In the DSR1 model with subluminal light-speed variation, a boosted box can overtake its own emitted photon above a critical rapidity, leading to tensions in particle counting and motion not resolved by relative locality.
Generalized Lorentz invariance with an invariant energy scale
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abstract
The hypothesis that the Lorentz transformations may be modified at Planck scale energies is further explored. We present a general formalism for theories which preserve the relativity of inertial frames with a non-linear action of the Lorentz transformations on momentum space. Several examples are discussed in which the speed of light varies with energy and elementary particles have a maximum momenta and/or energy. Energy and momentum conservation are suitably generalized and a proposal is made for how the new transformation laws apply to composite systems. We then use these results to explain the ultra high energy cosmic ray anomaly and we find a form of the theory that explains the anomaly, and leads also to a maximum momentum and a speed of light that diverges with energy. We finally propose that the spatial coordinates be identified as the generators of translation in Minkowski spacetime. In some examples this leads to a commutative geometry, but with an energy dependent Planck constant.
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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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On the Consistency of Covariant Light-Speed Variation in Doubly Special Relativity
In the DSR1 model with subluminal light-speed variation, a boosted box can overtake its own emitted photon above a critical rapidity, leading to tensions in particle counting and motion not resolved by relative locality.
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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.