scholarly journals Locality and evolution to equilibrium

2021 ◽  
Author(s):  
Marek Gazdzicki ◽  
Mark Gorenstein ◽  
Ivan Pidhurskyi ◽  
Oleh Savchuk ◽  
Leonardo Tinti
Keyword(s):  
Quantum Mechanics ◽  
Equilibrium State ◽  
Particle Transport ◽  
Transition Matrix ◽  
Complex Structure ◽  
Space Time ◽  
Quantum Statistics ◽  
Countable Space ◽  
Simple Matrix ◽  
Action At A Distance

Abstract Quantum statistics and non-locality are deeply rooted in quantum mechanics and go beyond our intuition reflected in classical physics. Quantum statistics can be derived using statistical methods for indistinguishable particles - particles of quantum mechanics. Violation of strong locality - colloquially called the ghostly action at a distance - is one of the most amazing properties of nature derived from quantum mechanics. An intriguing question is whether the non-local evolution of indistinguishable particles is needed to reach the equilibrium state given by quantum statistics. Motivated by the above and similar questions, we developed a simple framework that allows us to follow space-time evolution of assembly of particles. It is based on a discrete-time Markov chain on countable space for indistinguishable particles. We summarise well-known and introduced new constraints on the transition matrix that grant space-time symmetries, locality of particle-transport, strong locality, and equilibrium state. Then, within the framework, several important cases are considered. First, we show that the simplest transition matrix leads to equilibrium but violates particle transport and strong localities. Furthermore, we construct a simple matrix that leads to equilibrium obeying particle-transport locality and violating strong locality. This resembles the properties of quantum mechanics. Finally, we demonstrate that it is also possible to reach equilibrium by obeying both particle-transport and strong localities. Thus, within this framework, the violation of a strong locality is not needed to reach the equilibrium of indistinguishable particles. However, to obey strong locality, a complex structure of the transition matrix is needed. In addition, we comment on distinguishable particles and, in particular, show that their evolution seen by an observer blind to particle differences may look like the evolution of indistinguishable particles with the properties of quantum mechanics. We hope that this work may help to study the relation between symmetries, localities and the evolution to equilibrium for indistinguishable and distinguishable particles.

scholarly journals PROBABILITY IN RELATIVISTIC QUANTUM MECHANICS AND FOLIATION OF SPACE–TIME

2007 ◽  
Vol 22 (32) ◽  
pp. 6243-6251 ◽  
Author(s):  
HRVOJE NIKOLIĆ
Keyword(s):  
Quantum Mechanics ◽  
Wave Equations ◽  
Integral Curve ◽  
Relativistic Quantum ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Relativistic Wave ◽  
Probability Densities ◽  
The Many ◽  
Conserved Currents

The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be nonnegative and the integral of them over an entire hypersurface should be equal to one. To satisfy these requirements in a covariant manner, the foliation of space–time must be such that each integral curve of the current crosses each hypersurface of the foliation once and only once. In some cases, it is necessary to use hypersurfaces that are not spacelike everywhere. The generalization to the many-particle case is also possible.

Quantum Mechanics in Simple Matrix Form

1986 ◽  
Vol 54 (12) ◽  
pp. 1154-1155 ◽  
Author(s):  
Thomas F. Jordan ◽  
Kannan Jagannathan
Keyword(s):  
Quantum Mechanics ◽  
Matrix Form ◽  
Simple Matrix

scholarly journals Space time geometry in the atomic hydrogenoid system. Approach to a dust relativistic model from causal quantum mechanics

2018 ◽  
Vol 64 (1) ◽  
pp. 18
Author(s):  
G. Gómez ◽  
I. Kotsireas ◽  
I. Gkigkitzis ◽  
I. Haranas ◽  
M.J. Fullana
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
General Equation ◽  
System Approach ◽  
Space Time ◽  
Relativistic Model ◽  
Time Deformation ◽  
Non Local ◽  
De Broglie Bohm

Weintend to use the description oftheelectron orbital trajectory in the de Broglie-Bohm (dBB) theory to assimilate to a geodesiccorresponding to the General Relativity (GR) and get from itphysicalconclusions. ThedBBapproachindicatesustheexistenceof a non-local quantumfield (correspondingwiththequantumpotential), anelectromagneticfield and a comparativelyveryweakgravitatoryfield, togetherwith a translationkineticenergyofelectron. Ifweadmitthatthosefields and kineticenergy can deformthespace time, according to Einstein'sfield equations (and to avoidtheviolationoftheequivalenceprinciple as well), we can madethehypothesisthatthegeodesicsof this space-time deformation coincide withtheorbitsbelonging to thedBBapproach (hypothesisthat is coherentwiththestabilityofmatter). Fromit, we deduce a general equation that relates thecomponentsofthemetric tensor. Thenwe find anappropriatemetric for it, bymodificationofanexactsolutionofEinstein'sfield equations, whichcorresponds to dust in cylindricalsymmetry. Thefoundmodelproofs to be in agreementwiththebasicphysicalfeaturesofthehydrogenquantum system, particularlywiththeindependenceoftheelectronkineticmomentum in relationwiththeorbit radius. Moreover, themodel can be done Minkowski-like for a macroscopicshortdistancewith a convenientelectionof a constant. According to this approach, theguiding function ofthewaveontheparticlecould be identifiedwiththedeformationsofthespace-time and thestabilityofmatterwould be easilyjustifiedbythe null accelerationcorresponding to a geodesicorbit.

