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Aurélien Drezet

Publications and source records attributed to Aurélien Drezet.

At least 37 records · Page 2Linked to original sources
arXiv2022

Quantum solitodynamics: Non-linear wave mechanics and pilot-wave theory

In 1927 Louis de Broglie proposed an alternative approach to standard quantum mechanics known as the double solution program (DSP) where particles are represented as bunched fields or solitons guided by a base (weaker) wave. DSP evolved as the famous de Broglie-Bohm pilot wave interpretation (PWI) also known as Bohmian mechanics but the general idea to use solitons guided by a base wave to reproduce the dynamics of the PWI was abandonned. Here we propose a nonlinear scalar field theory able to reproduce the PWI for the Schrödinger and Klein-Gordon guiding waves. Our model relies on a relativistic `phase harmony' condition locking the phases of the solitonic particle and the guiding wave. We also discuss an extension of the theory for the $N$ particles cases in presence of entanglement and external (classical) electromagnectic fields.

quant-ph↗
arXiv2022

Indefinite causal order with fixed temporal order for electrons and positrons

We provide an analysis of indefinite causal orders in relativistic quantum mechanics based on the electron-positron picture of Feynman involving negative energy electrons moving backward in time. We show that genuine implementations of the paradigmatic quantum switch, but here violating some causal inequalities and with a fixed temporal order, become possible in extreme external electromagnetic field conditions allowing the presence of closed time-like curves.

quant-ph↗
arXiv2022

A classical analog of the quantum Zeeman effect

We extend a recent classical mechanical analog of Bohr's atom consisting of a scalar field coupled to a massive point-like particle [P. Jamet, A. Drezet, ``A mechanical analog of Bohr's atom based on de Broglie's double-solution approach'', Chaos 31, 103120 (2021)] by adding and studying the contribution of a uniform weak magnetic field on their dynamics. In doing so, we are able to recover the splitting of the energy levels of the atom called Zeeman's effect within the constraints of our model and in agreement with the semiclassical theory of Sommerfeld. This result is obtained using Larmor's theorem for both the field and the particle, associating magnetic effects with inertial Coriolis forces in a rotating frame of reference. Our work, based on the old `double solution' theory of de Broglie, shows that a dualistic model involving a particle guided by a scalar field can reproduce the normal Zeeman effect.

quant-ph↗
arXiv2021

The Quantum Eraser Non-Paradox: a comment on arXiv:2111.09347v1

This is a short reply to arXiv:2112.00436v1 and arXiv:2111.09347v1 by C. Bracken, J.R. Hance, and S. Hossenfelder. I precise some elements concerning i) the methodology of my previous version of the comment [arXiv:2111.13357v3] to arXiv:2111.09347v1, and ii) why the grand father-paradox (causal loop) presented in their article comes from a prejudice concerning retrocausality not from retrocausality or locality themselves.

quant-ph↗
arXiv2021

A mechanical analog of Bohr's atom based on de Broglie's double-solution approach

Motivated by recent developments of hydrodynamical quantum mechanical analogs [J. W. M. Bush, Annu. Rev. Fluid Mech. 47, 269-292 (2015)] we provide a relativistic model for a classical particle coupled to a scalar wave-field through a holonomic constraint. In presence of an external Coulomb field we define a regime where the particle is guided by the wave in a way similar to the old de Broglie phase-wave proposal. Moreover, this dualistic mechanical analog of the quantum theory is reminiscent of the double-solution approach suggested by de Broglie in 1927 and is able to reproduce the Bohr-Sommerfeld semiclassical quantization formula for an electron moving in a atom.

quant-ph↗
arXiv2021

Making sense of Born's rule $p_α=\lVertΨ_α\rVert^2$ with the many-minds interpretation

This work is an attempt to justify Born's rule within the framework of the many-minds interpretation seen as a development of the many-worlds interpretation of Everett. More precisely, here we develop a unitary model of many-minds based on the work of Albert and Loewer (Synthese \textbf{77}, 195 (1988)). At the difference of previous models ours is not genuinely stochastic and dualistic and also involves some classical-like randomness concerning the initial conditions of the Universe. We also compare the present method for recovering Born's rule with previous works based on decision theory \emph{à la }Deutsch, Wallace, and envariance \emph{à la} Zurek and show how these approaches are connected to our model

quant-ph↗
arXiv2021

Collapse of the many-worlds interpretation: Why Everett's theory is typically wrong

We analyze the objective meaning of probabilities in the context of the many-worlds interpretation of Everett. For this purpose we study in details the weak law of large numbers and the role of typicality and universally negligible probabilities (through the works of Cournot and Borel). We demonstrate that Everett's theory doesn't provide any clue for fixing a probability rule and therefore contradicts irrevocably empirical facts and Born's law.

quant-ph↗
arXiv2021

Justifying Born's rule $P_α=|Ψ_α|^2$ using deterministic chaos, decoherence, and the de Broglie-Bohm quantum theory

In this work we derive Born's rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to a environement made of "qubits" (i.e., Bohmian pointers) we show that entanglement together with deterministic chaos lead to a fast relaxation from any statistitical distribution $ρ(x)$ (of finding a particle at point $x$) to the Born probability law $|Ψ(x)|^2$. Our model is discussed in the context of Boltzmann's kinetic theory and we demonstrate a kind of H theorem for the relaxation to the quantum equilibrium regime.

