tom.stoer said:
To which indications are you referring to?
I think that a theory of holography with "boundary Hilbert spaces" seems to be a promising framework.
This again boils down to our disagreement about structural realism, so I expect that if you are self-consistent you should not accept the following arguments :) but anyways (sorry for the lenght, but it's not possible to condense more).
As there are not much experimental feedback here, the indications I see are piling up are from analysis of constructing principles and a general understanding of scientific knowledge evolves.
Thus the question I ask is not if timeless observer invariant statespaces are correct or wrong, I merely ask wether it's a rational expectation for further research. For me it's not so. But this doesn't mean that I exclude the possibility.
There is no a priori mathematical problem with picturing observer invariant and timeless state spaces in cases where the set of observers can be described. The problem is to identify these mathematical structures, if we believe they exists, which again brings us back to methodology.
One problem I see is when you consider the scientific perspective how
how to defend your expectations, and theories, and the process where you rationally would infer these structures. In the structural realism view, you don't demand this. Then any "mathematical existence" of timeless eternal true structures is accepted. I don't think these structures are impossible, but I think that the endavour of trying to find them is irrational. As you in any case would have to face the question of what structure, and why.
As I see it, the abstractions vectors and hilbert spaces, represent the information and the possible information states. And if we demand motivation for also the possibilities, then they are more or less "spanned" by the history of states; directly or indirectly by related information; but I have a hard time to see how a finite observer can encode an infinite history, not to mention that such a process would take infinite time. So it seems the constraints of finite information, and finite computations only yields a "window" of the set of possibilities. And from the inside view, there possible larger set of possibilities where we only see a window is not known. So any theories formulated from the inside will be bound to "live on" this evolving hilbert space. Moreoever it seems reasonable to think that each information processing agent will have a different window. This is in particularly clear when you consider a relatively speaking "simple observer" in a compelx environment; such as elementary particle vs lab environment, vs human vs entire universe.
Then reason to expect thta the observer invariant and start hilbert spaces does in fact work reasonably well when it comes to particle physics is that the observer is really the human laboratory, which is NOT "simple" relative in terms of complexity relative to the atom. Because we humans observer, these mini-observers interacting with each other. But the objection does become relevant if we try to understand the GUT models, ie. why the action between particles are what they are.
The objection is analogous to the ergodic hypothesis problem in classical physics - how do you INFER the equiprobable state space, in a real process in finite time? A structural realist is not worried about the inferrability constraint, but I am. My conclusion is that the inference of the statespce, is constrained to a complexity window, and therefor ongoing and we can never KNOW wether our "ergodic hypothesis" is right. The ergodic hypothesis is rather simply a basis for placing your bets.
This is why I think that the action of any observer, is "as if" it's distinguishable state/hilbert space, was fixed. But if it isn't (which it often isn't) the observer will face a backreaction, and sometimes this can be adjusted by a unitary correction, but sometimes it cna't, since there is no consistent correction withing the hilbert space, and thus
recovering consistency requires the hilbert space to deform. But the point here is that this does not always happen. There are cases where the interactions simply work fine withing the fixed hilbert spaces. For me this is a kind of equilibrium scenario. Now to assume this from start, is to assume a certain kind of equilibrium, and given this analysis about as rational as Einsteins original expectation that the universe should be static.
Most ways around this, just tries to consider a LARGER hilber space, where the prior one evolves (again unitarlity) but anyone that accepts my arguments sees that this is nto a solution as the size of the hilber space is constrained the by observers complexity. The larger and larger and ultimately infinitely large spaces violated the entire inference and complexity constraints (which I consider to be founding of an intriinsic mesurement theory) and again we're back to structural realism, which I ultimately consider to be a non-scientific stance.
In this view,
QM as we know it, with fixed hilbert space
is a measurement theory that is extrinsic and that lacks the information constraint condition, and assume infinite time to equuilibrate hte hilbert spaces. And the environment is assumed to be an infinite information sink. This in fact does make sense when we do study small subsystems (like we DO in in particle physics). This is a similar point Smolin also made.
This is one of the "indications" I see as to why QM as we know it, is a special limiting case of the correct inference theory I seek.
But clearly the proper inference theory I seek, will be really weird compare to QM. Those who had problems giving up on classical realism to accept the partial step of current QM, will IMO also have to have to give up structural realism which is far more radical.
/Fredrik
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