*v*and

*w*(in 1 dimension) in the relativistic mechanics needs to be done with the following formula: $$v\oplus w = \frac{v+w}{1+vw}$$ The speed of light is assumed c=1. The interval $(-1,1)$ together with $\oplus$ forms a group. Here is an example of such "addition": $$\frac{1}{2}\oplus\frac{1}{2}= \frac{1/2 + 1/2}{ 1+\frac{1}{2}\frac{1}{2}} = \frac{4}{5} $$ The following diagram is sort of a

**slide rule**for space travelers (like

**Ijon Tichy**). The horizontal line is the real axis for the values of velocities. Point labelled "

**v+w**" in the figure represents the relativistic sum of velocities

**v**and

**w**. Move "

**v**" or "

**w**" to see how the result changes.

You may even experiment with tachyons! Slide velocity

*v*to a value greater than 1 and see how adding a small velocity

*w*slows it down.

For more see this.

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