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Say two events happen in the same place according to one observer (1). They are separated in time by 3 years.

According to another observer (2) that is moving relative to the first, the events are separated by 5 years. We can calculate, using the invariance of the spacetime interval, that the events are separated in space by 4 lightyears, according to the second observer.

When we want to calculate the speed of observer 2 relative to observer 1, it is necessary to use the time separation of events according to observer 2. So, the relative speed would be

[itex] \frac{4yrs \cdot c}{5yrs} = \frac{4}{5}c[/itex]

Why does the time interval according to observer 2 give us relative speed of the frames? Isn't this time interval dilated due to the amount of time it takes light from the events to reach the traveling observer?

Thanks,

Russ

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# Measuring Relative Speed of Frames using Spacetime Interval

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