arXiv: General Relativity and Quantum Cosmology, 2018
In the framework of finite-dimensional Fock space models, for a fixed given mean number of partic... more In the framework of finite-dimensional Fock space models, for a fixed given mean number of particles \bar{n}_{k}, blackbody-like or another, it is shown that there are, in the space S of all pure states, a multi-dimensional subspace s_{\bar{n}_{k}} of initial pure states and a corresponding multi-dimensional subspace S_{\bar{n}_{k}} of final pure states yielding \bar{n}_{k}, which are mutually related by a unitary transformation. In consequence it follows that the blackbody form of the Hawking spectrum does not contradict unitarity of black hole evaporation.
In a recent paper Osuga and Page have presented an explicitly unitary toy qubit transport model f... more In a recent paper Osuga and Page have presented an explicitly unitary toy qubit transport model for transferring information from a black hole to the outgoing radiation. Following their idea we propose a unitary toy model which involves (fermionic) Hawking states.
A simple gedankenexperiment is proposed showing observability of radiation by an observer comovin... more A simple gedankenexperiment is proposed showing observability of radiation by an observer comoving with an accelerated charge.
The paper contains a talk given by the author at the Banach Center in Spring 1995. It recapitulat... more The paper contains a talk given by the author at the Banach Center in Spring 1995. It recapitulates author's approach to construction of topological invariants of the Reshetikhin-Turaev-Witten type of 3- and 4-dimensional manifolds in the framework of SU(2) Chern-Simons gauge theory and its hidden (quantum) gauge symmetry.
It has been shown that there is a small possibility to experimentally violate the CHSH Bell inequ... more It has been shown that there is a small possibility to experimentally violate the CHSH Bell inequality in a 'classical' context. The probability of such a violation has been estimated in the framework of a classical probabilistic model in the language of a random-walk representation.
A straightforward relationship between the two approaches to 3-dimensional topological invariants... more A straightforward relationship between the two approaches to 3-dimensional topological invariants, one of them put forward by Witten in the framework of topological quantum field theory, and the second one proposed by Kohno in terms of rational conformal field theory, is established.
A study of the partition function of a 3-dimensional scalar-vector model formally related via dua... more A study of the partition function of a 3-dimensional scalar-vector model formally related via duality to the Rozansky-Witten topological sigma-model is presented. The partition function is shown to consist of such topological quantities of a 3-dimensional manifold M like a lattice sum, the Reidemeister-Ray-Singer torsion and the Massey product.
A path-integral approach to non-perturbative topological invariants of knots, links and manifolds... more A path-integral approach to non-perturbative topological invariants of knots, links and manifolds of dimension three and four using topological quantum field theory of Schwarz (Chern-Simons) type is presented.
It has been shown that the primary, old-fashioned idea of Sakharov's induced gravity and gaug... more It has been shown that the primary, old-fashioned idea of Sakharov's induced gravity and gauge interactions, in the "one-loop dominance" version, works astonishingly well yielding phenomenologically reasonable results. As a byproduct, the issue of the role of the UV cutoff in the context of the induced gravity has been reexamined (an idea of self-cutoff induced gravity). As an additional check, the black hole entropy has been used in the place of the action. Finally, it has been explicitly shown that the induced coupling constants of gauge interactions of the standard model assume qualitatively realistic values.
The paper is a chapter of the above-mentioned book. It aims to give an expository presentation of... more The paper is a chapter of the above-mentioned book. It aims to give an expository presentation of author's version of the non-Abelian Stokes theorem in the framework of path-integral formalism.
It has been shown that Sakharov's induced, from the fields entering the standard model, Barbe... more It has been shown that Sakharov's induced, from the fields entering the standard model, Barbero-Immirzi parameter assumes, in the framework of euclidean formalism, the UV cutoff-independent value, 1/9. The calculus uses the Schwinger's proper-time formalism, the Seeley-DeWitt heat-kernel expansion, and it is akin to the derivation of the ABJ chiral anomaly in space-time with torsion.
The idea of the Michelson-Morley experiment is theoretically reanalyzed. Elementary arguments are... more The idea of the Michelson-Morley experiment is theoretically reanalyzed. Elementary arguments are put forward to precisely derive the most general allowable form of the directional dependence of the one-way velocity of light.
A practical implementation of the non-Abelian Stokes theorem for topologically nontrivial loops (... more A practical implementation of the non-Abelian Stokes theorem for topologically nontrivial loops (knots) with possible intersections is proposed.
A simple circuit implementation of the oracle for Grover's quantum search of a real unstructu... more A simple circuit implementation of the oracle for Grover's quantum search of a real unstructured classical database is proposed. The oracle contains a kind of quantumly accessible classical memory, which stores the database.
It has been shown that anisotropy of homogeneous spacetime described by the general Kasner metric... more It has been shown that anisotropy of homogeneous spacetime described by the general Kasner metric can be damped by quantum fluctuations coming from perturbative quantum gravity in one-loop approximation. Also, a formal argument, not limited to one-loop approximation, is put forward in favor of stability of isotropy in the exactly isotropic case.
