Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:gr-qc/0507093

The combination of de Broglie's Harmony of the Phases and Mie's theory of gravity results in a Principle of Equivalence for Quantum Gravity

de Haas, E. P. J.

Published Jul 21, 2005• 2 citations
arXivHTMLPDF

Abstract

Under a Lorentz-transformation, Mie's 1912 gravitational mass behaves identical as de Broglie's 1923 clock-like frequency. The same goes for Mie's inertial mass and de Broglie's wave-like frequency. This allows the interpretation of de Broglie's "Harmony of the Phases" as a "Principle of Equivalence" for Quantum Gravity. Thus, the particle-wave duality can be given a realist interpretation. The "Mie-de Broglie" interpretation suggests a correction of Hamilton's variational principle in the quantum domain. The equivalence of the masses can be seen as the classical "limit" of the quantum equivalence of the phases.

DOI
10.48550/arxiv.gr-qc/0507093

Related papers

Quantum violation of the equivalence principle and gravitationally modfied de Broglie relation

Dharam Vir Ahluwalia

The agreement between the predictions of general relativity and observations of the energy loss due to gravitational waves emitted by binary pulsars is just as impressive as the agreement between prediction of quantum electrodynamics and the measured value of Lamb shift in atoms. However, general relativity has not yet yielded to a successful quantised theory. There is a widespread belief that the two thories are incompatible at some deep level. The question is: where? Here, I show that the conceptual foundations of the theory of general relativity and quantum mechanics are so rich that they suggest concrete modifications into each other in the interface region. Specifically, I consider quantum states that have no classical counterpart and show that such states must carry an inherent violation of the principle of equivalence. On the other hand, I show that when gravitational effects are incorporated into the quantum measurement process one must induce a gravitationally induced modification to the de Broglie's wave-particle duality. The reported changes into the foundations of the two theories are far from in-principle modifications. These are endowed with serious implications for the understanding of the early universe and, in certain instances, can be explored in terrestrial laboratories.

•Feb 1, 2000•0 citations

Semiclassical gravity in the de Broglie-Bohm theory and the double scale theory

Michel Gondran, Alexandre Gondran

We present a semiclassical gravity in the framework of the double scale theory, a new interpretation of quantum mechanics which expands on the de Broglie-Bohm (dBB) theory. In this interpretation, any quantum system is associated with two wave functions, one external and one internal. The external wave function drives the center-of-mass, as in the dBB theory, and spreads with time. The internal wave function corresponds to the density of an extended particle. It remains confined in space and its average position corresponds to the center of mass of the particle. We define, for an N-body system, new semi-classical gravity equations called Einstein-de Broglie equations. The external wave function of each body depends only on the internal wave functions of the N--1 others. They are deduced from Einstein's semi-classical equation by using the internal wave functions instead of the usual wave function. If we restrict to the dBB interpretation, we find the Newton-de Broglie equations that Struyve and Lalo{ë} have recently proposed independently. We show that the Newton-de Broglie and Einstein-de Broglie equations converge to Newton's gravity when h $\rightarrow$ 0, which gives a theoretical validation.

arXiv:2302.10235•Jan 23, 2023•0 citations

The Other de Broglie Wave

Daniel Shanahan

In his famous doctoral dissertation, de Broglie assumed that a massive particle is surrounded in its rest frame by a standing wave. He argued that as observed from another inertial frame this wave becomes the superluminal wave now known as the de Broglie wave. It is shown here that under a Lorentz transformation, such a standing wave becomes, not the de Broglie wave, but a modulated wave moving at the velocity of the particle. It is the modulation that has the superluminal velocity of the de Broglie wave and should be recognized as the true de Broglie wave. De Broglie's demonstrations relied, variously, on his "theorem of the harmony of phases", on a mechanical model, and on a spacetime diagram. It is shown that in each case the underlying wave was inadvertently suppressed. Identified as a modulation, the de Broglie wave acquires a physically reasonable ontology, avoiding the awkward device of recovering the particle velocity from a superposition of such waves. The deeper wave structure implied by this de Broglie wave must also impinge on such issues in quantum mechanics as the meaning of the wave function and the nature of wave-particle duality.

•Mar 6, 2015•1 citation

Quantum Gravity Explanation of the de Broglie Pilot Wave

Friedwardt Winterberg

The particle-wave duality of the de Broglie pilot wave is explained by the emission of watt-less gravitational waves from Schroedinger's Zitterbewegung of elementary particles obeying the Dirac equation. In particular is shown that the quantum potential of the Madelung-transformed Schroedinger equation is gravitational in it's origin.

