Asymptotic approach to special relativity compatible with a relativistic principle

Abstract

We propose a general framework to describe Planckian deviations from special relativity compatible with a relativistic principle. They are introduced as the leading corrections in an asymptotic approach to special relativity going beyond the energy power expansion of effective field theories. We discuss the conditions in which these Planckian effects might be experimentally observable in the near future, together with the nontrivial limits of applicability of this asymptotic approach that such a situation would produce, both at the very high (ultraviolet) and the very low (infrared) energy regimes.

Relativistic kinematics beyond special relativity

“…There are some points in common between this work and Ref. [15], where a systematic approach to SR compatible with a relativistic principle was presented also at leading order of Planckian effects, referring to that framework as Asymptotic Special Relativity (ASR). That previous work tried to be more general in the sense of including arbitrary functions of energy or momentum instead of simple polynomials in the corrections to SR, but in fact was more restrictive than the present analysis because it only considered the definition of auxiliary (energy and momentum) variables as a way to go beyond SR. That this is not sufficiently general will be clear in Section IV, which therefore establishes that a criticism of DSR that is often heard (that it is just SR rewritten in another set of variables) is unfounded.…”

Minimal Length Scale Scenarios for Quantum Gravity

“…As discussed in Section 4.2.4, the addition law in this type of model has to be modified in order to obtain Lorentz-invariant conserved sums of momenta. This gives rise to the soccer-ball problem and can lead to changes in thresholds of particle interactions [19,20,78]. It had originally been argued that this would shift the GZK cut-off [17], but this argument has meanwhile been revised.…”

Does a deformation of special relativity imply energy dependent photon time delays?

“…7 We can then obtain the value oft B at that point from Eq. (14); this will give us the time-delayT ≡t B (x B = 0) with respect to the arrival of the low-energy photon (that took place att B = 0):…”

“…This means that DSR theories cannot produce a threshold for particle decays at a certain energy of the decaying particle, since the value of this energy would not be relativistically invariant. In the same way, the existence of a relativity principle implies cancellations between the effects of modified particle dispersion relations and modified conservation laws that evade many of the constraints of the Lorentz-violating case [7].…”