Abstract
We propose a mathematical structure, based on anoncommutative geometry, which combines essentialaspects of general relativity with those of quantummechanics, and leads to correct “limitingcases” of both these physical theories. Thenoncommutative geometry of the fundamental level isnonlocal with no space and no time in the usual sense,which emerge only in the transition process to thecommutative case. It is shown that because of the originalnonlocality, quantum gravitational observables should belooked for among correlations of distant phenomenarather than among local effects. We compute the Einstein–Podolsky–Rosen effect; itcan be regarded as a remnant or a “shadow”of the noncommutative regime of the fundamental level.A toy model is computed predicting the value of the“cosmological constant” (in the quantum sector) which vanishes whengoing to the standard spacetime physics.
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Heller, M., Sasin, W. Noncommutative Unification of General Relativity and Quantum Mechanics. International Journal of Theoretical Physics 38, 1619–1642 (1999). https://doi.org/10.1023/A:1026617913754
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DOI: https://doi.org/10.1023/A:1026617913754