On the origin of the weak equivalence principle in a theory of emergent quantum mechanics
Ricardo Gallego Torromé
备注：
25 pages; no figures. Accepted for publication in International Journal of Geometric Methods in Modern Physics. arXiv admin note: substantial text overlap with arXiv:1402.5070
We argue that in a framework for emergent quantum mechanics, the weak equivalence principle is a consequence of concentration of measure in large dimensional spaces of $1$-Lipshitz functions. Furthermore, as a consequence of the emergent framework and the properties that we assume for the fundamental dynamics, it is argued that gravity must be a classical, emergent interaction.
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A quantum particle moving in a gravitational field may penetrate the classically forbidden region of the gravitational potential. This raises the question of whether the time of flight of a quantum particle in a gravitational field might deviate systematically from that of a classical particle due to tunnelling delay, representing a violation of the weak equivalence principle. I investigate this using a model quantum clock to measure the time of flight of a quantum particle in a uniform gravitational field, and show that a violation of the equivalence principle does not occur when the measurem…
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Recently we showed that the postulated diffeomorphic equivalence of states implies quantum mechanics. This approach takes the canonical variables to be dependent by the relation p=\partial_q S_0 and exploits a basic GL(2,C)-symmetry which underlies the canonical formalism. In particular, we looked for the special transformations leading to the free system with vanishing energy. Furthermore, we saw that while on the one hand the equivalence principle cannot be consistently implemented in classical mechanics, on the other it naturally led to the quantum analogue of the Hamilton-Jacobi equation, …
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Gravitation, according to General Relativity, is an attribute of space-time's geometry and hence not a force in the Newtonian sense. This is a consequence of Einstein's equivalence principle, which so far passed all experimental tests with high precision. However, the search for possible violations continues, for they, as the case may be, are expected to point towards more fundamental theoretical extensions of General Relativity. In particular, it is expected that useful insights are gained by studying the interaction between gravitational fields and genuine quantum-mechanical systems, like at…
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In this paper we present 'Quantum Model Theory' (QMod), a theory we developed to model entities that entail the typical quantum effects of 'contextuality', 'superposition', 'interference', 'entanglement' and 'emergence'. The aim of QMod is to put forward a theoretical framework that is more general than standard quantum mechanics, in the sense that, for its complex version it only uses this quantum calculus locally, i.e. for each context corresponding to a measurement, and for its real version it does not need the property of 'linearity of the set of states' to model the quantum effect. In thi…
