Breaking of Lorentz invariance

[tom.stoer]

Today one tries to find indications for quantum gravity indirectly via low-energy effects induced by "foamy" or "discrete" structures replacing space-time at the Planck regime. It is by no means clear whether and how such discrete structures necessarily indice Lorentz symmery breaking, neither in the UV, nor in the IR. In addtion it is not clear how such UV effects manifest itslef (indirectly) in the IR.

Therefore the general conclusion that not observing these indirect effects at low energy automatically rule out these "discrete models" in the UV.

Two references regarding the relation of UV and IR effects:

http://arxiv.org/PS_cache/gr-qc/pdf/0403/0403053v4.pdf
Phys.Rev.Lett.93:191301,2004
Lorentz invariance and quantum gravity: an additional fine-tuning problem?
John Collins, Alejandro Perez, Daniel Sudarsky, Luis Urrutia, Héctor Vucetich
(Submitted on 12 Mar 2004 (v1), last revised 30 Oct 2004 (this version, v4))
Abstract: Trying to combine standard quantum field theories with gravity leads to a breakdown of the usual structure of space-time at around the Planck length, 1.6*10^{-35} m, with possible violations of Lorentz invariance. Calculations of preferred-frame effects in quantum gravity have further motivated high precision searches for Lorentz violation. Here, we explain that combining known elementary particle interactions with a Planck-scale preferred frame gives rise to Lorentz violation at the percent level, some 20 orders of magnitude higher than earlier estimates, unless the bare parameters of the theory are unnaturally strongly fine-tuned. Therefore an important task is not just the improvement of the precision of searches for violations of Lorentz invariance, but also the search for theoretical mechanisms for automatically preserving Lorentz invariance.

http://arxiv.org/abs/1106.6346v2
Comment on http://arxiv.org/abs/1106.1417" "Small Lorentz violations in quantum gravity: do they lead to unacceptably large effects?"
Joseph Polchinski
(Submitted on 30 Jun 2011 (v1), last revised 2 Sep 2011 (this version, v2))
Abstract: A recent paper by Gambini, Rastgoo and Pullin [arXiv:1106.1417 investigates the important issue of constraints from Lorentz invariance on Planck scale physics, arguing that the classic analysis of Collins, Perez, Sudarsky, Urrutia and Vucetich \cite{cpsuv} is not generally valid. We argue that the new work is based on models that do not capture the relevant physics, and that almost all models of observable high energy Lorentz violation, and proposed Lorentz-violating theories of quantum gravity, are ruled out by low energy tests; the only known exceptions are based on supersymmetry.

 

[AndyW]

Thank you for bringing up this interesting topic about the search for quantum gravity. As you mentioned, one approach to studying this elusive theory is through the investigation of low-energy effects induced by "foamy" or "discrete" structures at the Planck scale. However, as you pointed out, there are still many uncertainties surrounding these discrete models and the potential breaking of Lorentz symmetry in the UV and IR regimes.

In response to your statement about the general conclusion that not observing these indirect effects at low energy automatically rules out these "discrete models" in the UV, I would like to point out two references that further explore the relation between UV and IR effects in the search for quantum gravity. The first reference, "Lorentz invariance and quantum gravity: an additional fine-tuning problem?" by Collins, Perez, Sudarsky, Urrutia, and Vucetich, discusses the breakdown of the usual structure of space-time at the Planck length and the potential violations of Lorentz invariance. They argue that combining known elementary particle interactions with a preferred frame at the Planck scale can lead to Lorentz violation at the percent level, unless the parameters of the theory are finely tuned. This highlights the need for both improving the precision of searches for violations of Lorentz invariance and searching for theoretical mechanisms that can preserve Lorentz invariance.

The second reference, "Small Lorentz violations in quantum gravity: do they lead to unacceptably large effects?" by Polchinski, addresses the constraints on Lorentz invariance from Planck scale physics. They argue that most models of observable high energy Lorentz violation and proposed theories of quantum gravity are ruled out by low energy tests, with the exception of those based on supersymmetry.

In summary, while the search for quantum gravity through the study of low-energy effects induced by discrete structures is a promising avenue of research, there are still many open questions and uncertainties that need to be addressed. The references provided offer valuable insights into the relation between UV and IR effects and the potential constraints on Lorentz invariance in the search for quantum gravity. Thank you again for bringing up this important topic.