Special & General Relativity Questions and Answers
Without a fixed reference frame for judging speed in the universe, how do we know which 'twin' did the moving in the famous Twin Paradox?
Because the experiences of the two twins are not the same, there is not really any symmetry between the physical conditions of these two observers. So long as you agree to use ONE of them as the 'standard time keeper', the results of special relativity hold. It doesn't matter that there is no cosmic reference standard of motion, only the relative conditions of the two clocks matter.
Having said that, I now add that the Cosmic Microwave Background radiation left over from the Big Bang does seem to provide some form of standard of motion for every local observer. It has been known for decades that this background, which Big Bang cosmology says ought to be smooth, actually has a faint 'dipole' anisotropy caused by the movement of the Earth, Sun and Milky Way. In one direction it is slightly blue-shifted, in the opposite it is red-shifted, by about 300 kilometers per second. This means that our local reference system is moving relative to the cosmic background which provides a 'standard of rest' for all observers in the universe. Special relativity does not have much to offer about this, and so far as the measurements we make are concerned, the dipole effect is irrelevant until we start to inquire about how galaxies are moving through the universe.
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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.