Does the temperature of matter increase as it is accelerated to relativistic speeds?
Does the temperature of matter (e.g. a particle in an accelerator) increase as it is accelerated and in particular does it reach extremely high temperatures as it approaches the speed of light?
My background: I am a retired corporate counsel and have developed an interest in physics and related topics of the past 13 years.
It turns out that a single particle, like the kind of which you speak, does not have a definable temperature. Physicists call temperature a "macroscopic" quantity: it is a property of an "ensemble" (a technical term that essentially means a collection of something) of particles in an equilibrium state. So, we can talk about the temperature of a glass of water or that of a slab of metal, or that of any other collections of atoms that make up an object. The temperature that we measure is not caused by the atoms themselves, but rather their random motions in the object: the faster the random velocity of the atoms, the higher the temperature. Note the difference between random and net motion here: although the water molecules in a boiling kettle each have random motions of hundreds of metres per second, the kettle isn't going anywhere. All of these random motions cancel out (this is the definition of "random", of course) so that there is no net motion, only an increased temperature. Thus, temperature is not a fundamental physical quantity like an atom's charge or mass, but rather a convenient, measurable means of describing the random motions of a collection of particles.
Here's the catch: if you speak not of a collection of particles but of a single one, then you cannot define a random part of its motion and a net part (there is no reference frame with respect to which a random motion can be defined). So, you cannot really define assign a temperature to a particle in an accelerator, because it is a single particle. One could be tricky and state that the random motion of the particle would be the small deviations from its circular path in the accelerator, caused by fluctuations in the strong magnetic fields that accelerate the particles: taken at face value, this random motion translates into a temperature of a few degrees Kelvin at best.
What would happen if you heated a substance until its random motions approached that of light? The answer is that we don't know. The framework within which we define and understand temperature only holds when the random motions of the particles that make up the object of interest move slowly relative to the speed of light. If this condition is not met, the formalism that I described to you is no longer valid. Our theories of ensembles at high speeds are not well enough developed to be able to define temperature consistently at these speeds.
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