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Totally stolen from ABATC
Ah, I should have known it also exists on YouTube – brb, gotta embed now!
Very cool! I have a question – nothing can travel faster than the speed of light. Here we have two streams going head to head at nearly the speed of light. So their relative velocity will be nearly twice the speed of light. Does that create any problems?
sailor, no, no problem. their relative velocity (the speed of one of them as measured by the other one) is still slightly less than the speed of light, thanks to relativity.
Nothing can exceed the speed of light in a vacuum. It is possible to force particles to exceed the speed of light in other mediums such as air or water (resulting in an extremely cool phenomenon known as Cerenkov radiation). Two beams traveling at near-light speed would only approximate the speed of light in a vacuum, never exceed it.
Sailor: I’m sorry to say that my learnerd commenters here are missing the point of your question.
According to the Theory of Relativity standing at the time that Einstein started thinking about this (no this theory, but the original theory) the closing speed of two protons each going, say, 200 million meters a second would be … relative to either one … 400 million meters a second. That was an obvious fact. However, it was also just recently known at the time that every single time you measure light it is going at the same speed (in the measurement modalities of the day).
Einstein’s SPECIAL theory of relativity reconciles these two facts by assuming that both are true with respect everything but time. Well, initially. Once you do this, a LOT of other things suddenly either fall neatly into place or get very very spooky.
Einstein didn’t believe in spooky. He got around the whole notion of velocity addition by representing space-time as non-Euclidean. Hyperbolic geometry is meant to reconcile the conflicts since the particles would be traveling asymptotically.
Yea, and that gets pretty spooky. I mean, we are used to the concept of “spacetime”.
Thank you all for the comments. I am not sure I am wiser as I thought speed was a function of time. I am still not also sure how two things going in opposite directions at nearly the speed of light relative to their surroundings could also be going the same speed relative to each other. Something odd would have to happen to time, which maybe is what Greg was saying.
The way this works out is that the time itself is different for each proton. The protons are literally experiencing different time than an observer watching from, say, Geneva.
OK got it.
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