Timeline for The local Lorentz invariance is violated in Einstein-Aether theory, but not in Einstein-Maxwell theory. Why?

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Nov 2, 2017 at 13:10	history	edited	Drake Marquis	CC BY-SA 3.0	added 597 characters in body
Nov 2, 2017 at 13:02	comment	added	Drake Marquis		@ACuriousMind Thanks for your comment. I added a reference to Jacobson's original work on Einstein-aether theory. In his theory, $u^a$ never vanishes, so no matter whether in vacuum or not, there exists a special direction given by $u^a$. This special direction violates Lorentz invariance. So Aether theory violates Lorentz invariance in the sense of 2 and 3. Maxwell theory has a Lorentz invariant action, so it is always Lorentz invariant (as textbooks tell us), no matter whether a particular solution has a nonvanishing $A^a$ which defines a special direction.
Nov 2, 2017 at 12:57	history	edited	Drake Marquis	CC BY-SA 3.0	Add a citation.
Nov 2, 2017 at 12:46	comment	added	ACuriousMind♦		You (or rather the references you have read that claim this, which you should perhaps cite) need to be more precise what you mean by "Lorentz violation". There are at least three different notions of how a symmetry can be "violated": 1. The action is not invariant. 2. The ground/vacuum state is not invariant. 3. The state the system currently is in is not invariant. Aether theory appears to be in the sense of 2., while your reasoning about E-M theory appears to be in the sense of 3.
Nov 2, 2017 at 11:13	history	edited	Qmechanic♦	CC BY-SA 3.0	added 2 characters in body; edited tags
Nov 2, 2017 at 9:01	history	asked	Drake Marquis	CC BY-SA 3.0