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While looking for question about speed of light I saw this Physics.SE question where I found this:

$$v_\text{rel} = \frac{v_1 - v_2}{1 - \frac{v_1v_2}{c^2}}.\tag1$$

But in another answer there was this: $$v_2^{'} = \frac{v_1+v_2}{1+\frac{v_1v_2}{c^2}}.\tag2$$ Which is very similar to $(1)$. Which is correct and what are these formulas (I know that are related to special relativity but searching online I couldn't really find them!)?

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PunkZebra
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1 Answers1

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They are both correct but for slightly different things. The random mixture of not very consistent notation used in the two answers doesn't make it very clear what each is talking about.

They are the formula for the velocity of an object moving $u$ in the rest frame and $u'$ when measured in a frame moving at speed $v$. To transform between the two frame we have

$$u = \frac{v + u'}{1+\frac{vu'}{c^2}}$$

and the reverse is

$$u' = \frac{v-u}{1-\frac{vu}{c^2}}$$

Here is a simple explanation of what is going on with a nice diagram to help see what you're transforming between. This wikipedia page has a more in depth explanation and derivation of the first equation.

nivag
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