Building on QP from 5 reasonable axioms

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normvcr said:
Why is the probability of state transitions symmetric? i.e. P( S transitions to T) = P( T transitions to S )
Fra said:
How about the ergodic hypothesis applied to the histories in the state of microstates? ...
This got me to thinking. There is some principal that a system should be able to evolve to maximum entropy. Perhaps, this can form the core of an argument that the transition probabilities are symmetric. This might also not pan out at all ...
 
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normvcr said:
This got me to thinking. There is some principal that a system should be able to evolve to maximum entropy. Perhaps, this can form the core of an argument that the transition probabilities are symmetric. This might also not pan out at all ...
[bayes theorem] P(T|S) = P(S|T) * P(T)/P(S)
and
[ergodic hypothesis] P(S) = P(T)
=> P(T|S) = P(S|T)

or were you seeking something more subtle?, this applies only to pure microstates though.

/Fredrik
 
Fra said:
[bayes theorem] P(T|S) = P(S|T) * P(T)/P(S)
and
[ergodic hypothesis] P(S) = P(T)
=> P(T|S) = P(S|T)
... this applies only to pure microstates though.
/Fredrik
Clever argument. The fly in the ointment is that since P(T|S)=P(S|T), then we always will have P(T)=P(S), even when not at equilibrium. The analysis needs to take place in a somewhat more complex context: P(T|S) manifests itself when a measurement is done for T, in initial state S, and vice versa for P(S|T).
It is sufficient to work with microstates (pure states). Symmetry for mixed states would then follow from linearity of the transition probabilities.
 
normvcr said:
Clever argument. The fly in the ointment is that since P(T|S)=P(S|T), then we always will have P(T)=P(S), even when not at equilibrium.

Yes if we are introducing another state (some macrostate) which "equiliirium" refers to, then one needs to make that explicit in the formulas, ie we are then not just talking about an uncertaint microstate, but also an uncertain macrostate. Its also along these paths, and when associating the macrostate to an observer as an inferential agent in its envirnoment, and ponder about its "expectations on evolution", then you can connect arrow of time to the observer depedent directions
that you start to get into the objections i had before.But i will not ramble too much about that, becauase is am quote sure most arent going to see my point anyway and this is the wrong place to explain my whole idea anyway. But i think there is a lot of interesting stuff in these inferential structures! So good luck with your paper, without know what stance you take!

/Fredrik
 
normvcr said:
I will ... see if the journal is interested, and let you guys know how it turns out.
The paper was turned down by the journal, for reasons that I accept -- "this is an interesting mathematics article, but does not contain sufficient philosophical/conceptual insights to be publishable in ...". This is quite reasonable, given the nature of the journal. I raised two such insights in this thread
  1. Symmetry of probability of state transitions.
  2. The physical states (states that exist in reality) are topologically closed.
However, I did not make a point of underlining these, and other issues in the paper, as I am not trained in physics, and feel it would be presumptive of me to espouse physics to physicists. So, I am in something of a quandary ...