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.