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I know that some particles can go near or more than half the speed of light. So, say we shoot two particles in opposite directions at more than half the speed of light. Say one is moving at 50% the speed of light (Particle A), and another is moving at 60% the speed of light (Particle B). From the perspective of Particle B, Particle A would be moving at 110% of the speed of light. Is that possible? Isn't it impossible for something to travel faster than light? You could say, "Particle A technically isn't, that is just how it looks". But isn't it reality? I just want someone to explain this to me

This question isn't much related: Would light still travel the same speed relative to something traveling faster than the speed of light?

P.S. Excuse this question if it is hard to understand or is obvious, I am 11 and still have questions, after much research.

Qmechanic
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user392759
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3 Answers3

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Based on your intuition and everyday arithmetic, you would indeed conclude that it's possible to set up something like this demonstrating something going on at greater than the speed of light. Mathematically speaking, this is based on Galilean invariance where all speeds add and subtract in the usual way, and it works just fine for describing things like bowling balls hitting pins and cars colliding head-on.

But nature is not Galilean invariant at extremely high speeds; it obeys a different velocity-adding law called Lorentz invariance into which the speed of light enters the picture when you are going really fast, and seriously messes up your intuition.

Einstein wrote a short book called Relativity which explains these ideas with a minimum of math. I wish I had read it when I was 11 and recommend you give it a try.

niels nielsen
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No, particle A is not travelling faster than the speed of light, even in particle B's reference frame. The reason for this is that in special relativity, you can't naively add velocities. The correct speed is given by the velocity addition formula:

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

In our case, we can take $u$ to be the speed of A in the frame of B, $v$ the speed of the emitter of the two particles in the frame of B, and $u'$ the speed of A in the frame of the emitter. Evaluating $u$ we get:

$$u=\frac{0.6c+0.5c}{1+\frac{0.5c*0.6c}{c^2}}\approx0.85c$$

You can see for yourself that plugging in any sub-light speed $v$ and $u'$ will give you a sub-light speed $u$ as well. To understand where the formula comes from you'll have to read up on special relativity, but the gist of it is that at high speeds we're not allowed to just add them up.

Sturrum
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What happens is that the rules for finding relative velocities that we use are approximations. Very good approximations for ordinary speeds, that are much smaller than light speed.

The formula is: $$\beta_{12} = \frac{\beta_{01} - \beta_{02}}{1 - \beta_{01}\beta_{02}}$$ where $\beta$ is the ratio between the velocity and the light velocity.

In your example: $\beta_{01} = 0,5$, $\beta_{01} = -0,6$ (negative sign because goes to opposite direction), so $\beta_{12} = \frac{1.1}{1 + 0.3} = 0.85$

Claudio Saspinski
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