[gpsx]

I think people get confused when they think that each object has a wave function. This is not correct. The universe has one wave function. The wave function consists of a bunch of possible states along with the coefficient for each state. You can think of each state as being a distinct snapshot of what the universe might look like - including for example the position and spin of each particle. In the example of two electrons shown here, the wave function has non-zero coefficients only for states where the two electron spins are in opposite directions.

When we make a measurement, the state of the universe appears to collapse, meaning any state that is not consistent with that measurement disappears. This means the other electron is left in the opposite spin state. (Important aside here, some people believe the wave function collapses, "Copenhagen interpretation" and some people believe the wave function doesn't change but the the brain of the observer correlates/entangles with the electron, "Many Worlds Interpretation". Either way there is an operational collapse of the wave function.)

A special case for a wave function is when the coefficients are arranged so that state of one particle, say particle 1 spin, is symmetric no matter what the state of another particle, particle 2, is. This special case is when particles are NOT entangled.

(Edit: added paragraph on measurement)

[drpre]

I think what I get hung up on with explanations like this is, what changes once the wave function has collapsed? Are there observable characteristics before wave function collapse that become different after the wave function collapses?

Maybe this question just reduces to “how can we tell the difference between two entangled particles having always been in some state (but we didn’t know it) vs. being simultaneously in both states until we make a measurement?”

Based on other comments in this post, it seems like the answer may be: Bell’s theorem proves that classical explanations have an upper bound on correlations between the particles, but quantum mechanics predicts a correlation the violates the classical upper bound. And we can experimentally test the correlations in practice.

This is all very hard to wrap my head around.

[gpsx]

I want to add to my above comment. Non-entanglement is a special mathematical case, but it happens quite often. If the two particles never interact in any way, then the special condition will be true and they will not be entangled. There is another case where the particles _appear_ not to be entangled. This is when the wave function is so jumbled that even though the particles are entangled you can't detect it. This is called a decoherence. This also happens quite often and is why macroscopic quantities don't exhibit entanglement and hence quantum behavior.