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= fx (jv2j) · X mmmmwith mm fx (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.