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We resolve black hole information paradox within semiclassical gravity, in a manner that does not depend on details of unknown quantum gravity. Our crucial insight is that outgoing Hawking particles are physical only far from the black hole horizon, so they are created far from the horizon and entangled with degrees of freedom closer to the horizon. The latter degrees of freedom can be understood as quasi-classical coherent states, implying that Hawking radiation is accompanied with additional radiation similar to classical radiation by which the black hole loses hair during the classical gravitational collapse. The two kinds of radiation are entangled, which resolves black hole information paradox., Comment: 8 pages, accepted for publication in Class. Quantum Grav

We develop a general formulation of quantum statistical mechanics in terms of probability currents that satisfy continuity equations in the multi-particle position space, for closed and open systems with a fixed number of particles. The continuity equation for any closed or open system suggests a natural Bohmian interpretation in terms of microscopic particle trajectories, that make the same measurable predictions as standard quantum theory. The microscopic trajectories are not directly observable, but provide a general, simple and intuitive microscopic interpretation of macroscopic phenomena in quantum statistical mechanics. In particular, we discuss how various notions of entropy, proper and improper mixtures, and thermodynamics are understood from the Bohmian perspective., Comment: 32 pages, version accepted for publication in Physica A: Statistical Mechanics and its Applications

We develop a new method for finding the quantum probability density of arrival at the detector. The evolution of the quantum state restricted to the region outside of the detector is described by a restricted Hamiltonian that contains a non-hermitian boundary term. The non-hermitian term is shown to be proportional to the flux of the probability current operator through the boundary, which implies that the arrival probability density is equal to the flux of the probability current., Comment: 7 pages, accepted for publication in Universe

Conceptual difficulties in semiclassical and quantum gravity arise from diffeomorphism invariance of classical general relativity. With a motivation to shed some light on these difficulties, we study a class of toy models for which one-dimensional diffeomorphism invariance, namely time-reparametrization invariance, emerges at the classical level from energy conservation. An attempt to quantize the models while taking the invariance seriously leads to toy versions of the problem of time in quantum gravity, of the cosmological constant problem, and of the black hole firewall problem. Nevertheless, all these problems are easily resolved by taking into account that the invariance emerges only at the classical level, while the fundamental theory that needs to be quantized is not diffeomorphism invariant., Comment: 21 pages, accepted for publication in Fortsch. Phys

Classical measurements are passive, in the sense that they do not affect the physical properties of the measured system. Normally, quantum measurements are not passive in that sense. In the infinite dimensional Hilbert space, however, we find that quantum projective measurement can be passive in a way which is impossible in finite dimensional Hilbert spaces. Specifically, we find that expectation value of a hermitian Hamiltonian can have an imaginary part in the infinite dimensional Hilbert space and that such an imaginary part implies a possibility to avoid quantum Zeno effect, which can physically be realized in quantum arrival experiments. The avoidance of quantum Zeno effect can also be understood as avoidance of a quantum version of gambler's fallacy, leading to the notion of passive quantum measurement that updates information about the physical system without affecting its physical properties. The arrival time probability distribution of a particle is found to be given by the flux of the probability current. Possible negative fluxes correspond to regimes at which there is no arrival at all, physically understood as regimes at which the particle departs rather than arrives., Comment: 15 pages, 1 figure, version accepted for publication in Fortschr. Phys

Since Bohmian mechanics is explicitly nonlocal, it is widely believed that it is very hard, if not impossible, to make Bohmian mechanics compatible with relativistic quantum field theory (QFT). I explain, in simple terms, that it is not hard at all to construct a Bohmian theory that lacks Lorentz covariance, but makes the same measurable predictions as relativistic QFT. All one has to do is to construct a Bohmian theory that makes the same measurable predictions as QFT in one Lorentz frame, because then standard relativistic QFT itself guarantees that those predictions are Lorentz invariant. I first explain this in general terms, then I describe a simple Bohmian model that makes the same measurable predictions as the Standard Model of elementary particles, after which I give some hints towards a more fundamental theory beyond Standard Model. Finally, I present a short story telling how my views of fundamental physics in general, and of Bohmian mechanics in particular, evolved over time., Comment: 19 pages, version accepted for publication in Found. Phys

In Supplee's submarine paradox, a naive argument based on Lorentz contraction leads to a contradiction that a fast submarine should sink in the water's reference frame but float in the submarine's reference frame. Due to the submarine's rigidity constraints, it is not easy to resolve the paradox in a manifestly covariant form. To simplify the problem, we consider a version of the paradox in which one fluid moves through another fluid. An analysis of ideal relativistic fluids in a weak gravitational field shows that the moving fluid has a larger pressure and hence sinks, in agreement with known results for the rigid submarine., Comment: 8 pages, 1 figure, significantly revised and extended, accepted for publication in Am. J. Phys

