From: julio@diegidio.name   
      
   On Thursday, 1 September 2022 at 18:30:58 UTC+2, richali...@gmail.com wrote:   
   >   
   > Can anyone give a clear explanation why information has to be conserved   
   > in quantum mechanics?   
   >   
   > I was not taught this when first learning about QM in the 1970's. As   
   > best as I can tell the idea comes from the idea that the QM wave   
   > function evolves per a unitary operator that can, in principle, be   
   > reversed to recover the past state as well as calculate the future   
   > state of the system.   
      
   That information is conserved follows from unitarity which in turn   
   follows from reversibility, i.e. that the laws of physics are the same   
   whether we let the system evolve forwards or backwards in time (indeed,   
   except for the "measurement problem" as well as thermodynamics).   
      
   And *reversibility* itself is already present in classical physics,   
   namely since the Hamiltonian/Lagrangian approaches, where the dynamics   
   of a system are described in terms of the evolution of a *system state*   
   in a state space: *that* evolution has to be reversible, indeed lack of   
   reversibility would simply not be a state space: IOW, given a "law of   
   motion", there must be one and only one next state, and one and only one   
   previous state, or the whole state-space based approach becomes simply   
   meaningless.   
      
   > It seems to me that this argument is missing two important facts: -The   
   > wave function is not real, it is only a mathematical tool for predicting   
   > the probabilities of future states -The actual future is one of many   
   > predicted by the wave function, and likewise can be the result of many   
   > different possible past states.   
      
   No to the second part for the reasons said above.  The first part is an   
   issue of ontology: e.g. in pilot-wave theory the wave function *is* real.   
   And I'd personally agree that physics without a *solid* ontology is very   
   poor thing.   
      
   > It seems to me that each time the wave function "collapses" that   
   > information is lost. Is there a good argument why this is wrong?   
      
   That's exactly what happens with the standard interpretation, aka the   
   "shut up and calculate".  Is(n't) that wrong?  Many think that it in   
   fact means an open problem, just there is sort of a taboo against   
   wave-particle duality (as in pilot-wave theory), despite it *is*   
   ontologically solid, and we are rather offered multiverses...   
      
   Julio   
      
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