1,567 research outputs found
Minimal Length, Measurability and Gravity
The present work is a continuation of the previous papers written by the
author on the subject. In terms of the measurability (or measurable quantities)
notion introduced in a minimal length theory, first the consideration is given
to a quantum theory in the momentum representation. The same terms are used to
consider the Markov gravity model that here illustrates the general approach to
studies of gravity in terms of measurable quantities. This paper is dedicated
to the 75th Anniversary of Professor Vladimir Grigor'evich Baryshevsky.Comment: 34 pages, Late
Enlarged Bound on the Measurability of Distances and Quantum -Poincar\`e Group
When quantum mechanical and general relativistic effects are taken into
account in the analysis of distance measurements, one finds a measurability
bound. I observe that some of the structures that have been encountered in the
literature on the Quantum -Poincar\`e Group naturally lead to this
bound.Comment: 5 pages, LaTe
Imprint of quantum gravity in the dimension and fabric of spacetime
We here conjecture that two much-studied aspects of quantum gravity,
dimensional flow and spacetime fuzziness, might be deeply connected. We
illustrate the mechanism, providing first evidence in support of our
conjecture, by working within the framework of multifractional theories, whose
key assumption is an anomalous scaling of the spacetime dimension in the
ultraviolet and a slow change of the dimension in the infrared. This sole
ingredient is enough to produce a scale-dependent deformation of the
integration measure with also a fuzzy spacetime structure. We also compare the
multifractional correction to lengths with the types of Planckian uncertainty
for distance and time measurements that was reported in studies combining
quantum mechanics and general relativity heuristically. This allows us to fix
two free parameters of the theory and leads, in one of the scenarios we
contemplate, to a value of the ultraviolet dimension which had already found
support in other quantum-gravity analyses. We also formalize a picture such
that fuzziness originates from a fundamental discrete scale invariance at short
scales and corresponds to a stochastic spacetime geometry.Comment: 6 pages; v2: phenomenology section adde
Quantum Measurements and the kappa--Poincare Group
The possible description of the vacuum of quantum gravity through the so
called kappa--Poincare group is analyzed considering some of the consequences
of this symmetry in the path integral formulation of nonrelativistic quantum
theory. This study is carried out with two cases, firstly, a free particle, and
finally, the situation of a particle immersed in a homogeneous gravitational
field. It will be shown that the kappa--Poincare group implies the loss of some
of the basic properties associated to Feynman's path integral. For instance,
loss of the group characteristic related to the time dependence of the
evolution operator, or the breakdown of the composition law for amplitudes of
events occurring successively in time. Additionally some similarities between
the present idea and the so called restricted path integral formalism will be
underlined. These analogies advocate the claim that if the kappa--Poincare
group contains some of the physical information of the quantum gravity vacuum,
then this vacuum could entail decoherence. This last result will also allow us
to consider the possibility of analyzing the continuous measurement problem of
quantum theory from a group--theoretical point of view, but now taking into
account the kappa--Poincare symmetries.Comment: Accepted in General Relativity and Gravitation. Dedicated to Alberto
Garcia on the occasion of his 60th. birthda
Metric-scalar gravity with torsion and the measurability of the non-minimal coupling
The "measurability" of the non-minimal coupling is discussed by considering
the correction to the Newtonian static potential in the semi-classical
approach. The coefficient of the "gravitational Darwin term" (GDT) gets
redefined by the non-minimal torsion-scalar couplings. Based on a similar
analysis of the GDT in the effective field theory approach to non-minimal
scalar we conclude that for reasonable values of the couplings the correction
is very small.Comment: 10 pages, LaTex. Accepted for publication in Mod. Phys. Lett.
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