# what does it truly mean for there to be a max speed? [duplicate]

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Firstly, I apologize if this is the wrong place to post this question; I'm not a scientist, just curious. So: if the speed of light (299 792 458 m/s according to Google) is an absolute limit even for relative speeds, then what happens if I throw a rock such that it achieves the speed of light, and then throw another in exactly the opposite direction (at any speed I guess, but lets say speed of light)? What is their velocity relative to one another?

## marked as duplicate by ACuriousMind♦Nov 6 '17 at 11:59

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• "is an absolute limit even for relative speeds" - what do you mean by relative speeds? – Andrei Geanta Nov 6 '17 at 10:32
• well, if I throw two rocks in opposite directions at, say, 1 m/s then the speed of either rock relative to the other is 2 m/s. I meant it in that way. – Numi Nov 6 '17 at 10:34

## 1 Answer

If you want to calculate the relative velocity between two objects, you have to use composition law for velocities:

$$v=\frac{u+w}{1+\frac{uw}{c^2}}$$ where $c$ is the speed of light.

Even if the two objects travel at the speed of light (which is not possible for a massive particle) the relative velocity cannot exceed $c$.

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

Note that for low velocities, the term $\frac{uw}{c^2}\rightarrow 0$, so that $1+\frac{uw}{c^2}\rightarrow 1$. In the approximation of low velocities, the composition law for velocities reduces to:

$$v= u+w$$

• Ok fair enough, but I'm having extreme difficulty visualizing how this works: relative to me (the observer who threw both rocks, standing at say the origin), the rocks are going at light speed relative to each other AND relative to me? – Numi Nov 6 '17 at 10:42
• Is this where the whole time dilation thing comes into play? Please suggest something that I can read to gain a greater understanding of this. – Numi Nov 6 '17 at 10:43
• @Numi, Yes, the speed of light is $c$ relative to every inertial frame of reference. The speed of light is the same in every inertial frame of reference. This is one of the postulates of special relativity. – Andrei Geanta Nov 6 '17 at 10:45
• @Numi, Yes, this is the reason why space and time are not invariants. They form an invariant quantity called spacetime interval. But separately they are not invariants. – Andrei Geanta Nov 6 '17 at 10:49
• Could you please suggest some sort of further reading for me? – Numi Nov 6 '17 at 10:57