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Let me introduce this idea of Schrödinger's cat.

It always impresses me that Schrödinger, who was one of the inventors of quantum mechanics,

which has been an extremely successful theory,

early on he had the courage to come forth with expressing his discomfort with the theory.

The way he expressed that was this following example.

Suppose you had a system where there's a cat inside of a box,

and it's important that it doesn't interact with the outside world.

The example was suppose you also have a radioactive particle inside the box,

and if the particle decays it triggers some mechanism that releases poison and kills the cat.

In principle, although it would be impractical,

we can write down the quantum mechanical equations that describe the situation.

Basically, all quantum mechanics tells us is that after a time equal to the half-life,

the particle decays with 50% probability,

all quantum mechanics tells us that we have a so-called superposition state,

which is represented by these symbols, if you're not familiar with it.

But what it's telling us is that after this half-life of the particle,

quantum theory just says that the so-called wave function that describes the situation

is that the cat is neither alive nor dead, it's both alive and dead simultaneously.

I think this of course bothered Schrödinger and other founding fathers,

and they struggled this throughout their careers that maybe there's something missing in quantum mechanics.

So anyway, to give you an idea, maybe a little better example of I like,

which doesn't have much to do with physics, but it gives I think the flavor of this idea of superposition.

If we look at this box figure up here, it's drawn in such a way that there's some ambiguity

about whether this face here is in the foreground or this face here.

So you tend to see a situation like this where one of those two faces is in the foreground.

But in this situation up here, I think it conveys this idea of superposition,

because in some sense it's neither this nor this, it's both at the same time.

And I think this is very much like this idea of superposition that the quantum theory tells us about.

And the other, actually the other nice interesting thing about this example here is I think when you tend to see it in one orientation or the other,

that's very much like quantum measurement in, or measurement in quantum mechanics,

that when we measure a system, in this case looking at it a certain way,

it tends to be collapsed or be projected into one orientation or the other.

So, and this idea of entanglement, I won't talk too much about entanglement,

but this idea of entanglement expresses the idea that, for example, in Schrödinger's example here,

this superposition where the cat is both dead and alive, there's this correlation with the fact that

the situation is this superposition of the particle in decayed and the cat alive and the particle decayed and the cat dead.

And so this correlation is what was termed entanglement, that is, that the state of the cat was entangled or correlated with the state of the particle.

So let me go on, so I think that Schrödinger and others were bothered by what quantum mechanics was telling us,

this idea that all we can really say before we do a measurement is that the system is in superposition state.

So he struggled for this a long time, and in the early 50s he came up with a way out of this dilemma,

and he said, well, we've been thinking, we've been extrapolating these simple pictures,

we know how to write down the equations for small numbers of particles, and we discover this superposition,

but maybe we're fooling ourselves trying to extrapolate to the macroscopic world.

And so basically his one way out of that was, he said, well, maybe we're leading ourselves astray,

because even though we can think about these experiments, these so-called thought experiments,

we never really experiment with these small numbers of atoms or molecules,

and if we do, then this invariably leads to ridiculous consequences, this cat, this macroscopic superposition.

Well, that doesn't really work anymore, because now, of course, we can at least play these superposition games

with these small number of particles, and so we're forced to, in some ways,