## 15   The Transformation of Temperature

The decision as to whether we should leave entropy or temperature invariant, depends on how we want to understand temperature. One could also claim that this decision deepens the definition of temperature. The two possibilities are
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• temperature is defined first and foremost by the amount of heat energy, which is contained in a certain amount of material. Thus temperature must transform as Q jdoes, that is, by multiplying by the root term as we will show in the second part of this work (see "STR and Heat"). However, in the melting process heat is added without any change in temperature !

or

• temperature makes a statement about the ratio that different forms of energy in a certain piece of material have to each other. Then temperature is directly coupled with certain equilibrium states (in particular the triple points of the substances or the state of matter at standard pressure). And ratios of energies are invariant in the sense of STR.
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The energy of a particle is dependent on the relative velocity of the observer, and therefore in almost all of the proposed approaches heat is not invariant. If we tend to the first assumption, we must accordingly transform temperature by multiplying by the root factor and leave the entropy invariant. We have no other option. All those who divide heat and temperature by the root, are definitely barking up the wrong tree. We will show exactly where the decisive mistake is in their considerations in the second part of this e-paper. In the first approach triple points and melting points are dependent on relative velocities, while the fact that two or three phases coexist, of course, is not dependent on the speed of the observer.

In contrast, the second approach combines temperature with certain equilibrium conditions which are either present or not present, regardless of the relative speed of an observer. If at standard pressure pieces of aluminum are swimming around in a melting batch of aluminum, the soup has a temperature of 933.473 K. Temperature obtains a significance that is absolute in the relativistic sense. Critical temperatures of super-conductors, etc. retain their value, regardless of the reference system, because the concept of temperature is directly related to the internal structure of materials. Indeed, temperature initially is defined in this way, and by means of so-called fixed-point cells precisely calibrated reference temperatures are spread throughout the world (see section 7).

The first approach is in my view untenable, since, for example, while melting a metal bar considerable amounts of energy are supplied without any change in temperature of the material. Energy content and temperature can not be directly coupled!

The second approach establishes temperature as a fundamental unit of physics. We want to take this view as the basis of the following sections. We opt for

T' nT

Temperature is invariant in the sense of STR.

Avramov claims that astronomical observations speak against an increase and also against a decrease in temperature with increasing relative velocity [10]. According to his view distant galaxies should appear either very hot, or should no longer be observable because of their low temperature. The argument suffers, however, from the fact that the cosmic redshift is not the result of relative motion. So-called cosmic 'jets', gas or plasma clouds which are ejected from very young stars with very high relativistic velocities perpendicular to the accretion disc would perhaps provide better quantitative evidence.