|MadSci Network: Physics|
Dear Aditya, I'm sorry-- I thought I'd answered that part of the question. Let me try again.... The conservation of energy demands that no matter WHEN I do an experiment, I get the same result. The conservation of momentum demands that no matter WHERE I do an experiment, I get the same result. Therefore, if I accelerate an electron in China, and I use the same amount of energy to accelerate an electron in Illinois, I will get the same maximum velocity. The conservation laws demand this. Your question is of theoretical interest, but not really of experimental interest. Why? Because different machines (accelerators) use different magnets and radio frequency chambers to accelerate particles. They all have different energy use profiles (friction, heating, etc) and the rings or linear accelerators have slightly different radii, which means the same amount of energy will accelerate the same kind of particle to different final energies. However! This is due entirely to our inability to build exactly the same thing twice, not due to any fundamental laws of physics. The laws of physics say that, for a perfect system, the same amount of energy will accelerate the same type of particle to the same final energy no matter where it's done. To answer your question, I'd have to say that no one has ever been able to measure it well enough to tell, but no difference would be found. There's useful information on this in any quantum mechanics book-- I got this from pages 163-165 of Introductory Quantum Mechanics by Richard L. Liboff (Addison Wesley, 1988). I hope this helps!
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