A cat is kept in an impenetrable box, and no one can look inside. There is also a single radioactive atom. After exactly one half-life, there would be a 50% chance that the atom has decayed, and 50% chance that it hasn't decayed. But since we can't observe the atom, we must describe it in a quantum mechanical mixed state, 50% decayed and 50% not decayed. Within the box, there is a detector which determines whether it has decayed. If it has decayed, then the cat is killed. If not, then the cat is left alive.Before I get into explaining it in more detail, I'd like to ask, what's your favorite joke involving Schrodinger's cat? Mine is this Saturday Morning Breakfast Cereal comic.
However, since we have not opened the box, we must describe the cat in a quantum mechanical mixed state, 50% dead, and 50% alive. So the cat is dead and alive at the same time. When we open the box, the quantum state collapses, and we either find a completely dead cat or a completely alive cat.
Moving on!
Some people think that the takeaway message of the Schrodinger's Cat thought experiment is that it's completely absurd. "A cat which is dead and alive? Absurd!" But there's more to it than that. It's that the explanation seems unnecessarily absurd. Couldn't we just say that there's a 50% chance that the cat's dead and 50% chance that it's alive? Why do we need to add in this whole idea of being dead and alive simultaneously if no one ever sees the cat that way anyways? It's like we're saying that something really weird is going on, but only when we're not looking at it. It's as preposterous as painting my moustache green, only to hide it with a huge fan whenever anyone looks my way.
The thing is, the weirdness of quantum mechanics may seem unnecessary for the cat, but it is entirely necessary for smaller systems, such as single particles or photons. There's even a proof, known as Bell's Theorem, that at least some weirdness is absolutely required.
Consider single photon. If we build a detector to observe its polarity, we will always see it polarized vertically or horizontally.
Since we only see it one way or another, it would be quite absurd to say that it's simultaneously horizontal and vertical. We only see it one way or another, so why would we even consider that it could be both at once? But in fact, there is a quantum state which is a mix of horizontal plus vertical. There's also another quantum state which is horizontal minus vertical. And we can see both of these states if we just rotate our detector 45 degrees. Now we have the two diagonal polarizations.
If you try to measure either diagonal polarization without rotating the detector, then we will have a 50% chance of seeing horizontal and 50% chance of seeing vertical. But before we observed them, they were both vertical and horizontal simultaneously, so to speak.
But how is the cat anything like those photons? No matter how you look at the cat, it will always be either completely dead or completely alive. Rotating your head won't help. In principle, you can build a detector which can see the cat in a simultaneously dead and alive state. But in practice, such a detector is utterly impossible. You'd probably have to look at every single particle in the cat all at once. And you'd have to isolate the cat, making sure that no stray observers destroy the mixed state by looking at it.
Cat illustrations taken from Griffith's Introduction to Quantum Mechanics
But I could be wrong. As I said, the detector is utterly impossible to build. So if I can't build it, how would I prove that it's possible at least in principle? Perhaps there really is something fundamentally different happening to the cat which is not happening to the photons. It depends on which interpretation of quantum mechanics we take.
The most common interpretation is the Copenhagen interpretation. The Copenhagen interpretation says that at some point, the state of the system "collapses" into a definite state. So when we open the box and look at the cat, the cat "collapses" into a completely alive or a completely dead state. Or perhaps the collapsing happens earlier? Perhaps the cat observes its own survival/death, collapsing itself into a state that is either completely alive or completely dead. Or perhaps the collapse occurs even earlier than that? There is a detector inside the box which determines whether the radioactive atom decayed or not. Perhaps this detector collapsed the atom by observing it.
Might we go even further, and say that the atom collapses itself? Perhaps. But an atom is a relatively small set of protons, neutrons, and electrons. Perhaps we will eventually build a detector which can measure the atom in a simultaneously decayed and not decayed state. So we probably don't want to go as far as the atom.
We can go in the opposite direction too. Perhaps the quantum collapse happens even later than when you open the box. Perhaps you, too, are in a mixed state, simultaneously happy that the cat lived, and sad that the cat died. "Ridiculous," you say. "When I look at the cat, I am 100% sure that it is either dead or alive." That doesn't prove anything at all. You could be in a mixed state, simultaneously being absolutely sure the cat is alive, and absolutely sure that the cat is dead. Maybe you exist in this mixed state until you tell a friend about it, allowing your friend to "collapse" you.
