Gravitational Collapse in Quantum Einstein Gravity

The existence of spacetime singularities is one of the biggest problems of nowadays physics. According to Penrose, each physical singularity should be covered by a “cosmic censor” which prevents any external observer from perceiving their existence. However, classical models describing the gravitational collapse usually results in strong curvature singularities, which can also remain “naked” for a finite amount of advanced time. This proceedings studies the modifications induced by asymptotically safe gravity on the gravitational collapse of generic Vaidya spacetimes. It will be shown that, for any possible choice of the mass function, quantum gravity makes the internal singularity gravitationally weak, thus allowing a continuous extension of the spacetime beyond the singularity.     

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.     

Nordström’s scalar theory of gravity and the equivalence principle

General Relativity obeys the three equivalence principles, the “weak” one (all test bodies fall the same way in a given gravitational field), the “Einstein” one (gravity is locally effaced in a freely falling reference frame) and the “strong” one (the gravitational mass of a system equals its inertial mass to which all forms of energy, including gravitational energy, contribute). The first principle holds because matter is minimally coupled to the metric of a curved spacetime so that test bodies follow geodesics. The second holds because Minkowskian coordinates can be used in the vicinity of any event. The fact that the latter, strong, principle holds is ultimately due to the existence of superpotentials which allow to define the inertial mass of a gravitating system by means of its asymptotic gravitational field, that is, in terms of its gravitational mass. Nordström’s theory of gravity, which describes gravity by a scalar field in flat spacetime, is observationally ruled out. It is however the only theory of gravity with General Relativity to obey the strong equivalence principle. I show in this paper that this remarkable property is true beyond post-newtonian level and can be related to the existence of a “Nordström-Katz” superpotential.     

On the Gravitization of Quantum Mechanics 1: Quantum State Reduction

This paper argues that the case for “gravitizing” quantum theory is at least as strong as that for quantizing gravity. Accordingly, the principles of general relativity must influence, and actually change, the very formalism of quantum mechanics. Most particularly, an “Einsteinian”, rather than a “Newtonian” treatment of the gravitational field should be adopted, in a quantum system, in order that the principle of equivalence be fully respected. This leads to an expectation that quantum superpositions of states involving a significant mass displacement should have a finite lifetime, in accordance with a proposal previously put forward by Diósi and the author.     

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.     

About “black holes” and dark matter

It is shown that the complete system of classical gravitational equations for an isolated centrally symmetric body yields that: (1) in terms of Galilean coordinates all metric coefficients of the Riemannian space induced by the body cannot be equal to zero or infinity anywhere; (2) they, together with the first-order derivatives, should be continuous everywhere. The equations do not contain solutions corresponding to “black holes,” but admit solutions corresponding to objects for which the surface radius (in terms of standard coordinates) is equal to the double mass of matter under this surface. These objects can make the main contribution to the dark matter of the Universe and explain observed effects, such as gravitational microlensing and other effects. Under certain conditions they can become powerful X-ray sources.     

Comprehensive solution to the cosmological constant,zero-point energy,and quantum gravity problems

We present a solution to the cosmological constant, the zero-point energy, and the quantum gravity problems within a single comprehensive framework. We show that in quantum theories of gravity in which the zero-point energy density of the gravitational field is well-defined, the cosmological constant and zero-point energy problems solve each other by mutual cancellation between the cosmological constant and the matter and gravitational field zero-point energy densities. Because of this cancellation, regulation of the matter field zero-point energy density is not needed, and thus does not cause any trace anomaly to arise. We exhibit our results in two theories of gravity that are well-defined quantum-mechanically. Both of these theories are locally conformal invariant, quantum Einstein gravity in two dimensions and Weyl-tensor-based quantum conformal gravity in four dimensions (a fourth-order derivative quantum theory of the type that Bender and Mannheim have recently shown to be ghost-free and unitary). Central to our approach is the requirement that any and all departures of the geometry from Minkowski are to be brought about by quantum mechanics alone. Consequently, there have to be no fundamental classical fields, and all mass scales have to be generated by dynamical condensates. In such a situation the trace of the matter field energy-momentum tensor is zero, a constraint that obliges its cosmological constant and zero-point contributions to cancel each other identically, no matter how large they might be. In our approach quantization of the gravitational field is caused by its coupling to quantized matter fields, with the gravitational field not needing any independent quantization of its own. With there being no a priori classical curvature, one does not have to make it compatible with quantization.     

