Antony Valentini
It is argued that the natural kinematics of the pilot-wave theory is Aristotelian. Despite appearances, Galilean invariance is not a fundamental symmetry of the low-energy theory. Instead, it is a fictitious symmetry that has been artificially imposed. It is concluded that the search for a Lorentz-invariant extension is physically misguided.
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Generalized Uncertainty Principle (GUP) was obtained in string theory and quantum gravity and suggested the existence of a fundamental minimal length which, as was established, can be obtained within the deformed Heisenberg algebra. We use the deformed commutation relations or in classical case (studied in this paper) the deformed Poisson brackets, which are invariant with respect to the translation in configurational space. We have found transformations relating coordinates and times of moving and rest frames of reference in the space with GUP in the first order over parameter of deformation.…
Galilean relativity and wave-particle duality imply the Schrödinger equation
该研究利用 Galileo/Lorentz 协变性与 de Broglie 波粒二象性，导出 Schrödinger 方程及波函数助推变换，并在相对论情形得到 Klein–Gordon 方程与 Lorentz 协变 Schrödinger 方程。
Recently Dragan and Ekert [New. J. Phys 22, 033038, 2020] presented arguments that probabilistic dynamics inherent in the realm of quantum physics is related to the propagation of superluminal particles. Moreover they argue that existence of such particles is a natural consequence of the principle of relativity. We show that the proposed extension of Lorentz transformation can be interpreted in natural way without invoking superluminal phenomena.
Revisiting de Broglie's Double-Solution Pilot-Wave Theory with a Lorentz-Covariant Lagrangian Framework
本研究基于经典场论变分原理构建局域洛伦兹不变的导波系统族，重现德布罗意双解理论的核心特征，推导得出经典版海森堡不确定性原理。
The Galilean symmetry and the Poincare symmetry are usually taken as the fundamental (relativity) symmetries for `nonrelativistic' and `relativistic' physics, respectively, quantum or classical. Our fully group theoretical formulation approach to the theories, together with its natural companion of mechanics from symplectic geometry, ask for different perspectives. We present a sketch of the full picture here, emphasizing aspects which are different from the more familiar picture. The letter summarizes our earlier presented formulation while focusing on the part beyond, with an adjusted, or co…
Group Theoretical Approach to Pseudo-Hermitian Quantum Mechanics with Lorentz Covariance and $c \rightarrow \infty $ Limit
本文通过群论方法构建了具有洛伦兹协变性和c→∞极限的伪埃尔米特量子力学框架，利用相干态表示和扩展的群C*-代数定义可观测量子，展示了非厄米特性与闵氏度量的联系。
We compare and contrast two distinct approaches to understanding the Born rule in de Broglie-Bohm pilot-wave theory, one based on dynamical relaxation over time (advocated by this author and collaborators) and the other based on typicality of initial conditions (advocated by the 'Bohmian mechanics' school). It is argued that the latter approach is inherently circular and physically misguided. The typicality approach has engendered a deep-seated confusion between contingent and law-like features, leading to misleading claims not only about the Born rule but also about the nature of the wave fun…
We consider a electron in a external field in D=5, through the Dirac equation in the Galilean symmetry approach, and in the Lorentz symmetry approach; from these we perform the nonrelativistic limit, then we procede the supersymmetry of the same that is associated with the Galilean symmetry, we identify as a supersymmetry sector from the quantum-mechanical dynamics, and we got the algebra of fermionic charges. We naturally define as extra electrical vector E, and interpret the terms of energy coming from the fifth dimension. The energy from the fifth dimension, criate this extra electrical vec…
The Young double-slit interference pattern produced by quantum objects, like photons, that move through a double-slit is regarded, by the conventional Copenhagen interpretation of Quantum Mechanics, as the evidence of the wave-like behaviour potentially contained in the wave function. On the contrary, a more realistic view of this phenomenon considers the quantum object a particle accompanied by a pilot wave which would be the cause of the interference fringes. This paper proposes a feasible experiment, based on an easy variation of the nowadays common double-slit experimental set-ups, aimed a…
We obtain a Lorentz covariant wave equation whose complex wave function transforms under a Lorentz boost according to the following rule, $Ψ(x)\rightarrow e^{\frac{i}{\hbar}f(x)}Ψ(x)$. We show that the spacetime dependent phase $f(x)$ is the most natural relativistic extension of the phase associated with the transformation rule for the non-relativistic Schroedinger wave function when it is subjected to a Galilean transformation. We then generalize the previous analysis by postulating that $Ψ(x)$ transforms according to the above rule under proper Lorentz transformations (boosts or spatial rot…
The trouble with pilot-wave theory: a critical evaluation
本文批判性评估了pilot-波理论的争议，指出其与传统物理的差异、革命性动态及对测量的理解，同时探讨其与量子力学的区别和潜在影响。
We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski four-vectors under the Lorentz symmetry. The basic representation is identified as a coherent state representation, essentially an irreducible component of the regular representation, with the matching representation of an extension of the group $C^*$-algebra giving the algebra of observables. The key feature of the formulation is that it is not unitary but pseudo-un…
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