scholarly journals Is gravitational mass of a composite quantum body equivalent to its energy?

Open Physics ◽  
2013 ◽  
Vol 11 (8) ◽  
Author(s):  
Andrei Lebed
Keyword(s):  
Gravitational Field ◽  
Mass Operator ◽  
Energy Operator ◽  
Microscopic Level ◽  
Quantum States ◽  
Gravitational Mass ◽  
Expectation Values ◽  
The Earth ◽  
Stationary Quantum ◽  
Passive Gravitational Mass

AbstractWe define passive gravitational mass operator of a hydrogen atom in the post-Newtonian approximation of general relativity and show that it does not commute with energy operator, taken in the absence of gravitational field. Nevertheless, the equivalence between the expectation values of passive gravitational mass and energy is shown to survive for stationary quantum states. Inequivalence between passive gravitational mass and energy at a macroscopic level results in time dependent oscillations of the expectation values of passive gravitational mass for superpositions of stationary quantum states, where the equivalence restores after averaging over time. Inequivalence between gravitational mass and energy at a microscopic level reveals itself as unusual electromagnetic radiation, emitted by the atoms, supported and moved in the Earth gravitational field with constant velocity using spacecraft or satellite, which can be experimentally measured.

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 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.

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.

scholarly journals Breakdown of the Einstein’s Equivalence Principle for a quantum body

2020 ◽  
Vol 35 (20) ◽  
pp. 2030010
Author(s):  
Andrei G. Lebed
Keyword(s):  
Equivalence Principle ◽  
Gravitational Mass ◽  
Hydrogen Atoms ◽  
Expectation Values ◽  
Einstein's Equation ◽  
Stationary Quantum ◽  
Einstein's Equivalence Principle ◽  
Passive Gravitational Mass ◽  
Theoretical Results ◽  
Quantum Ensembles

We review our recent theoretical results about inequivalence between passive gravitational mass and energy for a composite quantum body at a macroscopic level. In particular, we consider macroscopic ensembles of the simplest composite quantum bodies — hydrogen atoms. Our results are as follows. For the most ensembles, the Einstein’s Equivalence Principle is valid. On the other hand, we discuss that for some special quantum ensembles — ensembles of the coherent superpositions of the stationary quantum states in the hydrogen atoms (which we call Gravitational demons) — the Equivalence Principle between passive gravitational mass and energy is broken. We show that, for such superpositions, the expectation values of passive gravitational masses are not related to the expectation values of energies by the famous Einstein’s equation, i.e. [Formula: see text]. Possible experiments at the Earth’s laboratories are briefly discussed, in contrast to the numerous attempts and projects to discover the possible breakdown of the Einstein’s Equivalence Principle during the space missions.

scholarly journals Inequivalence between gravitational mass and energy due to quantum effects at microscopic and macroscopic levels

2017 ◽  
Vol 26 (13) ◽  
pp. 1730022 ◽  
Author(s):  
Andrei G. Lebed
Keyword(s):  
Hydrogen Atom ◽  
Quantum Effects ◽  
Gravitational Mass ◽  
Expectation Values ◽  
Gedanken Experiment ◽  
Einstein's Equation ◽  
Experimental Possibility ◽  
Stationary Quantum ◽  
The Masses ◽  
Passive Gravitational Mass

In this paper, we review recent theoretical results, demonstrating breakdown of the equivalence between active and passive gravitational masses and energy due to quantum effects in general relativity. In particular, we discuss the simplest composite quantum body — a hydrogen atom — and define its gravitational masses operators. Using Gedanken experiment, we show that the famous Einstein’s equation, [Formula: see text], is broken with small probability for passive gravitational mass of the atom. It is important that the expectation values of both active and passive gravitational masses satisfy the above-mentioned equation for stationary quantum states. Nevertheless, we stress that, for quantum superpositions of stationary states in a hydrogen atom, where the expectation values of energy are constant, the expectation values of the masses oscillate in time and, thus, break the Einstein’s equation. We briefly discuss experimental possibility to observe the above-mentioned time-dependent oscillations. In this review, we also improve several drawbacks of the original pioneering works.

