# 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.