Noether's Theorem and the real world

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Discussion Overview

The discussion revolves around Noether's theorem and its applicability to real-world scenarios, particularly in the context of inhomogeneous distributions of galaxies and materials. Participants explore the implications of symmetries and invariance in physics, touching on theoretical and conceptual aspects.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant suggests that Noether's theorem does not apply to the real world due to the inhomogeneous distribution of galaxies and materials, implying that conservation laws may not hold exactly.
  • Another participant counters that the matter distribution does not need to be invariant under transformations for Noether's theorem to be relevant, emphasizing that the theorem relates to the invariance of the action.
  • A third participant reiterates that Noether's theorem is derived from the symmetries of the Lagrangian and that boundary conditions are considered separately.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of Noether's theorem to real-world scenarios, indicating that multiple competing perspectives remain unresolved.

Contextual Notes

Some assumptions about the nature of symmetries and their relationship to physical laws are not fully explored, and the discussion does not clarify the implications of boundary conditions on the application of Noether's theorem.

sweet springs
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Hi.

Noether's theorem comes from the symmetries of the world. In the real world the distribution of galaxies and materials are inhomogeneous. Noether's theorem does not stand for the real world, so conxervations of energy, momentum, angular momentum do not stand exactly. Is it OK? Thanks in advance for your teachings.
 
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sweet springs said:
In the real world the distribution of galaxies and materials are inhomogeneous.

This does not matter. The matter distribution does not need to be invariant under the transformation for it to be a symmetry, Noether's theorem relates to the invariance of the action.
 
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sweet springs said:
Noether's theorem comes from the symmetries of the world
Noether's theorem comes from the symmetries of the Lagrangian. In other words, the symmetries of the laws of physics.

The boundary conditions are added later.
 
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Thanks a lot!
 

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