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Oct
11
comment Einstein's special relativity beyond the speed of light
Okay, the absolute value of the metric is important for the speed of light. Thus it is indeed a notable observation that this approach depends on the signature in that way, thanks for the clarifications. However, even in 1+1d it has very limited physical meaning.
Oct
11
comment Einstein's special relativity beyond the speed of light
What do you mean by “you can’t”? Take the subgroup of GL(4) generated by SO(1,3) and permutation matrices, then you can exchange “time and x” or “time and y” etc. Then it does not even preserve the absolute value of the metric, but why should it, it is physically not that interesting in any case.
Oct
10
comment Einstein's special relativity beyond the speed of light
@Ron Maimon (sorry, not allowed to comment there) Well (I did not vote down), I do not think it is the central point that it only works in 2D, even in higher dimensions it is no problem to add time reversal/space-time-interchanging to the transformation group, in higher dimensions it would no longer preserve the absolute value of the metric, but it does violate causality in every case (even 2D). And it should not be surprising to any physicists that we can allow superluminal reference frames when we allow such violations.
Oct
10
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10
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