Very Special Relativity

Question

I just attended a talk where I learnt about a rather recent idea.

"Very Special relativity"

Andrew G. Cohen and Sheldon L. Glashow

I take all new ideas with intense skepticism. From the little that I understood it seems to be the case that it invokes the concept of a preferred direction that is fundamental to the theory.

I have not yet looked at every detail, but it seems to me as sufficient to debunk such an idea (maybe just on aesthetic grounds). But maybe I have not understood some essential aspects of it.

Given that a lot of attention (165 citations on march 25th) is currently being given to this idea, it would be nice to review it, and maybe even independently post a review on the reviews section.

Comments

Lubos has made a few comments on the issue on TRF such as [1] and [2]. I am completely new to this idea, and initially confused it with the "doubly special relativity" which I was about to write an answer for.

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I agree with Lubos when he says "it is a much much more well-defined and meaningful set of questions than e.g. doubly special relativity."

Some how I don't like the idea of having a prefered direction until confirmed by experimental evidence, for that reason I would place my bets somewhere else.

But certainly naive guesses have been shown to be wrong again and again, So I was hoping there would be some strong theoretical grounds to say otherwise.

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It is not completely meaningless to study theories where Poincare invariance is violated, since such theories point to things that can be tested experimentally for possible violations. 

For a 2005 Living Review of tests for Lorentz covariance see Modern Tests of Lorentz Invariance by D. Mattingly. The resumee there is ''Currently, we have no experimental evidence that Lorentz symmetry is not an exact symmetry in nature.''