Which Quantum Interpretation could make a difference?

[Ken G]

Does c squared equal 6 light years per second in "hypospace"? Multiple universes where physics works differently was bad enough, I'm not sure we need universes where math works differently too.

 

[Demystifier]

I think Ken wants to say that, even though all local interpretations of QM contain some "but", the "but" of the consistent histories interpretation is the biggest one. And I would agree with that.

 

[xristy]

I think Ken wants to say that, even though all local interpretations of QM contain some "but", the "but" of the consistent histories interpretation is the biggest one. And I would agree with that.

It would seem that there are other reasonable views on the matter of non-classical logic w.r.t. quantum mechanics.

Regarding the claim:

(a) Quantum mechanics prompts us to revise our classical logical notions in favour of ‘quantum logical’ ones. This is explained by analogy to geometry, in the sense that also general relativity prompts us to revise our Euclidean (or rather Minkowskian) geometrical notions in favour of Riemannian (or rather pseudo-Riemannian) geometrical notions.

- which is referred to in the Griffiths paper mentioned earlier; Bacciagaluppi remarks:

As regards Putnam’s claim (a), I take it that it is indeed justified, at least provided one takes ‘quantum logic’ as a local logic, suitable to describing a class of propositions in the context of quantum mechanical experiments (or the corresponding class of propositions about properties of quantum mechanical systems). This claim is analogous to the claim that intuitionistic logic is indeed suitable to describing a class of propositions dealing with mathematical constructions. This is distinct from the claim that intuitionistic logic is in fact the logic that underlies all rigorous human thought (and 2 is thus the ‘true’ logic). Claim (a) understood in this sense, I should think, is relatively uncontroversial, and shall be taken as such for purposes of further discussion. The explanation that quantum logic, suitably defined, has all the main formal properties required of a ‘good’ logic will also fall into this part of the discussion.

Griffiths does not appear to make the broader sorts of claims as Putnam did w.r.t. the sorts of reasoning that are appropriate in the context of quantum mechanics and so his use of a non-classical sort of reasoning would be reasonably considered justified as above.

 

[Ken G]

What's interesting is that if we open the door to different types of reasoning itself, not just different sets of propositions, we have a radically altered version of what physics itself is supposed to be. I'm not saying we shouldn't do that, I'm saying we should do that quite hesitantly! I would view that as a kind of last-resort flavor of "but." To give you some idea, what if we said that "fuzzy logic" was also a potentially valid type of reasoning to base physics on? To some extent we already do this-- we label things as "laws" that we know are not infinitely precise. But we can say that we are not using different logic, because we can set an accuracy target that our laws need to work within, without requiring they be exact, on the grounds that they idealize the reality. That's not fuzzy logic, it's precise logic applied to idealized outcomes.

Now, if we encounter a "law" that works a random 99% of the time, and fails a random 1% of the time, regarding that as a law is fuzzy logic. If we ever really encountered something like that, we might be forced to alter the types of logic we accept in physics, but most physicists would be loathe to do that-- they would say we need to look more carefully at that 1% and find some causative influence that is now being treated as random. So we recognize a difference between a law that makes statistical predictions, versus a law that itself has only a probability of being true. We hold the line as much as possible on our reasoning processes, even as we have to give ground on what we expect from our laws.

 

[xristy]

What's interesting is that if we open the door to different types of reasoning itself, not just different sets of propositions, we have a radically altered version of what physics itself is supposed to be. I'm not saying we shouldn't do that, I'm saying we should do that quite hesitantly! I would view that as a kind of last-resort flavor of "but."

Already in 1936 Birkhoff and von Neumann set out

to discover what logical structure one may hope to find in physical theories which, like quantum mechanics, do not conform to classical logic. Our main conclusion, based on admittedly heuristic arguments, is that one can reasonably expect to find a calculus of propositions which is formally indistinguishable from the calculus of linear subspaces with respect to set products, linear sums, and orthogonal complements - and resembles the usual calculus of propositions with respect to and, or, and not.

The door seems to have already been open rather a while.

Later in the above paper they observe that

The above heuristic considerations suggest in particular that the physically significant statements in quantum mechanics actually constitute a sort of projective geometry, while the physically significant statements concerning a given system in classical dynamics constitute a Boolean algebra.

They suggest even more strongly that whereas in classical mechanics any propositional calculus involving more than two propositions can be decomposed into independent constituents (direct sums in the sense of modem algebra), quantum theory involves irreducible propositional calculi of unbounded complexity. This indicates that quantum mechanics has a greater logical coherence than classical mechanics - a conclusion corroborated by the impossibility in general of measuring different quantities independently.

In essence the computational procedures of quantum mechanics already entail representations of non-classical modes of reasoning. The idea of quantum computation depends on the non-classical character of the logic of quantum mechanics for its anticipated effectiveness.

 

[Ken G]

Later in the above paper they observe that
In essence the computational procedures of quantum mechanics already entail representations of non-classical modes of reasoning. The idea of quantum computation depends on the non-classical character of the logic of quantum mechanics for its anticipated effectiveness.

Yet there is a big difference between having a classically operating mind build a quantum computer, and having a quantum computer for a mind. The idea behind the "Heisenberg cut" of the Copenhagen way of thinking is that even if we identify a certain new type of logic for quantum systems, the goal of physics is to bring external phenomena into contact with our own ways of perceiving and thinking. We don't "think quantum", we translate quantum phenomena into how we think, in the Searle's "Chinese room" kind of way. It's very much predicated on the idea that how we think is a given, and physics must conform to it, rather than the other way around. I don't say it has to be like that, perhaps the alternative is intriguing, but I think there is a certain demonstrable resonance with the Copenhagen approach that has made it the mainstream approach. I note in the above, the suggestions for a different approach at present are loaded with terms like "heuristic" and "hope to find". It doesn't sound like they've really succeeded in "thinking quantum" without the translation.