Isn't this distinction exactly what the article is about? By saying ahead of time, "one ball is red, the other is blue", you're describing a hidden-variables theory of entanglement. It may be unknowable (before measurement) which color the ball in your left hand is, but it has a color.

But Bell's theorem provides a very measureable counterexample to this type of explanation of entanglement. Sure, in the article they talk about electron spins instead of ball colors, but the analogy is that there isn't a well defined "color of the ball" before it's measured.

Of course, the analogy breaks down a bit: electron spin can be measured in multiple axes with somewhat complicated interactions.

> By saying ahead of time, "one ball is red, the other is blue", you're describing a hidden-variables theory of entanglement.

No, consider the case of neutral pion decay, which emits one spin up electron and one spin down electron. We can clearly say ahead of time one electron will be spin up, and the other will be spin down. But there is no hidden variable that determines which.

If there were a hidden variable, then knowledge of that hidden variable would let you predict which electron is spin up (which ball was red). In the macroscopic world, the hidden variable might be the state of my brain when it chose which hand to grab which ball. But if you replaced me with a robot, and that robot used the measurement of a quantum event (such as an electron's spin) to determine which ball to choose, then there is no hidden variable.

> No, consider the case of neutral pion decay, which emits one spin up electron and one spin down electron.

No, it does emit two electrons with total spin zero which is not the same thing.

> We can clearly say ahead of time one electron will be spin up, and the other will be spin down.

Let’s imagine that one was really up and the other was down. But you decide to measure instead the spins along a perpendicular axis. You would expect to find no correlation between them.

However, what you actually see is that if you measure both spins along any (common) axis they will point in opposite directions.

It doesn’t make any sense to say that before any measurement one was up and the other down. The red and blue balls analogy is very misleading and has nothing to do with entanglement.

> The red and blue balls analogy is very misleading and has nothing to do with entanglement.

this is exactly why classical analogies should not be used to describe quantum entanglement - it gives the layperson a wrong impression. Those analogies makes it easy for the layperson to imagine the hidden variable hypothesis, which is proven to be wrong.

This a good source for learning this stuff for real instead of pop-sci approximations:

https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-s...

OPs explanation is that entanglement is when there is a red ball and a blue ball and when you know which ball is red, you determine that the other ball must be blue.

My explanation is that entanglement is when there is no red ball or blue ball, there are simply two balls and the color of both balls is both red and blue simultaneously. It's not simply that one ball is red, the other is blue, but we don't know which one is which until we measure them. It's that fundamentally there is no red ball and blue ball, there are just two balls whose colors are in a superposition of red and blue.

I will try to come up with an observable difference but it's hard to do so with colors because the typical examples used for entanglement involve properties that can cancel one another out, so that two entangled particles exhibiting a superposition of two properties will, after many trials, end up forming some kind of destructive or constructive interference that would not be possible if those two particles were in a definite state.

Bell's experiment itself is readily understandable to most laypeople - and comparing the outcome to what you'd expect with e.g. hidden variables is really the easiest way to see why the red/blue explanation misses the point IMO.

Ah, but that’s the tough part - there IS a measurable difference in behavior of the universe between these two examples! (albeit hard to experimentally prove exists, but it has been!)

They really are in a superposition, not just ‘not known’ until one is measured.

Just like light was proven to (truly, actually) be both a light and a wave through the double slit experiments. It doesn’t feel right, but it is - and that is where the progress is made, and why the pushback on some examples. It hides the actual truth behind a misleading, but easy to understand example, that teaches people the opposite of what is really going on.

It could also be that we simply don’t understand something about light phase, and that’s causing us to get confused about superpositions. After all, the experiments aren’t on single photons, they are on beams of photons.

Not sure if we're confusing threads here - double slit experiments have been run on single photons and the results are pretty conclusive. Even a single photon is a wave that interferes with itself.

I would expect similar here. Intuition is terrible at understanding what is going on at the atomic and smaller level, or anywhere relativistic anything is happening.

Not confusing threads; the double slit experiment is often given as evidence of superposition. My attempts at replicating the experiment myself have been foiled because it inevitably goes to phase calculations on lasers, which I don't have any idea how to do. I keep looking for a way to do this famous and supposedly simple experiment, but haven't found a way yet. In any case, when I go deep on what is there (as a layman) it inevitably seems to result in phase measurements as the smoking gun proving superpositions exist at all.