- #141
PeterDonis
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TrickyDicky said:I still have problems with the bolded phrase. This seems like a coordinate condition.
It's true that you can define coordinates with either direction of time. For example, I could define "inverted" FRW coordinates where the sign of t was reversed and nothing else was changed; in those coordinates, the expansion would be negative and the universe would be "contracting". However, there would be no way to do a Lorentz transformation at any event between those "inverted" coordinates and standard FRW coordinates (more precisely, between a local patch of one and a local patch of the other). So local Lorentz invariance is enough to ensure that, if we pick a direction of time in one coordinate system, any others that we relate to it must have the same direction of time. I guess if we wanted to be really careful, we would have to say that local Lorentz invariance is part of "general covariance", so general covariance does require you to pick a time orientation. In principle you could pick either one (since the expanding and contracting FRW models are both valid solutions of the EFE), but since we actually observe the universe to be expanding in the same direction of time as we feel ourselves to be "moving", we pick that direction of time as the "future".