The concept of temperature becomes problematic when dealing with particles traveling near the speed of light. Temperature is a measure of the average kinetic energy of the particles in a system. In classical physics, temperature is well-defined and applicable to particles at rest or moving at low speeds compared to the speed of light.
However, when particles approach the speed of light, we encounter the realm of relativistic physics, where traditional concepts undergo significant changes. At relativistic speeds, the equations governing kinetic energy and momentum are altered due to time dilation and length contraction effects predicted by Einstein's theory of special relativity.
As an object approaches the speed of light, its relativistic mass increases, and the energy required to accelerate it further also increases significantly. At the speed of light, the relativistic mass would become infinite, making it impossible to accelerate a massive object to that speed.
Since the concept of temperature relies on the kinetic energy of particles and their velocity distribution in a reference frame, applying it to particles moving at or near the speed of light becomes problematic. It's not straightforward to define a meaningful temperature for such particles because their behavior is governed by relativistic dynamics, and classical thermodynamics doesn't adequately describe their properties.
In situations where relativistic effects are significant, such as with high-energy particles in particle accelerators or cosmic rays, other quantities and concepts are used to characterize their behavior, such as energy, momentum, and Lorentz factors. Traditional temperature concepts are not applicable in these extreme relativistic scenarios.