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.     

Inertial and gravitational mass in quantum mechanics

We show that in complete agreement with classical mechanics, the dynamics of any quantum mechanical wave packet in a linear gravitational potential involves the gravitational and the inertial mass only as their ratio. In contrast, the spatial modulation of the corresponding energy wave function is determined by the third root of the product of the two masses. Moreover, the discrete energy spectrum of a particle constrained in its motion by a linear gravitational potential and an infinitely steep wall depends on the inertial as well as the gravitational mass with different fractional powers. This feature might open a new avenue in quantum tests of the universality of free fall.     

对于“包含在连续谱量子体系中的决定论性”一文的讨论

对于具有连续能谱的单粒子量子体系,“包含在连续谱量子体系中的决定论性”一文用所谓“双波函数”来描述处于能量本征态的粒子系综中各粒子的量子行为,并且在所谓的“等价定理”中称:双波函数描述在经典极限下将化为经典力学描述.然而,此描述所给出的系综力学量观测值统计分布的预言与通常量子力学不相容;并且,该文对其“等价定理”的证明是不正确的,这个“定理”实际上不成立 关键词： 连续能谱量子体系 双波函数 经典极限     

Vacuum energy: Quantum hydrodynamics vs. quantum gravity

We compare quantum hydrodynamics and quantum gravity. They share many common features. In particular, both have quadratic divergences, and both lead to the problem of the vacuum energy, which, in quantum gravity, transforms to the cosmological constant problem. We show that, in quantum liquids, the vacuum energy density is not determined by the quantum zero-point energy of the phonon modes. The energy density of the vacuum is much smaller and is determined by the classical macroscopic parameters of the liquid, including the radius of the liquid droplet. In the same manner, the cosmological constant is not determined by the zero-point energy of quantum fields. It is much smaller and is determined by the classical macroscopic parameters of the Universe dynamics: the Hubble radius, the Newton constant, and the energy density of matter. The same may hold for the Higgs mass problem: the quadratically divergent quantum correction to the Higgs potential mass term is also cancelled by the microscopic (trans-Planckian) degrees of freedom due to the thermodynamic stability of the whole quantum vacuum.     

Quantum and classical divide: the gravitational case

We study the transition between quantum and classical behaviour of particles in a gravitational quantum well. We analyze how an increase in the particles mass turns the energy spectrum into a continuous one, from an experimental point of view. We also discuss the way these effects could be tested by conducting experiments with atoms and fullerene-type molecules.     

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

We 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.     

INVESTIGATION OF NON-LINFAR SCHRODINGER EQUATION SOLITON SOLUTION

Packet-like soliton solution of the non-linear Schrödinger's equation has been in-vestigated.We found that a state of a free particle can possibly be described by thissoliton solution,with the quantum property and the classical property of a particleas its limiting cases.A set of biorthogonal eigen-functions of non-hermitian opera-tor,which can be used in the pertubation expansion,has been found.We discoveredthat the discrete eigenvalue mode corresponds to the“classical”motion of a particle,and the continuous eigenvalue modes correspond to the“quantum”motion.Wesuggested that the parameter u describing the state of a system can be used to identifywhether the system is“quantum”or“classical”.     

Quantum statistical physics: A new approach

The new scheme employed (throughout the “thermodynamic phase space”), in the statistical thermodynamic investigation of classical systems, is extended to quantum systems. Quantum Nearest Neighbor Probability Density Functions (QNNPDF's) are formulated (in a manner analogous to the classical case) to provide a new quantum approach for describing structure at the microscopic level, as well as characterize the thermodynamic properties of material systems. Since QNNPDF's describe microstructure in “random neighborhoods”, the new scheme may be viewed as an “elastic cavity” approach (with “elastic” walls). A major point of this paper is that it relates the free energy of an assembly of interacting particles to QNNPDF's. Application to the simple case of dilute, weakly degenerate gases has been outlined.     

