Noether's Theorem and Conservation of Information

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SUMMARY

Noether's Theorem establishes a profound connection between symmetries in physical systems and conservation laws. In the context of quantum mechanics, Leonard Susskind articulates the concept of "conservation of information" as synonymous with unitarity, which ensures that the sum of probabilities remains conserved. This discussion highlights the need to identify specific symmetries that correspond to the conservation of probability amplitudes, suggesting a deeper relationship between these concepts in theoretical physics.

PREREQUISITES
  • Understanding of Noether's Theorem
  • Familiarity with quantum mechanics and unitarity
  • Basic knowledge of probability theory
  • Concept of symmetries in physics
NEXT STEPS
  • Explore the implications of Noether's Theorem in various physical theories
  • Research the concept of unitarity in quantum mechanics
  • Investigate the relationship between symmetries and conservation laws
  • Study the mathematical foundations of probability amplitudes
USEFUL FOR

Physicists, students of theoretical physics, and anyone interested in the intersection of symmetries and conservation principles in quantum mechanics.

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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