Building a case for a Planck-scale-deformed boost action: the Planck-scale particle-localization limit

TL;DR

This paper explores the inevitability of a Planck-scale-deformed relativistic framework, linking quantum gravity considerations with particle localization limits and black hole entropy corrections, suggesting that existing formalisms may be insufficient.

Contribution

It strengthens the argument that a Planck-scale-deformed Minkowski limit is inevitable, connecting particle localization limits, black hole entropy corrections, and the need for new relativistic formalisms.

Findings

Planck-scale particle localization limits imply a DSR Minkowski limit.

Logarithmic black hole entropy corrections relate to DSR frameworks.

Existing DSR formalisms may not be sufficiently general.

Abstract

"Doubly-special relativity" (DSR), the idea of a Planck-scale Minkowski limit that is still a relativistic theory, but with both the Planck scale and the speed-of-light scale as nontrivial relativistic invariants, was proposed (gr-qc/0012051) as a physics intuition for several scenarios which may arise in the study of the quantum-gravity problem, but most DSR studies focused exclusively on the search of formalisms for the description of a specific example of such a Minkowski limit. A novel contribution to the DSR physics intuition came from a recent paper by Smolin (hep-th/0501091) suggesting that the emergence of the Planck scale as a second nontrivial relativistic invariant might be inevitable in quantum gravity, relying only on some rather robust expectations concerning the semiclassical approximation of quantum gravity. I here attempt to strengthen Smolin's argument by observing that an analysis of some independently-proposed Planck-scale particle-localization limits, such as the "Generalized Uncertainty Principle" often attributed to string theory in the literature, also suggests that the emergence of a DSR Minkowski limit might be inevitable. I discuss a possible link between this observation and recent results on logarithmic corrections to the entropy-area black-hole formula, and I observe that both the analysis here reported and Smolin's analysis appear to suggest that the examples of DSR Minkowski limits for which a formalism has been sought in the literature might not be sufficiently general. I also stress that, as we now contemplate the hypothesis of a DSR Minkowski limit, there is an additional challenge for those in the quantum-gravity community attributing to the Planck length the role of "fundamental length scale".