The problem of moving thermometers

Abstract Three questions in special relativistic thermodynamics are relevant to the work reported here: (1) The transformation of heat Q. This question is not considered here, and we adopt the orthodox view (Q = Q0/β) as embodied in Pauli’s article. (2) The transformation of temperature. (3) The relativistic second law. If this is taken in the orthodox form TdS ≽ dQ, where the quantities involved refer to a relatively moving system, then the answers to (1) and (3) imply the answer T = T0/β to (2). In this paper we start by treating the answer to question (3) as unknown, and deal with question (2). The answer found to this question (T = T0) is shown to imply an answer to question (3) (TdS ≽ βdQ, β≡ (1 — v2/c2)–½). The examination of question (2) is carried out in a new way by considering measurements by a thermometer fixed in the observer’s frame and in brief interaction (by black body radiation only) with a moving black body. To ensure that no energy escapes, one body is taken to move inside the other. The definition of quasi-equilibrium adopted leads to temperature transformation laws, which depend on the body shapes involved. Also we find that quasi-equilibrium is not a transitive property. It is concluded that this approach must be rejected, and at present one can conceive of satisfactory measurements by a thermometer only if it is stationary in the system studied. (It may of course be manipulated electronically by a relatively moving observer.) This implies T = T0. It is also shown that Doppler effect arguments do not provide a guide to general temperature transformation laws.