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arXiv:gr-qc/0303116 · Physics Letters B

Space–time torsion contribution to quantum interference phases

Abel Camacho, Alfredo Macı́as

Published May 12, 2005• 2 citations
arXivHTMLPDF

Abstract

The field of neutron interferometry achieved one of its most significant successes with the detection of the influence of gravity in the quantum mechanical phase of a thermal neutron beam. From the latest experimental readouts in this context an intriguing discrepancy has been elicited. Indeed, theory and experiment dissent by one per cent, and though this fact could be a consequence of the mounting of the experimental device, it might also embody a difference between the way in which gravity behaves in classical and quantum mechanics. In this work the effects, upon the interference pattern, of space–time torsion will be analyzed heeding its coupling with the spin of the neutron beam. It will be proved that, even with this contribution, there is enough leeway for a further discussion of the validity of the equivalence principle in nonrelativistic quantum mechanics.

DOI
10.1016/j.physletb.2005.04.065

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The field of neutron interferometry achieved one of its most significant successes with the detection of the influence of gravity in the quantum mechanical phase of a thermal neutron beam. From the latest experimental readouts in this context an intriguing discrepancy has been elicited. Indeed, theory and experiment dissent by one per cent, and though this fact could be a consequence of the mounting of the experimental device, it might also embody a difference between the way in which gravity behaves in classical and quantum mechanics. In this work the effects, upon the interference pattern, of space–time torsion will be analyzed heeding its coupling with the spin of the neutron beam. It will be proved that, even with this contribution, there is enough leeway for a further discussion of the validity of the equivalence principle in nonrelativistic quantum mechanics.
The general theory of the influence of gravity, inertia (i.e. interferometer motion) and space-time torsion on the outcome of neutron interference experiments is presented. The exact results are obtained in a general relativistic treatment based on the description of a stationary working interferometer in Riemann-Cartan space-time and on the WKB approximation for the neutron waves. Particular attention is paid to the influence on the spinor amplitude. There are two types of resulting amplitude effects; one originates in the non-integrability of the spinor connection and represents the influence of a modified Riemann-Cartan curvature; the other is caused by the influence of the interferometer rotation and acceleration and of space-time torsion during the time interval between the emission of the two coherent neutron waves. For practical purposes small effects are treated in an approximation. Two examples of a global evaluation of the expressions are given. Applications including a gravitational Aharonov-Bohm effect are discussed.
The general theory of the influence of gravity, inertia (i.e. interferometer motion) and space-time torsion on the outcome of neutron interference experiments is presented. The exact results are obtained in a general relativistic treatment based on the description of a stationary working interferometer in Riemann-Cartan space-time and on the WKB approximation for the neutron waves. Particular attention is paid to the influence on the spinor amplitude. There are two types of resulting amplitude effects; one originates in the non-integrability of the spinor connection and represents the influence of a modified Riemann-Cartan curvature; the other is caused by the influence of the interferometer rotation and acceleration and of space-time torsion during the time interval between the emission of the two coherent neutron waves. For practical purposes small effects are treated in an approximation. Two examples of a global evaluation of the expressions are given. Applications including a gravitational Aharonov-Bohm effect are discussed.
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 confront against measurement readouts some of the principles behind metric theories of gravity will be analyzed, as well as 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.
The discrepancy of 0.80.8 %0.8 between theory and the COW-experiment is interpreted. This is done by using a new path equation other than the geodesic one. It is shown that this discrepancy is possibly due to a type of interaction between the torsion, of space-time generated by the background field, and the spin of the moving neutron. The results obtained are discussed and compared with the experimental interpretation suggested by Arif et al. in 1994. As a byproduct, an upper limit is imposed on the free parameter of the new path equation used.
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Quantum mechanics is a part of physics where experiment and theory are inseparably intertwined. This general theme permeates the 2nd edition of this book. It discusses more than 40 neutron interferometry experiments along with their theoretical motivations and explanations. The basic ideas and results of interference experiments related to coherence and decoherence of matter waves and certain post-selection variations, gravitationally induced quantum phase shifts, Berry’s geometrical phases, spinor symmetry and spin superposition, and Bell’s inequalities are all discussed in this book. Both the scalar and vector Aharonov-Bohm topological interference effects and the neutron version of the Sagnac effect are presented in a self-contained and pedagogical way. Interferometry with perfect crystals, artificial lattices, and spin-echo systems are described in some detail. The book includes the theoretical underpinning as well as connections to other areas of experimental physics, such as quantum optics, nuclear physics, gravitation, and atom interferometry. The observed phase shifts due to the Earth’s gravity and rotation indicate a close connection to relativity theory. Neutron interferometry can be considered as a central technique of quantum optics with massive particles. It has stimulated the development of interferometry with atoms, molecules, and clusters. Quantum interference experiments with massive particles have direct consequences on the discussion of epistemological questions since they show explicitly the wave-particle duality, and the entanglement and the contextuality of various parameters governing our modern view of nature.