A direct quote from the English translations of Chapter VIII, Page 199, 1st paragraph, Volume 3, 3rd Edition, Course of Theoretical Physics: Quantum Mechanics (Non-relativistic Theory) by L.D. Landau and E. M. Liftshitz at the Institute of Physics Problems, USSR Academy of Sciences, 1977, Pergamon Press:
In both classical and quantum mechanics, the law of conservation of angular momentum is a consequence of the isotropy of space with respect to a closed system. This already demonstrates the relation between the angular momentum and the symmetry properties under rotation. In quantum mechanics, however, the relation in question is a particularly far-reaching one, and essentially constitutes the basic content of the concept of angular momentum, especially as the classical definition of the angular momentum of a particle as the product r ´ p has no direct significance in quantum mechanics, owing to the fact that position and momentum cannot be simultaneously measured.
It is now understood that both authors did not believed the mathematical usefulness of topology for physical descriptions. Nevertheless, from a topology point of view it is the isotropy of spacetime that effected the laws of conservation not exclusively for angular momentum but for square of energy as well. The square of energy is derived from r ´ p by taking the time derivative r ´ dp/dt ® r ´ F where F is now the infinitesimal primary force and the quantity r ´ F is transformed into an infinitesimal torque. Furthermore, the scalar product of r ´ F with itself can be defined as the local infinitesimal quantity for the square of energy: E²= r ´ F × r ´ F. This quantity is experimentally discovered as the quantum vacuum fluctuation by a Casimir detector.


LinkBack URL
About LinkBacks
Reply With Quote


