Answer to Question #304415 in Mechanics | Relativity for Bob

Question

b) Show that there is a time dilation for a clock that moves at a relativistic velocity v relative to an

observer who is on the ground taking readings.

Answer 1

need:

-either a second observer in the same reference frame with the clock,

-either “an interactive clock”.

This “interactive clock” might be a complex instrument with a clock, that correlates signals with outer space beacons or with pulsars at the same time with the ground observer.

After that, it sends to the ground observer pieces of information about how the time flows for that clock. It is like somebody yelled to the ground observer and say:

“On my clock in thirty seconds, I have count five pulses from the pulsars AB or from the AB outer space beacon”

The ground observer counts also pulses from the same pulsar or beacon in 30 seconds, but he counts only three pulses.

In this way, the ground observer knows that his clock is ticking faster than “a clock that moves at a relativistic velocity relative” to the ground observer.

An observation about “a relativistic velocity v relative to a ground observer”

Two aliens pass by Earth in their spaceship at a very fast speed. One of them says:

“We just pass near Earth”

“No,” the other one replied. “The Earth passes near us at a very fast speed”

They both laughed.

This is a weird idea that the speed is relative and we have to work with a frame at rest and the other one in motion ( and vice versa). This idea has to be replaced by the fact that both frames are moving. And, for the time dilation or contraction, we have to know which frame is moving faster ( or slower) than the other one. Period.

In your question, we know sure that the clock is moving faster than Earth