0

I can't get this around my head it seem a paradox to me.

In my thought experiment. Suppose there are two guys John and Jack. John start throwing a ball at near speed of light

Meanwhile Jack stays very close to a black hole that the gravitational time dilation between the earth and black hole came out $\gamma = 22$. so $1$ second for Jack = $22$ seconds for John.

So Jack will say that John's ball velocity increased by $22$ times faster! so why couldn't Jack says that the ball is travelling faster than speed of light? can this broke the rule of all relativity that nothing can travel faster than light?

Ryo Lemon
  • 3
  • Angular velocity does not have the same dimensions as linear velocity, so it does not make sense to express it in terms of the speed of light. – Sandejo Dec 22 '20 at 09:23
  • Okay thanks! so i'll suppose if that John throw a ball straight ahead at near the speed of light then Jack at black hole sees time pass faster by 22 times,isn't that the ball moves faster than light to Jack frame? – Ryo Lemon Dec 22 '20 at 09:29
  • Sandejo Thanks for edited my answer and correcting my grammar! Edit : I changed my example from rotation to linear velocity. – Ryo Lemon Dec 22 '20 at 09:46

1 Answers1

1

You are quite correct. Jack will say that the ball John throws moves faster than light.

This is because in general relativity the definition of velocity is a lot more complicated than it is in special relativity. The velocity we are talking about here is called the coordinate velocity, and coordinate velocities can exceed the speed of light.

Explaining why this is rapidly gets us into some rather involved mathematics, but if you're interested have a look at my answer to Does light really travel more slowly near a massive body? For some extra background you might also be interested to read my answer to GR. Einstein's 1911 Paper: On the Influence of Gravitation on the Propagation of Light.

John Rennie
  • 355,118