## 19 Conditions and Limitations of this Work

- we assumed in section
**2**that there should be scalar transformations for the state variables*P**j*,*V**j*and*T**j*. This assumption appears justified in retrospect, since we have found two self-consistent sets of such transformations !

asd - the equations for an ideal gas (but not our transformation formulas !) cease to be valid at low temperature or if the pressure in the gas is too high. When the free path length is no longer significantly larger than the particle diameter, the preconditions for some statistical considerations no longer apply

sdd - if one defines temperature with Avramov in the meaning of section
**15**, then the constants*k*and*R*jmust transform by multiplying by the root factor. This is in no way restricted to the realm of ideal gases

sdfs - formally it
*is*possible to interpret entropy*S*fas a relativistic invariant. Then the Boltzmann constant is invariant, and the temperature*jT*jmust transform by multiplying by the root factor: 'Fast-moving objects appear cooler'. It is doubtful, however, that this version is compatible with astronomical observations. This would not influence the transformations of*j**P*and*V*

sdfgf - the zero point of the absolute temperature scale is in any case relativistically invariant. The position of the zero point does not depend on whether
*T*jis invariant or is multiplied by the root factor

sadas - today or in the near future, it is quite unlikely that these transformations will be tested in a terrestrial laboratory. How would one investigate a large hot ensemble of gas under controlled conditions at
*jv*j= 0.8 ·*c*j?

sad - however, astronomers observe very hot gases that move at high relativistic speeds (so-called 'jets', see the wikipedia contributions to astronomical (cosmic, or polar) jets and the keyword 'superluminal motion'). How do astronomers determine the temperature of such objects? What relativistic corrections do they apply?