Yesterday 06:15 PM
I've hijacked this video a bit .. the whole thing is good but my particular interest is the EPR and 'proof' of non-locality
5:38 Bohr wasn't the one who wrote the mathematical rules of quantum mechanics. Instead, he told everyone what they meant. While others were confused by the theory Bohr offered answers, his philosophy became known as the Copenhagen interpretation of quantum mechanics. My general understanding of the Copenhagen interpretation is you have the wave function, it describes everything that you can know about a particle or a system, and it evolves according to the Schrödinger equation. And at some point you're gonna make a measurement and at that point the wave function collapses. - I think that one bit of that that you said was like the wave function is all you can know about the particle, and I think that was like a pretty important point to Bohr. As Bohr would put it. 'It's wrong to think that the task of physics is to find out how nature is.' The job of physics is just to predict measurements in the lab, which quantum mechanics does incredibly well as for what the electron is doing when you're not looking well to Bohr, that question didn't even make sense to ask.
6:36
The wave function tells you everything physics can or should tell you. Einstein couldn't stand the Copenhagen interpretation In a letter to his ally Schrodinger, he called it a tranquilizing philosophy or religion. Einstein felt his thought experiment exposed a critical weakness in the Copenhagen interpretation. He'd shown that the way the wave function collapses is non-local, and so he reasoned maybe the wave function is the problem. Maybe it's not the best way to describe the electron.
9:16
So in 1935, he [Einstein] made one last attempt to convince the community that there was a contradiction between quantum mechanics and relativity. With the help of two younger colleagues, Boris Podolsky and Nathan Rosen, he formulated another even more striking thought experiment that shows the non-locality of quantum mechanics. This paper is now known as the EPR paper after its authors. Here is a simplified version of their thought experiment. Imagine a single high energy photon suddenly becomes two particles. One of them is an electron and to conserve total charge. The other is a positron since one is negative and the other is positive, they cancel out. But both electrons and positrons have a property called spin and like electric charge, this also needs to be conserved. If the light started out with zero spin, well then the two particles together must have zero total spin as well. For example, if the direction of the electron spin is this, the positron has to have spin in the opposite direction so that they perfectly cancel out. But the electron spin could have been this instead or this. All of these possibilities are valid. So the rules of quantum mechanics say that the electron does all of these possible things at once until it's measured. It's not just that we don't know what the spin is, the electron really is doing everything. The only restriction is whatever the electron is doing. The positron must do the exact opposite. This also means that when the electron is measured and its state is determined, so is the positrons. This is what we mean by entanglement. The two particles states depend on each other. But how do we measure the particles and force them to do one thing? Well for that we use the Stern-Gerlach machine. It's essentially a strangely shaped magnet and it's how we measure spin. The orientation of the magnets determines what axis you're measuring the spin in. For example, if the machine is like this and we shoot in a particle with spin in the positive Z direction, it will certainly go to this spot we'll call plus. If instead a particle has negative Z spin, it will certainly go down to minus. So this Stern-Gerlach machine measures spin in the Z axis. So what happens when we put in one of our entangled particles? When the electron goes into this machine, it either goes to plus or to minus. With 50/50 probability, let's say our electron goes to plus. Well, this means it went from being in an indeterminate state to positive Z spin. But what about the positron? Well, the only way to conserve spin is if it's now in the negative Z spin state. When it's measured, there is a 100% chance it's minus. It has to be that way to conserve spin. But the authors of the paper realized there's something very odd about this result. - To see what's wrong with this let's imagine that the electron and the positron carry these envelopes with them. These envelopes represent the state of the two particles. Until they're measured, both of the particles are in a superposition of being plus and minus at the same time. So both options are in the envelope, but now let's move the positron to someone who's far far away. In this analogy, opening the envelope is like measuring the spin of the electron, but that causes the wave function of the electron to collapse to just one possibility. In this case, it's plus, but what happens to the other envelope far away? Well, it needs to instantly collapse to minus because otherwise when the experimenter opens their envelope, they have a chance of seeing plus, which would violate the conservation of spin.But if it needs to collapse instantly when the electron is measured, then how does it know what to collapse to? It must receive intel from the far away electron, but that message has to travel much faster than the speed of light to get to the positron in time.
