The validity of the formulaE=mc 2 for gravitational energy

Theoretical evidence for the validity of the formulaE =mc ² for gravitational energy in general relativity is reviewed. For isolated bodies the formula applies to both the inertial mass and the mass as a source of gravity. The formula also holds for the case of the mass density (as a source of gravity) of an inhomogeneous medium with small-scale gravitational interactions.     

A new type of quantum interferometer for gravitational wave detection

We present an orientational quantum interferometer sensitive to gravitational waves that is based on orienting quantum objects like molecules, atoms, or nuclei in space. The detection principle is based on inducing non-sphericity to the corresponding wave functions by light-pulses. In the field of a gravitational wave these objects then possess spectra that depend on their orientation in space. In our measurement scheme we investigate the adiabatic influence of a monochromatic gravitational wave over a quarter gravitational wave period and compare the corresponding frequencies at instances with maximal and vanishing gravitational wave elongation. We therefore explore the effect over a quarter gravitational wave period (or wavelength) and the resulting frequency shift scales with the binding energy of the system times the amplitude of the gravitational wave. In particular, a gravitational wave with amplitude h = 10⁻²³ will induce a frequency shift of the order of 110 μHz for an atom interferometer based on a 91-fold charged uranium ion.     

Theory of Gravitational-Inertial Field of Universe

In this paper the basic proposition is a generalization of the metric tensor by introduction of an inertial field tensor satisfying ?_ig_lm ? g_lm;i ≠ 0. On the basis of variational equations a system of more general covariant equations of gravitational-inertial field is obtained. In Einstein's approximation these equations reduce to the field equations of Einstein. The solution of fundamental problems of generl taheory of relativity by means of the new equations give the same results as Einstein's equations. However application of these equations to the cosmologic problem leads to following results: 1. All Galaxies in the Universe (actually all bodies if gravitational attraction is not considered) “disperse” from each other according to Hubble's law. Thus contrary to Friedmann's theory (according to which the “expansion of Universe” began from the singular state with an infinite velocity) the velocity of “dispersion” of bodies begins from the zero value and in the limit tends to the velocity of light. 2. The “dispertion” of bodies represents a free motion in the inertial field and Hubble's law represents a law of motion of free bodies in the inertial field - the law of inertia. All critical systems (with Schwarzschild radius) are specific because they exist in maximal inertial and gravitational potentials. The Universe represents a critical system, it exists under the Schwarzschild radius. In the high-potential inertial and gravitational fields the material mass in a static state or in the process of motion with decelleration is subject to an inertial and gravitational “annihilation”. Under the maximal value of inertial and gravitational potentials (= c²) the material mass is completely “evaporated” transforming into a radiation mass. The latter is concentrated in the “horizon” of the critical system. All critical systems –“black holes”- represent geon systems, i.e., the local formations of gravitational-electromagnetic radiations, held together by their own gravitational and inertial fields. The Universe, being a critical system, is “wrapped” in a geon crown. The Universe is in a state of dynamical equilibrium. Near the external part of its boundary surface a transformation of matter into electromagnetic-gravitational-neutrineal energy (geon mass) takes place. Inside the Universe, in the galaxies takes place the synthesis of matter from geon mass, penetrating from the external part of the world (from geon crown) by means of a tunneling mechanism. The geon system may be considered as a natural entire cybernetic system.     

Mass Parameter Quantization in the FRW Cosmological Model

Using the canonical quantum theory apply to spherically symmetric pure gravitational systems, we present the study of the closed Friedmann-Robertson-Walker (FRW) cosmological model filled with pressureless matter (dust) content as a toy model. The Wheeler-DeWitt equation is view as the Schrödinger equation for the linear harmonic oscillator with energy E. We show that such type of universe has a quantized masses of the order of the Planck mass and harmonic oscillator wave functions, where a dual symmetry emerge among the quantum parameters.     

Unitary cocycle representations of the Galilean line group: Quantum mechanical principle of equivalence

We present a formalism of Galilean quantum mechanics in non-inertial reference frames and discuss its implications for the equivalence principle. This extension of quantum mechanics rests on the Galilean line group, the semidirect product of the real line and the group of analytic functions from the real line to the Euclidean group in three dimensions. This group provides transformations between all inertial and non-inertial reference frames and contains the Galilei group as a subgroup. We construct a certain class of unitary representations of the Galilean line group and show that these representations determine the structure of quantum mechanics in non-inertial reference frames. Our representations of the Galilean line group contain the usual unitary projective representations of the Galilei group, but have a more intricate cocycle structure. The transformation formula for the Hamiltonian under the Galilean line group shows that in a non-inertial reference frame it acquires a fictitious potential energy term that is proportional to the inertial mass, suggesting the equivalence of inertial mass and gravitational mass in quantum mechanics.     

