Noether's Theorem and Conservation of Information

AI Thread Summary
The discussion explores the relationship between Noether's Theorem and the conservation of information, particularly in the context of quantum mechanics. It raises the question of whether a specific symmetry corresponds to the conservation of information, as described by Leonard Susskind in relation to unitarity. Unitarity is noted for conserving probabilities, which are distinct from traditional conserved quantities like energy and momentum. The conversation seeks insights into whether there is a natural symmetry that reflects the conservation of probability amplitudes. Overall, the inquiry emphasizes the need for a deeper understanding of these concepts in physics.
Feeble Wonk
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I'm not sure if this is the appropriate forum, but I'm trying to find out if there is a specific symmetry (according to Noether's Theorem) that is reflected in the conservation of information?
 
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I am bumping this thread because I was wondering it myself. I can't claim the mathematical chops for understanding Noether's theorem, but perhaps someone can give me some idea/well-informed speculation about this question, or even if it's sensible.

Leonard Susskind is perhaps the most reputable physicist to use the term "conservation of information" as a synonym for unitarity in QM. Wikipedia tells me unitarity implies "probabilities are numbers between 0 and 1 whose sum is conserved". So we seem to have some sort of conserved quantity here... although probabilities seem quite different a sort of thing than energy or momentum. So can we point to a symmetry in nature that reflects the fact that the square of the magnitude of a probability amplitude is conserved?

Hope I've understood this correctly, thanks
 

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