According to the time = distance/velocity formula it would take him 0.33 microseconds to complete.

t = 100/(0.999 * 299 792 458) = 100/299 492 665.54 = 0.000000334 seconds (0.33 microseconds)

My question is, does The Flash experience running the 100 metres in 0.33 microseconds or does a stationary observer?

Depending on who does, how do I calculate how fast the other observer thinks The Flash ran?


closed as off-topic by AccidentalFourierTransform, Kyle Kanos, sammy gerbil, Emilio Pisanty, ACuriousMind May 26 '18 at 22:09

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Both the Flash and the observer stationary on the racetrack would agree that he was running ar 99.9%$c$. Where you have, as you often do in relativity, two observers in different inertial frames they must agree on their relative speed $v$. You can see that broadly from symmetry, the two are equivalent so how can one speed be greater than the other? They may disagree about the sign, of course: the observer will say the Flash is moving forwards with speed $v$, the Flash will see the track and the observer moving backwards with speed $-v$.

The observer says he travels 100m in 0.33 microseconds. The Flash's clock will run slow by a factor $\gamma$ so he will say it takes a much shorter time. But he will also see the 100m track, from start line to finishing tape, which is stationary in the observer's frame, shortened by the Lorentz contraction by exactly the same factor, so when he computes distance over time the factors cancel and the speed is the same.


The speed you've quoted ($0.999c$), where $c$ is the speed of light, is presumably the Flash's speed as seen in the stationary observer's frame of reference. Then the time you calculated (let's call it $t_0$) is the time that the stationary observer measures.

To find what time the Flash himself measures, simply use the time dilation formula $t_\mathrm{Flash} = \gamma t_0$, where $\gamma = (1-\frac{v^2}{c^2})^{-\frac{1}{2}}$, with $v=0.999c$.


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