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In any circular cyclotron, how can the proton projectiles approach each other at more than 50% of the speed of light without exceeding the speed of light relative to each other?

Qmechanic
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Karl Hemeyer
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    The basic gist is that adding velocities doesn't work in special relativity the way you think it does. See this article about velocity addition: https://en.wikipedia.org/wiki/Velocity-addition_formula – enumaris Apr 20 '18 at 21:42
  • We get this question and equivalent ones at least once a day at the moment. As @enumaris said it's simply the way velocity addition works in relativity. The cyclotron part makes no practical difference to this. – StephenG - Help Ukraine Apr 20 '18 at 21:52

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Good question! Before Einstein came along if you had two particles traveling traveling towards each other at about 300,000 km/s each, then we might indeed think that the other particle is traveling twice as fast as light does. Einstein showed that the speed of light in empty space is always the same, but space and time are not. They are relative. If we are travelling at different speeds, you and I will not agree on how large things are or how fast clocks tick but we will agree on the speed of light. So for those two protons, they will see that time has slowed down and distances have shortened in such a way that they will never measure themselves or the other proton as going faster than the speed of light.

Please also see this related question:

Accelerating particles to speeds infinitesimally close to the speed of light?

John
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  • That's fine for the "people on the protons," but what do I see as the operator of the cyclotron standing at the controls....and thanks. – Karl Hemeyer Apr 20 '18 at 21:43
  • What do you mean? You’d see two beams of protons each traveling at 50% the speed of light. From the point of view of the protons, though, life seems very different. – John Apr 20 '18 at 21:47
  • John, this can't be because I am observing each of these approaching protons at velocities of 99% of the speed of light given enough energy to propel them to that level which is what we constantly hear about associated with the LHC in/below/around Cern., similar to Einstein standing at that train station so long ago. – Karl Hemeyer Apr 21 '18 at 07:13