Spooky Action at a Distance (Bell's Inequality) - Sixty Symbols

Bell's

inequality

is a slightly obscure piece of quantum mechanics, but it turns out that it is actually very important to our understanding of the way the universe works, which is why the original paper was written in 1964 by John Bell and referred to Einstein Podolski's roses and paradox as the important theme. here is that John Bell essentially took on Einstein and surpassed him, a little background on John Bell, he was from Northern Ireland, he died in the early 1990s I think, but he was quite young, only a little over 60 years old at the time, but he did quite a bit of fundamental work on quantum mechanics, but this is what he's most famous for, so here's his paper, it's a bit intense.

I think that's the way to describe it in the sense that there are a lot of integral signs. and stuff in there and it's one of those bits of physics where I had a hard time understanding it, but I came across another wonderful article by a guy named David Merman called Bringing Home the Atomic Mysteries of the Quantum World for Anyone Who Actually Puts the Inequality of Bell and Bell's Theorem, which somehow underlies Belle's work in a much more understandable framework and gives us an example that we can look at without horrible amounts of mathematics. David Merman, another famous physicist, famous to most college physicists because he wrote a book with a guy named Ashcroft.

His name is Ashcroft and Merman, who a lot of people learned solid state physics from, so he's kind of a hated figure among college students, but he's a brilliant guy and he comes up with really clever ways to explain things, so that's That's what we're going to do. We use the moments experiment. We'll have to go back a little further and talk about quantum mechanics and how things are measured in quantum mechanics. There was a famous experiment from the 1920s by Stern and Gerlach where they did an experiment. to look at the properties of particles when you pass them through magnets, this is their apparatus where you essentially have a bunch of particles and you pass them between these pairs of magnets and this is kind of the endgame in view of what those magnets look like. so it's a very non-uniform magnetic field that you pass them through.

They were interested in the angular momentum of these particles as they pass by and the reason a magnet allows you to do that is if you have a particle that has, for example, a spin associated with it, but I think it's spinning, so if it's a charged particle, you basically have a little bit of current because you have a charge that's moving and every time you have a little loop of current, you essentially create a little magnet and then we can think of these particles as little magnets and When you put a magnet in a non-uniform magnetic field, the net effect is that it exerts a force on it and depending on which direction that magnet is facing, it will make it move. different directions, so they did this experiment with these passing particles and what they found is that when you pass them through what is now called a Stern girl type apparatus, the particles split up and it has to do with the direction that they go. point the spin and you You can think of them as little magnets and it just depends on which direction they move up the magnet, which direction they move when sorting them, it sorts them in a very discreet way and that's where the quantum mechanics because somehow Think well, if you have this thing that's going to attack things, you know that if it's the North Poles up, it's going to move them that way and there's no falling down, it's going to move them that way, you'd think that if there's something that's in the middle, it won't move them that far, that's not what happens in quantum mechanics, essentially it's either up or down, it's never somewhere in between if you measure it as up or down.

It's just going to be up or down and what they found was this unexpected result at the time of quantum mechanics, so instead of finding things scattered all over the place, they split into these two discrete groups of up or down. And that's a fundamental thing about quantum mechanical measurement: you tend to get discrete results rather than anything in between and this is kind of an early example of what are the particles passing through that magnet, so in the experiment Stone girl original. they actually use silver atoms, but there's a lot of things, so the property they're capturing is the spin of a particle and you could actually do that with electrons, for example, electrons have a spin, the reason why it does not work. very well in the classic stone girl type of experiment is because the charge of the electron also interacts with the magnets, which complicates the measurement, but basically there are a lot of things that will have this, so you can do it with hydrogen atoms . for example, as I say, the original experiment was with silver, but for most of the rest of what we can talk about, we'll just think about electrons because it makes life easier to think about them because they're kind of isolated particles. and we don't have to think about whole atoms or anything like that.

Well, we're going to use this type of device quite a bit and to avoid having to take it out every time during the rest of what I'm going to talk about, we're just going to draw it as an up or down arrow with a question mark next to it, so that's the first part we need to introduce, then we need to introduce another part of quantum mechanics, which is something called the entangled state. Okay, so, for example, let's think about electrons again because it's easier to think about electrons. You can create electrons in this called entangled state.

Remember the spins, either up or down, and you can create a kind of pair of electrons that are coupled. each other so if one of them is up the other one is down or if that one is down that one is up and usually you create them together but then you can separate them but they will still be in this intertwined state so if we go to an experiment, we're creating this entangled state, then we separate the electrons from each other and then we pass them through one of these sets of devices that measure the spin up or down, it will always come out up or down. never swims in the middle so you make the measurement one of them comes out upwards the other one comes out there or you make the measurement one of them comes out downwards the other one comes out upwards and that's the only possibility that always happens with these things, so One of the things you could do is, instead of measuring up or down, you could basically take your experimental apparatus and turn it on its side and then instead of asking if it's up or down, what you're asking is if The turn is to the left or to the right.

