The Spacetime View of the Information Paradox

In semiclassical gravity, the final state of black-hole evaporation cannot be described by a pure state. Nevertheless, we point out that the system can be described by a generalized pure state, which is not defined on a 3-dimensional hypersurface but on the 4-dimensional spacetime describing the whole Universe at all times. Unlike the conventional quantum state, such a generalized state treats time on an equal footing with space, which makes it well suited for systems that are both quantum and relativistic. In particular, such a generalized state contains a novel type of information encoded in the correlations between future and past, which avoids the black-hole information paradox.Comment: 7 pages, revised, to appear in Int. J. Quantum In

Non-equal-time Poisson brackets

The standard definition of the Poisson brackets is generalized to the non-equal-time Poisson brackets. Their relationship to the equal-time Poisson brackets, as well as to the equal- and non-equal-time commutators, is discussed.Comment: 4 pages, late

Many-fingered time Bohmian mechanics

The many-fingered time (MFT) formulation of many-particle quantum mechanics and quantum field theory is a natural framework that overcomes the problem of "instantaneous collapse" in entangled systems that exhibit nonlocalities. The corresponding Bohmian interpretation can also be formulated in terms of MFT beables, which alleviates the problem of instantaneous action at a distance by using an ontology that differs from that in the standard Bohmian interpretation. The appearance of usual single-time particle-positions and fields is recovered by quantum measurements.Comment: 7 page

Bohmian particle trajectories in relativistic fermionic quantum field theory

The de Broglie-Bohm interpretation of quantum mechanics and quantum field theory is generalized in such a way that it describes trajectories of relativistic fermionic particles and antiparticles and provides a causal description of the processes of their creation and destruction. A general method of causal interpretation of quantum systems is developed and applied to a causal interpretation of fermionic quantum field theory represented by c-number valued wave functionals.Comment: 12 pages, revised, to appear in Found. Phys. Let

Quantum nonlocality without hidden variables: An algorithmic approach

Is quantum mechanics (QM) local or nonlocal? Different formulations/interpretations (FI) of QM, with or without hidden variables, suggest different answers. Different FI's can be viewed as different algorithms, which leads us to propose an algorithmic definition of locality according to which a theory is local if and only if there exists at least one FI in which all irreducible elements of that FI are local. The fact that no such FI of QM is known strongly supports quantum nonlocality.Comment: 4 pages, corrected typo

Time and probability: From classical mechanics to relativistic Bohmian mechanics

Bohmian mechanics can be generalized to a relativistic theory without preferred foliation, with a price of introducing a puzzling concept of spacetime probability conserved in a scalar time. We explain how analogous concept appears naturally in classical statistical mechanics of relativistic particles, with scalar time being identified with the proper time along particle trajectories. The conceptual understanding of relativistic Bohmian mechanics is significantly enriched by this classical insight. In particular, the analogy between classical and Bohmian mechanics suggests the interpretation of Bohmian scalar time as a quantum proper time different from the classical one, the two being related by a nonlocal scale factor calculated from the wave function. In many cases of practical interest, including the macroscopic measuring apparatus, the fundamental spacetime probability explains the more familiar space probability as an emergent approximate description. Requiring that the quantum proper time in the classical limit should reduce to the classical proper time, we propose that only massive particles have Bohmian trajectories. An analysis of the macroscopic measuring apparatus made up of massive particles restores agreement with the predictions of standard quantum theory.Comment: 53 pages, 2 figures, new references, some statements sharpene

Time in quantum gravity by weakening the Hamiltonian constraint

We replace the usual Hamiltonian constraint of quantum gravity H|psi>=0 by a weaker one =0. This allows |psi> to satisfy the time-dependent functional Schrodinger equation. In general, only the phase of the wave function appears to be time independent. The resulting quantum theory has the correct classical limit and thus provides a viable theory of quantum gravity that solves the problem of time without introducing additional nongravitational degrees of freedom.Comment: 4 page

Gravitational crystal inside the black hole

Crystals, as quantum objects typically much larger than their lattice spacing, are a counterexample to a frequent prejudice that quantum effects should not be pronounced at macroscopic distances. We propose that the Einstein theory of gravity only describes a fluid phase and that a phase transition of crystallization can occur under extreme conditions such as those inside the black hole. Such a crystal phase with lattice spacing of the order of the Planck length offers a natural mechanism for pronounced quantum-gravity effects at distances much larger than the Planck length. A resolution of the black-hole information paradox is proposed, according to which all information is stored in a crystal-phase remnant with size and mass much above the Planck scale.Comment: 7 pages, revised, new references, accepted for publication in Mod. Phys. Lett.

On compatibility of Bohmian mechanics with standard quantum mechanics

It is shown that the apparent incompatibility of Bohmian mechanics with standard quantum mechanics, found by Akhavan and Golshani quant-ph/0305020, is an artefact of the fact that the initial wavefunction they use, being proportional to a $\delta$-function, is not a regular wavefunction.Comment: 3 page

Is particle creation by the gravitational field consistent with energy conservation?

If particle creation is described by a Bogoliubov transformation, then, in the Heisenberg picture, the raising and lowering operators are time dependent. On the other hand, this time dependence is not consistent with field equations and the conservation of the stress-energy tensor. Possible physical interpretations and resolutions of this inconsistency are discussed.Comment: 7 page