•Aug 1, 2015•0 citations

Analogue Gravity and the de Broglie wave: a Missed Opportunity

Shanahan, Daniel

In a small book entitled Ondes et Mouvements, published in February 1926, Louis de Broglie described the wave, now known as the de Broglie wave, as a modulation or beating effect of undulatory form induced in the structure of the particle by the failure of simultaneity. Considered in this way, the de Broglie wave is neither ontologically distinct, nor in any way separate, from the particle, but like the Fitzgerald-Lorentz contraction is a distortion in the structure of the particle itself. So understood, the de Broglie wave is a physically real phenomenon, capable of describing for the particle, a well-defined and physically realistic trajectory. In comparison, and as I argue in this paper, the wave functions that emerge as solutions to the Schrödinger and Klein-Gordon equations are better regarded as mathematical constructs, albeit constructs of significant utility, identifying the wave number and frequency that the particle would have at each point of space if it were in fact at that point of space. A particular concern of this paper will be to show that the de Broglie wave would emerge as such a distortion of structure in certain sonic quasiparticles proposed in the context of Analogue Gravity for the purpose of simulating the Lorentz transformation.

•Sep 16, 2024•0 citations

Clock, Boost, Wave: A Kinematic Origin of the de Broglie Relation

Ping Zhang

The de~Broglie relation $\lambda = h/p$ is among the most well-confirmed results in modern physics, yet the kinematic origin of the associated matter wave remains conceptually obscure. This paper presents a kinematic analysis leading to the de~Broglie relation. The only assumption is the existence of a globally defined phase field with uniform rest-frame oscillation, a structure known to occur in superfluids and Bose--Einstein condensates. Under a Lorentz boost, the scalar transformation of the phase field converts temporal periodicity directly into spatial periodicity, yielding a wave number $k' = \gamma\omega_0 v/c_s^2$ and a phase velocity $v_{\mathrm{phase}} = c_s^2/v$. No wave equation, dynamical model, or quantization procedure is required. The result follows solely from the relativity of simultaneity applied to a scalar phase field. When the characteristic frequency and invariant speed are identified as $\omega_0 = mc^2/\hbar$ and $c_s = c$, the resulting wavelength and phase velocity reproduce the standard de~Broglie relations. The logical architecture inverts that of de~Broglie's original construction: rather than postulating a separate clock and wave linked by phase harmony, the wave emerges as the Lorentz-transformed image of a single coherent phase clock. The phase harmony that de~Broglie introduced as an independent postulate becomes a consequence of Lorentz covariance. The analysis establishes a precise kinematic correspondence without asserting that the physical vacuum is a coherent medium. Whether this correspondence reflects a deeper physical principle or a mathematical analogy remains an open question.