In the context of the sensational results concerning superluminal velocities, announced recently ... more In the context of the sensational results concerning superluminal velocities, announced recently by the OPERA Collaboration, we have proposed a classical model yielding a statistically calculated measured velocity of a beam, higher than the velocity of the particles constituting the beam. The two key elements of our model, necessary and sufficient to obtain this curious result, are a time-dependent "transmission" function and statistical method of the maximum-likelihood estimation.
arXiv: General Relativity and Quantum Cosmology, 2018
In the framework of finite-dimensional Fock space models, for a fixed given mean number of partic... more In the framework of finite-dimensional Fock space models, for a fixed given mean number of particles \bar{n}_{k}, blackbody-like or another, it is shown that there are, in the space S of all pure states, a multi-dimensional subspace s_{\bar{n}_{k}} of initial pure states and a corresponding multi-dimensional subspace S_{\bar{n}_{k}} of final pure states yielding \bar{n}_{k}, which are mutually related by a unitary transformation. In consequence it follows that the blackbody form of the Hawking spectrum does not contradict unitarity of black hole evaporation.
In a recent paper Osuga and Page have presented an explicitly unitary toy qubit transport model f... more In a recent paper Osuga and Page have presented an explicitly unitary toy qubit transport model for transferring information from a black hole to the outgoing radiation. Following their idea we propose a unitary toy model which involves (fermionic) Hawking states.
A simple gedankenexperiment is proposed showing observability of radiation by an observer comovin... more A simple gedankenexperiment is proposed showing observability of radiation by an observer comoving with an accelerated charge.
The paper contains a talk given by the author at the Banach Center in Spring 1995. It recapitulat... more The paper contains a talk given by the author at the Banach Center in Spring 1995. It recapitulates author's approach to construction of topological invariants of the Reshetikhin-Turaev-Witten type of 3- and 4-dimensional manifolds in the framework of SU(2) Chern-Simons gauge theory and its hidden (quantum) gauge symmetry.
It has been shown that there is a small possibility to experimentally violate the CHSH Bell inequ... more It has been shown that there is a small possibility to experimentally violate the CHSH Bell inequality in a 'classical' context. The probability of such a violation has been estimated in the framework of a classical probabilistic model in the language of a random-walk representation.
A straightforward relationship between the two approaches to 3-dimensional topological invariants... more A straightforward relationship between the two approaches to 3-dimensional topological invariants, one of them put forward by Witten in the framework of topological quantum field theory, and the second one proposed by Kohno in terms of rational conformal field theory, is established.
A study of the partition function of a 3-dimensional scalar-vector model formally related via dua... more A study of the partition function of a 3-dimensional scalar-vector model formally related via duality to the Rozansky-Witten topological sigma-model is presented. The partition function is shown to consist of such topological quantities of a 3-dimensional manifold M like a lattice sum, the Reidemeister-Ray-Singer torsion and the Massey product.
A path-integral approach to non-perturbative topological invariants of knots, links and manifolds... more A path-integral approach to non-perturbative topological invariants of knots, links and manifolds of dimension three and four using topological quantum field theory of Schwarz (Chern-Simons) type is presented.
It has been shown that the primary, old-fashioned idea of Sakharov's induced gravity and gaug... more It has been shown that the primary, old-fashioned idea of Sakharov's induced gravity and gauge interactions, in the "one-loop dominance" version, works astonishingly well yielding phenomenologically reasonable results. As a byproduct, the issue of the role of the UV cutoff in the context of the induced gravity has been reexamined (an idea of self-cutoff induced gravity). As an additional check, the black hole entropy has been used in the place of the action. Finally, it has been explicitly shown that the induced coupling constants of gauge interactions of the standard model assume qualitatively realistic values.
The paper is a chapter of the above-mentioned book. It aims to give an expository presentation of... more The paper is a chapter of the above-mentioned book. It aims to give an expository presentation of author's version of the non-Abelian Stokes theorem in the framework of path-integral formalism.
It has been shown that Sakharov's induced, from the fields entering the standard model, Barbe... more It has been shown that Sakharov's induced, from the fields entering the standard model, Barbero-Immirzi parameter assumes, in the framework of euclidean formalism, the UV cutoff-independent value, 1/9. The calculus uses the Schwinger's proper-time formalism, the Seeley-DeWitt heat-kernel expansion, and it is akin to the derivation of the ABJ chiral anomaly in space-time with torsion.
The idea of the Michelson-Morley experiment is theoretically reanalyzed. Elementary arguments are... more The idea of the Michelson-Morley experiment is theoretically reanalyzed. Elementary arguments are put forward to precisely derive the most general allowable form of the directional dependence of the one-way velocity of light.
A practical implementation of the non-Abelian Stokes theorem for topologically nontrivial loops (... more A practical implementation of the non-Abelian Stokes theorem for topologically nontrivial loops (knots) with possible intersections is proposed.
A simple circuit implementation of the oracle for Grover's quantum search of a real unstructu... more A simple circuit implementation of the oracle for Grover's quantum search of a real unstructured classical database is proposed. The oracle contains a kind of quantumly accessible classical memory, which stores the database.
It has been shown that anisotropy of homogeneous spacetime described by the general Kasner metric... more It has been shown that anisotropy of homogeneous spacetime described by the general Kasner metric can be damped by quantum fluctuations coming from perturbative quantum gravity in one-loop approximation. Also, a formal argument, not limited to one-loop approximation, is put forward in favor of stability of isotropy in the exactly isotropic case.
In the context of the sensational results concerning superluminal velocities, announced recently ... more In the context of the sensational results concerning superluminal velocities, announced recently by the OPERA Collaboration, we have proposed a classical model yielding a statistically calculated measured velocity of a beam, higher than the velocity of the particles constituting the beam. The two key elements of our model, necessary and sufficient to obtain this curious result, are a time-dependent "transmission" function and statistical method of the maximum-likelihood estimation.
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