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On the polarization states of the de Broglie gravitational wave

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Abstract

The pilot-wave theory is an alternative, but less used, interpretation of Quantum Mechanics. In that framework, elementary particles are guided by a wave and move along well defined trajectories. A fascinating idea is the possibility to describe the de Broglie wave as oscillations of the gravitational field, thereby giving geometrical meaning to the pilot-wave of a quantum corpuscle. In this work we will investigate the polarizations of the de Broglie gravitational wave and we will find that the spin-2 metric perturbation breaks down into two tensor (helicity-2), two vector (helicity-1) and two scalar (helicity-0) components. We will show that these dynamical variables satisfy the equation of the harmonic oscillator, meaning that they represent the physical degrees of freedom of the wave. We will also propose a method to measure the scalar modes, containing longitudinal components that are absent in standard transverse gravitational waves.

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Notes

  1. de Broglie was actually trying to develop a new non-Newtonian form of dynamics based on the unification of Maupertuis’ variational principle for Mechanics and Fermat’s principle of least time for Optics. A detailed review of de Broglie’s work can be found in [2, 3].

  2. For a review of the recent results see [14].

  3. The analysis of the polarization modes of gravitational waves has recently received great attention, because any detection of non-tensorial polarizations is a signal of physics beyond the theory of Einstein, see [20, 21].

  4. The theory is linear in \(h_{ab}\), meaning that we neglect terms of order \(\vert h_{ab}\vert ^2\) and higher.

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Authors and Affiliations

  1. Independent Researcher, Lindau (Bodensee), Germany

    Luca D’Errico

  2. Department of Computer Science, University of Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano, SA, Italy

    Elmo Benedetto

  3. Department of Engineering, University of Sannio, Piazza Roma 21, 82100, Benevento, Italy

    Elmo Benedetto & Antonio Feoli

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  1. Luca D’Errico
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  2. Elmo Benedetto
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  3. Antonio Feoli
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D’Errico, L., Benedetto, E. & Feoli, A. On the polarization states of the de Broglie gravitational wave. Gen Relativ Gravit 55, 83 (2023). https://doi.org/10.1007/s10714-023-03132-5

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