Observability and Relativistic Fluid Mechanics
Boris S. Khots · 2021
The governing principles in Fluid Mechanics are the conservation laws for mass, momentum, and energy. And in classic Physics and Mathematics the conservation laws characterizing special relativistic fluid mechanics are invariant (in fact co-variant) under Poincare group of transformations. We consider this situation from Mathematics with Observers point of view. First of all we prove that the sets of all invertible 3 3, 4 4, 5 5 matrices are not the Lie groups in Mathematics with Observers, and group definition&s;s conditions take a place here with some probability less than 1. Also we prove that the sets of all orthogonal matrices O(3) is not the Lie groups in Mathematics with Observers, and group definition&s;s conditions take a place here with some probability less than And we prove that the sets of all Lorentz matrices L is not the Lie groups in Mathematics with Observers, and group definition&s;s conditions take a place here with some probability less than 1. And finally we prove that the sets of all Poincare matrices P is not the Lie groups in Mathematics with Observers, and group definition&s;s conditions take a place here with some probability less than 1. That means in Mathematics with Observers the probabilities of the conservation laws characterizing special relativistic fluid mechanics are invariant (in fact co-variant) under Poincare group of transformations are less than 1.