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In texts about special relativity the light clock is usually described as a tool to measure time $t$. It counts how often light travels along a given distance $d$, i.e. $t = d/c$, where $c$ is the speed of light.

In other contexts, distance is defined by how far light travels in a given time $t_d$, i.e. $d = c\cdot t_d$.

Now I wonder if we have a way to define distance and time such that that not each one relies on the other one?

Is an atomic clock sufficiently different from a light clock so that we can say we do not base time measurement on distance measurement?

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But light is essential to the theory of relativity. Yes you can measure distance in meters but time in space is not absolute. You could put a person on the start line and person on the finish lines with atomic clocks and they would not agree on when a person when the person started and finished. The person at the finish line would start the clock the speed of light late. And the person at the start line would stop the clock the speed of light late. They might agree it was 100 meters but they would not agree on the time. The guy on the start line would have a longer time. And if the runner had a clock he would also have a different time. On the start line they could agree the clocks are synchronized but once they are separated by space they would no longer agree the clocks are synchronized. Each would say the other clock is slow by the speed of light / distance.

The clock is not different but how we measure the clock is different as information only travels at the speed of light.

The basis for the theory of relativity is that regardless of your frame of reference you agree on the speed of light. I get it is kind of a circular definition but it works.

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