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I think general relativity will answer this in the negative. How about special relativity?

Consider a world line in A with the equation x=f(t) ; with f(t)= f(t+T) , T being the period. This won't transforms into x' = g(t') with a periodic g() as x,t depend on

*both*x',t' . What form must f have in order to preserve periodicity?

(For instance f(t) =ct transforms well , but f(t) = sin wt doesn't.)

Since we determine time by periodic phenomena, I'd also like to ask how the arguments involving 'clock synchronization' in special relativity are to hold valid.