# Ultimate Speed

## Main Question or Discussion Point

Like we have learned in school, the ultimate speed is a light speed. Do you belive that? We may be wrong. Lets take an example. There are two objects. They start in the same place and they start moving away from each other. They are travelling in a speed of a light. But isnt the speed they are moving away from each other two times light speed.
v1 C v2
<---O-----*-----O--->
v1 is light of speed and v2 is light of speed. C is where they started. v1+v2 is two times light speed. It seems to me that the distant is growing two times LS. It means that its bigger than light speed.

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Staff Emeritus
Gold Member
Dearly Missed
In relativity the formula for adding speeds is not the usual one. When you use that formula, derived from the Lorentz transformations, you never get the sum of speeds bigger than c.

The justification for the Lorentz transformations is hundreds of thousands of confirming experiments every day.

HallsofIvy
Homework Helper
Or, just possibly, YOU may be wrong. In this particular case, you simply did the arithmetic wrong.

If object A is moving away from point B at speed v1 and object C is moving away from point B with speed v2 in exactly the opposite direction, then the speed of A relative to B is given by

$$\frac{v_1+v_2}{1+\frac{v_1v_2}{c^2}}$$.

It is easy to see that if v1and v2 are both less than c, then so is this value. In your specifice example, where v1 and v2 are both equal to c (the speed of each relative to B is c) then the speed of each relative to the other is $$\frac{2c}{1+ \frac{c^2}{c^2}}= \frac{2c}{2}= c$$.

The only objection I have with SelfAdjoint's response is the phrase "In relativity the formula for adding speeds is not the usual one.". It is not the approximation that we commonly use for adding very very low speeds!