Quantum Systems under Gravitational Time Dilation by Magdalena Zych

Author:Magdalena Zych
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

5.3 General Relativistic and Quantum Aspects of the Proposals

The aim of the proposed experiments is to access a physical regime where the effects stemming from both quantum mechanics and general relativity (GR) cannot be neglected. To this end, experimental results should simultaneously falsify a model of quantum fields or particles evolving in a Newtonian potential and a model of classical fields or particles in curved space-time (see Fig. 5.5). Below it is analysed in which sense and how this can be achieved.

The effect of gravity can also be detected by observing a shift in the relative phase between the superposed amplitudes travelling along the two arms, in both massive, Sect. 5.1.2, and massless, Sect. 5.2.2, case. The observation of the phase shift alone could not be directly interpreted as a test of the time dilation, since it can be understood in terms of a coupling between the mass and a potential in a flat space-time, which would yield the same phase shift without the time dilation. There is a formal analogy between a massive particle in the Newtonian limit of gravity and a charged particle in a Coulomb electrostatic potential. In the latter, the notion of proper time unquestionably never enters, which suggests that only those gravitational effects which have no electrostatic analogues can be seen as genuinely general relativistic, in the present interferometric context. The gravitational phase shift effect does have an electrostatic analogue experimentally verified with electrons in a Coulomb potential, see e.g. [13]. Thus measurements of the gravitational phase-such alone, such as those of Refs. [6, 11], do not contradict non-metric, Newtonian gravity and cannot be seen as tests of general relativity. The interaction of photons with the Newton potential, however, requires an additional ingredient: it is necessary to assign an effective gravitational mass to the photon, whereas massless particles, or electromagnetic waves, do not interact with gravity in the non-relativistic mechanics. Such an interaction is a direct consequence of the mass-energy equivalence.

More precisely, the interaction necessary to obtain the gravitational phase shift follows from postulating the equivalence between the system’s mass and its average total energy, i.e. that internal energy contributes to the system’s rest mass: , where is the non-gravitational Hamiltonian of the system. This yields a gravitational energy term

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