I review the current status of phenomenological programs inspired by quantum-spacetime research. I stress in particular the significance of results establishing that certain data analyses provide sensitivity to effects introduced genuinely at the Planck scale. My main focus is on phenomenological programs that affect the directions taken by studies of quantum-spacetime theories.

https://link.springer.com/content/pdf/10.12942%2Flrr-2013-5.pdf

Quantum-Spacetime Phenomenology

In this article we develop a physical interpretation for the deformed (doubly) special relativity theories (DSRs), based on a modification of the theory of measurement in special relativity. We suggest that it is useful to regard the DSRs as reflecting the manner in which quantum gravity effects induce Planck-suppressed distortions in the measurement of the 'true' energy and momentum. This interpretation provides a framework for the DSRs that is manifestly consistent, nontrivial, and in principle falsifiable. However, it does so at the cost of demoting such theories from the level of fundamental physics to the level of phenomenological models - models that should in principle be derivable from whatever theory of quantum gravity one ultimately chooses to adopt.

Interpreting doubly special relativity as a modified theory of measurement

I briefly argue for logical necessity to incorporate, besides c, , two fundamental length scales in the symmetries associated with the interface of gravitational and quantum realms. Next, in order to clear the proverbial bush, I discuss the CPT and indistinguishability issue related to recent nonlinear deformations of special relativity and suggest why algebraically well-defined extensions of special relativity do not require nonlinear deformations. That done, I suggest why the stable Snyder–Yang–Mendes Lie algebra should be considered as a serious candidate for the symmetries underlying freely falling frames at the interface of gravitational and quantum realms; thus echoing, and complementing, arguments recently put forward by Chryssomalakos and Okon. In the process I obtain concrete form of uncertainty relations which involve above-indicated length scales and a new dimensionless constant. I draw attention to the fact that because superconducting quantum interference devices can carry roughly 1023 Cooper pairs in a single quantum state, Planck-mass quantum systems already exist in the laboratory. These may be used for possible exploration of the interface of the gravitational and quantum realms.

A freely falling frame at the interface of gravitational and quantum realms

We examine the transformation of particle trajectories in models with deformations of Special Relativity that have an energy-dependent and observer-independent speed of light. These transformations necessarily imply that the notion of what constitutes the same space-time event becomes dependent on the observer's inertial frame. To preserve observer-independence, the such arising nonlocality should not be in conflict with our knowledge of particle interactions. This requirement allows us to derive strong bounds on deformations of Special Relativity and rule out a modification to first order in energy over the Planck mass.

The Box-Problem in Deformed Special Relativity

In this paper we explore the problem of antiparticles in DSR1 and κ-Minkowski space-time following three different approaches inspired by the Lorentz invariant case: (a) the dispersion relation, (b) the Dirac equation in space-time and (c) the Dirac equation in momentum space. We find that it is possible to define a map Sdsr which gives the antiparticle sector from the negative frequency solutions of the wave equation. In κ-Poincare, the corresponding map Skp is the antipodal mapping, which is different from Sdsr. The difference is related to the composition law, which is crucial to define the multiparticle sector of the theory. This discussion permits to show that the energy of the antiparticle in DSR is the positive root of the dispersion relation, which is consistent with phenomenological approaches.

Particle and antiparticle sectors in DSR1 and kappa-Minkowski space-time

http://cds.cern.ch/record/638228/files/0308049.pdf

W G Unruh

Papers

Problems of "doubly special relativity" with variable speed of light