To see it, understand STR, the perfect model is sine-Gordon: just many coupled pendula - we get particles ("kinks") with rest mass, which are created/annihilated in pairs, the mass grows exactly like in STR and is released while annihilation ... while moving these particles undergo Lorentz contraction (speed is limited by speed of massless waves) and oscillating particles ("breathers") slow down (time dilation) - exactly like in STR.

https://en.wikipedia.org/wiki/Sine-Gordon_equation

"Universe model with a drill" ;) https://www.youtube.com/watch?v=nl5Qq5kUbEE

Animation of kink-antikink annihilation: https://en.wikipedia.org/wiki/Topological_defect#Images

2 very sensitive measurements conducted within the past year seem to suggest (if GR is true), that we are in a universe that lacks causality. 2/3 LIGO detections imply one of the merging pair of black holes should be a naked singularity.

GR allows naked singularities. It models them fine. GR just stops being globally deterministic.

If you look up the history of GR some mathematicians in 50's made some really weird proposals for non-causal universes that would appear locally causal. But there isn't a way to test this. So it is more pure mathematics or philosophy then physics.

http://mnras.oxfordjournals.org/content/162/4/307.abstract discusses observables of such metrics, especially Gödel's.

A 2009 overview (postdating COBE, for example): http://iopscience.iop.org/article/10.1088/0004-637X/703/1/35... (preprint: https://arxiv.org/abs/0902.4575)

> 2/3 LIGO detections imply one of the merging pair of black holes should be a naked singularity.

Where did you get that from?

It's sure not prominent on the caltech or mit sites, or indeed in Pretorius et al. https://arxiv.org/abs/1603.08955

Where did you get this impression? All of the LIGO results are consistent with "standard" GR black holes whose event horizons merge.

Background: https://en.wikipedia.org/wiki/Gravastar

This creates more interest, but can obfuscate what the real situation in the field is. In this case, while Gravastars are certainly something many scientists actively do and should consider, there is no real evidence from the LIGO data that favors the hypothesis of "we are in a universe that lacks causality" over the observation of the merger of two Kerr black holes.

Yes.

http://journals.aps.org/prd/abstract/10.1103/PhysRevD.94.084... (preprint: https://arxiv.org/abs/1602.08759)

So you're still left with gravastar models that can co-exist with black holes.

One of the key assumptions of GR is that spacetime is globally hyperbolic. This implies causality. You can’t guarantee solutions of the Einstein or Maxwell equations w/o this assumption.

link?

ED: This is the starting point of the Causal Set [1] program. Don’t ask me for details, I don’t know any. But the wikipedia article looks interesting. Seems they are trying to figure out how causality restricts models with some level of discreteness.

[1] https://en.wikipedia.org/wiki/Causal_sets

> "Furthermore, so far, it has been impossible to conciliate in one common theory these two aspects of physics. To succeed in this quest, almost all unification theories predict a breaking of Lorentz symmetry."

(Note that it's actually talking about Lorentz symmetry without rotations (called "Lorentz boosts"), because rotations are associated with another conservation, as you mentioned.)

[1] http://physics.stackexchange.com/questions/12559/what-conser...

For example, a minimal SME photon Lagrangian is developed in section II. A. of Kostelcky and Mewes @ https://arxiv.org/abs/0905.0031

The difference between a minimal SME (mSME) and the full SME is that the latter admits terms of any mass dimension greater than two, while mSME requires power-counting renormalizability (in order to be an effective field theory) so mSME admits only terms of dimension four. As a result mSME can only have a finite number of Lorentz invariance violation parameters, while SME can have an infinite number of them.

The bright side is that mSME can represent locally the Lagrangian in the physics.se answer you link to with a fixing of parameters; the dim side is that in general one does not want to do this a priori, precisely because the mSME is a tool to investigate whether the Lorentz SO(3,1; R) group is an exact feature of nature at every point, rather than postulating that it is (as the Standard Model does, and indeed as Special Relativity and General Relativity do).

For example, SME is useful for dealing with things like this: https://www.wikiwand.com/en/Bumblebee_models#/Lagrangian where the non-matter term might not reduce (via GL(4, R)) to the groupoid of local coordinate transforms on the manifold and the local SO(3, 1; R) Lorentz group on the orthonormal frames (tetrad formalism) which are the symmetries of General Relativity. The point is to find out under what conditions any such model does vary from General Relativity. (We already have a good EFT for GR itself, and the result of the Bourgoin et al. paper is that it remains good.)

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).

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.

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.