Quantum decoherence and an adiabatic process in macroscopic and mesoscopic systems

Quantum decoherence is of primary importance for relaxation to an equilibrium distribution and, accordingly, for equilibrium processes. We demonstrate how coherence breaking implies evolution to a microcanonical distribution (``microcanonical postulate'') and, on that ground, consider an adiabatic process, in which there is no thermostat. We stress its difference from a zero-polytropic process, i.e., a process with zero heat capacity but involving a thermostat. We find the distribution for the adiabatic process and show that (i) in the classical limit this distribution is canonical, (ii) for macroscopic systems, the mean values of energy for adiabatic and zero-polytropic processes are the same, but its fluctuations are different, and (iii) in general, adiabatic and zero-polytropic processes are different, which is particularly essential for mesoscopic systems; for those latter, an adiabatic process is in general irreversible.Comment: 4 pages, LATEX, Elsevier style espcrc1.sty, to appear in Proceedings of ISQM-Tokyo '9

Cosmological Quantum Jump Dynamics I. The Principle of Cosmic Energy Determinacy, Equations of Motion, and Jumps Probabilities

The universe, as a closed system, is for all time in a state with a determinate value of energy, i.e., in an eigenstate of the Hamiltonian. That is the principle of cosmic energy determinacy. The Hamiltonian depends on cosmic time through metric. Therefore there are confluence and branch points of energy levels. At branch points, quantum jumps must happen to prevent the violation of energy determinacy. Thus quantum jumps are a reaction against the propensity of the universe dynamics to that violation. On the basis of this idea, an internally consistent quantum jump dynamics is developed.Comment: 11 pages, LATEX 2

General Relativity and Quantum Jumps: The Existence of Nondiffeomorphic Solutions to the Cauchy Problem in Nonempty Spacetime and Quantum Jumps as a Provider of a Canonical Spacetime Structure

It is shown that in spite of a generally accepted concept, there exist nondiffeomorphic solutions to the Cauchy problem in nonempty spacetime, which implies the necessity for canonical complementary conditions. It is nonlocal quantum jumps that provide a canonical global structure of spacetime manifold and, by the same token, the canonical complementary conditions.Comment: 13 pages, LATEX 2

Quantum Fields in Curved Spacetime: Quantum-Gravitational Nonlocality and Conservation of Particle Numbers

We argue that the conventional quantum field theory in curved spacetime has a grave drawback: The canonical commutation relations for quantum fields and conjugate momenta do not hold. Thus the conventional theory should be denounced and the related results revised. A Hamiltonian version of the canonical formalism for a free scalar quantum field is advanced, and the fundamentals of an appropriate theory are constructed. The principal characteristic feature of the theory is quantum-gravitational nonlocality: The Schroedinger field operator at time t depends on the metric at t in the whole 3-space. Applications to cosmology and black holes are given, the results being in complete agreement with those of general relativity for particles in curved spacetime. A model of the universe is advanced, which is an extension of the Friedmann universe; it lifts the problem of missing dark matter. A fundamental and shocking result is the following: There is no particle creation in the case of a free quantum field in curved spacetime; in particular, neither the expanding universe nor black holes create particles.Comment: 17 pages, no figures, LATEX 2.0

On Cosmological Spacetime Structure and Symmetry: Manifold as a Lie Group, Spinor Structure and Symmetry Group, Minkowski Metric, and Unnecessariness of Double-Valued Representations

It is shown that cosmological spacetime manifold has the structure of a Lie group and a spinor space. This leads naturally to the Minkowski metric on tangent spaces and the Lorentzian metric on the manifold and makes it possible to dispense with double-valued representations.Comment: 12 pages, LaTeX 2

Indeterministic Quantum Gravity and Cosmology IX. Nonreality of Many-Place Gravitational Autolocalization: Why a Ball Is Not Located in Different Places at Once

This paper is a sequel to the series of papers [gr-qc/9409010, gr-qc/9505034, gr-qc/9603022, gr-qc/9609035, gr-qc/9609046, gr-qc/9704033, gr-qc/9704038, gr-qc/9708014], being an immediate continuation and supplement to the last of them, where gravitational autolocalization of a body has been considered. A resulting solution, which describes a one-place location, has been called gravilon. Here it is shown that a gravilon is the only solution, i.e., that many-place gravitational autolocalization is unreal. This is closely related to nonreality of tunneling in the conditions under consideration.Comment: 5 pages, LATEX 2.0

Indeterministic Quantum Gravity and Cosmology VIII. Gravilon: Gravitational Autolocalization

This paper is a sequel to the series of papers [gr-qc/9409010, gr-qc/9505034, gr-qc/9603022, gr-qc/9609035, gr-qc/9609046, gr-qc/9704033, gr-qc/9704038]. Gravitational autolocalization of a body is considered. A self-consistent problem is solved: A quantum state of the center of mass of the body gives rise to a classical gravitational field, and the state, on the other hand, is an eigenstate in the field. We call a resulting solution gravilon. Gravilons are classified, and their properties are studied. Gravitational autolocalization is predominantly a macroscopic effect. The motion of a gravilon as a whole is classical.Comment: 7 pages, LATEX 2e, uses amssym

The Indeterministic Einstein Equation: Quantum Jumps, Spacetime Structure, and Dark Pseudomatter

Current physics is faced with the fundamental problem of unifying quantum theory and general relativity, which would have resulted in quantum gravity. The main effort to construct the latter has been bent on quantizing spacetime structure, in particular metric. Meanwhile, taking account of the indeterministic aspect of the quantum description of matter, which manifests itself in quantum jumps, essentially affects classical spacetime structure and the Einstein equation. Quantum jumps give rise to a family of sets of simultaneous events, which implies the existence of universal cosmological time. In view of the jumps, the requirement for metric and its time derivative to be continuous implies that the Einstein equation should involve pseudomatter along with matter. Pseudomatter manifests itself only in gravitational effects, being thereby an absolutely dark ``matter''.Comment: 10 pages, LATEX 2

Indeterministic Quantum Gravity and Cosmology VII. Dynamical Passage through Singularities: Black Hole and Naked Singularity, Big Crunch and Big Bang

This paper is a continuation of the papers [gr-qc/9409010, gr-qc/9505034, gr-qc/9603022, gr-qc/9609035, gr-qc/9609046, gr-qc/9704033]. The aim of the paper is to incorporate singularities---both local (black hole and naked singularity) and global (big bang and big crunch)---into the dynamics of indeterministic quantum gravity and cosmology. The question is whether a singularity is dynamically passable, i.e., whether a dynamical process which ends with a singularity may be extended beyond the latter. The answer is yes. A local singularity is trivially passable, while the passableness for a global singularity may invoke CPT transformation. The passableness of the singularities implies pulsating black holes and the oscillating universe. For the local singularity, the escape effect takes place: In a vicinity of the singularity, quantum matter leaves the gravitational potential well. Keywords: tempered singularity, strong singularity, trivial passage, CPT passage, pulsating black hole, escape effect, oscillating universeComment: 12 pages, LATEX 2.0

On Quantum Nonlocality: Using Prediction of a Distant Measurement Outcome

We assume that an event caused by a correlation between outcomes of two causally separated measurements is, by definition, a manifestation of quantum nonlocality, or superluminal influence. An example of the Alice-Bob type is given, with the characters replaced. The relationship between quantum nonlocality and relativity theory is touched upon.Comment: 5 pages, LATEX 2.0