scholarly journals Gravity to Electricity as Quantum

2020 ◽  
Author(s):  
Jong-hoon Lee
Keyword(s):  
Quantum Mechanics ◽  
Magnetic Fields ◽  
Potential Energy ◽  
Equilibrium State ◽  
Opposite Direction ◽  
Repulsive Force ◽  
The Earth ◽  
Gravity And Magnetic ◽  
The Relationship ◽  
Renormalization Theory

When gravity exists in magnetic fields, gravity interacts with magnetic fields to generate electricity Earth direction or opposite direction. In this experiment, we demonstrate it and explain why need the renormalization theory. And in this experimental model, the relationship between electricity, voltage and time were redefined through the analysis of data for 0.1 second. Voltage and time are in a 1: 1 matching relationship. The voltage can be recorded on the x-axis and time on the y-axis. It explains two expressions of the Schrödinger equation. According to these experiments, the electric potential energy generated in gravity and magnetic fields is not reflected in quantum mechanics. The renormalization theory has modified the quantum mechanics in four-dimensional systems. If gravity and electromagnetic force are particles, they are in a symmetrical balance of supersymmetric particles in the gravity generator. Gravity generator was voltage (0) and electricity (0) in Excel 6380 data of experiment F4 when it was in equilibrium state in the direction of the Earth by gravity force and in the opposite direction by the magnetic repulsive force.

Bell’s theorem

2018 ◽  
Author(s):  
Arthur Fine
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Experimental Tests ◽  
Bell Inequalities ◽  
Bell’S Theorem ◽  
Bell's Theorem ◽  
Bell Theorem ◽  
System Of Inequalities ◽  
Action At A Distance ◽  
High Degree

Bell’s theorem is concerned with the outcomes of a special type of ‘correlation experiment’ in quantum mechanics. It shows that under certain conditions these outcomes would be restricted by a system of inequalities (the ‘Bell inequalities’) that contradict the predictions of quantum mechanics. Various experimental tests confirm the quantum predictions to a high degree and hence violate the Bell inequalities. Although these tests contain loopholes due to experimental inefficiencies, they do suggest that the assumptions behind the Bell inequalities are incompatible not only with quantum theory but also with nature. A central assumption used to derive the Bell inequalities is a species of no-action-at-a-distance, called ‘locality’: roughly, that the outcomes in one wing of the experiment cannot immediately be affected by measurements performed in another wing (spatially distant from the first). For this reason the Bell theorem is sometimes cited as showing that locality is incompatible with the quantum theory, and the experimental tests as demonstrating that nature is nonlocal. These claims have been contested.

Bell’s theorem and its tests: Proof that nature is superdeterministic—Not random

2020 ◽  
Vol 33 (2) ◽  
pp. 216-218
Author(s):  
Johan Hansson
Keyword(s):  
Quantum Mechanics ◽  
Reference Frames ◽  
Space Time ◽  
Bell’S Theorem ◽  
Quantum Mechanical ◽  
Bell's Theorem ◽  
Fundamental Level ◽  
Global Space ◽  
Mechanical Measurements

By analyzing the same Bell experiment in different reference frames, we show that nature at its fundamental level is superdeterministic, not random, in contrast to what is indicated by orthodox quantum mechanics. Events—including the results of quantum mechanical measurements—in global space-time are fixed prior to measurement.

GALILEAN AND DISCRETE SPACE-TIME SYMMETRIES OF ROY-SINGH DETERMINISTIC QUANTUM MECHANICS

1995 ◽  
Vol 10 (32) ◽  
pp. 4641-4650
Author(s):  
ARVIND KUMAR
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Time Reversal ◽  
Space Time ◽  
Discrete Space ◽  
Galilean Space

The recent deterministic quantum theory of Roy and Singh is shown to be covariant with respect to Galilean, space reflection and time reversal transformations.

HOLOMORPHIC QUANTUM MECHANICS, CONFORMAL REFLECTION AND THE INTERNAL SYMMETRY OF HADRONS

1989 ◽  
Vol 04 (17) ◽  
pp. 4449-4467 ◽  
Author(s):  
PRATUL BANDYOPADHYAY
Keyword(s):  
Quantum Mechanics ◽  
Minkowski Space ◽  
Composite System ◽  
Conformal Geometry ◽  
Reflection Group ◽  
Internal Symmetry ◽  
Space Time ◽  
Internal Space ◽  
Minkowski Space Time ◽  
Antiparticle State

It is shown here that the holomorphic quantum mechanics in a complexified Minkowski space-time helps us to study the geometrical feature of the internal space of a particle and its relevance with conformal geometry. It is noted that the conformal reflection can be depicted in the formalism of an internal helicity which takes the value [Formula: see text] and [Formula: see text] for the particle and antiparticle state. This again can be described in the framework of holomorphic quantum mechanics in terms of the half-orbital angular momentum of a constituent in an anisotropic space in the sense of Minkowski space-time with a fixed lz value for the particle and antiparticle configuration when a composite system is considered. A massive or massless spinor moving with such characteristic in the configuration of a composite system can be depicted as a Cartan semispinor and behaves as a twistor. The doublet of such spinors with opposite helicities represent an eight-component conformal spinor. The internal symmetry group SU(3) for a composite system of hadrons can then be realized from the reflection group. This formalism reveals the microlocal region of a complexified Minkowski space-time as a twistor space.

Sign in / Sign up

Export Citation Format

Share Document