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It's a statement I've seen thrown around here and there. Essentially, under relativity, everything can be said to move at c, some part of it is motion through space, some of it through time, and when we speed up or slow down we are merely exchanging one motion for another. However, I never understood what is meant by "speed" or "motion" here.
Specifically what confuses me is the idea of "motion through time". "Speed" to me normally means the rate in which an object varies in space over time, and to talk about something "moving" we talk about it changing it's position with respect to time. But what does it mean when we say that an object "moves" through time (or space-time) or has a "speed"? Speed with respect to what? And what would it mean for something to move through spacetime at a different rate?
Right now, the only way I can make sense of the idea of a speed through spacetime is by introducing some sort of meta-time or hypertime, with which we can talk about movement through space-time, but that sounds a bit extreme. Can someone help explain it for me? Hope this all sounds clear enough for you guys. Thank you in advance.