Question

In a lot of laymen explanations of general relativity it is implied that the four dimensions of the space-time are equivalent, and we perceive time as different only because it is embedded in our human perception to do so.

My question is: is that really how general relativity treats the 4 dimensions?

If so - what are the implications (if any) this has on causality?

If no - can the theory support more than one time dimension?

Answer 1

That statement, that space and time are equivalent, is not really correct. In special relativity there is a distinction between spacelike and timelike events, those are events that cannot or can (respectively) be causally connected. This replaces the notion of "simultaneous" and "before or after" to something all inertial observers can agree on. In general relativity, this distinction is made locally - causal influence propagates locally in speeds less than c, but that constraints changes from point to point according to the local metric (which encodes the force of gravity).

All of this is encoded in the statement that the metric is indefinite, with a specific signature that supports one time direction. While the mathematics of GR can be generalized to other signatures, the physics cannot - the Lorentzian signature is essential in correctly interpreting the theory. Anyone can play all kinds of mathematical games, but those are meaningless unless you are very clear on how the calculations you perform are related (at least in principle) to physically observable quantities.