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Generalized Uncertainty Principle, Classical Mechanics, and General Relativity
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The Generalized Uncertainty Principle (GUP) has been directly applied to the motion of (macroscopic) test bodies on a given space-time in order to compute corrections to the classical orbits predicted in Newtonian Mechanics or General Relativity. These corrections generically violate the Equivalence Principle. The GUP has also been indirectly applied to the gravitational source by relating the GUP modified Hawking temperature to a deformation of the background metric. Such a deformed background metric determines new geodesic motions without violating the Equivalence Principle. We point out here that the two effects are mutually exclusive when compared with experimental bounds. Moreover, the former stems from modified Poisson brackets obtained from a wrong classical limit of the deformed canonical commutators.
Forward citations
Cited by 2 Pith papers
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Bounded compactness from G(E)UP
The generalized uncertainty principle bounds the compactness of any object much heavier than the Planck mass by about 1/α, and the existence of black holes forces the GUP parameter to satisfy α ≲ 2.
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Generalized Uncertainty Principle mimicking dynamical Dark Energy: matter perturbations and gravitational wave data analysis
In a GUP-modified cosmology, matter fluctuations grow more slowly and the primordial gravitational wave spectrum is enhanced at high frequencies, leading to a claimed bound β ≲ 10^39.
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