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The first paragraph of the Wikipedia article on the angular momentum operator states that

In both classical and quantum mechanical systems, angular momentum (together with linear momentum and energy) is one of the three fundamental properties of motion.

I guess it makes sense intuitively. Motion can be described as a combination of translation and rotation. Such movements cause those bodies, per definition, to have angular and linear momentum. Those bodies also have kinetic energy.

However, "one of the three fundamental properties" sounds like it would be something well known, well used. I have never seen this being said before.

Is it possible to elaborate on why these are the so called "fundamental properties"?

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1 Answer 1

up vote 2 down vote accepted

"Fundamental properties of motion" is not a standard term, but there are ten conserved quantities associated (via Noether's theorem) to the ten generators of the Poincare group of spacetime symmetries:

  • 1 (1) Energy (associated with time translations)
  • 3 ($D$) Momentum components (associated with translations)
  • 3 ($\frac{1}{2}D(D-1)$) Angular momentum components (associated with rotations)
  • 3 ($D$) quantities which I have never heard a name for, which basically say that the center of mass velocity is constant (associated with boosts)

In brackets I've put the generalisation to $D+1$ spacetime dimensions, just cause. :)

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