Or maybe you never collapse at all, and nothing ever collapses. Perhaps the entire universe is in a mixed state of having simultaneously N living cats and N+1 living cats. This interpretation is known as the Many Worlds interpretation, because it implies that the world is simultaneously in many different states. It's like we're all together in this huge box which will never be opened. (FYI, this is the interpretation I advocate, so I might be biased in my presentation.)
So that's the basic idea of Schrodinger's Cat. I hope this raised all sorts of new questions... you can always ask.
Some people think that the takeaway message of the Schrodinger's Cat thought experiment is that it's completely absurd. "A cat which is dead and alive? Absurd!" But there's more to it than that. It's that the explanation seems unnecessarily absurd. Couldn't we just say that there's a 50% chance that the cat's dead and 50% chance that it's alive? Why do we need to add in this whole idea of being dead and alive simultaneously if no one ever sees the cat that way anyways? It's like we're saying that something really weird is going on, but only when we're not looking at it. It's as preposterous as painting my moustache green, only to hide it with a huge fan whenever anyone looks my way.
The thing is, the weirdness of quantum mechanics may seem unnecessary for the cat, but it is entirely necessary for smaller systems, such as single particles or photons. There's even a proof, known as Bell's Theorem, that at least some weirdness is absolutely required.
Consider single photon. If we build a detector to observe its polarity, we will always see it polarized vertically or horizontally.
Since we only see it one way or another, it would be quite absurd to say that it's simultaneously horizontal and vertical. We only see it one way or another, so why would we even consider that it could be both at once? But in fact, there is a quantum state which is a mix of horizontal plus vertical. There's also another quantum state which is horizontal minus vertical. And we can see both of these states if we just rotate our detector 45 degrees. Now we have the two diagonal polarizations.
If you try to measure either diagonal polarization without rotating the detector, then we will have a 50% chance of seeing horizontal and 50% chance of seeing vertical. But before we observed them, they were both vertical and horizontal simultaneously, so to speak.But how is the cat anything like those photons? No matter how you look at the cat, it will always be either completely dead or completely alive. Rotating your head won't help. In principle, you can build a detector which can see the cat in a simultaneously dead and alive state. But in practice, such a detector is utterly impossible. You'd probably have to look at every single particle in the cat all at once. And you'd have to isolate the cat, making sure that no stray observers destroy the mixed state by looking at it.
Cat illustrations taken from Griffith's Introduction to Quantum MechanicsThe most common interpretation is the Copenhagen interpretation. The Copenhagen interpretation says that at some point, the state of the system "collapses" into a definite state. So when we open the box and look at the cat, the cat "collapses" into a completely alive or a completely dead state. Or perhaps the collapsing happens earlier? Perhaps the cat observes its own survival/death, collapsing itself into a state that is either completely alive or completely dead. Or perhaps the collapse occurs even earlier than that? There is a detector inside the box which determines whether the radioactive atom decayed or not. Perhaps this detector collapsed the atom by observing it.
Might we go even further, and say that the atom collapses itself? Perhaps. But an atom is a relatively small set of protons, neutrons, and electrons. Perhaps we will eventually build a detector which can measure the atom in a simultaneously decayed and not decayed state. So we probably don't want to go as far as the atom.
We can go in the opposite direction too. Perhaps the quantum collapse happens even later than when you open the box. Perhaps you, too, are in a mixed state, simultaneously happy that the cat lived, and sad that the cat died. "Ridiculous," you say. "When I look at the cat, I am 100% sure that it is either dead or alive." That doesn't prove anything at all. You could be in a mixed state, simultaneously being absolutely sure the cat is alive, and absolutely sure that the cat is dead. Maybe you exist in this mixed state until you tell a friend about it, allowing your friend to "collapse" you.
Or maybe you never collapse at all, and nothing ever collapses. Perhaps the entire universe is in a mixed state of having simultaneously N living cats and N+1 living cats. This interpretation is known as the Many Worlds interpretation, because it implies that the world is simultaneously in many different states. It's like we're all together in this huge box which will never be opened. (FYI, this is the interpretation I advocate, so I might be biased in my presentation.)
So that's the basic idea of Schrodinger's Cat. I hope this raised all sorts of new questions... you can always ask.
