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Observer-independent quanta of mass and length
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abstract
It has been observed recently by Giovanni Amelino-Camelia \cite{gac1, gac2} that the hypothesis of existence of a minimal observer-independent (Planck) length scale is hard to reconcile with special relativity. As a remedy he postulated to modify special relativity by introducing an observer-independent length scale. In this letter we set forward a proposal how one should modify the principles of special relativity, so as to assure that the values of mass and length scales are the same for any inertial observer. It turns out that one can achieve this by taking dispersion relations such that the speed of light goes to infinity for finite momentum (but infinite energy), proposed e.g., in the framework of the quantum $\kappa$-Poincar\'e symmetry. It follows that at the Planck scale the world may be non-relativistic.
Forward citations
Cited by 4 Pith papers
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Complex scalar field in \kappa-Minkowski noncommutative spacetime
The canonical Noether charges for the κ-deformed complex scalar match the covariant phase space results, and the earlier C-breaking is traced to using the twisted-cyclic Lagrangian L_C1 instead of the manifestly symme...
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A winding number analysis of Schwarzschild black hole stability in light of Planck-scale modified kinematics
For the cubic entropy correction S=πr_h²−αr_h³ arising from a Planck-scale modified dispersion relation, all physically allowed Schwarzschild-like branches have winding number w=−1, so no stable phase appears.
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On the Meaning of Localization in Non-Local Quantum Field Theory and On the Limits of a Space-Time Description and the Physical Meaning of Phase Space in a Nonlocal Continuum
The paper derives a nonlocal phase-space uncertainty relation implying a minimal measurable length of order L_M and a finite phase-space cell in nonlocal QFT.
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Revisiting Varying Speed of Light in Cosmology: Insights from the Friedmann-Lema\^itre-Robertson-Walker Metric
A varying speed of light in FLRW is presented as gauge freedom via the lapse function, but the key variational derivation omits the √-g measure and the claimed Hubble-tension resolution contradicts Eq. (30).
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