative values of the effective squared-mass parameter. Our results establish an experimental basis for investigating the physical meaning of quantum trajectories and their role in describing motion in relativistic spacetime.