Related papers: A Machian reformulation of Quantum Mechanics

A Machian reformulation of Quantum Mechanics

URL: http://arxiv.org/abs/2202.11561v2
Date: Tue, 8 Mar 2022 13:04:56 GMT
Title: A Machian reformulation of Quantum Mechanics
Authors: Kostas Glampedakis
Abstract summary: We reformulate the Schr"odinger equation of non-relativistic quantum mechanics in a fully Machian way. Just like its classical counterpart, the resulting quantum theory is fully relational in the positions and momenta of the bodies comprising a given physical system.
Score: 0.0
License: http://creativecommons.org/licenses/by-sa/4.0/
Abstract: The widely known but also somewhat esoteric Mach principle envisages a fully relational formulation of physical theories without any reference to a concept of `absolute space'. When applied to classical mechanics, under the guise of an extended symmetry group, this procedure is known to lead to an equation of motion with inertial-like forces that are sourced by the mass distribution of the system itself. In this paper we follow a similar procedure and reformulate the Schr\"odinger equation of non-relativistic quantum mechanics in a fully Machian way. Just like its classical counterpart, the resulting quantum theory is fully relational in the positions and momenta of the bodies comprising a given physical system, leaving no room for the notion of absolute space.

Related papers

Second-Order Moment Quantum Fluctuations and Quantum Equivalence Principle [0.0]
We find that the second-order moment quantum fluctuations are actually distinguished into two parts: a dynamic part and a geometric part. The dynamic part is indeed mass-dependent and governed by a non-zero Hamiltonian in a non-general sigma-covariant inertial frame. The geometric part is mass-independent and universal, so it is only this part measures the universal second-order moment quantum fluctuation of the spacetime.
arXiv Detail & Related papers (2024-08-19T01:26:01Z)
A Theory of Quantum Jumps [44.99833362998488]
We study fluorescence and the phenomenon of quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field. Our results amount to a derivation of the fundamental randomness in the quantum-mechanical description of microscopic systems.
arXiv Detail & Related papers (2024-04-16T11:00:46Z)
Stochastic Mechanics and the Unification of Quantum Mechanics with Brownian Motion [0.0]
We show that non-relativistic quantum mechanics of a single spinless particle on a flat space can be described by a process that is rotated in the complex plane. We then extend this theory to relativistic theories on integrals using the framework of second order geometry.
arXiv Detail & Related papers (2023-01-13T10:40:27Z)
Does the Universe have its own mass? [62.997667081978825]
The mass of the universe is a distribution of non-zero values of gravitational constraints. A formulation of the Euclidean quantum theory of gravity is also proposed to determine the initial state. Being unrelated to ordinary matter, the distribution of its own mass affects the geometry of space.
arXiv Detail & Related papers (2022-12-23T22:01:32Z)
Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
arXiv Detail & Related papers (2022-05-24T20:51:03Z)
Wave Functional of the Universe and Time [62.997667081978825]
A version of the quantum theory of gravity based on the concept of the wave functional of the universe is proposed. The history of the evolution of the universe is described in terms of coordinate time together with arbitrary lapse and shift functions.
arXiv Detail & Related papers (2021-10-18T09:41:59Z)
Open-system approach to nonequilibrium quantum thermodynamics at arbitrary coupling [77.34726150561087]
We develop a general theory describing the thermodynamical behavior of open quantum systems coupled to thermal baths. Our approach is based on the exact time-local quantum master equation for the reduced open system states.
arXiv Detail & Related papers (2021-09-24T11:19:22Z)
Quantum superposition of spacetimes obeys Einstein's Equivalence Principle [0.0]
We argue that the Equivalence Principle can be generalised so that it holds for reference frames associated to quantum systems in a superposition of spacetimes. This procedure reconciles the principle of linear superposition in Quantum Theory with the principle of general covariance and the Equivalence Principle of General Relativity.
arXiv Detail & Related papers (2021-09-03T09:51:18Z)
Fully Symmetric Relativistic Quantum Mechanics and Its Physical Implications [0.0]
A new formulation of relativistic quantum mechanics is presented and applied to a free, massive, and spin zero elementary particle in the Minkowski spacetime. The reformulation requires that time and space, as well as the timelike and spacelike intervals, are treated equally, which makes the new theory fully symmetric and consistent with the Special Theory of Relativity.
arXiv Detail & Related papers (2021-05-31T19:13:19Z)
There is only one time [110.83289076967895]
We draw a picture of physical systems that allows us to recognize what is this thing called "time" We derive the Schr"odinger equation in the first case, and the Hamilton equations of motion in the second one.
arXiv Detail & Related papers (2020-06-22T09:54:46Z)
The Non-Hermitian quantum mechanics and its canonical structure [7.784991832712813]
The non-Hermitian Schr"odinger equation is re-expressed generally in the form of Hamilton's canonical equation without any approximation. The conventional difficulties in non-Hermitian quantum mechanics are totally overcome by the reformulation.
arXiv Detail & Related papers (2020-05-21T05:52:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.