So you got it right, your entangled pair will leave one of our Stone girl experiments the same, but we'll put one of them on its side and suppose, for example, we measure this particle and it's on top and then the question is whether it stays. or, well, what you really want it to be is down, because it's measured, this one is up and this one is down, but we're not asking that question, we're not asking up or down, we're asking left or right. right and the answer. It doesn't matter, so if you do this experiment, you will see that if this one is up, it will be some kind of 50 50, either to the left or to the right, and similarly, if this one is down, it will be some kind of 50 50, whether it is facing left or right. is it left or right, okay, we've taken our operators, we've turned it on its side now we're going to turn it over just to take it to its natural conclusion, so now again we ask if we're actually doing the same measurement that they were before, but it's just that one of our sets of operators is now upside down, so it's pretty sure that if this one is up, this one will be down, but because we turned the thing upside down, it's like upside down, okay, in terms of colors that I put on these things just when this one is red this one is also red just because it is measuring the opposite but with the device upside down or it could be that this one will be down, in which case this one will be up again all of these things are possible but They always come in these pairs now okay so we took the thing we turned it on its side we turned it upside down now I want to turn it around a little so it's not completely upside down anymore here's the story when we're not in any particular sense and in particular, I'm going to turn it 120 degrees, which is a third of the way, so now if this measures one electron up, then it really wants to measure it down here, but again we're not asking if it's up or down. below, we're asking something slightly in between, but you can see one of these arrows pointing down, so what happens is that down is more likely than up and in particular for this 120 degree angle, it turns out that 75 of the Sometimes if this one is up, this one will point down, so it will be the red arrow again. 25 of the time, if this one is red, this one will point down. be green, okay, so it's somewhere in between and if you want the mass for the cap regulation of quantum mechanics pretty simple, it turns out that if that angle is Theta, then the probability of this 25 is the cosine of theta divided by 2 squared. it's always that formula, okay, so to summarize, if this one is active, 25 of the time it will be active, in other words, because we rotate the operators, it will be the other color and 75 of the time it will be something like this. down so that it's the same color because we rotate the operators around one of these.

I promise that at the moment all we've done is spin this thing, but of course, we can also play with this thing, so last thing. What I want to show you is that if this guy is about 120 degrees, if we turn it 120 degrees, we're basically doing the same experiment that we were doing before because we're just measuring the fixtures now they're measuring the same direction, so it's nice. It is exactly the same as the first example, but only with the head turned to the side, so if it points to the right, it will always point to the left and vice versa.

It was a quick counterattack through quantum entanglement. and the ways in which spin can be measured from the particles that come out of it. Now we come to David Merman's brilliant experiment and, in particular, here is the machine David Merman came up with. This is kind of a thought experiment, but you know it's actually an experiment that you could actually do in practice, and this is the machine that they came up with, it's a box, it has a switch with three positions on the side and it has two lights on the back, red and green and if you move the switch to different positions, all you have to do is take one of these stone gerlock devices and turn it 120 degrees or 240 degrees, so it's like a third of the way or two-thirds of the way and then if you do a quantum measurement of the spin of a particle, remember that it will always come out red or green and if it comes out red, the red light turns on and if it comes out green, the green light turns off, so that's the device.

What he came up with and the experiment he wanted to do with his device is that he wanted two of these configured so that they would create two particles in a quantum entangled state, send one of them towards this detector, the other towards this detector and then all of them. . What happens is that depending on where the switch is, you've just placed your Stern device in different orientations, so you're going to get different results, and in particular, if the two switches are in the same position, that means that at both Stone girls like it. The fixtures are oriented the same way, either that way or that way or that way, but they are always oriented the same way, which means that if one light is red, the other will be green 100 of the time. times because that's what we just did.

Showing before if they are in different configurations, that means that they are 120 degrees apart from each other in one orientation or another and whatever combination has the difference is that they are always 120 degrees apart from each other and that means that the lights will be different 25 of the times they will be the same 75 this brings us back to the paradox of Einstein Podolski and Rosen because what happens is that somehow the particles come out in this direction in this direction and the answer that you get is random, right, if we start with them with the switches in the same position that means if one is red the other will always be green okay you can't know until you do the measurement which ones are red you will know if they are it's going to be red this end with this end or vice versa, suppose we set this operator so that one of these devices is a little bit further away, so that, in fact, the particle reaches this one a little bit before reaching this one, which means that if this one is red, then this one will always be green, in other words if this particle spin is up this particle spin will always be down, somehow the particle knows what orientation it should be in instantly and you can set things up. so the reason why any information passes from here to here between one measurement and the other measurement and so on in some wayBell, which is displayed as soon as you perform the measurement you have written. of things fundamentally changed in a way that you wouldn't have if it were something deterministic, so it's kind of fundamental to a lot of things that are happening now, so I guess what I'm saying is that if there are a lot of particles in the Milky Way that are entangled with a bunch of particles somewhere else in the universe and something happens to those particles.

I don't know what something means that particles here in the Milky Way would react and could have an implication for us here in our environments, so this is a whole other area of ​​quantum mechanics in terms of where you go from quantum mechanics to kind of a classical universe and this is the idea of ​​decoherence in terms of how long it can be maintained. things in these entangled states when you move them apart from each other and do other things to them and if these entangled states are quite delicate, it's quite easy to break them, so we're probably not affecting what's happening in the Andromeda galaxy right now because someone is doing it.

An experiment by Stern Gerlach somewhere in the UK, if some alien species came up with a way to destroy matter and they erased their matter, the entangled matter on this side of the universe could also be erased. I hope I'm not sorry, I didn't mean put that back here and then you would have all these problems that you know sometimes your Earth would be here and the satellite would be here and they wouldn't be able to communicate with each other, so what do you want to do? in some ways it's finding an orbit that puts your satellite a decent

distance

from the Earth, but also maintaining a station with the Earth while the two orbit the Sun, so a geostationary satellite is where you have something that stays above the same point. the earth