Information Symmetry

Full Title or Meme

Conservation of information seems to be a deep physical principle. Per Noether's theorm, that must be an underlying symmetry, in some space, which may explain this conservation of information

Context

Unitarity is a key concept in Quantum Mechanics and Quantum Field Theory.

Entropy. It's not a symmetry, but there's the second law of thermodynamics. I am not talking about entropy, which is the unknown information about some system, for a particular observer. I talk about information. –

Are the known information and the loss thereof (entropy) about a system not related by something like "as the entropy increases the information decreases" ...? Could it be that you are right when one talks about a fine grained microscopic description of the system which is reversible and therefore both, information and entropy are conserved (such that it is very interesting to ask for a symmetry corresponding to the conservation of information +1), and Lunge is right when talking about course grained systems that don't conserve entropy and information when not in equilibrium ? –

Well, I am maybe wrong, but I think that information is always conserved, but entropy always increases. And I think also, that this applies to microscopic systems as well as to macroscopic systems.

References

• See the wiki page AI for Quantum Physics