Allow me to give a more (but not perfectly) accurate analogy.

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.

It sounds like an interesting, if very expensive, way to get around primes for key exchange, in the world where prime factorization is much more efficient. Need a random number, look a bun of shared digits in a predefined order. You now have a shared random number that's perfectly secure, as long as you shipped out your shared state in advance.

With quantum entanglement, what happens to one particle prior to measurement affects the other even if the effect occurred after they were parted. That's where it gets really spooky.

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.

What is the equivalent to "shaking" in QM? I'm trying to figure out why it matters whether you shake the box or not (i.e. could the shaking simply not have an effect if you're not looking?)

The shaking represents any sort of action that doesn't perform a measurement. It was the first thing I thought of that could affect the ball without opening the box.

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.

But isn't it possible that performing "shaking" might not affect any "ball" when it's "inside of a box"?

Sounds like they never were two separate entities to begin with or never parted location. Which is spooky too, in a different way.

When I first started to be interested in this area, it occurred to me that it might be something like a 'stretchy' spacetime i.e. the particles are actually locally connected but appear unconnected if you use a static spacetime as a reference as we tend to. I guess something analogous to the idea that someone moving close to c experiences time different from someone in a slow moving reference frame.

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 like they never were two separate entities to begin with or never parted location. Which is spooky too, in a different way.

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.

> Sounds like they never were two separate entities to begin with

“Separate entities” may just be an artifact of intelligences trying to divide sense data about the universe into chunks they are capable of processing.

Experimentally, when they entangle photons, they just pick two random photons.

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.

Too build on this thought - is it possible that these quantum properties aren't affected by locality? Which is obviously true given the explanation above... I guess I'm asking if there are other intuitions that can be made if locality is explicitly considered unrelated.

If I understand right, this starts to touch on Bell's Theorem.

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.

That this example has very little to do with entanglement, which is not merely "knowing without direct proof". We do that everyday.

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...