What is the temperature of a moving body?

Abstract

The construction of a relativistic thermodynamics theory is still controversial after more than 110 years. To the date there is no agreement on which set of relativistic transformations of thermodynamic quantities is the correct one, or if the problem even has a solution. Starting from Planck and Einstein, several authors have proposed their own reasoning, concluding that a moving body could appear cooler, hotter or at the same temperature as measured by a local observer. In this article we present a review of the main theories of relativistic thermodynamics, with an special emphasis on the physical assumptions adopted by each one. We also present a set of relativistic transformations that we have derived by assuming the laws of Thermodynamics to be covariant. We found that under such assumptions a moving body appears to be hotter. Since relativistic thermodynamics is a topic that can be treated as part of an undergraduate course of classical thermodynamics or modern physics, the review and our own derivations presented here aim to encourage undergraduate physics students to open a discussion on the fundamental assumptions in thermodynamics and to engage in research activities early in their scientific career.

Time and thermodynamics extended discussion on “Time & clocks: A thermodynamic approach”

“…Since, action is an invariant under Lorentz transformation, therefore entropy is a Lorentz invariant. Further, temperature should satisfy the Lorentz transformation as, T = T /γ, which is in agreement with the authors proposal [1,17,18].…”

The Zeroth Law of Thermodynamics in Special Relativity

“…The root of the Planck-Ott imbroglio was the disagreement on the relativistic transformation of the heat [12]. The two views, and a simple way of deriving them, are summarized in Appendix C. Now we are able to clarify this issue.…”

“…(129) one finds that in a given frame where we have employed the definition (29). This formula is the relativistic transformation of the heat proposed by Ott [12].…”

“…The long-lasting debate on the definition of the temperature of moving bodies, traditionally called Planck-Ott imbroglio [32], originates at this point. At first [28,35,41,44], the discussion was oriented in the direction of defining a transformation law of the temperature under Lorentz boosts and work in this direction is still ongoing (see [12] for a recent review). Supporters of both Planck's and Ott's views agree on the fact that the transformation should involve a Lorentz factor, however the opinions diverge on its position (at the denominator according to Planck [41], at the numerator according to Ott [35]).…”

Mutual Derivation Between Arbitrary Distribution Forms of Momenta and Momentum Components

“…A recent review article [25] had not made a conclusion on the relative size of f T and 0 T . We insist on the Planck-Einstein relation to be correct due to invariant T p spectra in high energy collisions [20].…”