# A question about movement in 4D

1. Jan 10, 2005

### curiouschemist

Okay, I understand that if you dedicate some motion to one dimension at a constant rate you consequently pull motion from another dimension. Like driving at an angle rather than a straight line traveling a longer distance to a said stopping line (traveling in two dimensions rather than one). I understand how this translates to time dilation at fast acceleration, the more you move through space the less you move through time. This has only been given to me in one spacial dimension and the time dimension. What happens if a rotor spins at close to the speed of light? It is, in turn (no pun intended), spinning in two spacial dimensions, would you only be able to spin the rotor at 1/2 the speed of light since you are distributing motion to two spatial dimensions from one time dimension? In this respect, what about the third spatial dimension? Like, say, a collapsing massive star. Would it only have to accelerate to 1/3 the speed of light? Anyway... I hope you see my question, I hope you (anyone) can give me some clarity. Thanks!

2. Jan 10, 2005

### JesseM

No--it's not as if an individual atom in a solid object "knows" whether other atoms in the same object are moving in different directions (as with a rotor) or if they are all at rest with respect to each other (as with a solid object moving in a linear way).

I don't think the idea of explaining relativity in terms of "movement in space vs. movement in time" should be taken too literally, it's really just a sort of mathematical trick. Brian Greene is the only author I have seen who describes relativity this way, and he explains the justification in an endnote in The Elegant Universe (p. 392):

I don't really like the idea of labelling $$d\tau/dt$$ the "speed through time", since it's really just the speed that a clock is ticking as seen in a different reference frame, and labelling the magnitude of the 4-vector $$u$$ above (usually known as the '4-velocity') as the "speed through spacetime" makes even less sense to me.

Last edited: Jan 11, 2005