Now we can, we can go back and try to understand this, this strange behavior of
photons and electrons a little bit more closely. By trying to understand this
proposition which says electron. Either. Went through. Slit one or it went through
slit two. So to try to test this proposition, what we can do, is we can run
this experiment again with electrons. But now we are trying to detect which slit it
went through. So what we can do is, put a little source of light, here. You know,
across slit one, or across each of the slits. So that, when the electron is going
through the slit, you know, the light actually bounces off of it, and, and we
get to see that the electron went by. So now, what we'd imagine is, not only are we
going to get the interference pattern. But we're also going to actually detect what
actually happened. But, the, you know, this proposition that the electron went
through either slit one or through slit two. So when you actually do this
experiment, what you realize is that in fact, and that it didn't go through both
slits. And in fact what you realize is, you know, the result of this experiment
does show you that every time you see, the electron go pass through slit one. In fact
it doesn't go through slit two. Every time you measure, it is going through slip two,
it doesn't go through slit one. But on the other hand, when you do the experiment
this way. The count at this detector suddenly changes. You know longer see this
interference pattern. But instead, you see, you see this, this, this pattern we
saw with bullets. So this is a very strange thing. As long as you don't try to
see which slit the electron went through, then you get the interference pattern. But
if you try to see. If you try to see which slit it went through. To confirm this, you
know, to confirm this hypothesis that the electrons either went through slit one or
slit two. Well then you, you, you, you do actually detect that it went through
either one or the other but now the interference pattern disappears. Of course
you can turn dow n the intensity of light here by these two slits to make sure that
you, you try not to disturb the electron as it's going through. And as you turn
down the intensity. What you end up getting. Is, some combination of this
interference pattern and the straight addition. And, in fact, the extent of this
combination you get is exactly proportional to how, what fraction of the,
of the electrons you [inaudible], you, you, you are able to detect at the slit
point of slit two. So nature perfectly hides her tracks. So if you try to measure
which slit the electron went, went through, then the interference pattern
disappears. If you try to detect only a little bit. Then the interference pattern
disappears a little bit. Exactly when you actually do the detection. Okay, so. So
let's summarize what we've learned about quantum mechanics. First thing we've
learned is in quantum mechanics measurement outcomes are probabilistic. So
where the, electron or photon ends up, to detect it you'll have to do a measurement
and the measurement is inherently a probabilistic process. Second thing you
can not measure without disturbing the system. Whenever you make a measurement
you can, you can make the measurement as subtle as you want but you'd still disturb
the system. The third thing we learned is that elementary particles behave in a very
strange way. They behave like no classical entities that we've seen. They behave
neither like particles, nor like waves. But they behave in a completely strange
way. Some of the characteristics seem as though they are like characteristics of
particles They behave like bullets. Other characteristics are those of waves. But
really the, they behave like some funny combination of the two, which is like
neither of the two at all. The fourth thing is that, when we do this experiment.
We can say that there's a moment when the electron leaves the source, the electron
[inaudible]. And then, from then on, we cannot really see what path the electron
took, or whether it took multiple parts at the same time to arri ve at the point x.
And so we really cannot say what the trajectory of this electron is. So what
quantum mechanics allows us to do is it's, you know, we start the experiment, it
happens quantumly and as soon as we look, as soon as we measure, that disturbs the
system, that gives us the outcome, the outcome of the experiment. So there is
this black box nature to a quantum experiment. When we start the experiment,
the source of electrons, and then something happens and then we do this, do
our measurement. And we see the outcome, that the electron ended up at the point x.
But in the middle here, we cannot really say what happened. And what the formalism
tells us is that, if you had a double slit here, then the electron has some
amplitude. A1, with which it goes through slit one and ends up at x, some amplitude.
A2, with which it goes through slit two, and ends up at x. And the amplitude with
which it ends up at x is a1 of x+ a2 of x. And the probability of detecting it there
is the square of this amplitude. Okay. So that's the strange behavior of [inaudible]
particles. And okay. So starting next time, we'll start from scratch, and talk
about quantum bits, and the basic axioms of quantum mechanics.