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> I cannot make any sense of your reference to “which aspect of Bell’s theorem doesn’t go through” somehow associated with “statistical independence of the allowed histories”. Would you care to clarify?
I have a detailed but very simple toy-Ising model showing how statistical independence can fail at the level of allowed histories in http://www.mdpi.com/2078-2489/5/1/190 . If you’re interested, it probably will also better explain what I mean about finite-edge effects, because it is built from a perfectly-analogous model that doesn’t have time in it at all. (The histories are analogous to instantaneous global states.)
> Regarding your views (A) and (B). View (A) I think I understand and probably agree with, but (B) seems confused. There is, to begin with, no “proper” CH framework; have you a particular task in mind?
Instead of “proper”, I guess I should have said whatever “chosen” framework one uses to calculate probabilities. (You may be able to choose one arbitrarily, which is a great feature of CH, but you still have to choose one.)
>I am not sure what you mean by “real”. Various incompatible frameworks can be assigned probabilities, but they cannot be combined. Regarding “existence” I don’t understand what you are getting at.
It’s the failure-to-combine that concerns me; I want to retrodict which history really happens (or at least a set of histories for which one of them has really happened). This is the same goal that Gell-Mann and Hartle started with in a recent piece they did on CH.
I think the biggest difference between us is that you (and Gell-Mann/Hartle) are willing to bend the rules of classical probability, and I’m not. In your Am. J. Phys piece you clearly explain that there’s this new type of quantum logic where you’re simply not allowed to consider the probability of histories that lie outside of any “chosen” framework. If you’re willing to give up on classical probability theory, maybe that’s fair.
But consider this: CH doesn’t fall apart if one sticks with classical probability! Instead, it works in almost the same way. There’s always some natural history framework, as you note, determined by the future measurement settings. Even when using classical-probability, the results of CH go through if *these*, special histories are the only ones that are allowed to really happen. (The other histories aren’t ruled out on the basis of some new “single framework rule”, they’re ruled out by the future boundary constraints from the future settings.) In other words, you can swap out non-classical probability for retrocausality.
Whether or not you’re inclined to explore this trade-off, I hope you at least see that your single-framework-rule can be effectively replicated by a truly retrocausal theory, without such a rule. (The only difference is that there would have to be one “proper” framework, not any “chosen” framework.)
But this raises the question: if your “quantum-logic” can be replicated by “classical-logic + retrocausality”, is there retrocausality hiding in your quantum logic in the first place? I’m sure you would say no, but perhaps that’s because you’ve already come to terms with this new style of thinking about histories that lie in different frameworks. But I haven’t come to terms with it. And because it’s impossible to tell which histories lie in different frameworks until one knows the future settings, your logic looks retrocausal to me.