Is conservation of charge ever violated like conservation of energy is violated during cosmological expansion? I am trying to understand this with respect to Noether's Theorem.
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related: https://physics.stackexchange.com/q/13577/ conservation of energy is NOT violated during cosmological red shift – Alex Robinson Oct 11 '19 at 10:44
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1@Alex Robinson the OP is asking with respect to Noether’s theorem, and he/she is correct. Since the LCDM spacetime is not static there is no globally conserved energy per Noether’s theorem. – Dale Oct 11 '19 at 11:10
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During the cosmological redshift, that is on the larger scale, time symmetry is broken and when it is broken conservation of energy is also violated. – Samyak Raj Oct 11 '19 at 11:20
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When and why would you expect charge conservation to break? – my2cts Oct 11 '19 at 13:52
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Possible duplicate of What is the symmetry which is responsible for preservation/conservation of electrical charges? – John Rennie Oct 11 '19 at 14:14
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With Noether’s theorem any conserved quantity is associated with some differential symmetry of the Lagrangian. For energy, the relevant symmetry is time translation symmetry. The laws of physics are generally symmetric under time translations, so usually energy is conserved. However, the LCDM model’s spacetime is not time translation symmetric, so on cosmological scales there is no conserved energy. (Note, locally energy is still conserved, including along the worldline of a redshifting photon, just not globally)
For charge conservation the Noether symmetry is the gauge invariance of the electromagnetic potential. That is an independent symmetry from the time translation symmetry, so you can still have charge conservation even in the LCDM model spacetime. As far as I know there is no known realistic scenario where the gauge invariance is lost and therefore charge is not conserved.
Dale
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Yes hawking radiation exists but charge conservation is not violated. – MiltonTheMeme May 08 '20 at 01:15
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This is a common view but I find it unsatisfying. Even though it's convenient to talk about electrons locally without considering "the other end of the Wilson line", charges are zero in a gauge theory. So energy conservation would be violated in GR even if we didn't live in a universe whose initial condition happened to break time translation symmetry spontaneously. – Connor Behan Dec 13 '21 at 10:29
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Charge is a global (integral) quantity. You have to integrate the charge density over the whole space in order to obtain a conserved quantity; otherwise the (local) charge may "leak away", for example. – Vladimir Kalitvianski Apr 15 '22 at 16:28
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As far as the present is concerned charge has not been violated. However in the Big bang charge might have been violated because of the way quantum mechanics was not like today. Certain symmetries must have been broken and so charge might have been violated. Of course I am not too sure about this.
MiltonTheMeme
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