Does quantum mechanics tell an atomistic spacetime?
arXiv:0906.1101 · doi:10.1088/1742-6596/174/1/012009
Abstract
The canonical answer to the question posed is "Yes." -- tacitly assuming that quantum theory and the concept of spacetime are to be unified by `quantizing' a theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics arise as a coarse-grained reflection of the atomistic nature of spacetime? -- We speculate that this may indeed be the case. We recall the similarity between evolution of classical and quantum mechanical ensembles, according to Liouville and von Neumann equation, respectively. The classical and quantum mechanical equations are indistinguishable for objects which are free or subject to spatially constant but possibly time dependent, or harmonic forces, if represented appropriately. This result suggests a way to incorporate anharmonic interactions, including fluctuations which are tentatively related to the underlying discreteness of spacetime. Being linear and local at the quantum mechanical level, the model offers a decoherence and natural localization mechanism. However, the relation to primordial deterministic degrees of freedom is nonlocal.
Based on invited talks at Fourth International Workshop DICE2008, held at Castello Pasquini / Castiglioncello, Italy, 22-26 September 2008 and at DISCRETE'08 - Symposium on Prospects in the Physics of Discrete Symmetries, held at IFIC, Valencia, Spain, 11-16 December 2008 - to appear in respective volumes of Journal of Physics: Conference Series
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