## 2 Transformation of State Variables

We

*assume*that at least for the state variables

*P*,

*V*and

*T*jtransformations exist that are given by a multiplicative factor whose value depends only on relative speed:

*X' * *j*= *f*_{x} (*jv ^{2}*

*j*) ·

*X*mmmmwith mm

*f*

_{x}(0) = 1

A priori it is not certain that a set of such transformations can be found. For example take the pressure of a gas. A fast-moving observer could measure a different pressure in the direction of his velocity than in a direction perpendicular to it. Would that not explain the deformation of the gas balloon to an ellipsoid of revolution ? The at-rest spherical balloon is indeed subjected to the Lorentz contraction.

In fact, the change of momentum of a given particle bouncing against the balloon wall must be calculated for all directions relative to the balloon wall, and therefore the considerations in section **5** for the transformation of the pressure are direction independent. That the balloon loses its spherical shape has more to do with how one must measure lengths of fast-moving objects. Ultimately this can be traced back to the different observer's assessment of simultaneity. The fast-moving observer easily determines that the balloon must have a spherical shape in the rest frame, even when it presents itself as somewhat flattened.