Lorentz Invariance as local limit of Bigger Manifold
Is it possible that Lorentz invariance is just a lower limit of a larger manifold that has a priveleged frame?
Even if Bell's experiments can't transmit signal faster than light. The spirit of relativity is still violated by say instantaneous correlation between 10 billion light years. As Popper said "we have to give up Einsteinís interpretation of special relativity and return to Lorentzís interpretation and with it to . . . absolute space and time. . . . The reason for this assertion is that the mere existence of an infinite velocity entails [the existence] of an absolute simultaneity and thereby of an absolute space. Whether or not an infinite velocity can be attained in the transmission of signals is irrelevant for this argument: the one inertial system for which Einsteinian simultaneity coincides with absolute simultaneity . . . would be the system at absolute rest Ė whether or not this system of absolute rest can be experimentally identified. (Popper 1982: xviii, 20)"
Has anyone encountered a theory wherein Lorentz Invariance is just a lower limit of a another bigger manifold that allows Bell-like instantaneous correlations? Of course by default the bigger manifold can't transmit signal. But supposed signal can be transmitted. We can modify the manifold in such a way that a signal that reaches the other party 10 billion light years away instantaneously in the bigger manifold will take time (equal to the time it takes light to travel) to reach the smaller manifold that is lorentz invariance? Has anyone heard such a thing or close to it?
Does anybody really think that instantaneous, non-local, space-like, universe-wide
relations of absolute simultaneity (and EPR causal correlations) are logically, mathematically and ontologically consistent with Einsteinís GTR?