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Are the velocities in particle accelerators equal to or less than those found outside the accelerator.
You mean, immediately outside where we have access, or somewhere we don't-- like within an exploding star? The velocities are much much greater than anything that occurs in most parts of space.
But it doesn't matter. The accelerator still accelerates the particles inside it. Scientists don't capture a fast moving particle. They grab one from an ion source-- part of the machine-- and speed it up.
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For example, are gasses in a sun given enough kinetic energy (velocity) from heat so that matter/anti-matter are created due to their impact with each other? If so, the results from the particle accelerator are valid with respect to natural events.
Whatever the answer to the first question, conclusion does not follow.
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