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Now we can, we can go back and try to
understand this, this strange behavior of

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photons and electrons a little bit more
closely. By trying to understand this

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proposition which says electron. Either.
Went through. Slit one or it went through

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slit two. So to try to test this
proposition, what we can do, is we can run

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this experiment again with electrons. But
now we are trying to detect which slit it

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went through. So what we can do is, put a
little source of light, here. You know,

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across slit one, or across each of the
slits. So that, when the electron is going

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through the slit, you know, the light
actually bounces off of it, and, and we

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get to see that the electron went by. So
now, what we'd imagine is, not only are we

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going to get the interference pattern. But
we're also going to actually detect what

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actually happened. But, the, you know,
this proposition that the electron went

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through either slit one or through slit
two. So when you actually do this

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experiment, what you realize is that in
fact, and that it didn't go through both

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slits. And in fact what you realize is,
you know, the result of this experiment

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does show you that every time you see, the
electron go pass through slit one. In fact

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it doesn't go through slit two. Every time
you measure, it is going through slip two,

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it doesn't go through slit one. But on the
other hand, when you do the experiment

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this way. The count at this detector
suddenly changes. You know longer see this

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interference pattern. But instead, you
see, you see this, this, this pattern we

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saw with bullets. So this is a very
strange thing. As long as you don't try to

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see which slit the electron went through,
then you get the interference pattern. But

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if you try to see. If you try to see which
slit it went through. To confirm this, you

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know, to confirm this hypothesis that the
electrons either went through slit one or

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slit two. Well then you, you, you, you do
actually detect that it went through

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either one or the other but now the
interference pattern disappears. Of course

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you can turn dow n the intensity of light
here by these two slits to make sure that

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you, you try not to disturb the electron
as it's going through. And as you turn

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down the intensity. What you end up
getting. Is, some combination of this

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interference pattern and the straight
addition. And, in fact, the extent of this

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combination you get is exactly
proportional to how, what fraction of the,

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of the electrons you [inaudible], you,
you, you are able to detect at the slit

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point of slit two. So nature perfectly
hides her tracks. So if you try to measure

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which slit the electron went, went
through, then the interference pattern

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disappears. If you try to detect only a
little bit. Then the interference pattern

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disappears a little bit. Exactly when you
actually do the detection. Okay, so. So

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let's summarize what we've learned about
quantum mechanics. First thing we've

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learned is in quantum mechanics
measurement outcomes are probabilistic. So

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where the, electron or photon ends up, to
detect it you'll have to do a measurement

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and the measurement is inherently a
probabilistic process. Second thing you

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can not measure without disturbing the
system. Whenever you make a measurement

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you can, you can make the measurement as
subtle as you want but you'd still disturb

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the system. The third thing we learned is
that elementary particles behave in a very

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strange way. They behave like no classical
entities that we've seen. They behave

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neither like particles, nor like waves.
But they behave in a completely strange

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way. Some of the characteristics seem as
though they are like characteristics of

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particles They behave like bullets. Other
characteristics are those of waves. But

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really the, they behave like some funny
combination of the two, which is like

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neither of the two at all. The fourth
thing is that, when we do this experiment.

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We can say that there's a moment when the
electron leaves the source, the electron

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[inaudible]. And then, from then on, we
cannot really see what path the electron

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took, or whether it took multiple parts at
the same time to arri ve at the point x.

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And so we really cannot say what the
trajectory of this electron is. So what

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quantum mechanics allows us to do is it's,
you know, we start the experiment, it

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happens quantumly and as soon as we look,
as soon as we measure, that disturbs the

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system, that gives us the outcome, the
outcome of the experiment. So there is

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this black box nature to a quantum
experiment. When we start the experiment,

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the source of electrons, and then
something happens and then we do this, do

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our measurement. And we see the outcome,
that the electron ended up at the point x.

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But in the middle here, we cannot really
say what happened. And what the formalism

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tells us is that, if you had a double slit
here, then the electron has some

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amplitude. A1, with which it goes through
slit one and ends up at x, some amplitude.

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A2, with which it goes through slit two,
and ends up at x. And the amplitude with

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which it ends up at x is a1 of x+ a2 of x.
And the probability of detecting it there

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is the square of this amplitude. Okay. So
that's the strange behavior of [inaudible]

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particles. And okay. So starting next
time, we'll start from scratch, and talk

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about quantum bits, and the basic axioms
of quantum mechanics.