late comment, I was on vacation for a week, and am still catching up on this deep QM thread.
Very nice explanation of Bell’s inequality. For the first time I’m fully grokking how hidden variables are disproved. (I have that “aha” that is not going away when I stop thinking about it for five seconds). My first attempt to figure out QM via Penrose, I managed to figure out what the wave function meant mathematically, but was still pretty confused about the implications for physical reality, probably in similar fashion to physicists of the 30s and 40s, pre Bell. I got bogged down and lost before getting to Bell’s, which I’d heard of, but had trouble believing. Your emphasis on configurations and the squared modulus business and especially focusing on the mathematical objects as “reality”, while our physical intuitions are “illusions” was important in getting me to see what’s going on.
Of course the mathematical objects aren’t reality anymore than the mathematical objects representing billiard balls and water waves are. But the key is that even the mathematical abstractions of QM are closer to the underlying reality than what we normally think of as “physical reality”, i.e. our brain’s representation thereof.
late comment, I was on vacation for a week, and am still catching up on this deep QM thread.
Very nice explanation of Bell’s inequality. For the first time I’m fully grokking how hidden variables are disproved. (I have that “aha” that is not going away when I stop thinking about it for five seconds). My first attempt to figure out QM via Penrose, I managed to figure out what the wave function meant mathematically, but was still pretty confused about the implications for physical reality, probably in similar fashion to physicists of the 30s and 40s, pre Bell. I got bogged down and lost before getting to Bell’s, which I’d heard of, but had trouble believing. Your emphasis on configurations and the squared modulus business and especially focusing on the mathematical objects as “reality”, while our physical intuitions are “illusions” was important in getting me to see what’s going on.
Of course the mathematical objects aren’t reality anymore than the mathematical objects representing billiard balls and water waves are. But the key is that even the mathematical abstractions of QM are closer to the underlying reality than what we normally think of as “physical reality”, i.e. our brain’s representation thereof.