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This question already has an answer here:

I'm familiar with Einstein's formulae $V=\frac{u+v}{1+ \frac{uv}{c^2}}$ and $\Delta t'=\frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}$, the former being velocity addition and the latter being time dilation. Each of these equations imply that you can't go faster than light; the former cannot exceed $c$, and the latter will give an imaginary number in the denominator if you try.

But why are these formulae true? I understand it numerically, but how would you explain this conceptually?

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marked as duplicate by John Rennie special-relativity Dec 21 '18 at 16:31

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    $\begingroup$ What sort of answer do you expect to a "why" question? If you look at how the equations are derived you will have the best answer you can get. $\endgroup$ – m4r35n357 Dec 21 '18 at 16:35
  • $\begingroup$ @m4r35n357 That would be fine as an answer. But I don't understand the derivation. $\endgroup$ – DonielF Dec 21 '18 at 16:53
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The key concept is: space-time is 4 dimensional Minkowski space, and not 3 dimensional Euclidean space with a universal time parameter for all.

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  • $\begingroup$ English please? $\endgroup$ – DonielF Dec 21 '18 at 16:23
  • $\begingroup$ @DonielFwhat do you mean by "conceptually", then? $\endgroup$ – JEB Dec 21 '18 at 16:52
  • $\begingroup$ Explaining what you mean by a "4-dimensional Minkowski space," etc., for starters... $\endgroup$ – DonielF Dec 21 '18 at 16:54
  • $\begingroup$ @DonielF There are plenty of explanations out there, e.g. en.wikipedia.org/wiki/Minkowski_space the key conceptual point is that time is not a universal parameter that ticks uniformly for everyone, it's part of space-time. With that, the formulae make complete sense. $\endgroup$ – JEB Dec 21 '18 at 16:57
  • $\begingroup$ So...why didn't you include that in your answer? At least the link? $\endgroup$ – DonielF Dec 21 '18 at 17:27

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