Earthquake Quantization

Benjamin Koch1,2 and Enrique Muñoz2

1Institut für Theoretische Physik and Atominstitut, Technische Universität Wien, Wiedner Hauptstrasse 8–10, A-1040 Vienna, Austria
2Facultad de Física, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago, Chile

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Abstract

In this homage to Einstein's 144th birthday we propose a novel quantization prescription, where the paths of a path-integral are not random, but rather solutions of a geodesic equation in a random background. We show that this change of perspective can be made mathematically equivalent to the usual formulations of non-relativistic quantum mechanics. To conclude, we comment on conceptual issues, such as quantum gravity coupled to matter and the quantum equivalence principle.

Imagine that you are sitting on a balloon and observing the motion of few people walking on a square. Surprisingly, you do not see a smooth flow but rather a random zigzag. When trying to make sense of this crazy motion you might conclude that
the people are
+ actually drunk and are thus moving strangely on their own cause;
+ sober, but they have a hard time trying to move steadily since they are suffering from a massive
earthquake, which you in your safe balloon, can not perceive directly.

The first alternative of this analogy corresponds to intrinsic random motion of the path integral (PI) quantization, while the second alternative corresponds to random motion caused by a random background.

The idea of this short comment is that the paths of the PI could actually not be random
by themselves, instead they are the result of a law of motion which is intimately linked to a random nature of space-time itself.

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► References

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