INFLUENCE OF THE GRAVITATIONAL FIELD ON THE QUANTUM STATES OF THE ELECTRON IN A PENNING TRAP

1996 ◽  
Vol 11 (17) ◽  
pp. 1429-1443
Author(s):  
R. STAUDT ◽  
U.E. SCHRÖDER
Keyword(s):  
Electromagnetic Field ◽  
Gravitational Field ◽  
Dirac Equation ◽  
Penning Trap ◽  
Energy Levels ◽  
Quantum States ◽  
Minimal Coupling ◽  
Relative Shift ◽  
The Earth ◽  
Resulting Effect

Starting from the general covariant Dirac equation with minimal coupling of an electromagnetic field the corrections to the energy levels of the electron in a Penning trap caused by the gravitational field of the Earth are computed. Our discussion shows that the resulting effect is detectable only at the specific eigenfrequencies of the electron. The relative shift of these frequencies due to the gravitational field is found to be 2.1×10–9. It is briefly indicated how this effect in principle could be observed in suitable experiments performed with higher precision.

scholarly journals A spectroscopy approach to measure the gravitational mass of antihydrogen

2014 ◽  
Vol 30 ◽  
pp. 1460266 ◽  
Author(s):  
A. Yu. Voronin ◽  
V. V. Nesvizhevsky ◽  
G. Dufour ◽  
P. Debu ◽  
A. Lambrecht ◽  
...  
Keyword(s):  
Applied Field ◽  
Free Fall ◽  
Time Measurement ◽  
Quantum States ◽  
Gravitational Mass ◽  
Spatial Density ◽  
Material Surface ◽  
A Value ◽  
The Earth ◽  
Resonant Transitions

We study a method to induce resonant transitions between antihydrogen [Formula: see text] quantum states above a material surface in the gravitational field of the Earth. The method consists of applying a gradient of magnetic field, which is temporally oscillating with the frequency equal to a frequency of transition between gravitational states of antihydrogen. A corresponding resonant change in the spatial density of antihydrogen atoms could be measured as a function of the frequency of applied field. We estimate an accuracy of measuring antihydrogen gravitational states spacing and show how a value of the gravitational mass of the [Formula: see text] atom could be deduced from such a measurement. We also demonstrate that a method of induced transitions could be combined with a free-fall-time measurement in order to further improve the precision.

The analysis is geometrically stable orbits of spacecraft remote sensing of the Еarth

2018 ◽  
Vol 15 (1) ◽  
pp. 12-22
Author(s):  
V. M. Artyushenko ◽  
D. Y. Vinogradov
Keyword(s):  
Remote Sensing ◽  
Gravitational Field ◽  
State Vector ◽  
Semimajor Axis ◽  
The State ◽  
Zonal Harmonics ◽  
The Earth ◽  
Conditions Of Stability

The article reviewed and analyzed the class of geometrically stable orbits (GUO). The conditions of stability in the model of the geopotential, taking into account the zonal harmonics. The sequence of calculation of the state vector of GUO in the osculating value of the argument of the latitude with the famous Ascoli-royski longitude of the ascending node, inclination and semimajor axis. The simulation is obtained the altitude profiles of SEE regarding the all-earth ellipsoid model of the gravitational field of the Earth given 7 and 32 zonal harmonics.

Spheric radial basis functions in Mahalanobis measuring for displaying local field features

2019 ◽  
Vol 952 (10) ◽  
pp. 2-9
Author(s):  
Yu.M. Neiman ◽  
L.S. Sugaipova ◽  
V.V. Popadyev
Keyword(s):  
Gravitational Field ◽  
Quadratic Form ◽  
Local Field ◽  
Euclidean Distance ◽  
Basis Functions ◽  
Spherical Functions ◽  
Local Models ◽  
Stationary Field ◽  
Modeling Process ◽  
The Earth

As we know the spherical functions are traditionally used in geodesy for modeling the gravitational field of the Earth. But the gravitational field is not stationary either in space or in time (but the latter is beyond the scope of this article) and can change quite strongly in various directions. By its nature, the spherical functions do not fully display the local features of the field. With this in mind it is advisable to use spatially localized basis functions. So it is convenient to divide the region under consideration into segments with a nearly stationary field. The complexity of the field in each segment can be characterized by means of an anisotropic matrix resulting from the covariance analysis of the field. If we approach the modeling in this way there can arise a problem of poor coherence of local models on segments’ borders. To solve the above mentioned problem it is proposed in this article to use new basis functions with Mahalanobis metric instead of the usual Euclidean distance. The Mahalanobis metric and the quadratic form generalizing this metric enables us to take into account the structure of the field when determining the distance between the points and to make the modeling process continuous.

scholarly journals Comment on “Measurement of quantum states of neutrons in the Earth’s gravitational field”

2003 ◽  
Vol 68 (10) ◽  
Author(s):  
Johan Hansson ◽  
David Olevik ◽  
Christian Türk ◽  
Hanna Wiklund
Keyword(s):  
Gravitational Field ◽  
Quantum States ◽  
Earth’S Gravitational Field
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