scholarly journals Space-Time in Quantum Theory

2021 ◽  
Vol 51 (2) ◽  
Author(s):  
H. Capellmann
Keyword(s):  
Quantum Theory ◽  
Quantum Physics ◽  
Equations Of Motion ◽  
Universal Constant ◽  
Space Time ◽  
Relativity Theory ◽  
Integer Number ◽  
Commutation Relations ◽  
Quantum Transitions ◽  
Quantum Equations

AbstractQuantum Theory, similar to Relativity Theory, requires a new concept of space-time, imposed by a universal constant. While velocity of light c not being infinite calls for a redefinition of space-time on large and cosmological scales, quantization of action in terms of a finite, i.e. non vanishing, universal constant h requires a redefinition of space-time on very small scales. Most importantly, the classical notion of “time”, as one common continuous time variable and nature evolving continuously “in time”, has to be replaced by an infinite manifold of transition rates for discontinuous quantum transitions. The fundamental laws of quantum physics, commutation relations and quantum equations of motion, resulted from Max Born’s recognition of the basic principle of quantum physics: To each change in nature corresponds an integer number of quanta of action. Action variables may only change by integer values of h, requiring all other physical quantities to change by discrete steps, “quantum jumps”. The mathematical implementation of this principle led to commutation relations and quantum equations of motion. The notion of “point” in space-time looses its physical significance; quantum uncertainties of time, position, just as any other physical quantity, are necessary consequences of quantization of action.

scholarly journals A contribution to modern ideas on the quantum theory

1927 ◽  
Vol 115 (770) ◽  
pp. 208-214
Keyword(s):  
Quantum Theory ◽  
Kinetic Energy ◽  
Line Element ◽  
Natural Extension ◽  
Space Time ◽  
Relativity Theory ◽  
Unit Mass ◽  
The World ◽  
Free Particles ◽  
Theory Of Gravitation

The relativity theory of gravitation indicates that space-time is a four dimensional continuum in which the line element is measured by the equation ( ds ) 2 = g mn dx m dx n , (1) the notation being that generally adopted. The world-lines or natural tracks of free particles in this space are geodesics. From (1) we have g mn dx m /ds . dx n /ds = 1, (2) the quantity on the left being an expression corresponding to the kinetic energy of ordinary dynamics for a particle of unit mass. This correspondence is readily appreciated if it be noted that dx m /ds is the natural extension of the velocity, dx m /dt .

scholarly journals Notes on Conservation Laws, Equations of Motion of Matter, and Particle Fields in Lorentzian and Teleparallel de Sitter Space-Time Structures

2016 ◽  
Vol 2016 ◽  
pp. 1-27 ◽  
Author(s):  
Waldyr A. Rodrigues ◽  
Samuel A. Wainer
Keyword(s):  
Equations Of Motion ◽  
Killing Vector ◽  
De Sitter Space ◽  
Momentum Conservation ◽  
Space Time ◽  
Relativity Theory ◽  
De Sitter ◽  
Metric Tensor ◽  
Clifford Bundle ◽  
Time Structures

We discuss the physics of interacting fields and particles living in a de Sitter Lorentzian manifold (dSLM), a submanifold of a 5-dimensional pseudo-Euclidean (5dPE) equipped with a metric tensor inherited from the metric of the 5dPE space. The dSLM is naturally oriented and time oriented and is the arena used to study the energy-momentum conservation law and equations of motion for physical systems living there. Two distinct de Sitter space-time structuresMdSLandMdSTPare introduced given dSLM, the first equipped with the Levi-Civita connection of its metric field and the second with a metric compatible parallel connection. Both connections are used only as mathematical devices. Thus, for example,MdSLis not supposed to be the model of any gravitational field in the General Relativity Theory (GRT). Misconceptions appearing in the literature concerning the motion of free particles in dSLM are clarified. Komar currents are introduced within Clifford bundle formalism permitting the presentation of Einstein equation as a Maxwell like equation and proving that in GRT there are infinitely many conserved currents. We prove that in GRT even when the appropriate Killing vector fields exist it is not possible to define a conserved energy-momentum covector as in special relativistic theories.

scholarly journals On the Reality of Quantum Collapse and the Emergence of Space-Time

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 323
Author(s):  
Andreas Schlatter
Keyword(s):  
Quantum Physics ◽  
Space Time ◽  
Relativity Theory ◽  
Unitary Symmetry ◽  
Open Questions ◽  
New Perspective

We present a model, in which quantum-collapse is supposed to be real as a result of breaking unitary symmetry, and in which we can define a notion of “becoming”. We show how empirical space-time can emerge in this model, if duration is measured by light-clocks. The model opens a possible bridge between Quantum Physics and Relativity Theory and offers a new perspective on some long-standing open questions, both within and between the two theories.

EQUATIONS OF MOTION FOR SPACE-TIME-MATTER THEORY

2013 ◽  
Vol 10 (06) ◽  
pp. 1350018
Author(s):  
AUREL BEJANCU
Keyword(s):  
Equations Of Motion ◽  
Space Time ◽  
Relativity Theory ◽  
Covariant Form ◽  
General Relativity Theory ◽  
Full Generality ◽  
New Approach ◽  
Base Manifold ◽  
Matter Theory ◽  
Kaluza Klein

The purpose of this paper is to present, in a covariant form and in their full generality, the equations of motion for space-time-matter (STM) theory. The whole study is based on the new approach of STM theory developed in our first paper [1] of this series. We show that the theory of geodesics in a general Kaluza–Klein space is best presented and explained by splitting the set of all geodesics into horizontal and non-horizontal geodesics. It is noteworthy that the horizontal geodesics (respectively, non-horizontal geodesics) project on the base manifold on motions which generalize the motions from general relativity theory (respectively, motions from Lorentz force equations).