If you're grabbed by the story so .. I'd pick up the vid at
https://youtu.be/NIk_0AW5hFU?t=760
The Youtube is 'There Is Something Faster Than Light' with Looking Glass Darkly as star and is at https://www.youtube.com/watch?v=NIk_0AW5hFU
5:38 Bohr wasn't the one who wrote the mathematical rules of quantum mechanics. Instead, he told everyone what they meant. While others were confused by the theory Bohr offered answers, his philosophy became known as the Copenhagen interpretation of quantum mechanics. My general understanding of the Copenhagen interpretation is you have the wave function, it describes everything that you can know about a particle or a system, and it evolves according to the Schrödinger equation. And at some point you're gonna make a measurement and at that point the wave function collapses. - I think that one bit of that that you said was like the wave function is all you can know about the particle, and I think that was like a pretty important point to Bohr. As Bohr would put it. 'It's wrong to think that the task of physics is to find out how nature is.' The job of physics is just to predict measurements in the lab, which quantum mechanics does incredibly well as for what the electron is doing when you're not looking well to Bohr, that question didn't even make sense to ask.
6:36
The wave function tells you everything physics can or should tell you. Einstein couldn't stand the Copenhagen interpretation In a letter to his ally Schrodinger, he called it a tranquilizing philosophy or religion. Einstein felt his thought experiment exposed a critical weakness in the Copenhagen interpretation. He'd shown that the way the wave function collapses is non-local, and so he reasoned maybe the wave function is the problem. Maybe it's not the best way to describe the electron.
9:16
So in 1935, he [Einstein] made one last attempt to convince the community that there was a contradiction between quantum mechanics and relativity. With the help of two younger colleagues, Boris Podolsky and Nathan Rosen, he formulated another even more striking thought experiment that shows the non-locality of quantum mechanics. This paper is now known as the EPR paper after its authors. Here is a simplified version of their thought experiment. Imagine a single high energy photon suddenly becomes two particles. One of them is an electron and to conserve total charge. The other is a positron since one is negative and the other is positive, they cancel out. But both electrons and positrons have a property called spin and like electric charge, this also needs to be conserved. If the light started out with zero spin, well then the two particles together must have zero total spin as well. For example, if the direction of the electron spin is this, the positron has to have spin in the opposite direction so that they perfectly cancel out. But the electron spin could have been this instead or this. All of these possibilities are valid. So the rules of quantum mechanics say that the electron does all of these possible things at once until it's measured. It's not just that we don't know what the spin is, the electron really is doing everything. The only restriction is whatever the electron is doing. The positron must do the exact opposite. This also means that when the electron is measured and its state is determined, so is the positrons. This is what we mean by entanglement. The two particles states depend on each other. But how do we measure the particles and force them to do one thing? Well for that we use the Stern-Gerlach machine. It's essentially a strangely shaped magnet and it's how we measure spin. The orientation of the magnets determines what axis you're measuring the spin in. For example, if the machine is like this and we shoot in a particle with spin in the positive Z direction, it will certainly go to this spot we'll call plus. If instead a particle has negative Z spin, it will certainly go down to minus. So this Stern-Gerlach machine measures spin in the Z axis. So what happens when we put in one of our entangled particles? When the electron goes into this machine, it either goes to plus or to minus. With 50/50 probability, let's say our electron goes to plus. Well, this means it went from being in an indeterminate state to positive Z spin. But what about the positron? Well, the only way to conserve spin is if it's now in the negative Z spin state. When it's measured, there is a 100% chance it's minus. It has to be that way to conserve spin. But the authors of the paper realized there's something very odd about this result. - To see what's wrong with this let's imagine that the electron and the positron carry these envelopes with them. These envelopes represent the state of the two particles. Until they're measured, both of the particles are in a superposition of being plus and minus at the same time. So both options are in the envelope, but now let's move the positron to someone who's far far away. In this analogy, opening the envelope is like measuring the spin of the electron, but that causes the wave function of the electron to collapse to just one possibility. In this case, it's plus, but what happens to the other envelope far away? Well, it needs to instantly collapse to minus because otherwise when the experimenter opens their envelope, they have a chance of seeing plus, which would violate the conservation of spin.But if it needs to collapse instantly when the electron is measured, then how does it know what to collapse to? It must receive intel from the far away electron, but that message has to travel much faster than the speed of light to get to the positron in time.
If you're grabbed by the story so .. I'd pick up the vid at
https://youtu.be/NIk_0AW5hFU?t=760
The Youtube is 'There Is Something Faster Than Light' with Looking Glass Darkly as star and is at https://www.youtube.com/watch?v=NIk_0AW5hFU
