Post #1035196

2026-04-08 16:00 UTC

Noether’s Theorem ✍️ This equation reveals that every continuous symmetry in nature, a change you can make to a system without affecting its physical laws, brings about a conservation law. In simple terms, if the universe does not react to a certain change in perspective, it must keep a related physical quantity constant. For example, since the laws of physics remain unchanged no matter when you are (Time Symmetry), energy is conserved. Since the laws are the same regardless of where you are (Space Symmetry), momentum is conserved. Because they stay the same regardless of which way you face (Rotation Symmetry), angular momentum is conserved. This insight shifted our view of the universe. We no longer see conservation as just a series of lucky observations, but as a necessary outcome of the symmetry of space and time.

Replies (3)

@pustam_egr@mathstodon.xyz 2026-04-08 16:04

Each conservation law is associated with a symmetry in the underlying physics (Noether's Theorem): ‣ Translation Symmetry in Space ➡️ Conservation of Momentum ‣ Translation Symmetry in Time ➡️ Conservation of Energy ‣ Rotation Symmetry in Space ➡️ Conservation of Angular Momentum ‣ Boosts and Rotations Symmetry in Spacetime (Lorentz transformations) ➡️ Conservation of 4-Momentum (energy + linear momentum). ‣ Change in Phase of Wavefunction (Gauge transformations) ➡️ Conservation of Electric Charge ‣ Simultaneous Reversal of Charge, Parity, and Time ➡️ Conservation of CPT parity

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@xameer@mathstodon.xyz 2026-04-08 16:40

@pustam_egr@mathstodon.xyz by you here , you mean electron or photon? Maxwell laws state almost the same

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@fazalmajid@social.vivaldi.net 2026-04-08 18:34

@pustam_egr@mathstodon.xyz at y employer Dirac Software, one of the interview questions is "what is your favorite theorem?", and Noether's is the runaway leader.

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