•Jun 1, 2026•0 citations
Under a Lorentz-transformation, Mie's 1912 gravitational mass behaves identical as de Broglie's 1923 clock-like frequency. The same goes for Mie's inertial mass and de Broglie's wave-like frequency. This allows the interpretation of de Broglie's "Harmony of the Phases" as a "Principle of Equivalence" for Quantum Gravity. Thus, the particle-wave duality can be given a realist interpretation. The "Mie-de Broglie" interpretation suggests a correction of Hamilton's variational principle in the quantum domain. The equivalence of the masses can be seen as the classical "limit" of the quantum equivalence of the phases.
The agreement between the predictions of general relativity and observations of the energy loss due to gravitational waves emitted by binary pulsars is just as impressive as the agreement between prediction of quantum electrodynamics and the measured value of Lamb shift in atoms. However, general relativity has not yet yielded to a successful quantised theory. There is a widespread belief that the two thories are incompatible at some deep level. The question is: where? Here, I show that the conceptual foundations of the theory of general relativity and quantum mechanics are so rich that they suggest concrete modifications into each other in the interface region. Specifically, I consider quantum states that have no classical counterpart and show that such states must carry an inherent violation of the principle of equivalence. On the other hand, I show that when gravitational effects are incorporated into the quantum measurement process one must induce a gravitationally induced modification to the de Broglie's wave-particle duality. The reported changes into the foundations of the two theories are far from in-principle modifications. These are endowed with serious implications for the understanding of the early universe and, in certain instances, can be explored in terrestrial laboratories.
We present a semiclassical gravity in the framework of the double scale theory, a new interpretation of quantum mechanics which expands on the de Broglie-Bohm (dBB) theory. In this interpretation, any quantum system is associated with two wave functions, one external and one internal. The external wave function drives the center-of-mass, as in the dBB theory, and spreads with time. The internal wave function corresponds to the density of an extended particle. It remains confined in space and its average position corresponds to the center of mass of the particle. We define, for an N-body system, new semi-classical gravity equations called Einstein-de Broglie equations. The external wave function of each body depends only on the internal wave functions of the N--1 others. They are deduced from Einstein's semi-classical equation by using the internal wave functions instead of the usual wave function. If we restrict to the dBB interpretation, we find the Newton-de Broglie equations that Struyve and Lalo{ë} have recently proposed independently. We show that the Newton-de Broglie and Einstein-de Broglie equations converge to Newton's gravity when h →\rightarrow→ 0, which gives a theoretical validation.
In his famous doctoral dissertation, de Broglie assumed that a massive particle is surrounded in its rest frame by a standing wave. He argued that as observed from another inertial frame this wave becomes the superluminal wave now known as the de Broglie wave. It is shown here that under a Lorentz transformation, such a standing wave becomes, not the de Broglie wave, but a modulated wave moving at the velocity of the particle. It is the modulation that has the superluminal velocity of the de Broglie wave and should be recognized as the true de Broglie wave. De Broglie's demonstrations relied, variously, on his "theorem of the harmony of phases", on a mechanical model, and on a spacetime diagram. It is shown that in each case the underlying wave was inadvertently suppressed. Identified as a modulation, the de Broglie wave acquires a physically reasonable ontology, avoiding the awkward device of recovering the particle velocity from a superposition of such waves. The deeper wave structure implied by this de Broglie wave must also impinge on such issues in quantum mechanics as the meaning of the wave function and the nature of wave-particle duality.
In a small book entitled Ondes et Mouvements, published in February 1926, Louis de Broglie described the wave, now known as the de Broglie wave, as a modulation or beating effect of undulatory form induced in the structure of the particle by the failure of simultaneity. Considered in this way, the de Broglie wave is neither ontologically distinct, nor in any way separate, from the particle, but like the Fitzgerald-Lorentz contraction is a distortion in the structure of the particle itself. So understood, the de Broglie wave is a physically real phenomenon, capable of describing for the particle, a well-defined and physically realistic trajectory. In comparison, and as I argue in this paper, the wave functions that emerge as solutions to the Schrödinger and Klein-Gordon equations are better regarded as mathematical constructs, albeit constructs of significant utility, identifying the wave number and frequency that the particle would have at each point of space if it were in fact at that point of space. A particular concern of this paper will be to show that the de Broglie wave would emerge as such a distortion of structure in certain sonic quasiparticles proposed in the context of Analogue Gravity for the purpose of simulating the Lorentz transformation.
The de~Broglie relation λ=h/p\lambda = h/pλ=h/p is among the most well-confirmed results in modern physics, yet the kinematic origin of the associated matter wave remains conceptually obscure. This paper presents a kinematic analysis leading to the de~Broglie relation. The only assumption is the existence of a globally defined phase field with uniform rest-frame oscillation, a structure known to occur in superfluids and Bose--Einstein condensates. Under a Lorentz boost, the scalar transformation of the phase field converts temporal periodicity directly into spatial periodicity, yielding a wave number k′=γω0v/cs2k' = \gamma\omega_0 v/c_s^2k′=γω0​v/cs2​ and a phase velocity vphase=cs2/vv_{\mathrm{phase}} = c_s^2/vvphase​=cs2​/v. No wave equation, dynamical model, or quantization procedure is required. The result follows solely from the relativity of simultaneity applied to a scalar phase field. When the characteristic frequency and invariant speed are identified as ω0=mc2/ℏ\omega_0 = mc^2/\hbarω0​=mc2/ℏ and cs=cc_s = ccs​=c, the resulting wavelength and phase velocity reproduce the standard de~Broglie relations. The logical architecture inverts that of de~Broglie's original construction: rather than postulating a separate clock and wave linked by phase harmony, the wave emerges as the Lorentz-transformed image of a single coherent phase clock. The phase harmony that de~Broglie introduced as an independent postulate becomes a consequence of Lorentz covariance. The analysis establishes a precise kinematic correspondence without asserting that the physical vacuum is a coherent medium. Whether this correspondence reflects a deeper physical principle or a mathematical analogy remains an open question.