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 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 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 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 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.

scholarly journals Instantaneous Quantum Description of Photonic Wavefronts and Applications

2018 ◽  
Author(s):  
Andre Vatarescu
Keyword(s):  
Quantum States ◽  
Expectation Values ◽  
Direct Evaluation ◽  
Expectation Value ◽  
Quantum Description ◽  
Instantaneous Phase ◽  
Consecutive Number ◽  
Phase Sensitive ◽  
Pure States ◽  
Phase Sensitive Amplification

By imposing the condition of non-vanishing expectation values for the amplitude and phase of field operators, pure quantum states are identified composed of two consecutive number states.  These pure states also deliver noise-free radiation modes restricting the “half-photon noise” to the expectation value of the lowest level of dynamic and coherent number states. As a result, instantaneous phase-sensitive amplification of photons is easily controlled   and   direct evaluation of time or distance - varying wavefront distributions of photons and phases can be carried out for sub-Poissonian distributions of photons without the need for quasi-probabilities.

Reversibly Sampling Conformations and Binding Modes Using Molecular Darting

2020 ◽  
Author(s):  
Samuel C. Gill ◽  
David Mobley
Keyword(s):  
Monte Carlo ◽  
Ligand Binding ◽  
Binding Sites ◽  
Degrees Of Freedom ◽  
Dynamics Simulation ◽  
Hiv Integrase ◽  
Binding Modes ◽  
System A ◽  
Multiple Binding ◽  
Internal Degrees Of Freedom

<div>Sampling multiple binding modes of a ligand in a single molecular dynamics simulation is difficult. A given ligand may have many internal degrees of freedom, along with many different ways it might orient itself a binding site or across several binding sites, all of which might be separated by large energy barriers. We have developed a novel Monte Carlo move called Molecular Darting (MolDarting) to reversibly sample between predefined binding modes of a ligand. Here, we couple this with nonequilibrium candidate Monte Carlo (NCMC) to improve acceptance of moves.</div><div>We apply this technique to a simple dipeptide system, a ligand binding to T4 Lysozyme L99A, and ligand binding to HIV integrase in order to test this new method. We observe significant increases in acceptance compared to uniformly sampling the internal, and rotational/translational degrees of freedom in these systems.</div>

scholarly journals A novel class of translationally invariant spin chains with long-range interactions

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
B. Basu-Mallick ◽  
F. Finkel ◽  
A. González-López
Keyword(s):  
Long Range ◽  
Degrees Of Freedom ◽  
Spin Chains ◽  
Open Chain ◽  
New Class ◽  
Spin Interactions ◽  
Long Range Interactions ◽  
Spin Reversal ◽  
Twisted Yangian ◽  
Internal Degrees Of Freedom

Abstract We introduce a new class of open, translationally invariant spin chains with long-range interactions depending on both spin permutation and (polarized) spin reversal operators, which includes the Haldane-Shastry chain as a particular degenerate case. The new class is characterized by the fact that the Hamiltonian is invariant under “twisted” translations, combining an ordinary translation with a spin flip at one end of the chain. It includes a remarkable model with elliptic spin-spin interactions, smoothly interpolating between the XXX Heisenberg model with anti-periodic boundary conditions and a new open chain with sites uniformly spaced on a half-circle and interactions inversely proportional to the square of the distance between the spins. We are able to compute in closed form the partition function of the latter chain, thereby obtaining a complete description of its spectrum in terms of a pair of independent su(1|1) and su(m/2) motifs when the number m of internal degrees of freedom is even. This implies that the even m model is invariant under the direct sum of the Yangians Y (gl(1|1)) and Y (gl(0|m/2)). We also analyze several statistical properties of the new chain’s spectrum. In particular, we show that it is highly degenerate, which strongly suggests the existence of an underlying (twisted) Yangian symmetry also for odd m.

scholarly journals Complex Langevin calculations in QCD at finite density

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Yuta Ito ◽  
Hideo Matsufuru ◽  
Yusuke Namekawa ◽  
Jun Nishimura ◽  
Shinji Shimasaki ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Expansion Method ◽  
Finite Density ◽  
Fermi Sphere ◽  
Expectation Value ◽  
Sign Problem ◽  
Zero Momentum ◽  
Effective Theories ◽  
Severe Sign

Abstract We demonstrate that the complex Langevin method (CLM) enables calculations in QCD at finite density in a parameter regime in which conventional methods, such as the density of states method and the Taylor expansion method, are not applicable due to the severe sign problem. Here we use the plaquette gauge action with β = 5.7 and four-flavor staggered fermions with degenerate quark mass ma = 0.01 and nonzero quark chemical potential μ. We confirm that a sufficient condition for correct convergence is satisfied for μ/T = 5.2 − 7.2 on a 83 × 16 lattice and μ/T = 1.6 − 9.6 on a 163 × 32 lattice. In particular, the expectation value of the quark number is found to have a plateau with respect to μ with the height of 24 for both lattices. This plateau can be understood from the Fermi distribution of quarks, and its height coincides with the degrees of freedom of a single quark with zero momentum, which is 3 (color) × 4 (flavor) × 2 (spin) = 24. Our results may be viewed as the first step towards the formation of the Fermi sphere, which plays a crucial role in color superconductivity conjectured from effective theories.

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