#### questfortruth

##### Well-Known Member

Indeed, consider hypothetical two nuclear bombs explosions: Moscow and NY. Suppose, they started to happen almost simultaneously. Then the interval between them is space-like: ds*ds>0. But for a coordinate system, which origin O moves with super-luminal speed v>c between Moscow and NY, the explosions have started at the same point in space, but in different times; thus, the interval is time-like. However still holds ds*ds>0. Thus, we have lost definition of space-like interval. Therefore, the v>c is not logical, it violates the first law of Aristotle.

There is mathematical definition of space-like vector: U*U=1, the definition of time-like vector is U*U=-1.

But if the motion v>c is allowed, then U can be called both space-like and time-like. Space-like according to Earth, and time-like according to the ship's captain.

But if the motion v>c is allowed, then U can be called both space-like and time-like. Space-like according to Earth, and time-like according to the ship's captain.