Imagine a spacecraft that leaves Mars and heads for Earth. When it gets here
and decelerates into our own frame of reference, we find that it's clock has
only measured half the time that a similar clock here on Earth has since the
spacecraft began it's trip. Now imagine that a second spacecraft leaves Mars
headed for Earth. Only this time, instead of the spacecraft decelerating
into our own frame of reference, we accelerate the earth up to it's frame of
reference. The question quite simply is How would both clocks compare now?
If you argue that the spacecraft's clock would still register half the
elapsed time, then you have just assigned to the Earth a privileged frame of
reference. After all, instead of the spacecraft decelerating into our frame
of reference, it would be just as valid to say that the Earth decelerated
into the spacecraft's frame of reference.
If you say that both clocks would read the same or that the Earth's clock
would run slower, then we could modify this experiment so that the Earth
only spends one second accelerating into the spacecraft's frame of
reference, comparing the two clocks and then decelerating both the Earth and
the spacecraft at the same rate until they both occupied the same frame of
reference that the Earth was in before. Since both clocks (in this second
scenario) remain in the same frame of reference after they have been
compared, the spacecraft's clock could not lose time compared to the Earth's
clock as both are decelerating.
So, what gives? Does any Relativist really understand the Theory of