Prequantum Classical Statistical Field Theory: Schrödinger Dynamics of Entangled Systems as a Classical Stochastic Process

The idea that quantum randomness can be reduced to randomness of classical fields (fluctuating at time and space scales which are essentially finer than scales approachable in modern quantum experiments) is rather old. Various models have been proposed, e.g., stochastic electrodynamics or the semiclassical model. Recently a new model, so called prequantum classical statistical field theory (PCSFT), was developed. By this model a “quantum system” is just a label for (so to say “prequantum”) classical random field. Quantum averages can be represented as classical field averages. Correlations between observables on subsystems of a composite system can be as well represented as classical correlations. In particular, it can be done for entangled systems. Creation of such classical field representation demystifies quantum entanglement. In this paper we show that quantum dynamics (given by Schrödinger’s equation) of entangled systems can be represented as the stochastic dynamics of classical random fields. The “effect of entanglement” is produced by classical correlations which were present at the initial moment of time, cf. views of Albert Einstein.     

Covariant gauges and point sources in general relativity

The tree graph contributions to the vacuum expectation value of the quantized gravitational field produced by a point mass source are found to diverge. These divergences can be removed only by giving the source a finite extension, and it is first necessary to analyze the corresponding classical situation before making a comparison with the quantum theory. In this paper, the model for such an extended particle is taken to be a spherical shell of initially static pressure-free dust. Without solving the Einstein equations explicity, a coordinate-independent mass renormalization formula can be derived, valid at the moment of time symmetry, which relates the total mass of the system to the bare mass of the source and its invariant radius. The equations are then solved for various choices of coordinate systems, allowing the invariant radius of the shell to be expressed in terms of its coordinate dependent extension. The results are in agreement with those obtained previously by Arnowitt, Deser, and Misner. The work of these authors is generalized to include coordinate frames for which the metric is discontinuous across the shell. Aside from any intrinsic interest, such a generalization is necessary since the most convenient coordinate system for the quantum calculations, namely the covariant de Donder (harmonic) gauge, falls into this category. By expanding the total mass of the source in terms of its bare mass and harmonic coordinate extension, the classical Schwarzschild solution may be cast into a form which facilitates a direct comparison with the quantum theory in the de Donder gauge.     

Quantum Discreteness is an Illusion

I review arguments demonstrating how the concept of “particle” numbers arises in the form of equidistant energy eigenvalues of coupled harmonic oscillators representing free fields. Their quantum numbers (numbers of nodes of the wave functions) can be interpreted as occupation numbers for objects with a formal mass (defined by the field equation) and spatial wave number (“momentum”) characterizing classical field modes. A superposition of different oscillator eigenstates, all consisting of n modes having one node, while all others have none, defines a non-degenerate “n-particle wave function”. Other discrete properties and phenomena (such as particle positions and “events”) can be understood by means of the fast but continuous process of decoherence: the irreversible dislocalization of superpositions. Any wave-particle dualism thus becomes obsolete. The observation of individual outcomes of this decoherence process in measurements requires either a subsequent collapse of the wave function or a “branching observer” in accordance with the Schrödinger equation—both possibilities applying clearly after the decoherence process. Any probability interpretation of the wave function in terms of local elements of reality, such as particles or other classical concepts, would open a Pandora’s box of paradoxes, as is illustrated by various misnomers that have become popular in quantum theory.     

Comparison Between the Full Quantum Dynamics and the Quantum—Semiclassical Models to Many—Particle Systems

We consider a simple collinear collision of a “classical“ particle with a harmonic oscillator within quantumsemiclassical model and full quantum dynamics model,in which the latter is solved analytically in squeezed state and exact diagonalization methods and acts as the exact solution of such a system.A comparison of these two models for different mass ratios between the “classical“ particle and the quantum particle is done,which gives a criterion when using the quantum-semiclassical model.     

Quantum vacuum cosmology

It is shown for the case of a conformally flat vacuum that the curvature of space-time may be viewed as the observable consequence of particle interactions involving a scalar field φ, rather than the independent agency of the gravitational field by itself. The quantum nature of gravity comes in as a consequence of the quantum properties of the φ-field (“vacuum fluctuation”), and a direct analogy is drawn between the renormalizations of charge and mass. Cosmological solutions are derived: These being just the conventional Friedmann solutions, or the de Sitter solution. It is pointed out that a totally empty universe must be Minkowskian.