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Note that when this article says “Lorentz symmetry” it really means “spacetime is a Lorentzian manifold”. This is bad physicists slang. We know that Lorentz s

• raattgift 10y ago
  No, it means (local) Lorentz invariance violation (LIV) under the Standard Model Extension (SME) in curved spacetime. In SME you write down an observer Lagrangian incorporating tensors, spinors, covariant derivatives, and so forth, and SME coefficients: L = L_gravity + L_SM + L_LIV + ... where SM is the Standard Model. You can write down an L_LIV that is an extension of GR with or without torsion. The second you introduce nonvanishing torsion you are no longer in Riemann spacetime. Without torsion, however, you can keep yourself in a Lorentzian manifold and still introduce e.g. spontaneous (and thus preserving geometrical identities) Lorentz breaking in the L_LIV, as in Bumblebee models. In General Relativity, Lorentz invariance is what you get when you put a metric with a signature of (-+++) or (+---) into the Einstein Field Equations and then look at the local isometries induced on the tangent spaces and find the O(3,1) group. But you could just as easily plug any signature into the EFEs - there's no mathematical restriction, and there are researchers who use all sorts of signatures (e.g. (+++++), which is manifestly not Lorentz invariant).
  • jessriedel 10y ago
    How does your comment conflict with hansen's? He's just pointing out that Lorentz symmetries in GR are only local; there's no global conservations of energy.
    • raattgift 10y ago
      Honestly, it's been a couple of days and I don't know what exactly I was on about when I should have been sleeping, except probably making the point that the Bourgoin et al paper was about the SME -- which is after all a modification of GR and the Standard Model in which it's normal to quantify arbitrary departures from Lorentz and CPT invariance -- rather than GR sensu strictissimo. An SME model that preserves local Lorentz invariance everywhere that GR does (or at least, everywhere in the EFT limits) does not necessarily carry a Lorentzian manifold in its mathematical structure (e.g. LIFs might arise due to suppressed LIV effects in a more fundamental theory), and conversely, an SME model that does have a Lorentzian manifold background might still have some Lorentz invariance breaking term. I think we're all in agreement but talking past each other in English a bit when it comes to GR itself.
  • hansen 10y ago
    > (local) Lorentz invariance This is also very misleading terminology, as curvature is a local invariant of a (semi) Riemannian manifold. Lorentz invariance is violated locally, even though the “magnitude” of this violation goes to zero if the volume of the neighborhood goes to zero. > In General Relativity, Lorentz invariance is what you get when you put a metric with a signature of (-+++) or (+---) into the Einstein Field Equations and then look at the local isometries induced on the tangent spaces and find the O(3,1) group. Local or not, isometries preserve curvature and Minkowski space has zero curvature.