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When a person experiences higher speeds, the light must travel a greater distance to reach the person whom is moving compared to that whom is staying still. Right? So therefore, light takes slightly longer to reach the moving body compared to the still, right? But at what minimum velocity would a body have to be traveling at to experience a noticeable difference in time? (Maybe like a couple of minutes/hours). If I am wrong in my thinking please do correct me.

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  • $\begingroup$ The 'travelling' body is at rest with respect to itself and it's everything else that is travelling. (Uniform) motion is relative and time dilation is symmetric. $\endgroup$ – Alfred Centauri Feb 23 '15 at 12:07
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You are asking about time dilation. Using $$\Delta t' = \gamma \Delta t$$ where $$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$ We can rearrange for $v$ to get: $$v = \sqrt{c^2 - \frac{\Delta t^2}{\Delta t'^2} c^2 }$$ or maybe better $$\frac{v}{c} = \sqrt{1-\frac{\Delta t^2}{\Delta t'^2}}$$ to get the speed as a fraction of the speed of light. Plugging in some numbers, you'll see that you need to be pretty close to the speed of light to see time dilation at the order of minutes. For example, say one second in the space ship should look like one minute to me as a stationary observer. The space ship would have to travel with 99.986% the speed of light. If one second should look like two seconds, you'd find a speed of 86.6% c. So, in essence you need to go really really fast.

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