A circular particle collider like CERN gets particles going in two directions around a circle at nearly the speed of light and then gets them to do a head on collision. Popular science reporting describes this as nearly twice the speed of light. Can our physicist weigh in massively here and tell us whether this is nearly twice the speed of light or whether relativity makes it nearly the speed of light? I vote for the speed of light is not exceeded with respect to these two particles, but rather that the merely collide with a lot of energy (and mass) but with respect to each other they do not singly or together in their frame of reference exceed the speed of light.
Just to get things started (because I’m not qualified to comment) your instincts are right. From here:
But I look forward to someone coming along and explaining the math to us all.
Yes, in relativity there is a special rule for adding two velocities. If a and b are the speeds of the two approaching particles (relative to us). The speed of approach to each other is:
(a+b)/(1 + ab/c^2), where c is the speed of light.
For speeds that are small compared to the speed of light, the ab/c^2 term is very small so the approach speed is a+b as common sense would expect. If a and b are close to the speed of light, the equation guarantees that the approach speed never exceeds the speed of light. If either a or b or both are equal to the speed of light, the approach speed is also the speed of light.
Yes. The theory of relativity is named because at it’s core, everything is relative. Because we see two particles closing a gap at twice the speed of light, does not mean observers on either particle sees the same. They see a universe around them zipping by at almost the speed of light, and another particle approaching at a slightly higher speed.
As a frame of reference approaches the speed of light - distance (in direction of motion) decreases, time slows, and mass apparently increases.
The idea of relativistic mass is outdated. For several reasons, it makes more sense to talk about mass of a particle as simply its rest mass, and move the various relativistic factors into momentum, etc.
An observer at rest with respect to the collider would see the distance between the particles shrink at twice the speed of light, which is presumably what the pop. sci stuff you were reading was referring to.
But from the perspective of either particle, the other oncoming particle would be slightly less than the speed of light, for reasons explained upthread.
So two particles moving towards each other at c, relative to an outside observer, close at c , relative to themselves. Which is the same as if one is moving at c and the other is stationary?
Since the physics has been addressed…
Despite all the half-truths and outright falsehoods that can appear in pop sci articles, I’ve never seen this particular error before. There are a handful of things that pop sci writers “know” and fold into any article they can: Einstein was brilliant, the speed of light can’t be passed, quantum mechanics is spooky, and a couple others. Do you have an example where this particular mistake was made?
Huh?
I saw it in my surfing earlier today and cannot find it now. I’ve seen it before too.
If you’re standing in the collider at the point where the collisions happen, you’d see one particle coming from your right at (close to) the speed of light, and one coming from your left at the same speed. So you’d see the two objects close the distance between them at twice the speed of light. This doesn’t violate relativity, since that only limits the speed of objects, and the distance between two objects isn’t itself an object.
This speed is often given as the speed of collision in colliders, since we usually think of collisions as happening in the rest frame of the Earth (or in the frame of the Center of mass of the colliding objects, which in this case is the same thing), so I’d be willing to bet that’s what the article the OP was reading was talking about.
Examples? As above, I’ve never seen this used formally or informally, and a cursory Google search didn’t get me any cases.
The physics question in the OP is of course a good one. The reason I’m interested in examples is that I find myself curious if they are in fact cases of bad physics or just bad writing (but technically correct physics that’s misinterpreted due to the bad writing).
There is nothing in relativity that says it’s impossible for a velocity higher than c to exist.
I’m assuming we are talking about inertial reference frames.
If particle A is approaching me (at position B) at .99c and particle C is approaching me from the opposite direction at .99c, then from my point of view, the two particles are approaching each other at 1.98c. There’s nothing wrong with that.
But, from A’s point of view, B is approaching A at .99c and C is approaching A at .99995c. Also, from C’s point of view, B is approaching C at .99c and A is approaching C at .99995c. There’s nothing wrong here either.
All three points of view are valid.
What relativity actually DOES say is that no matter what frame of reference you are in, you will always observe c to be the same value, therefore all inertial reference frames are equally valid, and if it’s possible to send information faster than c then there would be at least one inertial reference frame where the information is traveling backwards through time, which could violate causality, allowing an effect to precede its cause. Hence, whatever frame you’re in, if you observe an object carrying information towards you or away from you, that object’s velocity will always be c or smaller, from your point of view.
But when you observe two objects moving relative to you there’s a way to calculate what they would measure as their relative velocities from their own points of view, and it’s not the same answer as what you observe their relative velocities to be from your point of view. There’s no reason you can’t measure their closing velocity as being higher than c, from your point of view. But it will always be less than c from their points of view.
Nah, you wouldn’t see anything. They’re way too small! 