Lorentz Invariance with an Invariant Energy Scale

Abstract

We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a non-linear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants, and we highlight the similarities between the group action found and a transformation previously proposed by Fock. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity. smolin@ic.ac.uk, j.magueijo@ic.ac.uk 1

Quantum-Gravity phenomenology and high energy particle propagation

“…This deformed dispersion relation has been proposed by several authors [17,18,19,20] and is the most popular in the literature. Just for completeness we note that another possibility compatible with the dimensional analysis exists: it refers to the so called conformal models of LI breaking and was considered by Kirzhnits and Chechin in their paper.…”

“…The (non linear) deformed boost in momentum space require a change in the dispersion relation as the one previously considered but also a different definition of total energy and momentum in multiparticle states. For the DSR1 [19] and DSR2 [20] models we have [21]:…”

Entropy and temperature of black holes in a gravity’s rainbow

“…DSR theories are characterized by the inclusion of a Lorentz invariant energy and/or momentum scale, in addition to the fundamental scale provided by the speed of light [28][29][30][31][32][33][34]. The invariance of this new scale (supposed to be related to the Planck scale) is possible thanks to a nonlinear action of the Lorentz group in momentum space.…”

“…Let us check now if the conditions demanded on the function H are fulfilled in some of the DSR models that are more often found in the literature (see the appendix for details). The first of these DSR models can be considered the prototype of the DSR2 family [32,33] (i.e., theories with bounded physical energy and momentum). It is seen in the appendix that H ; g = f ; 1 in this model for the MS proposal.…”

“…In addition, one encounters deformed dispersion relations in the so-called doubly special relativity (DSR) theories [28][29][30][31][32][33][34]. The initial motivation for these theories was to solve the apparent inconsistency that exists between the relativity principle and the emergence of a fundamental scale (Planck scale), suggested by most approaches to quantum gravity [35].…”