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Building blocks of space time continuum

Does spacetime comprises of any smallest “frames” units? E.g. Planck units? 

If so, how is it compatible with relativity? I.e. consider e.g. the twins “paradox” in which twin B returned younger than twin A, meaning after each Planck time unit – or any other natural unit contender – a smaller time unit passes for the other twin. Same goes for an atomic clocks, when clock A ticks 1 Planck unit, what did clock B ticked relative to it?

Asked Adam

Since it converges to zero, is it falty to conclude that spacetime is continuous?

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