apeiron
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Ken G said:Yes, the important thing about distinguishing an image space from the inverse-image space is that the evolution seen in the image space does not have to map backward onto the evolution in the inverse-image space.
I get you. And I agree. Are you basing this view on any sources in particular?
To me, this is the basic Peircean argument based on a logic of vagueness. And Prigogine makes the same essential case in the End of Certainty. As does Salthe in his Development and Evolution.
So our reductionist models (based on statements of local symmetry) create the impression that time is simply reversible. The current state predicts all future states deterministically, and also retrodicts all prior states. The block universe view of reality. The inverse view works equally well.
But a developmental ontology says real novelty and surprise occurs in some fashion. Our current map of the situation cannot capture all the information. So although we might feel there is a discrete series of events that got us to where we are, history cannot in fact be run backwards. We don't have the "hidden variables" that would allow us to recover those prior events in deterministic fashion.
The question then is what is the source of this uncertainty and unpredictability? Are there just hidden variables (discrete local infomation that we simply have not measured, but which in the god's eye view exists to ensure determinism). Or is nature inherently spontaneous in some way that defies complete measurement?
Well even if that is so, it would still seem that that spontaneity (for example, the probablistic collapse of a wavefunction into some discrete outcome) is still localisable as an event in time. But then what came before is a blur. So this would be a reason why the view backwards becomes indeterminate.
In complex systems - the kind with evolving rather than fixed global constraints - this would then be a second kind of blurring of the view. If the view based on states of the system can only capture the local information, and not see the global information - the story of how global constraints are changing - then that introduces a second kind of unpredictability into the story. You can't run the global state of the system backwards (or forwards) unless you have been recording that information properly.
In the short term, projections based on local state information can be used to predict the next state, and the state after that. But eventually the global constraints have changed in some way and prediction errors start to mount up. As Prigogine argues, the future becomes vague and approximate, not deterministic, because you cannot see global change from localised measurements.
Having said all this, I think the local QM errors and the lack of information about evolving global constraints are just two sides of the same coin.
As for example in Cranmer's transactional intepretation of QM, the future does constrain the past. How things will be, acts backwards to determine the events that arose to make them so. There is strong downward constraint from the global to the local scale.
So take the quantum eraser experiment. Things that happen in the future of an emission event - like some fool experimenter fiddling around with the flight path open to a photon - act backwards to constrain the probabilities for that "spontaneous" event. Top-down constraint (the total shape of the path of the event as it exists in the history of the universe) acts downwards to constrain what actually happens at the universe's locations.
Accepting Cranmer's approach is accepting strong downwards causation at the deepest level of reality. The alternative is some locality-preserving ontology like many worlds where every history just happens and there are no developing constraints.
[edit: sorry, that may have got confusing. What I was saying that there would be both a genuine local indeterminacy in QM spontaneity, and also a global lack of determination due to failure to measure global scale variables.
So the lack of an inverse image would be due both to a local ontic indeterminacy, and a global epistemological indeterminacy. But a systems view of causality - as implied in a transactional interpretation - can at least fix the history of a particular event in a fashion that is fully reversible within the timescope of that event.]
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