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Register a new userThe shadows of quantum gravity on quantum non-locality
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Bells inequality is a strong criterion to distinguish classic and quantum mechanical aspects of reality. Its violation is the net effect of the non-locality stored in the Heisenberg uncertainty principle (HUP) generalized by quantum gravity scenarios, called generalized uncertainty principle (GUP). Here, the effects of GUP on Bell-like operators of two, and three outcomes, as well as continuous cases, are studied. The achievements claim that the violation quality of Bells and Bell-like inequalities may be a proper tool to get better understanding of the quantum features of gravity and its effects on reality. Indeed, it is obtained that the current accuracy of Stern-Gerlach experiments implies $beta_0ll10^{23}$.
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This paper points out the importance of the assumption of locality of physical interactions, and the concomitant necessity of propagation of an entity (in this case, off-shell quanta - virtual gravitons) between two non-relativistic test masses in unveiling the quantum nature of linearized gravity through a laboratory experiment. At the outset, we will argue that observing the quantum nature of a system is not limited to evidencing $Oleft(hbarright)$ corrections to a classical theory: it instead hinges upon verifying tasks that a classical system cannot accomplish. We explain the background concepts needed from quantum field theory and quantum information theory to fully appreciate the previously proposed table-top experiments: namely forces arising through the exchange of virtual (off-shell) quanta, as well as Local Operations and Classical Communication (LOCC) and entanglement witnesses. We clarify the key assumption inherent in our evidencing experiment, namely the locality of physical interactions, which is a generic feature of interacting systems of quantum fields around us, and naturally incorporates micro-causality in the description of our experiment. We also present the types of states the matter field must inhabit, putting the experiment on firm relativistic quantum field theoretic grounds. At the end we use a non-local theory of gravity to illustrate how our mechanism may still be used to detect the qualitatively quantum nature of a force when the scale of non-locality is finite. We find that the scale of non-locality, including the entanglement entropy production in local/ non-local gravity, may be revealed from the results of our experiment.
We show that the atom interferometric coherence revival test suggested in [arXiv:2101.11629 [quant-ph] (2021)] does not test the quantum nature of the gravitational field when the atoms are coupled to a mechanical oscillator prepared in a thermal state. Specifically we clarify that the same coherence revivals take place in a model where the atoms are coupled to a classical oscillator through a classical gravitational field. We further elucidate the quantum mechanical calculation, showing that entanglement is not the source of the revivals. The suggested test is thus only relevant for pure initial quantum states of the oscillator. In this regime, numerical estimates show that it is unfeasible to do a test of the proposed type.
We analyse a gedankenexperiment previously considered by Mari et al. that involves quantum superpositions of charged and/or massive bodies (particles) under the control of the observers, Alice and Bob. In the electromagnetic case, we show that the quantization of electromagnetic radiation (which causes decoherence of Alices particle) and vacuum fluctuations of the electromagnetic field (which limits Bobs ability to localize his particle to better than a charge-radius) both are essential for avoiding apparent paradoxes with causality and complementarity. We then analyze the gravitational version of this gedankenexperiment. We correct an error in the analysis of Mari et al. and of Baym and Ozawa, who did not properly account for the conservation of center of mass of an isolated system. We show that the analysis of the gravitational case is in complete parallel with the electromagnetic case provided that gravitational radiation is quantized and that vacuum fluctuations limit the localization of a particle to no better than a Planck length. This provides support for the view that (linearized) gravity should have a quantum field description.
We introduce a protocol for a quantum switch in the gravitational field of a spherical mass and determine the time interval required for its realization in the gravity of Earth. One of the agents that perform operations with indefinite order is a quantum system in a path superposition state. Entanglement between its proper time and position is explored as a resource for the implementation of the quantum switch. The realization of the proposed protocol would probe the physical regime described by quantum mechanics on curved spacetimes, which has not yet been explored experimentally.
During the last two decades or so much effort has been devoted to the discussion of quantum mechanics (QM) that in some way incorporates the notion of a minimum length. This upsurge of research has been prompted by the modified uncertainty relation brought about in the framework of string theory. In general, the implementation of minimum length in QM can be done either by modification of position and momentum operators or by restriction of their domains. In the former case we have the so called soccer-ball problem when the naive classical limit appears to be drastically different from the usual one. Starting with the latter possibility, an alternative approach was suggested in the form of a band-limited QM. However, applying momentum cutoff to the wave-function, one faces the problem of incompatibility with the Schr{o}dinger equation. One can overcome this problem in a natural fashion by appropriately modifying Schr{o}dinger equation. But incompatibility takes place for boundary conditions as well. Such wave-function cannot have any more a finite support in the coordinate space as it simply follows from the Paley-Wiener theorem. Treating, for instance, the simplest quantum-mechanical problem of a particle in an infinite potential well, one can no longer impose box boundary conditions. In such cases, further modification of the theory is in order. We propose a non-local modification of QM, which has close ties to the band-limited QM, but does not require a hard momentum cutoff. In the framework of this model, one can easily work out the corrections to various processes and discuss further the semi-classical limit of the theory.
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