There are lots of non-relativistic models using waves. Nothing special
about them. The most compelling argument for relativity is causality.
You can reconstruct spacetime – up to conformal transformations – just
from the causality relations. I can’t even imagine what physics would
be like w/o causality.
GR does not imply causality nor does it enforce it. In fact GR works in a non-causal universe without a problem.
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.
Thanks for the links. I find it unfortunate that often in science (and especially with the LIGO data) much is written about what could possibly be lurking in the data but isn't actually favored over our current understanding.
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.
I think you're being a bit harsh. Is there any empirical evidence that favors classic black holes over gravastars, or is our "current understanding" just a matter of what we thought of first? If the latter, take a chill pill and let us enjoy the possibilities. :)
> GR does not imply causality nor does it enforce it. In fact GR works in a non-causal universe without a problem.
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.
If you restrict the speed of propagation of interactions (of massless waves), you nearly automatically get STR ... like in sine-Gordon model - speed of massive kinks becomes limited, and kinks are being contracted to zero while approaching this limit.
This was covered in my undergraduate (second-year) SR course. The idea is that if you accept that Maxwell's equations apply in all inertial frames (speed of light is constant) and that causality is conserved in all frames, the result is that Newtonian mechanics requires adjustments for effects that are called "special relativity".
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.
