Historical research guide · 1118 · 2013
Tests of Lorentz invariance: a 2013 update
Stefano Liberati
In one minute
Every approach to quantum gravity has to say something about what happens to spacetime symmetry at the Planck scale, and for two decades the most productive way to test those approaches has been to look for the tiny consequences a broken Lorentz symmetry would leave in ordinary particle physics. Liberati's review is the field's standing map of that effort. He starts by taking the symmetry apart: the Lorentz transformations do not have to be derived from the constancy of the speed of light at all, but follow from homogeneity, isotropy, the relativity principle and causality alone, a result going back to Ignatowski. He then lays out the effective-field-theory frameworks in which a violation would show up as an extra term in a particle's energy-momentum relation, collects the observational limits on those terms from gamma-ray bursts, cosmic rays and neutrinos, and works through two case studies — the OPERA faster-than-light neutrino episode and Hořava-Lifshitz gravity — to show how the machinery is used and where it bites.
Connection
Chapter 5 is about what it would mean for spacetime to be an emergent medium rather than a primitive, and Lorentz symmetry is the sharpest experimental handle anyone has on that question: if spacetime has constituents, the symmetry is an approximation, and this review is where the size of the allowed approximation is written down. Liberati also states the problem that any emergent-spacetime programme inherits — that relativistic behaviour of the underlying constituents does not by itself guarantee an exactly relativistic emergent system.
From the source
The Lorentz transformations need not be derived by assuming the invariance of the speed of light. They follow from four assumptions alone — spatial and temporal homogeneity, spatial isotropy, the relativity principle, and pre-causality — in the axiomatic derivation associated with Ignatowski.Section 2, The von Ignatovski theorem (arXiv:1304.5795)
Within effective field theory, radiative corrections let higher-dimension Lorentz-violating operators percolate down into the lower-dimension ones, so a dispersion relation carrying only a cubic or quartic violating term is not stable: unsuppressed linear and quadratic terms are induced and naturally dominate. Where the renormalisation-group running has been computed it is only logarithmic, giving no reason to expect those coefficients to be driven to zero at low energy.Section 5, Lorentz breaking and naturalness (arXiv:1304.5795)
Liberati's summary table of the rotationally invariant Standard Model Extension gives the typical strengths of current constraints by operator order: for photons, order ten to the minus sixteen at n equals 3 from gamma-ray bursts and ten to the minus eight at n equals 4 from cosmic rays; for electrons and positrons, ten to the minus sixteen at both n equals 2 and n equals 3; for protons, ten to the minus twenty at n equals 2.Section 11, Table 2 (arXiv:1304.5795)
The OPERA episode is treated as a worked example rather than as an embarrassment. The original apparent early arrival was withdrawn after a flaw was found, and the repeated measurement together with the ICARUS and MINOS results now functions as a constraint on neutrino velocities in the GeV range. The most convincing theoretical objection, from Cohen and Glashow, was that a superluminal neutrino would shed most of its energy to electron-positron pair production on the way from CERN to Gran Sasso, making the reported result internally inconsistent.Section 8, The Opera affaire (arXiv:1304.5795)
The constraints are not all equally robust. Liberati singles out the limits on dimension-six operators as resting on the composition of ultra-high-energy cosmic rays and on the observation of the GZK cutoff, both still unsettled between the Telescope Array and Auger pictures, and asks for constraints that do not depend on cosmic rays at all.Section 11.1, Uncertainties on n equals 4 constraints (arXiv:1304.5795)
He names naturalness as the field's most pressing theoretical challenge and almost a selection tool among candidate theories, and notes that any emergent-gravity scenario must be predictive about it, because relativistic behaviour of the fundamental constituents does not on its own guarantee an exactly relativistic emergent system.Section 11.2, The naturalness of Lorentz violations (arXiv:1304.5795)
The way in
https://doi.org/10.1088/0264-9381/30/13/133001How to cite it
Stefano Liberati (2013) Tests of Lorentz invariance: a 2013 update doi:10.1088/0264-9381/30/13/133001