36   Summary for the Sections 1 to 35

 
If one defines temperature as a fundamental unit of physics, as in section 15 of this treatise, then the following values are relativistically invariant:

The following values are transformed by multiplying by the root factor:

The following values are transformed by dividing by the root factor:

There is no simple transformation in the sense of section 2 for the following process variable:

Taking into account these transformations, all the essential relationships of thermodynamics persist !
The following relationships are invariant:

For non-relativistic ideal gases we further have the invariant relationships


It should be noted that we have not assumed the validity of these relationships for a fast moving observer in order to derive the transformation rules ! We only assumed that such a transformation exists for  T , and in addition we have chosen a definition of temperature within the limiting conditions of
k' · T' n=   k · T · √    so that temperature is relativistically invariant. Most of the results were established even before this decision ( see section 33 ).

Planck, Einstein, Hasenöhrl and von Mosengeil made no errors (unlike many others) in the derivation of their results. They just decided that jk'  =   k  should apply, and then they derived the other results in a logically correct way.

Avramov, however, made the better choice !