3,663 research outputs found
On the General Covariance in the Bohmian Quantum Gravity
It is shown explicitly that in the framework of Bohmian quantum gravity, the
equations of motion of the space-time metric are Einstein's equations plus some
quantum corrections. It is observed that these corrections are not covariant.
So that in the framework of Bohmian quantum gravity the general covariance
principle breaks down at the individual level. This principle is restored at
the statistical level.Comment: 17 pages, LaTe
Which quantum theory must be reconciled with gravity? (And what does it mean for black holes?)
We consider the nature of quantum properties in non-relativistic quantum
mechanics (QM) and relativistic QFTs, and examine the connection between formal
quantization schemes and intuitive notions of wave-particle duality. Based on
the map between classical Poisson brackets and their associated commutators,
such schemes give rise to quantum states obeying canonical dispersion
relations, obtained by substituting the de Broglie relations into the relevant
(classical) energy-momentum relation. In canonical QM, this yields a dispersion
relation involving but not , whereas the canonical relativistic
dispersion relation involves both. Extending this logic to the canonical
quantization of the gravitational field gives rise to loop quantum gravity, and
a map between classical variables containing and , and associated
commutators involving . This naturally defines a "wave-gravity duality",
suggesting that a quantum wave packet describing {\it self-gravitating matter}
obeys a dispersion relation involving , and . We propose an
ansatz for this relation, which is valid in the semi-Newtonian regime of both
QM and general relativity. In this limit, space and time are absolute, but
imposing allows us to recover the standard expressions for
the Compton wavelength and the Schwarzschild radius within
the same ontological framework. The new dispersion relation is based on
"extended" de Broglie relations, which remain valid for slow-moving bodies of
{\it any} mass . These reduce to canonical form for , yielding
from the standard uncertainty principle, whereas, for ,
we obtain as the natural radius of a self-gravitating quantum object.
Thus, the extended de Broglie theory naturally gives rise to a unified
description of black holes and fundamental particles in the semi-Newtonian
regime.Comment: 38 pages, 5 figures. Invited contribution to the Universe special
issue "Open questions in black hole physics" (Gonzalo J. Olmo, Ed.). Matches
published versio
The Compton-Schwarzschild correspondence from extended de Broglie relations
The Compton wavelength gives the minimum radius within which the mass of a
particle may be localized due to quantum effects, while the Schwarzschild
radius gives the maximum radius within which the mass of a black hole may be
localized due to classial gravity. In a mass-radius diagram, the two lines
intersect near the Planck point , where quantum gravity effects
become significant. Since canonical (non-gravitational) quantum mechanics is
based on the concept of wave-particle duality, encapsulated in the de Broglie
relations, these relations should break down near . It is unclear
what physical interpretation can be given to quantum particles with energy , since they correspond to wavelengths or time
periods in the standard theory. We therefore propose a correction
to the standard de Broglie relations, which gives rise to a modified Schr{\"
o}dinger equation and a modified expression for the Compton wavelength, which
may be extended into the region . For the proposed modification,
we recover the expression for the Schwarzschild radius for and
the usual Compton formula for . The sign of the inequality
obtained from the uncertainty principle reverses at , so that
the Compton wavelength and event horizon size may be interpreted as minimum and
maximum radii, respectively. We interpret the additional terms in the modified
de Broglie relations as representing the self-gravitation of the wave packet.Comment: 40 pages, 7 figures, 2 appendices. Published version, with additional
minor typos corrected (v3
Replacing the Singlet Spinor of the EPR-B Experiment in the Configuration Space with two Single-Particle Spinors in Physical Space
Recently, for spinless non-relativistic particles, Norsen, Marian and Oriols
show that in the de Broglie-Bohm interpretation it is possible to replace the
wave function in the configuration space by single-particle wave functions in
physical space. In this paper, we show that this replacment of the wave
function in the configuration space by single-particle functions in the
3D-space is also possible for particles with spin, in particular for the
particles of the EPR-B experiment, the Bohm version of the
Einstein-Podolsky-Rosen experiment.Comment: 17 pages, 5 figures, accepted in Foundations of Physics 201
The de Broglie-Bohm weak interpretation
We define the de Broglie-Bohm (dBB) weak interpretation as the dBB
interpretation restricted to particles in unbound states whose wave function is
defined in the three-dimensional physical space, and the dBB strong
interpretation as the usual dBB interpretation applied to all wave functions,
in particular to particles in bound states whose wave function is defined in a
3N-dimensional configuration space in which N is the number of particules. We
show that the current criticisms of the dBB interpretation do not apply to this
weak interpretation and that, furthermore, there are theoritical and
experimental reasons to justify the weak dBB interpretation. Theoretically, the
main reason concern the continuity existing for such particles between quantum
mechanics and classical mechanics: we demonstrate in fact that the density and
the phase of the wave function of a single-particle (or a set of identical
particles without interaction), when the Planck constant tends to 0, converges
to the density and the action of a set of unrecognizable prepared classical
particles that satisfy the statistical Hamilton-Jacobi equations. As the
Hamilton-Jacobi action pilots the particle in classical mechanics, this
continuity naturally concurs with the weak dBB interpretation. Experimentally,
we show that the measurement results of the main quantum experiments (Young's
slits experiment, Stern and Gerlach, EPR-B) are compatible with the de
Broglie-Bohm weak interpretation and everything takes place as if these
unbounded particles had trajectories. In addition, we propose two potential
solutions to complete the dBB weak interpretation.Comment: arXiv admin note: text overlap with arXiv:1311.146
Quantum theory of microworld and the reality
The mathematical model of orthodox quantum mechanics has been critically
examined and some deficiencies have been summarized. The model based on the
extended Hilbert space and free of these shortages has been proposed;
parameters being until now denoted as "hidden" have been involved. Some earlier
arguments against a hidden-variable theory have been shown to be false, too. In
the known Einstein-Bohr controversy Einstein has been shown to be true. The
extended model seems to be strongly supported also by the polarization
experiments performed by us ten years ago.Comment: 30 pages, 1 figur
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