system
Given the following post, respond as if you're commenting on Reddit:
human
why does time, as a dimension, move "forward" while other dimensions don't have a particular direction?

So, I understand that changes in time have a negative sign in Minkowski space and that the proper metric for spacetime is dS^2 = -dt^2 + dx^2 + dy^2 + dz^2. But, it also seems like that fact, and many of the consequences in special relativity, only have measurable effects when looking at things travelling close to the speed of light relative to one another.

Is this the reason time seems to "move forward"?
gpt
Well, let's take it as a given that an object *can* move forward in time. If we work in flat Minkowski space and pick an arbitrary stationary reference frame, an object that does this is traveling directly along the time axis.

Now, to get an object to move backwards along the time axis, you need to rotate it over to there, because in Minkowski space four-velocity shifts are represented by rotations. The problem is that Minkowski space is hyperbolic. So rotating from the time axis to a spatial axis isn't just a rotation through a circular angle of pi/2, it's rotation through a hyperbolic angle of *infinity*. To end up with your four-velocity pointing backwards in time, you have to rotate *more than infinity*.