Summary
In this paper we distinguish between the relativistic concepts of internal (inside a particle) and external (outside a particle) temperatures. Whereas the former is inversely related to the frequency associated with the particle and transforms as predicted by the Planck law, the latter is proportional to that frequency and transforms according to the Ott law. In the Newtonian limit (v/c→0) these two concepts become the same and are both discussed in the framework of a canonical scheme of thermodynamics.
Riassunto
In questo lavoro si opera una distinzione tra concetti relativistici di temperatura interna (dentro la particella) ed esterna (fuori dalla particella). Mentre la prima è inversamente correlata con la frequenza associata con la particella e si trasforma come previsto dalla legge di Planck, la seconda è proporzionale a quella frequenza e si trasforma secondo la legge di Ott. Nel limite newtoniano (v/c→0) questi due concetti diventano un solo concetto e sono entrambi discussi nel contesto di uno schema canonico della termodinamica.
Резюме
В этой статье мы проводим различие между релятивистскими концепциями внутренней (внутри частицы) и внешней (вне частицы) температуры. В то время как первая температура обратно пропорциональна частоте, связанной с частицей, и преобразуется согласно закону Планка, то вторая температура пропорциональна этой частоте и преобразуется согласно закону Отта. В ньютоновском пределе (v/c→0) эти две концепции являются одинаковьми. Обе концепции обсуждаются в рамках канонической схемы термодинамики.
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References
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There exists still a third approach to the question of temperature transformation which considers temperature to be Lorentz invariant. First proposed byP. T. Landsberg:Nature (London),212, 571 (1966), this approach has found its best treatment in an excellent paper byG. Cavalleri andG. Salgarelli:Nuovo Cimento A,62, 722 (1969), where these authors discuss also the implications of the Lorentz invariance of temperature in the realm of temperature measurement from the operational point of view.
The time period associated to a particle must also correspond to the timelike part of a timelike four-vector because it is the time elapsed between two, causally connected, consecutive events occurring in the particle (see, for example,H. M. Schwartz:Introduction to Special Relativity (New York, N. Y., 1977), p. 51). Now, since the wave frequency of the particle transforms according to the first of eqs. (6), the corresponding time period of the wave does inversely.
From the operational point of view there are no doubts that 1) one cannot situate a thermometer within such a small and experimentally indivisible object as an «elementary» particle and 2) temperature must be measured by a thermometer at rest with the element considered. However, one can imagine the following «thought experiment»: consider a moving extended particle which crosses through a microscopic rest thermometer (which may be assumed to pass along the internal empty spaces of the particle and to operate very rapidly). Accordingly, because of the finite value of the speed of the light signal, the thermometer will be inside the particle during a—of necessity—finite time interval in which it can reach thermal equilibrium with the internal matter of the particle. The laboratory observer could then measure the internal temperature of the moving particle.
Although it is now known that hadrons are actually composed by quarks, the confinement of such objects inside the hadrons may justify what we are asserting. Generalizing this idea, we consider any elementary particle as an object having an internal structure from which we may obtain theoretical or even indirect experimental information. (In this respect, we point out that the existence of at least five flavours of quarks, each appearing in three colours, and the discovery of at least five different leptons have already raised the possibility of a «lepton-quark physics» in which these two—up to now—different kinds of particles become unified by attributing to the particles some further sustructure (for a review of the proposed models seeH. Terazawa:Phys. Rev. D,22, 184 (1980)) In particular,H. Harari:Phys. Lett. B,86, 83 (1979), and, independently,A. Shupe:Phys. Lett. B,86, 87 (1979), have considered the most interesting of these models: all quarks and leptons are formed by «confined» further components—the rishons in Harari’s notation. It can be thought that, in order to account for a deeper unification of matter, further division of these rishons should be required, and so on.) In this way, the concept of clementary particle becomes (like those ofc with respect to velocity orh with respect to action) the limit after which we cannot experimentally detect further divisions of matter. Therefore, the physics associated to quarks—or,e.g., rishons—and the thermodynamics associated to the quantitiesT i,Q i andS i should be essentially theoretical and hidden in a direct experimental sense.
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González-Díaz, P.F. Internal and external temperatures. Nuov Cim B 64, 347–357 (1981). https://doi.org/10.1007/BF02903294
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DOI: https://doi.org/10.1007/BF02903294