Theory of Gravitational-Inertial Field of Universe. II. On Critical Systems in Universe

Application of the equations of the gravitational-inertial field to the problem of free motion in the inertial field (to the cosmologic problem) leads to results according to which 1. all Galaxies in the Universe “disperse” from each other according to Hubble's law, 2. the “dispersion” of bodies represents a free motion in the inertial field and Hubble's law represents a law of motion of free body in the inertial field, 3. for arbitrary mean distribution densities of space masses different from zero the space is Lobachevskian. All critical systems (with Schwarzschild radius) are specific because they exist in maximalinertial and gravitational potentials. The Universe represents a critical system, it exists under the Schwarzschild radius. In high-potential inertial and gravitational fields the material mass in a static state or in motion with deceleration is subject to an inertial and gravitational “annihilation”. At the maximal value of inertial and gravitational potentials (= c²) the material mass is being completely “evaporated” transforming into radiation mass. The latter is being concentrated in the “horizon” of the critical system. All critical systems-black holes-represent geon systems, i.e. local formations of gravitational-electromagnetic radiations, held together by their own gravitational and inertial fields. The Universe, being a critical system, is “wrapped” in a geon crown.     

On the intrinsic entropy of the gravitational field

I show that in linearized general relativity it is impossible to construct a detector by the use of which the quantum state of the linearized gravitational field could be reliably determined. This is because there is no material satisfying the positive energy condition which can serve as a good conductor or absorber of gravitational radiation over a finite range of frequencies. If this property is true of the full theory then one can conclude that a certain proportion of both the energy and information carried by a gravitational wave is irreversibly lost, and that there is a correspondingintrinsic entropy associated with any distribution of gravitational radiation.     

Gravitational and inertial mass of bodies of interacting electrical charges

Starting from the equations of motion of particles interacting with both electromagnetic and gravitational fields, the (passive) gravitational mass (M _g) and the inertial mass (M _i) of the total system of interacting charges is calculated. It is found that in both Einstein's General Relativity and the scalar-tensor gravitational theory of Brans and Dicke,M _g andM _i are both equal to the Special Relativistic energy of the system of interacting charged particles. Therefore, both theories are compatible with the high accuracy measurements of theM _g/M _i ratio of laboratory objects. This work was supported by National Aeronautics and Space Administration grant NGR 27-001-035.     

Once upon a time,in the Soviet Union …

Radiation reaction (but, more generally, fluctuations and dissipation) occurs when a system interacts with a heat bath, a particular case being the interaction of an electron with the radiation field. We have developed a general theory for the case of a quantum particle in a general potential (but, in more detail, an oscillator potential) coupled to an arbitrary heat bath at arbitrary temperature, and in an external time-dependent c-number field. The results may be applied to a large variety of problems in physics but we concentrate by showing in detail the application to the blackbody radiation heat bath, giving an exact result for the radiation reaction problem which has no unsatisfactory features such as the runaway solutions associated with the Abraham–Lorentz theory. In addition, we show how atomic energy and free energy shifts due to temperature may be calculated. Finally, we give a brief review of applications to Josephson junctions, quantum statistical mechanics, mesoscopic physics, quantum information, noise in gravitational wave detectors, Unruh radiation and the violation of the quantum regression theorem.     

The End Results of General Relativity Theory Via Just Energy Conservation and Quantum Mechanics

Herein we present a whole new approach that leads to the end results of the general theory of relativity via just the law of conservation of energy (broadened to embody the mass and energy equivalence of the special theory of relativity) and quantum mechanics. We start with the following postulate. Postulate: The rest mass of an object bound to a celestial body amounts less than its rest mass measured in empty space, and this, as much as its binding energy vis-á-vis the gravitational field of concern.     