We study the conditions under which an analog acoustic geometry of a relativistic fluid in flat spacetime can take the same form as the Schwarzschild black hole geometry. We find that the speed of sound must necessarily be equal to the speed of light. Since the speed of the fluid cannot exceed the speed of light, this implies that analog Schwarzschild geometry necessarily breaks down behind the horizon., Comment: 8 pages, minor revision, discussion on previous works expanded, conclusions expanded, typos corrected, results unchanged

We further develop the general theory of quantum time distributions introduced in arXiv:2010.07575 and apply it to find the distribution of arrival times at the detector. Even though the Hamiltonian in the absence of detector is hermitian, the time evolution of the system before detection involves dealing with a non-hermitian operator obtained from the projection of the hermitian Hamiltonian onto the region in front of the detector. Such a formalism eventually gives rise to a simple and physically sensible analytical expression for the arrival time distribution, for arbitrary wave packet moving in one spatial dimension with negligible distortion., Comment: 10 pages, improved version accepted for publication in Eur. Phys. J. Plus

We develop a general theory of the time distribution of quantum events, applicable to a large class of problems such as arrival time, dwell time and tunneling time. A stopwatch ticks until an awaited event is detected, at which time the stopwatch stops. The awaited event is represented by a projection operator $\pi$, while the ideal stopwatch is modeled as a series of projective measurements at which the quantum state gets projected with either $\bar{\pi}=1-\pi$ (when the awaited event does not happen) or $\pi$ (when the awaited event eventually happens). In the approximation in which the time $\delta t$ between the subsequent measurements is sufficiently small (but not zero!), we find a fairly simple general formula for the time distribution ${\cal P}(t)$, representing the probability density that the awaited event will be detected at time $t$., Comment: 18 pages, 3 figures, version accepted for publication in Phys. Lett. A

An important step to incorporate information in the second law of thermodynamics was done by Landauer, showing that the erasure of information implies an increase in heat. Most attempts to justify Landauer's erasure principle are based on thermodynamic argumentations. Here, using just the time-reversibility of classical microscopic laws, we identify three types of the Landauer's erasure principle depending on the relation between the two final environments: the one linked to a logical input 1 and the other to the logical input 0. The strong type (which is the original Landauer's formulation) requires the final environments to be in thermal equilibrium. The intermediate type giving the entropy change of $k_B \ln 2$ occurs when the two final environments are identical macroscopic states. Finally, the weak Landauer's principle, providing information erasure with no entropy change, when the two final environments are macroscopically different. Even though the above results are formally valid for classical erasure gates, a discussion on their natural extension to quantum scenarios is presented. This paper strongly suggests that the original Landauer's principle (based on the assumption of thermalized environments) is fully reasonable for microelectronics, but it becomes less reasonable for future few-atoms devices working at THz frequencies. Thus, the weak and intermediate Landauer's principles, where the erasure of information is not necessarily linked to heat dissipation, are worth investigating., Comment: 41 pages, 8 figures

In a microscopic quantum system one cannot perform a simultaneous measurement of particle and wave properties. This, however, may not be true for macroscopic quantum systems. As a demonstration, we propose to measure the local macroscopic current passed through two slits in a superconductor. According to the theory based on the linearized Ginzburg-Landau equation for the macroscopic pseudo wave function, the streamlines of the measured current should have the same form as particle trajectories in the Bohmian interpretation of quantum mechanics. By an explicit computation we find that the streamlines should show a characteristic wiggling, which is a consequence of quantum interference., Comment: 9 pages, 2 figures, version accepted for publication in Mod. Phys. Lett. A

Bell's theorem implies that any completion of quantum mechanics which uses hidden variables (that is, preexisting values of all observables) must be nonlocal in the Einstein sense. This customarily indicates that knowledge of the hidden variables would permit superluminal communication. Such superluminal signaling, akin to the existence of a preferred reference frame, is to be expected. However, here we provide a protocol that allows an observer with knowledge of the hidden variables to communicate with her own causal past, without superluminal signaling. That is, such knowledge would contradict causality, irrespectively of the validity of relativity theory. Among the ways we propose for bypassing the paradox there is the possibility of hidden variables that change their values even when the state does not, and that means that signaling backwards in time is prohibited in Bohmian mechanics., Comment: Minorly revised version

