STATIONARY QUANTUM STATES OF THE DIRAC FERMIONS IN THE REISSNER-NORDSTRÖM METRIC

2015 ◽  
Author(s):  
V. I. Dokuchaev ◽  
Yu. N. Eroshenko
Keyword(s):  
Quantum States ◽  
Dirac Fermions ◽  
Stationary Quantum

Bohm's Mysterious 'Quantum Force' and 'Active Information': Alternative Interpretation and Statistical Properties

2001 ◽  
Vol 56 (1-2) ◽  
pp. 205-207 ◽  
Author(s):  
Boon Leong Lan
Keyword(s):  
Time Series ◽  
Power Spectrum ◽  
Important Implication ◽  
Alternative Interpretation ◽  
Quantum States ◽  
Statistical Properties ◽  
Numerical Evidence ◽  
Stationary Quantum ◽  
Non Gaussian ◽  
Quantum Force

AbstractAn alternative interpretation to Bohm’s ‘quantum force’ and ‘active information’ is proposed. Numerical evidence is presented, which suggests that the time series of Bohm’s ‘quantum force’ evaluated at the Bohmian position for non-stationary quantum states are typically non-Gaussian stable distributed with a flat power spectrum in classically chaotic Hamitonian systems. An important implication of these statistical properties is briefly mentioned

scholarly journals Does the Equivalence between Gravitational Mass and Energy Survive for a Composite Quantum Body?

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
A. G. Lebed
Keyword(s):  
Hydrogen Atom ◽  
Mass Operator ◽  
Energy Operator ◽  
Quantum States ◽  
Gravitational Mass ◽  
Hydrogen Atoms ◽  
Expectation Values ◽  
Direct Experiment ◽  
Stationary Quantum ◽  
Passive Gravitational Mass

We define passive and active gravitational mass operators of the simplest composite quantum body—a hydrogen atom. Although they do not commute with its energy operator, the equivalence between the expectation values of passive and active gravitational masses and energy is shown to survive for stationary quantum states. In our calculations of passive gravitational mass operator, we take into account not only kinetic and Coulomb potential energies but also the so-called relativistic corrections to electron motion in a hydrogen atom. Inequivalence between passive and active gravitational masses and energy at a macroscopic level is demonstrated to reveal itself as time-dependent oscillations of the expectation values of the gravitational masses for superpositions of stationary quantum states. Breakdown of the equivalence between passive gravitational mass and energy at a microscopic level reveals itself as unusual electromagnetic radiation, emitted by macroscopic ensemble of hydrogen atoms, moved by small spacecraft with constant velocity in the Earth’s gravitational field. We suggest the corresponding experiment on the Earth’s orbit to detect this radiation, which would be the first direct experiment where quantum effects in general relativity are observed.

scholarly journals Breakdown of the equivalence between gravitational mass and energy due to quantum effects

2019 ◽  
Vol 28 (12) ◽  
pp. 1930020 ◽  
Author(s):  
Andrei G. Lebed
Keyword(s):  
Degrees Of Freedom ◽  
Quantum States ◽  
Gravitational Mass ◽  
Electron Mass ◽  
Expectation Values ◽  
Expectation Value ◽  
State Formula ◽  
Stationary Quantum ◽  
Passive Gravitational Mass ◽  
Internal Degrees Of Freedom

We review our recent theoretical results about inequivalence between passive and active gravitational masses and energy in the semiclassical variant of general relativity, where the gravitational field is not quantized but matter is quantized. To this end, we consider the simplest quantum body with internal degrees of freedom — a hydrogen atom. We concentrate our attention on the following physical effects, related to electron mass. The first one is the inequivalence between passive gravitational mass and energy at the microscopic level. Indeed, the quantum measurement of gravitational mass can give a result which is different from the expected one, [Formula: see text], where the electron is initially in its ground state; [Formula: see text] is the bare electron mass. The second effect is that the expectation values of both the passive and active gravitational masses of stationary quantum states are equivalent to the expectation value of the energy. The most spectacular effects are the inequivalence of the passive and active gravitational masses and the energy at the macroscopic level for an ensemble of coherent superpositions of stationary quantum states. We show that, for such superpositions, the expectation values of passive and active gravitational masses are not related to the expectation value of energy by Einstein’s famous equation, [Formula: see text]. In this paper, we also improve several drawbacks of the original pioneering works.

Construction of stationary quantum states with targeted energies

2011 ◽  
Vol 49 (9) ◽  
pp. 1937-1948
Author(s):  
Chandrachur Das ◽  
Kamal Bhattacharyya
Keyword(s):  
Quantum States ◽  
Stationary Quantum

scholarly journals Breakdown of the equivalence between gravitational mass and energy for a quantum body: Theory and suggested experiments

2015 ◽  
Vol 24 (11) ◽  
pp. 1530027 ◽  
Author(s):  
Andrei G. Lebed
Keyword(s):  
Microscopic Level ◽  
Quantum States ◽  
Gravitational Mass ◽  
Expectation Values ◽  
Expectation Value ◽  
Stationary Quantum ◽  
Body Theory ◽  
Passive Gravitational Mass ◽  
Theoretical Results ◽  
Active Gravitational Mass

In this paper, we review recent theoretical results, obtained for the equivalence between gravitational mass and energy of a composite quantum body as well as for its breakdown at macroscopic and microscopic levels. In particular, we discuss that the expectation values of passive and active gravitational mass operators are equivalent to the expectation value of energy for electron stationary quantum states in hydrogen atom. On the other hand, for superpositions of the stationary quantum states, inequivalence between the gravitational masses and energy appears at a macroscopic level. It reveals itself as time-dependent oscillations of the expectation values of passive and active gravitational masses, which can be, in principle, experimentally measured. Inequivalence between passive gravitational mass and energy at a microscopic level can be experimentally observed as unusual electromagnetic radiation, emitted by a macroscopic ensemble of the atoms. We propose the corresponding experiment, which can be done on the Earth's orbit, using small spacecraft. If such experiment is done it would be the first direct observation of quantum effects in general relativity.

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