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... c/2-(-c/2)=c relative to the other object? (title character limit)

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If my speed is c/n to the object behind me, which also has c/n to the one behind it and so on I should have a speed of c to the observation of the nth or so object behind. If n is a large number none of the objects are moving unreasonably fast themselves. There's a bunch of stuff in the universe so there should be an object moving with c with respect to another, maybe even faster.

And if this is wrong does it mean that c is the maximum relative speed something can reach, so there's a region of possible speed differences that are possible such as (x,x+c), so everything in the universe is limited to a speed "range"?

I barely know anything about relativity and this might be a little ignorant of a question, but I don't know a way to efficiently research something like this other than asking people.

Qmechanic
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shiddingatspeedoflight
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2 Answers2

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In special relativity, velocities do not simply add up just as in galilean physics.

Because special relativity is constructed on the principle of invariant speed of light $c$, and that speeds strictly smaller than $c$ in one reference frame will be smaller than $c$ in any reference frame, it makes sense that composing velocities is not as simple as just adding them up classically.

If you call $u' = c/2$ your velocity to the first object, and that object has a velocity $v = c/2$ with respect to the other object, then your velocity $u$ with respect to the other object will be:

$$u = \frac{u' + v}{1 + \frac{u'v}{c^2}} = \frac{c}{1 + \frac{1}{4}} = \frac{4}{5} c < c$$

You can check that this formula yields velocities $u < c$ as long as $u' < c$ and $v < c$, and if $u' = c$ or $v = c$, $u = c$. Similarly, for $n$ successive velocity composition (like a chain of $n+1$ objects moving at a given velocity $v$ each from the previous object), you would need to apply the formula $n$ times.

zonksoft
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QuantumApple
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So lets say you start from earth with c/2 in one direction and somebody else (B) with c/2 in the opposite direction. From earth the relative velocity is c. If on earth an observer waits 1 second, you and B are 1 lightsecond apart. This even works if you start with c and B also start with c. Then from earth the relative velocity is 2c, and if an observer on earth waits 2 seconds you and B were 2 lightsecond apart.

When you start to view the thing from your point of view, then it all looks very different, and special relativity is telling you how different.

lalala
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