By entangling soft massless particles one can create an arbitrarily large amount of entanglement entropy that carries an arbitrarily small amount of energy. Dropping this entropy into the black hole (b.h.) one can increase the b.h. entropy by an amount that violates Bekenstein bound or any other reasonable bound, leading to a version of b.h. information paradox that does not involve Hawking radiation. Among many proposed solutions of the standard b.h. information paradox with Hawking radiation, only a few can also resolve this version without the Hawking radiation. The assumption that both versions should be resolved in the same way significantly helps to reduce the space of possible resolutions., Comment: 11 pages, revised and improved, accepted for publication in Universe

The analog acoustic metric has been originally derived for adiabatic acoustic perturbations propagating in an isentropic irrotational ideal fluid. In the framework of a Lagrangian hydrodynamic description we demonstrate that under certain conditions the usual acoustic metric can be derived for nonisentropic fluids. In a special case when the pressure takes a special form and the nonadiabatic perturbations are neglected the adiabatic acoustic perturbations corresponding to massless phonons propagate in an analog metric of the usual type., Comment: 15 pages, major revision to match the version accepted in CQG, a section on planar black holes added, a few clarifications added, references added, typos corrected

Statistical physics cannot explain why a thermodynamic arrow of time exists, unless one postulates very special and unnatural initial conditions. Yet, we argue that statistical physics can explain why the thermodynamic arrow of time is universal, i.e., why the arrow points in the same direction everywhere. Namely, if two subsystems have opposite arrow-directions at a particular time, the interaction between them makes the configuration statistically unstable and causes a decay towards a system with a universal direction of the arrow of time. We present general qualitative arguments for that claim and support them by a detailed analysis of a toy model based on the baker's map., Comment: 21 pages, 5 figures, In English and in Russian

We study the infrared effective theory of gravity that stems from the quantum trace anomaly. Quantum fluctuations of the metric induce running of the cosmological constant and the Newton constant at cosmological scales. By imposing the generalized Bianchi identity we obtain a prediction for the scale dependence of the dark matter and dark energy densities in terms of the parameters of the underlying conformal theory. For certain values of the model parameters the dark energy equation of state and the observed spectral index of the primordial density fluctuations can be simultaneously reproduced., Comment: 11 pages, equation (4) corrected, discussions expanded, references added, results unchanged, to appear in PLB

We study the propagation of pions at finite temperature and finite chemical potential in the framework of the linear sigma model with 2 quark flavors and $N_c$ colors. The velocity of massless pions in general differs from that of light. One-loop calculations show that in the chiral symmetry broken phase pions, under certain conditions, propagate faster than light., Comment: 8 pages, 3 figures included. Considerably revised, discussions expanded, one figure added, typos corrected, results unchanged. To be published in Phys. Rev. D

A system of charged bosons at finite temperature and chemical potential is studied in a general-relativistic framework. We assume that the boson fields interact only gravitationally. At sufficiently low temperature the system exists in two phases: the gas and the condensate. By studying the condensation process numerically we determine the critical temperature $T_c$ at which the condensate emerges. As the temperature decreases, the system eventually settles down in the ground state of a cold boson star., Comment: 21 pages, 11 figures included, revised, to appear in Nucl. Phys. B

We study in detail gravitational lensing caused by a supermassive fermion star and compare it with lensing by a black hole of the same mass. It is argued that lensing effects, being very distinct, may shed some light on the yet unexplained nature of the compact dark massive object at the Galactic center., Comment: revised, 17 pages, 13 figures included, to appear in Astrophys. J

All differences between the role of space and time in nature are explained by proposing the principles in which none of the spacetime coordinates has an {\it a priori} special role. Spacetime is treated as a non-dynamical manifold, with a fixed global $\mathbb{R}^D$ topology. Dynamical theory of gravity determines only the metric tensor on a fixed manifold. All dynamics is treated as a Cauchy problem, so it {\em follows} that one coordinate takes a special role. It is proposed that {\em any} boundary condition that is finite everywhere leads to a solution which is also finite everywhere. This explains the $(1,D-1)$ signature of the metric, the boundedness of energy from below, the absence of tachyons, and other related properties of nature. The time arrow is explained by proposing that the boundary condition should be ordered. The quantization is considered as a boundary condition for field operators. Only the physical degrees of freedom are quantized., Comment: 22 pages. I have written the first version (v1) 20+ years ago when I was young and bold, but then forgotten it and worked on other stuff. Now with some maturity I have looked at it again and concluded that it is still worth publication, with a minimal revision. The reviewers and editors of Symmetry agreed

We study the chiral phase transition in the linear sigma model with 2 quark flavors and $N_c$ colors. One-loop calculations predict a first-order phase transition at both $\mu=0$ and $\mu\neq 0$. We also discuss the phase diagram and make a comparison with a thermal parametrization of existing heavy-ion experimental data., Comment: 12 pages, 6 ps-figures, LaTex