Thermodynamics of relativistic quantum fields confined in cavities

We investigate the quantum thermodynamical properties of localised relativistic quantum fields, and how they can be used as quantum thermal machines. We study the efficiency and power of energy transfer between the classical gravitational degrees of freedom, such as the energy input due to the motion of boundaries or an impinging gravitational wave, and the excitations of a confined quantum field. We find that the efficiency of energy transfer depends dramatically on the input initial state of the system. Furthermore, we investigate the ability of the system to extract energy from a gravitational wave and store it in a battery. This process is inefficient in optical cavities but is significantly enhanced when employing trapped Bose Einstein condensates. We also employ standard fluctuation results to obtain the work probability distribution, which allows us to understand how the efficiency is related to the dissipation of work. Finally, we apply our techniques to a setup where an impinging gravitational wave excites the phononic modes of a Bose Einstein condensate. We find that, in this case, the percentage of energy transferred to the phonons approaches unity after a suitable amount of time. These results give a quantitative insight into the thermodynamic behaviour of relativistic quantum fields confined in cavities.     

Dirac equation for the Hulthén potential within the Yukawa-type tensor interaction

Using the Nikiforov-Uvarov (NU) method, pseudospin and spin symmetric solutions of the Dirac equation for the scalar and vector Hulthén potentials with the Yukawa-type tensor potential are obtained for an arbitrary spin-orbit coupling quantum number κ. We deduce the energy eigenvalue equations and corresponding upper- and lower-spinor wave functions in both the pseudospin and spin symmetry cases. Numerical results of the energy eigenvalue equations and the upper- and lower-spinor wave functions are presented to show the effects of the external potential and particle mass parameters as well as pseudospin and spin symmetric constants on the bound-state energies and wave functions in the absence and presence of the tensor interaction.     

Theoretical Study of the Energies of the Oscillating System with a Well- Distributed Mass of the Spring

The energy of a spring with a well-distributed mass m_s is theoretically studied in this paper. The solution of the wave equation is derived in detail, and then the kinetic energy and potential energy of the spring are studied with the wave equation, as well as the kinetic energy of the oscillating mass M. The kinetic energy and potential energy of the spring, and total energy are numerically simulated for different ratios m_s/M with considering the spring’s mass, which makes the property of energy of the oscillating system understood easily.     

有效质量差异和电场对GaN/AlxGa1-xN球形量子点电子结构的影响

用平面波展开法对GaN/Al_xGa_1-xN球形量子点中类氢杂质态能级随量子点半径、Al组分以及结合能随Al组分的变化规律进行了详细讨论.计算了量子点内外有效质量差异对杂质态能级和结合能的修正,结果表明对于Al组分较高的GaN/Al_xGa_1-xN球形量子点,电子有效质量差异对杂质能级和结合能的修正不能忽略.考虑电子有效质量差异后,进一步具体计算了杂质结合能随量子点半 关键词： 球形量子点 平面波展开法 有效质量     

New gravitational experiment with ultracold neutrons

The results of a new neutron gravitation experiment are reported. The change in the energy of a neutron falling to a known height in the Earth’s gravitational field is compensated by an energy quantum ?Θ transferred to the neutron as a result of the phase modulation of the neutron wave. A phase diffraction grating moving across the direction of the propagation of the neutron wave is used as a modulator. The experiment has been carried out with ultracold neutrons Interference filters, neutron analogues of Fabry-Perot interferometers, are used for the spectrometry of ultracold neutrons. The force m _g g _n acting on the neutron in the Earth’s gravitational field has been measured with an accuracy of about 0.2%.     

Gravitational mass and energy gradient in the ultra-strong magnetic fields

The paper aims to apply the complex octonion to explore the influence of the energy gradient on the Eötvös experiment, impacting the gravitational mass in the ultra-strong magnetic fields. Until now the Eötvös experiment has never been validated under the ultra-strong magnetic field. It is aggravating the existing serious qualms about the Eötvös experiment. According to the electromagnetic and gravitational theory described with the complex octonions, the ultra-strong magnetic field must result in a tiny variation of the gravitational mass. The magnetic field with the gradient distribution will generate the energy gradient. These influencing factors will exert an influence on the state of equilibrium in the Eötvös experiment. That is, the gravitational mass will depart from the inertial mass to a certain extent, in the ultra-strong magnetic fields. Only under exceptional circumstances, especially in the case of the weak field strength, the gravitational mass may be equal to the inertial mass approximately. The paper appeals intensely to validate the Eötvös experiment in the ultra-strong electromagnetic strengths. It is predicted that the physical property of gravitational mass will be distinct from that of inertial mass.     

