Identity and conservation of information


Well, I was reading about conservation of information these days and I have to say that I am troubled by it.

First what is information and how do we know that it is conserved. Information is something which explains distinction between systems/things. Now consider a system. The law of motion, Schrodinger equation, is deterministic meaning that given the initial state of system we can predict future state of system. One can of course reverses the dynamic and ask what would be the initial state of system if we know the state of system in future. He would find an initial state of system, after reversing time, identical with what he started with. This means that there is something especial about this system which makes the system what it is, information. We now consider two systems. One can easily show that the state of these systems cannot become equal in future if we start with different initial states since one unique finals state does always reach to one single initial state if he reverses the time. This, forktion, is not allowed in deterministic system. Therefore information cannot be created or destroyed. In simple word two systems which are distinguishable and stay distinguishable.

Now, lets come back to the problem of identity. We know who we are internally. That state of affair doesn’t change with time therefore identity is sort information. It however goes off and on when we are asleep and awake. It seems that it didn’t exist in past. So how one can resolve the problem of conservation of information with a changing identity.


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