Atoms of Space and Time

2020 ◽  
pp. 135-151
Author(s):  
Demetris Nicolaides
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Physics ◽  
Space Time ◽  
Heisenberg Uncertainty Principle ◽  
Quantum Jump ◽  
Time And Motion ◽  
Scientific Hypothesis ◽  
Heisenberg Uncertainty

Epicurus argued that the Democritean atoms couldn’t move, unless space, time, and motion were radically reimagined. In addition to material atoms (smallest cuts of matter), there exist space “atoms” (smallest spatial expanses) and time “atoms” (smallest time intervals)! Also, he thought an atom’s motion is quantum! It moves from here to there without passing through the points in between—exactly the meaning of a quantum jump in quantum physics (presuming motion does occur). An atom spontaneously swerves (creating uncertainty in its whereabouts), a feature added by Epicurus in a first-ever attempt to escape Democritean determinism and subject human free will to a scientific hypothesis. Space atoms are required by loop quantum gravity (which unifies quantum theory with general relativity). The cause of the most consequential premise of quantum mechanics—the Heisenberg uncertainty principle—will be cautiously speculated with an original idea, using the Epicurean theory of space, time, and motion.

Emergences in Quantum Measurement Processes

KronoScope ◽  
2013 ◽  
Vol 13 (1) ◽  
pp. 85-95 ◽  
Author(s):  
Roger Balian
Keyword(s):  
Quantum Mechanics ◽  
Quantum Physics ◽  
Equations Of Motion ◽  
Quantum Measurements ◽  
Dynamical Process ◽  
Measuring Apparatus ◽  
Fundamental Theory ◽  
Quantum Equations ◽  
Probabilistic Nature ◽  
Standing Problem

Abstract Quantum mechanics is acknowledged as the fundamental theory on which the whole fabric of physics is supposed to rely. And yet, the features of quantum measurements, processes that provide information about microscopic objects, seem to contradict the principles of quantum mechanics. We make a qualitative presentation of this long standing problem and give an idea of recent progress in the elucidation of the paradox. Although governed solely by the quantum equations of motion, the dynamical process involving the tested system and the measuring apparatus veils the quantum oddities that oppose our standard logic and gives rise to the expected properties of measurements. In spite of the irreducibly probabilistic nature of the underlying quantum physics, classical concepts emerge, such as standard probabilities, ordinary correlations, disappearance of quantum fluctuations, and the possibility of making statements about individual systems.

Modified field equations from a complexified nonlocal metric

2019 ◽  
Vol 97 (8) ◽  
pp. 816-827
Author(s):  
Rami Ahmad El-Nabulsi
Keyword(s):  
General Relativity ◽  
Covariant Derivative ◽  
Equations Of Motion ◽  
Space Time ◽  
Relativity Theory ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
General Relativity Theory ◽  
Higher Derivative ◽  
Tangent Vectors

We argue that it is possible to obtain higher-derivative Einstein’s field equations by means of an extended complexified backward–forward nonlocal extension of the space–time metric, which depends on space–time vectors. Our approach generalizes the notion of the covariant derivative along tangent vectors of a given manifold, and accordingly many of the differential geometrical operators and symbols used in general relativity. Equations of motion are derived and a nonlocal complexified general relativity theory is formulated. A number of illustrations are proposed and discussed accordingly.

Topology knots and hierarchy problem

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Dimensional Space ◽  
Space Time ◽  
Elementary Particles ◽  
Hierarchy Problem ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
New Formula

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.

scholarly journals A brief review of E theory

2016 ◽  
Vol 31 (26) ◽  
pp. 1630043 ◽  
Author(s):  
Peter West
Keyword(s):  
Infinite Number ◽  
Equations Of Motion ◽  
Space Time ◽  
Unified Theory ◽  
Dynamical Equations ◽  
Supergravity Theory ◽  
Maximal Supergravity ◽  
Abdus Salam ◽  
Strings And Branes ◽  
Time Lead

I begin with some memories of Abdus Salam who was my PhD supervisor. After reviewing the theory of nonlinear realisations and Kac–Moody algebras, I explain how to construct the nonlinear realisation based on the Kac–Moody algebra [Formula: see text] and its vector representation. I explain how this field theory leads to dynamical equations which contain an infinite number of fields defined on a space–time with an infinite number of coordinates. I then show that these unique dynamical equations, when truncated to low level fields and the usual coordinates of space–time, lead to precisely the equations of motion of 11-dimensional supergravity theory. By taking different group decompositions of [Formula: see text] we find all the maximal supergravity theories, including the gauged maximal supergravities, and as a result the nonlinear realisation should be thought of as a unified theory that is the low energy effective action for type II strings and branes. These results essentially confirm the [Formula: see text] conjecture given many years ago.

scholarly journals Relativity and the quantum theory

1928 ◽  
Vol 117 (778) ◽  
pp. 630-637 ◽  
Keyword(s):  
Quantum Theory ◽  
Space Time ◽  
Theory Of Gravitation ◽  
The Law

In Einstein’s theory of gravitation it is assumed that the geometry of space- time is characterised by the following equation for the measurement of displacement:— ds 2 = g mn dx m dx n { m n = 1, 2, 3, 4, the sign of summation being omitted for convenience. It is supposed that the coefficients, of which g mn is the type, are dependent upon the content of space, and the relation existing between them is the law of gravitation.

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