The difference is that spin is a quantum mechanical concept, and this result becomes surprising in light of other things we know about quantum mechanics. Specifically, in quantum mechanics, it’s not just that we don’t know a particle’s properties (like spin) before we measure them, it’s that the particle has both properties, it has both spin up and spin down, until we measure it. We know this from things like the double slit experiment, where a single particle goes through two different slits at the same time and then interferes with itself. So when we have these two particles whose spins sum to 0, and we move them far away, and two observers measure their spin at the same time (so that the observers are outside of each others light cones), how do the particles coordinate so that their spins still sum to 0? They both had both spins when they were together, they didn’t pick individual spins until the measurement occurred, and yet they still somehow coordinated to have opposite spins, despite being outside each others light cones. That means information must have moved between the particles faster than the speed of light. That violates one of the fundamental premises of special relativity. That is the surprise.
I feel like this is missing something. How do we know they have both spins before we measure them and that they haven’t “decided” their spin beforehand?
Because this is how all properties work in quantum mechanics. This was the point of my reference to the double slit experiment, which is the classic example of this idea (called “superposition”). In the double slit experiment, you shoot a particle at a barrier that has two openings in it, and watch where it goes. If you shoot a bunch of particles through at once, then they interact with each other and produce a particular pattern. If you shoot them through one at a time, and they randomly picked one of the two holes to go through, you would expect to see them cluster in two places. This is not what you actually see. What you actually see when you shoot them through one at a time is exactly the same pattern that you saw when you shot them through all at once. Therefor, individual particles actually go through both holes at once and interact with themselves, they are in two different states simultaneously until someone observes them, and forces them to be in one. This is how all quantum mechanical properties work, including spin.
The difference is that spin is a quantum mechanical concept, and this result becomes surprising in light of other things we know about quantum mechanics. Specifically, in quantum mechanics, it’s not just that we don’t know a particle’s properties (like spin) before we measure them, it’s that the particle has both properties, it has both spin up and spin down, until we measure it. We know this from things like the double slit experiment, where a single particle goes through two different slits at the same time and then interferes with itself. So when we have these two particles whose spins sum to 0, and we move them far away, and two observers measure their spin at the same time (so that the observers are outside of each others light cones), how do the particles coordinate so that their spins still sum to 0? They both had both spins when they were together, they didn’t pick individual spins until the measurement occurred, and yet they still somehow coordinated to have opposite spins, despite being outside each others light cones. That means information must have moved between the particles faster than the speed of light. That violates one of the fundamental premises of special relativity. That is the surprise.
I feel like this is missing something. How do we know they have both spins before we measure them and that they haven’t “decided” their spin beforehand?
Because this is how all properties work in quantum mechanics. This was the point of my reference to the double slit experiment, which is the classic example of this idea (called “superposition”). In the double slit experiment, you shoot a particle at a barrier that has two openings in it, and watch where it goes. If you shoot a bunch of particles through at once, then they interact with each other and produce a particular pattern. If you shoot them through one at a time, and they randomly picked one of the two holes to go through, you would expect to see them cluster in two places. This is not what you actually see. What you actually see when you shoot them through one at a time is exactly the same pattern that you saw when you shot them through all at once. Therefor, individual particles actually go through both holes at once and interact with themselves, they are in two different states simultaneously until someone observes them, and forces them to be in one. This is how all quantum mechanical properties work, including spin.