Abel Camacho

White dwarfs as test objects of Lorentz violations

In the present work, the thermodynamical properties of bosonic and fermionic gases are analysed under the condition that a modified dispersion relation is present. This last condition implies a breakdown of Lorentz symmetry. The implications for the condensation temperature will be studied, as well as for other thermodynamical variables such as specific heat, entropy, etc. Moreover, it will be argued that those cases entailing a violation of time reversal symmetry of the motion equations could lead to problems with the concept of entropy. Concerning the fermionic case, it will be shown that Fermi temperature suffers a modification due to the breakdown of Lorentz symmetry. The results will be applied to white dwarfs and the consequences upon the Chandrasekhar mass–radius relation will be shown. The possibility of resorting to white dwarfs for the testing of modified dispersion relations is also addressed. It will be shown that the comparison of the current observations against the predictions of our model allows us to discard some values of one of the parameters appearing in the modifications of the dispersion relation.

Generalized uncertainty principle and quantum electrodynamics

In the present work the role that a generalized uncertainty principle could play in the quantization of the electromagnetic field is analyzed. It will be shown that we may speak of a Fock space, a result that implies that the concept of photon is properly defined. Nevertheless, in this new context the creation and annihilation operators become a function of the new term that modifies the Heisenberg algebra, and hence the Hamiltonian is not anymore diagonal in the occupation number representation. Additionally, we show the changes that the energy expectation value suffers as result of the presence of an extra term in the uncertainty principle. The existence of a deformed dispersion relation is also proved.

Generalized Uncertainty Principle and Deformed Dispersion Relation Induced by Nonconformal Metric Fluctuations

Considering the existence of nonconformal stochastic fluctuations in the metric tensor a generalized uncertainty principle and a deformed dispersion relation (associated to the propagation of photons) are deduced. Matching our model with the so called quantum κ-Poincaré group will allow us to deduce that the fluctuation-dissipation theorem could be fulfilled without needing a restoring mechanism associated with the intrinsic fluctuations of spacetime. In other words, the loss of quantum information is related to the fact that the spacetime symmetries are described by the quantum κ-Poincaré group, and not by the usual Poincaré symmetries. An upper bound for the free parameters of this model will also be obtained.

Thermodynamics of a photon gas and deformed dispersion relations

We resort to the methods of statistical mechanics in order to determine the effects that a deformed dispersion relation has upon the thermodynamics of a photon gas. The ensuing modifications to the density of states, partition function, pressure, internal energy, entropy, and specific heat are calculated. It will be shown that the breakdown of Lorentz invariance can be interpreted as a repulsive interaction, among the photons. Additionally, it will be proved that the presence of a deformed dispersion relation entails an increase in the entropy of the system. In other words, as a consequence of the loss of the aforementioned symmetry the number of microstates available to the corresponding equilibrium state grows.

SOME CONSEQUENCES OF A GENERALIZATION TO HEISENBERG ALGEBRA IN QUANTUM ELECTRODYNAMICS

In this essay it will be shown that the introduction of a modification to Heisenberg algebra (here this feature means the existence of a minimal observable length), as a fundamental part of the quantization process of the electrodynamical field, renders states in which the uncertainties in the two quadrature components violate the usual Heisenberg uncertainty relation. Hence in this context it may be asserted that any physically realistic generalization of the uncertainty principle must include, not only a minimal observable length, but also a minimal observable momentum.

Critical points in a relativistic bosonic gas induced by the quantum structure of spacetime

It is well known that phase transitions arise if the interaction among particles embodies an attractive as well as a repulsive contribution. In this work it will be shown that the breakdown of Lorentz symmetry, characterized through a deformation in the relation dispersion, plus the bosonic statistics predict the emergence of critical points. In other words, in some quantum gravity models the structure of spacetime implies the emergence of critical points even when no interaction among the particles has been considered.

Test of some fundamental principles in physics via quantum interference with neutrons and photons

The limitations and possibilities that the concept of quantum interference offers as a tool for testing fundamental physics are explored here. The use of neutron interference as an instrument to compare measurement readouts with some of the principles behind metric theories of gravity will be analyzed, as will some discrepancies between theory and experiment. The main restrictions that this model embodies for the study of some of the features of the structure of space–time will be explicitly pointed out. For instance, the conditions imposed by the necessary use of the semiclassical approximation. Additionally, the role that photon interference could play as an element in this context is also considered. In this realm we explore the differences between first-order and second-order coherence experiments, and underline the fact that the Hanbury–Brown–Twiss effect could open up some interesting experimental possibilities in the analysis of the structure of space–time. The void, in connection with the description of wave phenomena, implicit in the principles of metric theories is analyzed. The conceptual difficulties that this void entails are commented upon.

Decoherence and Bare Mass Induced by Nonconformal Metric Fluctuations

The effects, upon the Klein–Gordon field, of nonconformal stochastic metric fluctuations, are analyzed. It will be shown that these fluctuations allow us to consider an effective mass, i.e., the mass detected in a laboratory is not the parameter appearing in the Klein–Gordon equation, but a function of this parameter and of the fluctuations of the metric. In other words, in analogy to the case of a nonrelativistic electron in interaction with a quantized electromagnetic field, we may speak of a bare mass, where the observed mass shows a dependence upon the stochastic terms included in the metric. Afterwards, we prove, resorting to the influence functional, that the energy–momentum tensor of the Klein–Gordon field inherites this stochastic behavior, and that this feature provokes decoherence upon a particle immersed in the region where this tensor is present.

Letter: Sagnac Interferometry and Non–Newtonian Gravity

Sagnac interferometry has been employed in the context of gravity as a proposal for the detection of the so called gravitomagnetic effect. In the present work we explore the possibilities that this experimental device could open up in the realm of non–Newtonian gravitation. It will be shown that this experimental approach allows us to explore an interval of values of the range of the new force that up to now remains unexplored, namely, λ ≥ 1014 m.

Letter: Coupling Gravitomagnetism—Spin and Berry's Phase

Resorting to Berrys phase, a new idea to detect, at quantum level, the gravitomagnetic field of any metric theory of gravity, is put forward. It is found in this proposal that the magnitude of the gravitomagnetic field appears only in the definition of the adiabatic regime, but not in the magnitude of the emerging geometric phase. In other words, the physical parameter to be observed does not involve, in a direct way, (as in the usual proposals) the tiny magnitude of the gravitomagnetic field.