Who is Schroedinger’s Cat?

The light was ebbing, and the observer could not distinguish the cat’s state…

Knorozov’s Cat

Schroedinger’s cat occupies a weird space in popular knowledge of science. It is familiar to many people, partly because the name has an aura of mystery, and partly because the internet is a machine for spreading cat-related things. Schroedinger’s Cat-themed webcomics, for example, are a popular and fertile field. And most people have probably heard of the thought experiment, and have an idea that it involves a cat in a black box that is both dead and alive until you check. But it’s not always clear to me that people get the significance. Because Schroedinger’s Cat is a startling thought experiment, and something you don’t know about until you check isn’t necessarily all that startling. After all, people have no difficulty accepting a coin in flight. That coin could land either heads or tails with equal probability, and you don’t know until it lands. There is nothing strange about that. Or how about a black box that contains either a cabbage or a set of car keys? Depending on how you feel about cats, cabbages and cars, that may have a similar emotional effect to the Schroedinger’s Cat experiment. Yet there’s nothing strange about the cabbage-car box at all.

Lenin’s Cat

Schroedinger’s Cat experiment as conceived by Schroedinger has a radioactive isotope and a hammer and a vial of poison, but let’s make it even simpler, if less realistic. There is a quantum particle, say an electron, with a spin that can be either negative or positive. The cat is deathly allergic to isolated positive spin particles, so if the spin is positive, the cat dies. Otherwise, the cat lives.  So in what way does this situation differ from the cabbage-car box? If we want to get at the quantum mechanical explanation, we have to talk about two quantum mechanical concepts: superposition, and the difference between a pure state and an ensemble state.

First, superposition. Quantum superposition is just the statement that a quantum particle can be in a combination of states. Imagine a guitar string that’s just been plucked. Is it vibrating at the fundamental frequency, or at an overtone? The answer, of course, is that it’s doing both. Because quantum particles have wave-like properties, it’s not a stretch to imagine that the same logic can apply to two different quantum states of the same system. Mathematically, it’s the statement that if you have two solutions to an equation, a linear combination of the solutions is also a solution. Thus the spin of our electron in the cat’s box can be a superposition of negative and positive.

Harper’s Cat

Now let’s talk about pure and ensemble states. I like to think of it like this: imagine that we have two coins. We will take one of these coins, flip it, and see whether it comes up heads. We would get a 50% chance of getting heads if we have two fair coins (pure state), or one coin that has both sides heads, and another that has both sides tails (ensemble state). Let’s go through what happens in both of these situations. In both cases, we pick one coin, but we don’t look at it before flipping it. If we had to guess our probability of getting heads at this point, we would guess 50%. In the case of two fair coins, that’s actually true. With maximally unfair coins, though, it’s that in 50% of the cases our chance for heads is in reality 0%, and in the other 50% of cases, it’s 100%. Another way to say it is that if after a flip where we got heads, we went back in time and performed that flip again, we would get heads 100% of the time in the unfair (ensemble) case, but only 50% of the time in the fair (pure) case.

The cabbage-car box behaves like a box picked out of an ensemble state. If you took the box, got a cabbage, went back in time and opened the same box again, it would always contain a cabbage. The Schroedinger’s Cat box is a pure state. If you got a dead cat, went back in time to right before you opened the box, and tried again, you might get a live cat. OK, you may say, that’s not so strange – it’s like a coin that hasn’t been flipped yet. Except it’s not: this is where superposition becomes important again. The experiment with the cat and the electron – the analogue of flipping the coin – is already performed inside the box. Only both results exist in superposition. So it’s a coin that’s already been flipped, but is both heads and tails – until you look at it. This is shocking: we are used to things in the future being indeterminate, but things in the past and present either are or aren’t – even if we don’t know which it is.

Monroe’s Cat

One way to react to this result is to say that cats can’t exist in superposition. It’s very easy to imagine a string that’s vibrating both at a fundamental and an overtone. You can maybe accept that an electron can behave similarly and have both positive and negative spin simultaneously. We know that electrons behave like waves (you can perform the double slit experiment with them for instance). But it’s impossible to imagine a cat that’s both dead and alive, because that can’t happen in reality. So what the experiment shows is that there is some threshold after which thinking about superpositions doesn’t make sense. But then you have another mystery: where along the line between an electron and a cat is that threshold – and what’s so special about that point?

And in any case it doesn’t get rid of a fundamental problem. Suppose you built a tiny cat that can exist in a superposition of states. You then opened the box, and you saw the cat was alive. And then you decided to measure the spin of the electron. You would for sure measure that it was negative – because if it was positive, the cat would have been dead. This is what is called entanglement – the spin of the electron is entangled with the state of the cat, so that if we measure one, we also have information about the other. If you are discussing the quantum states of the box, then, there are two possible ones: negative spin electron with living cat, and positive spin electron with dead cat. So by looking at the cat and determining that it is alive, we have also “collapsed” the superposition of spins into one definite value – negative. But what’s so special about measuring? How is it that we are fixing the spin of an electron by looking at a cat?

The cat that walked by himself

The most straightforward answer possible – but not the most popular one – is that there is in fact nothing special about looking at stuff. Instead, what has happened is that we’ve become entangled with the cat and the electron. So there is still a superposition of two states: negative spin, living cat, person who thinks cat is alive is one state, and positive spin, dead cat, person who thinks cat is dead is the other. There hasn’t been any collapse – this is just what it feels like to be in one state of a superposition. This is a simple and elegant answer, except that it leads us to the conclusion that we are living in one branch of very very many universes which all exist at the same time. This is called the Everett Many World interpretation of quantum mechanics. The other possibility – that there is only one universe and when we see the cat is alive it’s not dead somewhere else – means that there is in fact something specific about measurement that causes collapse. This leads to what are termed collapse theories, of which the most famous and popular is the Copenhagen interpretation. There is a third possibility – that what we assumed about superpositions was incorrect. This mostly leads to hidden variable theories. Very quickly then, we have gotten ourselves mixed up in the interpretation of quantum mechanics. And that’s why the Schrodinger’s Cat thought experiment is so ubiquitous – it’s a fast way to get to some very fundamental questions about how reality works.

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One Response to Who is Schroedinger’s Cat?

  1. Pingback: The Unexpected and the Unexplainable | Rated Zed

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