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General Relativity and Gravitation

Some remarks concerning the equivalence principle of general relativity with respect to quantum mechanical one-particle state

Gerhard Börner, Siegfried Schlieder

Published Jan 1, 1980• 9 citations
Publisher
DOI
10.1007/bf00756165

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FLAVOR-OSCILLATION CLOCKS, CONTINUOUS QUANTUM MEASUREMENTS AND A VIOLATION OF EINSTEIN EQUIVALENCE PRINCIPLE

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The relation between Einstein equivalence principle and a continuous quantum measurement is analyzed in the context of the recently proposed flavor-oscillation clocks, an idea pioneered by Ahluwalia and Burgard (Gen. Rel. Grav.29, 681(E) (1997)). We will calculate the measurement outputs if a flavor-oscillation clock, which is immersed in a gravitational field, is subject to a continuous quantum measurement. Afterwards, resorting to the weak equivalence principle, we obtain the corresponding quantities in a freely falling reference frame. Finally, comparing this last result with the measurement outputs that would appear in a Minkowskian space–time it will be found that they do not coincide, in other words, we have a violation of Einstein equivalence principle. This violation appears in two different forms, namely: (i) the oscillation frequency in a freely falling reference frame does not match with the case predicted by general relativity, a feature previously obtained by Ahluwalia; (ii) the probability distribution of the measurement outputs, obtained by an observer in a freely falling reference frame, does not coincide with the results that would appear in the case of a Minkowskian space–time. Concerning this last difference, the probability distribution differs in two directions. Firstly, the maximum, as function of the energy of the system (that emerges if we calculate first the probability distribution in the original curved manifold and then, resorting to the weak equivalence principle, we find the corresponding expression in a freely falling reference frame) is shifted with respect to the case in which the system is in a Minkowskian space–time. Secondly, the magnitude of this maximum is not equal to the respective quantity predicted by general relativity. In other words, we obtain two new theoretical results that predict a violation of Einstein equivalence principle, and that could be measured.

arXiv:gr-qc/9911112•Modern Physics Letters A•Nov 30, 1999•9 citations

On the Comparison of the Quantum and Relativity Theories

Mendel Sachs

Springer eBooks•Jan 1, 1986•0 citations
Hawking's black hole evaporation process suggests that we may need to choose between quantum unitarity and other basic physical principles such as no-signalling, entanglement monogamy, and the equivalence principle. We here provide a quantum model for Hawking pair black hole evaporation within which these principles are all respected. The model does not involve exotic new physics, but rather uses quantum theory and general relativity. The black hole and radiation are in a joint superposition of different energy states at any stage of the evaporation process. In the particular branch where the black hole mass is 0, the radiation state is pure and one-to-one with the initial state forming the black hole. Thus there is no information loss upon full evaporation. The original Hawking's pair entanglement between infalling and outgoing particles gets transferred to outgoing particles via entanglement swapping, without violation of no-signalling or the entanglement's monogamy. The final state after the full black hole evaporation is pure, without loss of information, violation of monogamy, or the equivalence principle.
The agreement between the predictions of general relativity and observations of the energy loss due to gravitational waves emitted by binary pulsars is just as impressive as the agreement between prediction of quantum electrodynamics and the measured value of Lamb shift in atoms. However, general relativity has not yet yielded to a successful quantised theory. There is a widespread belief that the two thories are incompatible at some deep level. The question is: where? Here, I show that the conceptual foundations of the theory of general relativity and quantum mechanics are so rich that they suggest concrete modifications into each other in the interface region. Specifically, I consider quantum states that have no classical counterpart and show that such states must carry an inherent violation of the principle of equivalence. On the other hand, I show that when gravitational effects are incorporated into the quantum measurement process one must induce a gravitationally induced modification to the de Broglie's wave-particle duality. The reported changes into the foundations of the two theories are far from in-principle modifications. These are endowed with serious implications for the understanding of the early universe and, in certain instances, can be explored in terrestrial laboratories.
The relation between Einstein equivalence principle and a continuous quantum measurement is analyzed in the context of the recently proposed flavor-oscillation clocks, an idea pioneered by Ahluwalia and Burgard (Gen. Rel. Grav.29, 681(E) (1997)). We will calculate the measurement outputs if a flavor-oscillation clock, which is immersed in a gravitational field, is subject to a continuous quantum measurement. Afterwards, resorting to the weak equivalence principle, we obtain the corresponding quantities in a freely falling reference frame. Finally, comparing this last result with the measurement outputs that would appear in a Minkowskian space–time it will be found that they do not coincide, in other words, we have a violation of Einstein equivalence principle. This violation appears in two different forms, namely: (i) the oscillation frequency in a freely falling reference frame does not match with the case predicted by general relativity, a feature previously obtained by Ahluwalia; (ii) the probability distribution of the measurement outputs, obtained by an observer in a freely falling reference frame, does not coincide with the results that would appear in the case of a Minkowskian space–time. Concerning this last difference, the probability distribution differs in two directions. Firstly, the maximum, as function of the energy of the system (that emerges if we calculate first the probability distribution in the original curved manifold and then, resorting to the weak equivalence principle, we find the corresponding expression in a freely falling reference frame) is shifted with respect to the case in which the system is in a Minkowskian space–time. Secondly, the magnitude of this maximum is not equal to the respective quantity predicted by general relativity. In other words, we obtain two new theoretical results that predict a violation of Einstein equivalence principle, and that could be measured.