On 2/4/2014 2:35 PM, LizR wrote:
You said we don't need a coordinate system at all, we can just use 4-momenta and 4-intervals - so using those doesn't imply or define a 4D coordinate system?
Sure they imply that a 4D coordinate system is possible, in fact many different ones. This is just like map surveyors who measure a lot of distance and angles between points can infer that they're on a spheroid and hence can introduce a consistent coordinate system. But the distances and angles are more fundamental, i.e. operational, than the coordinate system which has a lot of arbitrariness in it. But we don't say we know we live on a spheroid because of the relativity of latitude.
The point only makes a difference when people are asking things like does SR mean that the block universe is really real. I think even the phrase "relativity of simultaneity" is kind of misleading. It seems to imply that distant events are simultaneous with local ones relative to some frame. But in general it's only that given two spacelike events there exists a frame in which they are simultaneous. If you add a third event then there may not be any frame that will make the three simultaneous. So I'd rather say there is no such thing as simultaneity for distant events.
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