1

Carl von Weizsäcker, who worked on the topic of Quantum Logic several times, said that Quantum Logic was temporal in contrast with Classical Logic which would be atemporal (that would mean that truth values would change with time in the first case but not in the second) And also, in von Weizsäcker's article of "Classical and Quantum Descriptions", he says:

(...) Yet there are grave objections against the idea of a quantum logic. First, a lattice of propositions is not yet a logic. It corresponds to the lowest type in Russell's hierarchy of logical types, it contains no predicates of predicates, no propositions about propositions.

My questions are:

  1. Is Quantum Logic really temporal as Weizsäcker claims? Or that was his particular interpretation? Was Birkhoff's and von Neumann's original proposal of Quantum Logic temporal or atemporal?

  2. When Weizsäcker says that Quantum Logic is not yet a logic because it contains no predicates of predicates, is he exaggerating his claim? I mean, I have read everywhere that Quantum Logic is just another type of logic but this is the first time I read that it is not really a logic. Weizsäcker himself says that it belongs to the lowest types of Russell's hierarchy of logical types. So, was he exaggerating his claim?

  3. Does Quantum Logic really not contain propositions about propositions? I have read that it can be formulated as a propositional logic. Wouldn't that mean the it would contain that? Was Weizsäcker talking about some other types of Quantum Logic (maybe his own version of it)?

Link to Weizsäcker article: https://link.springer.com/chapter/10.1007/978-94-010-2602-4_31

  • 1
    Quantum logic, as in the Birkhoff and von Neumann proposal, isn't temporal. Alain Connes, does however, point out that some von Neumann algebras, which came out of a formalisation of the algebra of observables in quantum theory, do appear to have a natural temporal property, this relies on Isawasa theory - personally I'd take all this with a pinch of salt... – Mozibur Ullah Feb 29 at 4:54
  • The main problem with quantum logic, is that it doesn't tell us much about the quantum world at all, and this is because of its high level of abstraction. Its rather like taking a book, say the Arabian Nights, and removing all the stories and all the words, until you're left with just a bare and blank book, and then exulting isn't this book great ... it was greater before all the words and stories were taken out. – Mozibur Ullah Feb 29 at 5:07
  • To put it bluntly, there is much more to the quantum world (physics), to logic (reasoning), and to time (temporality) than can be found in 'quantum logic'. – Mozibur Ullah Feb 29 at 5:45
  • Weizsäcker is not alone, Abramsky and others also call it a "non-logic". Some of the problems are that there is no reasonable notion of implication, and hence deduction, or that it is hard to interpret multi-place predicates or universal quantifiers due to non-commuting observables not taking values simultaneously. nLab article has some useful references on recent approaches towards resolving those issue. – Conifold Feb 29 at 11:11
  • @Conifold but is that claim literal? Or do they mean that it is not as helpful as classical logic (according to their views), and therefore compared to it it would be as if it was not considered a logic? I mean, isn't Quantum Logic formally a kind of non-classical logic? – vengaq Feb 29 at 21:16
0
  1. Is Quantum Logic really temporal as Weizsäcker claims? Or that was his particular interpretation? Was Birkhoff's and von Neumann's original proposal of Quantum Logic temporal or atemporal?

Its quantum theory that Weisecker is claiming to be temporal, and this because he writes, right in the introduction:

I take a particular approach in starting from the idea of a quantum logic. This is in my view not a peculiar 'empirical' logic, but a specification of a general logic of temporal statements, that is of statements on facts and possibilities.

In other words, he's taking the position that quantum physics as opposed to classical physics, is ontologically temporal, because it takes possibility as a basic ontology, whereas in classical physics it is a derived fact.

  1. When Weizsäcker says that Quantum Logic is not yet a logic because it contains no predicates of predicates, is he exaggerating his claim? I mean, I have read everywhere that Quantum Logic is just another type of logic but this is the first time I read that it is not really a logic. Weizsäcker himself says that it belongs to the lowest types of Russell's hierarchy of logical types. So, was he exaggerating his claim?

He's not exaggerating his claim. Quantum logic, as Birkhoff and von Neumann then articulated, is a travesty of a logic. However, the important point they were making is that perhaps classical notions of logic may need reinvestigating in the light of what quantum physics teaches us about the nature of change; and it is this point, which stands. (Having said this, it is a point that stood from at least Hegels day, and perhaps even earlier, since Aristotle - but quantum physics gave the question new urgency).

  1. Does Quantum Logic really not contain propositions about propositions? I have read that it can be formulated as a propositional logic. Wouldn't that mean the it would contain that? Was Weizsäcker talking about some other types of Quantum Logic (maybe his own version of it)?

Well, a little later from the introduction Weizsäcker writes:

In physics we can speak of an iteration of this process. The mathematics of Hilbert space presupposes a mathematical semantics of its symbols: the letter phi means a complex vector, the letter H means a self-adjoined linear operator, etc. Yet for the physicist this is still an uninterpreted 'formalism'...

It's a truth that is generally unackowledged by many formally minded physicists, that the formalism of Hilbert spaces isn't enough to describe even the very basic quantum physics of Bohr and Diracs day. This is why, Dirac, very astutely came up with his own formalism, which is aligned with von Neumanns Hilbert spaces, but actually goes beyond it. This is why, for the physicist, interested in physics rather than formalism, the formalism is 'uninterpreted'. Essentially, the correct, mathematically rigorous, formalism, for Quantum Mechanics, is yet to be sorted out (in the sense, we can teach it to under-graduates).

The link only gives the first two pages of Weizsäcker's paper, so I can't be more expansive than this. But it seems to me that Weizsäcker is far from endorsing quantum logic per se, and going by his table of contents:

  1. The Problem
  2. Classical and Temporal Logic
  3. Quantum Theory of Probability
  4. Reality in Quantum Theory
  5. Concluding Remarks

he is not particularly interested in quantum logic per se, but the nature of possibility, and how that, in some sense, already ontologises temporality, in a way that classical physics does not. Take for instance Newtons Laws of Motion, the paradigm of classical physics; it is well-known that this is time-reflective; however, this time-reflection is not valid in quantum physics - and this appears to be what he is focusing on.

| improve this answer | |
  • Thank you for your answer, I would like to ask you some more questions to clarify some points. Referring to: 1. And do you know if Weizsäcker changed his mind towards time being fundamental or if he eventually considered quantum models based on non-temporal quantum logics? 2a. But is that claim literal? Or do they mean that it is not as helpful as classical logic (according to their views), and therefore compared to it it would be as if it was not considered a logic? I mean, isn't Quantum Logic formally a kind of non-classical logic? @MoziburUllah – vengaq Feb 29 at 21:23
  • 2b. What do you exactly mean when you say that Quantum Logic is a travesty of logic? That it is not as helpful as other logics (according to you)? 3. I did not understand your answer in this point (#3). Does Quantum Logic really lack of propositions about propositions? If it can be formulated as a propositional logic, wouldn't it have this in that case? @MoziburUllah – vengaq Feb 29 at 21:23
  • @vengaq: I suggest you ask them on the main stack which gives other people a chance to answer them. – Mozibur Ullah Mar 2 at 17:20
  • could you answer 2b at least (since it was you who said that quantum logic is a travesty of logic)? What do you exactly mean when you say that Quantum Logic is a travesty of logic? That it is not as helpful as other logics (according to you)? @MoziburUllah – vengaq Mar 2 at 21:07

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.