Special & General Relativity Questions and Answers
Why can't you choose the reference frame where time moves fastest as the one at absolute rest?
Imagine if you had 5 different spacecraft separated by 1 million miles, and called this the Alpha Cluster. They would use doppler radar to determine their relative velocities and directions of motion, and by using their thrusters, arrange to cancel their relative motions so that they are all in the same 'inertial' reference frame. They would then synchronize their clocks so that they marked the same initial time. Special relativity says that these spacecraft can now be considered to be elements of the same proper reference frame because their relative speeds are zero and each clock is at rest with respect to this agreed upon reference frame.
Now imagine, billions of miles away, there is a second set of 5 spacecraft within 1 million miles of each other called the Beta Cluster, and they also set up an identical reference frame among themselves so that their relative speeds are exactly zero, and all of their clocks keep the same time. Now comes the hard part, the relative velocity between the Alpha and Beta Clusters is 90 percent the speed of light! Although the clocks within each Cluster the clocks are synchronized, when Alpha and Beta try to compare their time keeping by sending laser pulses at, say, 1 second intervals, they notice that the Alpha and Beta clocks are pretty badly out of whack. When Alpha sends its 1-second interval pulses to Beta, Beta receives them, but stretched out from 1 second intervals to :
1 second
T = --------------------- = 2.29 seconds
( 1 - (.9c/c)^2)^1/2
This is because, from Beta's frame of reference, Alpha is moving away/towards
Beta at 0.9c. On the other hand, when Beta sends their pulses 1 second apart
to Alpha, Alpha sees them 2.29 seconds apart because from their frame of
reference, Beta is moving away/towards Alpha at 0.9c. Surely one or the other
of these reference frames, Alpha or Beta, must be closer to the 'absolute
standard of rest', but which one? Neither of them can agree on which of them
is in motion, just based on the measurement of pulse arrival times, unless
they can use some external reference points like distant stars, galaxies, or
the cosmic background radiation itself. They can measure each others relative
speeds by, say Beta bouncing a high-power doppler radar off of the ships in
the Alpha Cluster and then firing the thrusters of each ship in the Beta
Cluster until the relative speeds are zeroed, but then all we have done is to
put Alpha and Beta Clusters into the same inertial reference frame. We do not
know if this is the one closer to the 'absolute rest frame' or not. Like
a set of nested Russian dolls, one inside the other, we cannot use special
relativity to tell us anything about some absolute frame of rest or motion.
All we can do is to talk about relative motion and 'locally-inertial reference
frames'. As for using the local proper time as a gauge of which frame is
moving slowest, we can never determine absolutely which proper time is running
the slowest because we can never resolve the ambiguity of which reference
frame is 'at rest'.
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All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the NASA Astronomy Cafe, part of the NASA Education and Public Outreach program.