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Register a new userForce-Free Gravitational Redshift: Proposed Gravitational Aharonov-Bohm experiment
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We propose a feasible laboratory interferometry experiment with matter waves in a gravitational potential caused by a pair of artificial field-generating masses. It will demonstrate that the presence of these masses (and, for moving atoms, time dilation) induces a phase shift, even if it does not cause any classical force. The phase shift is identical to that produced by the gravitational redshift (or time dilation) of clocks ticking at the atoms Compton frequency. In analogy to the Aharonov-Bohm effect in electromagnetism, the quantum mechanical phase is a function of the gravitational potential and not the classical forces.
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We study the Hamiltonian describing two anyons moving in a plane in presence of an external magnetic field and identify a one-parameter family of self-adjoint realizations of the corresponding Schr{o}dinger operator. We also discuss the associated model describing a quantum particle immersed in a magnetic field with a local Aharonov-Bohm singularity. For a special class of magnetic potentials, we provide a complete classification of all possible self-adjoint extensions.
In this paper we investigate the scalar Aharonov-Bohm (AB) effect in two of its forms, i.e., its electric form and its gravitational form. The standard form of the electric AB effect involves having particles (such as electrons) move in regions with zero electric field but different electric potentials. When a particle is recombined with itself, it will have a different phase, which can show up as a change in the way the single particle interferes with itself when it is recombined with itself. In the case where one has quasi-static fields and potentials, the particle will invariably encounter fringing fields, which makes the theoretical and experimental status of the electric AB effect much less clear than that of the magnetic (or vector) AB effect. Here we propose using time varying fields outside of a spherical shell, and potentials inside a spherical shell to experimentally test the scalar AB effect. In our proposal a quantum system will always be in a field-free region but subjected to a non-zero time-varying potentials. Furthermore, our system will not be spatially split and brought back together as in the magnetic AB experiment. Therefore there is no spatial interference and hence no shift in a spatial interference pattern to observe. Rather, there arises purely temporal interference phenomena. As in the magnetic AB experiments, these effects are non-classical. We present t
Spinor fields are written in polar form so as to compute their tensorial connection, an object that contains the same information of the connection but which is also proven to be a real tensor. From this, one can still compute the Riemann curvature, encoding the information about gravity. But even in absence of gravity, when the Riemann curvature vanishes, it may still be possible that the tensorial connection remains different from zero, and this can have effects on matter. This is shown with examples in the two known integrable cases: the hydrogen atom and the harmonic oscillator. The fact that a spinor can feel effects due to sourceless actions is already known in electrodynamics as the Aharonov-Bohm phenomenon. A parallel between the electrodynamics case and the situation encountered here will be drawn. Some ideas about relativistic effects and their role for general treatments of quantum field theories are also underlined.
A test of a cornerstone of general relativity, the gravitational redshift effect, is currently being conducted with the RadioAstron spacecraft, which is on a highly eccentric orbit around Earth. Using ground radio telescopes to record the spacecraft signal, synchronized to its ultra-stable on-board H-maser, we can probe the varying flow of time on board with unprecedented accuracy. The observations performed so far, currently being analyzed, have already allowed us to measure the effect with a relative accuracy of $4times10^{-4}$. We expect to reach $2.5times10^{-5}$ with additional observations in 2016, an improvement of almost a magnitude over the 40-year old result of the GP-A mission.
Future generation of gravitational wave detectors will have the sensitivity to detect gravitational wave events at redshifts far beyond any detectable electromagnetic sources. We show that if the observed event rate is greater than one event per year at redshifts z > 40, then the probability distribution of primordial density fluctuations must be significantly non-Gaussian or the events originate from primordial black holes. The nature of the excess events can be determined from the redshift distribution of the merger rate.
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