I give you a magic piece of paper with a two binary digits (00/01/10/11) on it. I also keep such a paper for myself. If we both start by looking at our first digits then those will mysteriosly match, but if we then look at our second digits they will have just a 50% chance of matching. However, if we both start by looking at the last digits, then those will match, and our first digits will have a 50% chance of matching. If you and I start by looking at different digits, then the digits we read are just standard random bits.
The cool thing about this is that our magic paper will also work instantly even if we are lightyears apart. However, if you decide to look at the last digit and you see a 1, then that tells you nothing about me or which digits (if any) I have looked at, so I can't send you a message with this paper.
To belabour the colours and boxes analogy:
We have 2 balls, if one is orange the other is always purple and vice versa.
Now these balls have an extra property. If you shake them vigorously they may or may not change colour randomly.
So, we put them in boxes without looking and take them far away from each other. Now, some time after they are far apart and before you look in the box, you shake one of the boxes. You then look.
In QM, if the ball you observe is orange(purple) then you know the other is purple(orange). But the other ball can't have known ahead of time that a) you were going to shake your one and b) that it changed colour (or didn't). That's why it's spooky.
It could be that the shaking didn't have an effect. But equally, it could have had an effect. The spooky bit is that the other ball 'knows' whether it did or not in a non-local way.
Unfortunately, I have neither the experience nor ability to progress that thought much further so, if someone wants to go off and get a Nobel from it, feel free...
Sounds interesting. I wouldn't be surprised if it turns out that these two particles are really just a single particle in a different dimension that we don't know it exists yet.
“Separate entities” may just be an artifact of intelligences trying to divide sense data about the universe into chunks they are capable of processing.
If two random photons used in an experiment weren't ever really separate entities to being with, even before the experiment ever started, then one should probably conclude that /all/ photons are not really separate entities.
Otherwise, every quantum experiment we've ever done has just /happened/ to pick two photons that were actually one entity, unlike most other photons.
The description as is means that the situation is identical if there's "spooky action at a distance" or if there's none and you just don't know what's in each box until you open one (and therefore can guarantee what's in the other). There are predictions from this however that when tested just don't work. There is something else going on. I would go further but I'm sure my explanations would contain huge inaccuracies that probably would cause more problems with understanding what's happening so will link you to a couple of things:
https://en.wikipedia.org/wiki/Bell%27s_theorem
http://www.askamathematician.com/2010/06/q-how-it-is-that-be...
I'm sure there are others here who are well versed in this who can chip in.
The same way, the issue with Shroedigger's cat is not that "the cat is in a single state, but we just don't know whether that's dead or alive unless we open the box" (as many laymen try to explain it).
That's just "I don't know yet" and has nothing to do with the issue Shroedigger tried to highlight or quantum mechanics (not to mention that this we encounter everyday and we can replicate perfectly with say, a box and a person that throws a dice and based on that releases or not a gas in the box with a cat -- that's not what the paradox is about).
For entanglement, see this:
https://www.sciencealert.com/watch-this-is-how-quantum-entan...