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here is what i have read. the observer on Earth measures the relativistic frame's ruler as being less than his own, and measures the relativistic frame's clock ticking slower than his own.

but this is also true of the relativistic frame, measuring the ruler and clock of the Earth observer's frame as being smaller and ticking more slowly than his relativistic frame's ruler and clock.

i have read that if one was traveling on a beam of light, that one would measure no elapse of time and no distance covered, no matter how far the observer on Earth measured the light beam to go. but if the guy on the light beam measures no time elapsed and no distance travelled, how could he at the same time, measure the Earth observer's clock to be going more slowly than his own, which has measured no time at all ? ditto for distance.