Question

Modern Physics: Special Relativity

Twin A travels to a planet 12 light-years away and back at 0.6c while twin B remains on Earth. Each twin sends a message to the other every year in their own frame of reference.

a) How many messages does each twin send?
b) How many messages does each twin receive?

Answer 1

a] The distance in twin A's reference frame will be Lorentz contracted and so the distance to be traveled will be:

this distance will be covered with a speed of v = 0.6c

So, the time it took for Twin A to return to earth in its own frame of reference is:

t = d/v = 9.6ly/0.6c = 16 years

Therefore, the number of messages sent by A is 16 [since a message is sent every year].

For twin B, the distance which A will travel is 12 light-year and so the time in which A will return is:

t = 12/0.6 = 20 years

therefore, the number of messages sent by twin B is 20.

b] Twin A will receive 20 messages while B will receive 16 messages.