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- W1701888477 abstract "We derive a Lorentz invariant distribution of velocities for a relativistic gas. Our derivation is based on three pillars: the special theory of relativity, the central limit theorem and the Lobachevskyian structure of the velocity space of the theory. The rapidity variable plays a crucial role in our results. For $v^2/c^2 ll 1$ and $1/beta=kT/2 m_0 c^2 ll 1$ the distribution tends to the Maxwell-Boltzmann distribution. The mean $langle v^2 rangle$ evaluated with the Lorentz invariant distribution is always smaller than the Maxwell-Boltzmann mean and is bounded by $langle v^2 rangle/c^2=1$. This implies that for a given $langle v^2 rangle$ the temperature is larger than the temperature estimated using the Maxwell-Boltzmann distribution. For temperatures of the order of $T sim {10^{12}}~ K$ and $T sim {10^{8}}~ K$ the difference is of the order of $10 %$, respectively for particles with the hydrogen and the electron rest masses." @default.
- W1701888477 created "2016-06-24" @default.
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- W1701888477 date "2014-06-03" @default.
- W1701888477 modified "2023-09-27" @default.
- W1701888477 title "A Lorentz invariant velocity distribution for a relativistic gas" @default.
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