Equivalence Postulate and Quantum Origin of Gravitation

We suggest that quantum mechanics and gravity are intimately related. In particular, we investigate the quantum Hamilton–Jacobi equation in the case of two free particles and show that the quantum potential, which is attractive, may generate the gravitational potential. The investigation, related to the formulation of quantum mechanics based on the equivalence postulate, is based on the analysis of the reduced action. A consequence of this approach is that the quantum potential is always non-trivial even in the case of the free particle. It plays the role of intrinsic energy and may in fact be at the origin of fundamental interactions. We pursue this idea, by making a preliminary investigation of whether there exists a set of solutions for which the quantum potential can be expressed with a gravitational potential leading term which alone would remain in the limit 0. A number of questions are raised for further investigation.     

GaAs/AlxGa1-xAs球形量子点中的电子结构

详细讨论了GaAs/Al_xGa_1-xAs球形量子点内的单电子束缚能级随量子点半径、Al组分以及外电场的变化规律,并计算了考虑量子点内外电子有效质量不同后对电子能级的修正. 另外,用解析和平面波展开两种方法对球形量子点内的电子能级进行了计算,并对计算结果做了比较,发现它们符合的很好. 结论和方法为量子点的研究和应用提供了有益的信息和指导. 关键词： 球形量子点 解析方法 平面波展开方法 有效质量     

Aspects of electrostatics in a weak gravitational field

Several features of electrostatics of point charged particles in a weak, homogeneous, gravitational field are discussed using the Rindler metric to model the gravitational field. Some previously known results are obtained by simpler and more transparent procedures and are interpreted in an intuitive manner. Specifically: (a) We discuss possible definitions of the electric field in curved spacetime (and noninertial frames), argue in favour of a specific definition for the electric field and discuss its properties. (b) We show that the electrostatic potential of a charge at rest in the Rindler frame (which is known and is usually expressed as a complicated function of the coordinates) is expressible as A ₀ = q/λ where λ is the affine parameter distance along the null geodesic from the charge to the field point. (c) This relates well with the result that the electric field lines of a charge coincide with the null geodesics; that is, both light and the electric field lines ‘bend’ in the same manner in a weak gravitational field. We provide a simple proof for this result as well as for the fact that the null geodesics (and field lines) are circles in space. (d) We obtain the sum of the electrostatic forces exerted by one charge on another in the Rindler frame and discuss its interpretation. In particular, we compare the results in the Rindler frame and in the inertial frame and discuss their consistency. (e) We show how a purely electrostatic term in the Rindler frame appears as a radiation term in the inertial frame. (In part, this arises because charges at rest in a weak gravitational field possess additional weight due to their electrostatic energy. This weight is proportional to the acceleration and falls inversely with distance—which are the usual characteristics of a radiation field.) (f) We also interpret the origin of the radiation reaction term by extending our approach to include a slowly varying acceleration. Many of these results might have possible extensions for the case of electrostatics in an arbitrary static geometry.     

Quantum information paradox: Real or fictitious?

One of the outstanding puzzles of theoretical physics is whether quantum information indeed gets lost in the case of black hole (BH) evaporation or accretion. Let us recall that quantum mechanics (QM) demands an upper limit on the acceleration of a test particle. On the other hand, it is pointed out here that, if a Schwarzschild BH exists, the acceleration of the test particle would blow up at the event horizon in violation of QM. Thus the concept of an exact BH is in contradiction with QM and quantum gravity (QG). It is also reminded that the mass of a BH actually appears as an integration constant of Einstein equations. And it has been shown that the value of this integration constant is actually zero! Thus even classically, there cannot be finite mass BHs though zero mass BH is allowed. It has been further shown that during continued gravitational collapse, radiation emanating from the contracting object gets trapped within it by the runaway gravitational field. As a consequence, the contracting body attains a quasi-static state where outward trapped radiation pressure gets balanced by inward gravitational pull and the ideal classical BH state is never formed in a finite proper time. In other words, continued gravitational collapse results in an ‘eternally collapsing object’ which is a ball of hot plasma and which is asymptotically approaching the true BH state with M = 0 after radiating away its entire mass energy. And if we include QM, this contraction must halt at a radius suggested by the highest QM acceleration. In any case no event horizon (EH) is ever formed and in reality, there is no quantum information paradox.