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Journal of Theoretical Physics & Mathematics Research

A Pilot Wave Model of the Invariant Speed of Light and Apparent Time Dilation

Michael R. Emmert‐Buck

Published Jun 11, 2026• 0 citations
Publisher

Abstract

Special relativity, general relativity, and de Broglie-Bohm (pilot wave) theory are explanations of fundamental aspects of nature. For the most part, special and general relativity concern observations at large scale, whereas pilot wave theory addresses atomic processes. A feature that is unique to relativity is time dilation, the slowing of time with; a) relative movement in an inertial reference frame, and b) the effect of a gravitational field. At present, time dilation remains a difficult notion to intuitively understand, although it can be derived from general principles and characterized by straightforward mathematics. Canonical pilot wave theory is less well known than relativity and does not address time dilation; however, the theory can be conceptually expanded to cover additional phenomena. Described here is an expanded pilot wave model proposing time dilation does not occur in nature, but rather the slowing of clocks or other objects is due to a mechanical change in atomic efficiency. In other words, atoms, structures composed of atoms, and emergent properties of objects operate more slowly with motion or gravity due to a functional decrease in the effect of pilot waves, but time always elapses at a constant rate for all observers. Idealized pilot wave and standing wave models are used to explain a mechanism for the invariant speed of light and apparent slowing of time due to motion or gravity.

DOI
10.64030/3065-8802.04.03.04

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Special relativity, general relativity, and de Broglie-Bohm (pilot wave) theory are explanations of fundamental aspects of nature. For the most part, special and general relativity concern observations at large scale, whereas pilot wave theory addresses atomic processes. A feature that is unique to relativity is time dilation, the slowing of time with; a) relative movement in an inertial reference frame, and b) the effect of a gravitational field. At present, time dilation remains a difficult notion to intuitively understand, although it can be derived from general principles and characterized by straightforward mathematics. Canonical pilot wave theory is less well known than relativity and does not address time dilation; however, the theory can be conceptually expanded to cover additional phenomena. Described here is an expanded pilot wave model proposing time dilation does not occur in nature, but rather the slowing of clocks or other objects is due to a mechanical change in atomic efficiency. In other words, atoms, structures composed of atoms, and emergent properties of objects operate more slowly with motion or gravity due to a functional decrease in the effect of pilot waves, but time always elapses at a constant rate for all observers. Idealized pilot wave and standing wave models are used to explain a mechanism for the invariant speed of light and apparent slowing of time due to motion or gravity.
The de Broglie-Bohm (pilot wave) formulation of quantum theory appears to be free from the conceptual problems specific to quantum mechanics (problem of measurement) and to quantum cosmology (problem of time). We further study the extension of this formulation to the case of gravity and demonstrate that the foliation of spacetime by spacelike hypersurfaces obtained during the solution of the quantum problem turns out to be distinguished in general. This means that quantum pilot wave dynamics is not invariant with respect to an arbitrary change of foliation, or, in other terms, that quantum nonlocality takes place. We also discuss the general structure of a realistic pilot wave theory that could describe the universe.
The alternative pilot-wave theory of quantum phenomena—associated especially with Louis de Broglie, David Bohm, and John Bell—reproduces the statistical predictions of ordinary quantum mechanics but without recourse to special ad hoc axioms pertaining to measurement. That (and how) it does so is relatively straightforward to understand in the case of position measurements and, more generally, measurements, whose outcome is ultimately registered by the position of a pointer. Despite a widespread belief to the contrary among physicists, the theory can also account successfully for phenomena involving spin. The main goal of this paper is to explain how the pilot-wave theory's account of spin works. Along the way, we provide illuminating comparisons between the orthodox and pilot-wave accounts of spin and address some puzzles about how the pilot-wave theory relates to the important theorems of Kochen and Specker and Bell.
Abstract The pilot-wave theory of de Broglie and Bohm has a special place in the history of contemporary physics, being it the very first alternative formulation of quantum mechanics. As is well-known, such a framework established itself as a leading interpretation of the quantum formalism in virtue of the solutions provided to the major technical and conceptual challenges affecting the orthodox view. The de Broglie-Bohm theory in fact not only solves the famous measurement problem, one of the most cogent issues faced by standard quantum mechanics, but also it clarifies the formal structure of the latter theory as a consequence of a consistent set of principles and an precise, unambiguous ontology. This volume aims to provide the reader with a discussion of the pilot-wave perspective which is as informative, comprehensive and accessible as possible, while at the same time clarifying confusions and misunderstandings that are unfortunately still common in literature despite the long history of this theoretical framework. The book features chapters about the various perspectives on the pilot-wave theory, its extensions to relativity and quantum field theory, and its experimental applications to various branches of physics, as for instance quantum electrodynamics, quantum chemistry, and quantum engineering. Moreover, the volume includes essays on the history and philosophy of de Broglie-Bohm theory in order to delineate its developments and the vicissitudes of its pioneers, as well as to understand the scientific image of the universe it provides.
The Lorentz transformation (LT) is explained by changes occurring in the wave characteristics of matter as it changes inertial frame. This explanation is akin to that favoured by Lorentz, but informed by later insights, due primarily to de Broglie, regarding the underlying unity of matter and radiation. To show the nature of these changes, a massive particle is modelled as a standing wave in three dimensions. As the particle moves, the standing wave becomes a travelling wave having two factors. One is a carrier wave displaying the dilated frequency and contracted ellipsoidal form described by the LT, while the other (identified as the de Broglie wave) is a modulation defining the dephasing of the carrier wave (and thus the failure of simultaneity) in the direction of travel. The superluminality of the de Broglie wave is thus explained, as are several other mysterious features of the optical behaviour of matter, including the physical meaning of the Schrödinger equation and the relevance to scattering processes of the de Broglie wave vector. Consideration is given to what this Lorentzian approach to relativity might mean for the possible existence of a preferred frame and the origin of the observed Minkowski metric.
The Lorentz transformation (the LT) is explained by changes occurring in the wave characteristics of matter as it changes inertial frame. This explanation is akin to that favoured by Lorentz, but informed by later insights, due primarily to de Broglie, regarding the underlying unity of matter and radiation. To show the nature of these changes, a massive particle is modelled as a standing wave in three dimensions. As the particle moves, the standing wave becomes a travelling wave having two factors. One is a carrier wave displaying the dilated frequency and contracted ellipsoidal form described by the LT, while the other (identified as the de Broglie wave) is a modulation defining the dephasing of the carrier wave (and thus the failure of simultaneity) in the direction of travel. The superluminality of the de Broglie wave is thus explained, as are several other mysterious features of the optical behaviour of matter, including the physical meaning of the Schrödinger Eqn. and the relevance to scattering processes of the de Broglie wave number. Consideration is given to what this Lorentzian approach to relativity might mean for the possible existence of a preferred frame and the origin of the observed Minkowski metric.
Both quantum mechanics and general relativity are based on principles that defy our daily intuitions, such as time dilation, quantum interference and entanglement. Because the regimes where the two theories are typically tested are widely separated, their foundational principles are rarely jointly studied. Recent works have found that novel phenomena appear for quantum particles with an internal structure in the presence of time dilation, which can take place at low energies and in weak gravitational fields. Here we briefly review the effects of time dilation on quantum interference and generalize the results to a variety of systems. In addition, we provide an extended study of the basic principles of quantum theory and relativity that are of relevance for the effects and also address several questions that have been raised, such as the description in different reference frames, the role of the equivalence principle and the effective irreversibility of the decoherence. The manuscript clarifies some of the counterintuitive aspects arising when quantum phenomena and general relativistic effects are jointly considered.