Special Relativity

Saturday at 9:34 AM #7 Ibix

NEW Imagine driving at 30mph along a straight road. Another car drives at 30mph along another straight road that makes an angle θ with yours. The other car will fall behind because it’s speed in your direction is only 30 cos θ. Of course, the other driver will say it’s you who is falling behind, and for the exact same reason. There’s no logical problem with both of you saying the other falls behind - it’s just that you have slightly different definitions of going forwards.

This is very closely analogous to the difference of opinion over time in relativity. You have different notions of what “not moving in space, only time” means, so disagreeing over clock rates is like observing that mile markers on the other road don’t measure miles on your road. The relevant factor is the hyperbolic cosine of the velocity rather than the trigonometric cosine of the angle, though, because spacetime is Minkowski, not Euclidean.