Can red shift compare which clock go faster?

[wangyi]

Hi,
We often say, an observer near the horizon of a BH finds the light traveling from far outside the horizon blue shifted, or an observer away from the BH finds the red shift of light from near the horizon. We get a conclusion that a clock near the horizon goes faster than a clocker far outside the horizon.

But can red shift alone determine the time rate? As we know, in special relatity, when two men move toward each other, one finds blue shift of light from the other, but he also finds the clock of the other observer slower, not faster.

best regards.
Thank you :)

 

[Ibix]

No, red shift alone does not determine the clock rate one would measure. First you need a clock synchronisation convention, which is necessary to relate an observed redshift to a clock rate.

A procedure for defining a synchronisation convention would involve a process equivalent to exchanging light signals. During that process you'd discover that the round trip time for the signals would vary in different ways under various different scenarios. And you might experience different proper accelerations. All of this would serve to differentiate between gravitational and kinematic time dilation, or more complex situations where one canmot cleanly separate them.

 

[PeterDonis]

We get a conclusion that a clock near the horizon goes faster than a clocker far outside the horizon.

Actually, it's the opposite: with the most natural choice of simultaneity convention (as @Ibix notes, you have to choose a simultaneity convention for a comparison of clock rates to make sense), a clock at rest near the horizon runs slower than a clock at rest far from the horizon.