quant-ph↗
arXiv2021

A no-go theorem for $Ψ-$anomic models under the restricted ontic indifference assumption

We address the question of whether a non-nomological (i.e., anomic) interpretation of the wavefunction is compatible with the quantum formalism. After clarifying the distinction between ontic, epistemic, nomic and anomic models we focus our attention on two famous no-go theorems due to Pusey, Barrett, and Rudolph (PBR) on the one side and Hardy on the other side which forbid the existence of anomic-epistemic models. Moreover, we demonstrate that the so called restricted ontic indifference introduced by Hardy induces new constraints. We show that after modifications the Hardy theorem actually rules out all anomic models of the wavefunction assuming only restricted ontic indifference and preparation independence.

quant-ph↗
arXiv2021

A causal and continuous interpretation of the quantum theory: About an original manuscript by David Bohm sent to Louis de Broglie in 1951

The aim of this article is reproduce and analyze an original article of David Bohm sent to Louis de Broglie in 1951. This article is the older document of David Bohm about his well known hidden variable theory based on the pilot wave interpretation of Louis de Broglie. We analyse the chronology and the history of this fascinating document.

physics.hist-ph↗
arXiv2020

The guidance theorem of de Broglie

We review some aspects of the double solution theory proposed by de Broglie at the beginning of the quantum era (i.e., in the period 1924-28). We specifically analyze and rederive the so called guidance theorem which is a key element of the full theory. We compare the double solution approach to the most known pilot-wave interpretation, also known as de Broglie-Bohm or Bohmian mechanics. We explain why de Broglie rejected the pilot wave interpretation and advocated the double solution. We also discuss some philosophical issues related to difference of strategies between de Broglie on the one side and Bohm on the other side.

quant-ph↗
arXiv2019

Entangled-photon decision maker

The competitive multi-armed bandit (CMAB) problem is related to social issues such as maximizing total social benefits while preserving equality among individuals by overcoming conflicts between individual decisions, which could seriously decrease social benefits. The study described herein provides experimental evidence that entangled photons physically resolve the CMAB in the 2-arms 2-players case, maximizing the social rewards while ensuring equality. Moreover, we demonstrated that deception, or outperforming the other player by receiving a greater reward, cannot be accomplished in a polarization-entangled-photon-based system, while deception is achievable in systems based on classical polarization-correlated photons with fixed polarizations. Besides, random polarization-correlated photons have been studied numerically and shown to ensure equality between players and deception prevention as well, although the CMAB maximum performance is reduced as compared with entangled photon experiments. Autonomous alignment schemes for polarization bases were also experimentally demonstrated based only on decision conflict information observed by an individual without communications between players. This study paves a way for collective decision making in uncertain dynamically changing environments based on entangled quantum states, a crucial step toward utilizing quantum systems for intelligent functionalities.

physics.optics↗
arXiv2019

Lorentz-invariant, retrocausal, and deterministic hidden variables

We review several no-go theorems attributed to Gisin and Hardy, Conway and Kochen purporting the impossibility of Lorentz-invariant deterministic hidden-variable model for explaining quantum nonlocality. Those theorems claim that the only known solution to escape the conclusions is either to accept a preferred reference frame or to abandon the hidden-variable program altogether. Here we present a different alternative based on a foliation dependent framework adapted to deterministic hidden variables. We analyse the impact of such an approach on Bohmian mechanics and show that retrocausation (that is future influencing the past) necessarily comes out without time-loop paradox.

quant-ph↗
arXiv2018

About Wigner Friend's and Hardy's paradox in a Bohmian approach: a comment of `Quantum theory cannot' consistently describe the use of itself'

This is an analysis of the recently published article `Quantum theory cannot consistently describe the use of itself' by D. Frauchiger and R. Renner~\cite{1}. Here I decipher the paradox and analyze it from the point of view of de Broglie-Bohm hidden variable theory (i.e., Bohmian mechanics). I also analyze the problem from the perspective obtained by the Copenhagen interpretation (i.e., the Bohrian interpretation) and show that both views are self consistent and do not lead to any contradiction with a `single-world' description of quantum theory.

quant-ph↗
arXiv2018

Category Theoretic Analysis of Photon-based Decision Making

Decision making is a vital function in this age of machine learning and artificial intelligence, yet its physical realization and theoretical fundamentals are still not completely understood. In our former study, we demonstrated that single-photons can be used to make decisions in uncertain, dynamically changing environments. The two-armed bandit problem was successfully solved using the dual probabilistic and particle attributes of single photons. In this study, we present a category theoretic modeling and analysis of single-photon-based decision making, including a quantitative analysis that is in agreement with the experimental results. A category theoretic model reveals the complex interdependencies of subject matter entities in a simplified manner, even in dynamically changing environments. In particular, the octahedral and braid structures in triangulated categories provide a better understanding and quantitative metrics of the underlying mechanisms of a single-photon decision maker. This study provides both insight and a foundation for analyzing more complex and uncertain problems, to further machine learning and artificial intelligence.

physics.optics↗
arXiv2017

Reciprocity and optical chirality

In this text we describe the role of optical chirality in the context of plasmonics. We clearly distinguish between 2D an 3D optical chirality and connect the problem with reciprocity and time symmetry. We compare our analysis with recent experimental results in nano-plasmonics and photonics.

physics.optics↗