Quantum physicist here. I can only say that reality down there at the quantum level is really really weird. You can get used to it, but forget making sense of it.
A delayed choice setup is not too dissimilar than a Bell inequality violation experiment. The weirdness there is that you can set things up such that no signal can travel between the systems being measured, and yet the outcomes are more correlated than any classical joint state can be.
So the conclusion is that either locality fails (i.e. it’s not true that outcomes on one side are independent of how you measure the other side) or realism fails (i.e. you can’t assign values to properties before the measurement, or in other words a measurement doesn’t merely “reveal” a pre-existing value: the values pop into existence in a coordinated fashion). Both of these options are crazy, and yet at least one of them must be true.
> either locality fails of realism fails
Or statistical independence fails, no? The CHSH derivation, for example, requires commuting expectation value with conjunction and similar for other Bell-like's that I'm aware of.
This always gets pooh-poohed away with with vague appeals to absurdism, "Alice and Bob's free will blah blah", but I don't really know of a priori reasons why the global state space needs to be Hilbert instead of a more complicated manifold with some Bell-induced metric. If you know of prior art here, I'd love some pointers.
That way lies superdeterminism, which has stood out to me as the most satisfactory explanation for years.
I’m not sure I understand. Expectation values are just scalars, why wouldn’t they commute? Can you explain what you mean?
I feel like one of the lucky 10,000 today! Thanks for asking.
Jump up an abstraction layer.
Multiplication and addition are each commutative, but performing multiplication followed by addition is not the same as addition followed by multiplication (in the real numbers), so they don't commute. Said another way, the operation of composing multiplication with addition isn't commutative.
Similarly, we can perform various operations on random variables, one being expectation value and another being multiplication (or conjunction): E(X•Y) ≠ E(x)•E(y) unless x and y are independent, so E and • don't commute.
When we say "commute" we often are directly or indirectly thinking of commutative diagrams, which capture a very general which of commutativity and allows us to precisely write down all the above.
Fun fact: associativity is also just commutativity of binary operator composition.
Yes I know addition and multiplication don't commute, but what does that have to do with the discussion above? Do you mean that repeated measurements on different systems might not be independent because they come from the same source?
> Do you mean that repeated measurements on different systems might not be independent because they come from the same source?
More that the measurement settings could be correlated somehow. So called "cosmic Bell tests" try to push back how far said correlations would have to be, though, by determining measurement settings from distant antipodal astronomical objects, e.g. see the famous Rauch paper [0].
On the surface it seems a bit absurd to consider conspiracies from 7 billion years ago, but that's the whole deal with conservation laws, which introduce correlations between otherwise free parameters and constrain the state space to some submanifold.
[0]:https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.12...
To me, it is not hard to make sense of quantum reality and it’s not weird at all, it actually makes sense. And it makes sense to me because we are living in it.
If you’ve ever looked into the theory of Orch-OR I’m sure you’d understand what I’m talking about. The minute you think of the quantum being different from the classical is where the problems begin.
Classical physics is the only process we have to understand quantum physics. Our brains are quantum computers that collapse wave functions so we can navigate the universe. And by collapsing the wave function I just mean we make a probability the best certainty we can.
Light as a wave is a probability. Light as a particle is a certainty.
It's the measurement problem, I think? Energy is moving as a wave, but the energy can only be transferred in quantum-sized values. At some point it "collapses" to a particular interaction with some other wave, and we can only probabilistically calculate where this may occur.
Edit: the Bell experiment is something else. It's like a wave can exist as an entity outside of time and space and only comes back to reality when it interacts. Perhaps it would make sense for electromagnetic waves if the distance and local time elapsed contracts to zero per relativity when travelling at the speed of light.
The measurement problem is a different kind of weirdness, that may or may not reduce to the same explanation after we have it.
The problem with the double slit (and Bell inequality) is that real things that we can see are correlated, not about mixed states and state erasure.
My impression about reality is the opposite. The quantum world makes perfect sense while it's the emergence of the classical world which is unfathomable. The crazy "pop into existence" part is still incomprehensible, so I guess it's essentially the same.