Somehow the answer to these questions must be explicable in terms other than it "comes out of a subtle result on the structure of Hilbert spaces".Stephen says:
It would be nice, but I'm not sure that it "must be" explicable so easily. We really lack the intuitions and therefore the vocabulary here in the macrocosm. I think it would be important to be able to do it simply, but no-one has managed it to my knowledge.
@Stephen
I cannot believe that an intricate mathematical subtletly can be at the bottom of the conundrum that something about the nature of making a measurement demands a sudden re-zeroing of the state of the universe. On measurement one deterministic process suddenly ceases and a new one begins! The answer must, indeed, have a mathematical embodiment but we ask what specific character of the structure of hilbert space connects with these interminable splittings of the universe at each measurement event.
1 comment:
This is just a preliminary reply about a point you raise, namely, that you "cannot believe that an intricate mathematical subtlety can be at the bottom of the conundrum that something about the nature of making a measurement demands a re-zeroing of the state of the universe" is one I take issue with. On the contrary, I believe that it is exactly as an "intricate mathematical subtlety" that ANYTHING involving the nexus between our classical minds and the quantum regime is likely to appear to us macroscopic beings. That is, in a form counter to our intuitions, which is what I take to be your meaning of the words "intricate" and "subtle". We do not have the internal epistemology to apprehend the quantum world as it actually is. We would not have evolved if we had had it. All classical reductions like hidden variables theories, etc., have been disposed of. We are left with no classical fall-back positions to explain anything, so why should this punctus crucis of classical-quantum interchange appear simple to us in any way? Particularly as the classical "world" does not exist. It is a fiction of our particular evolutionary tree. All is quantum, as David Finkelstein was fond of saying. What words would you use to simply describe something like this? It would have to be entirely within the vocabulary of QM: and then you are back with Hilbert space and its intricacies, which are real. This is not a proof that it cannot be done, but it is strong evidence to my mind. For further evidence, I would direct you to two of the best theorems in the subject: the Kochen-Specker No Go Theorem, and Gleason's Theorem on the representability of states in terms of density matrices in Hilbert spaces of dimension greater than 2. A lot of the best things we know about QM are based on these results, which are intricate in the extreme.
Suppose the proofs of whatever for instance Bub has done could be much simplified. Would you be happier? Or must it be an entirely non-mathematical explanation?
My own view is one of extreme operationalism adopted from Finkelstein. There are no objects in the actual world, only possible experiments. Therefore no "objective" observers. No observers, actually, only primitives called "experiments". Quantum theory is a language for describing possible experiments.
Post a Comment