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Now let's look at the situation when we
have a source of electrons or photons. So,

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let's say it's a source of electrons. It's
an electron gun and again we have, you

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know we have the same sort of set up with
the detector in the back here which we can

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think of as, you know the screen in the
back is fluorescent so that whenever an

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electron hits you get, you get little
burst of light. And now, we can ask what's

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the intensity of the electrons arriving
at, at point x? How much light do we see?

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How many do we detect? And the, the thing
that happens here is that, well, one thing

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that you noticed is as you turn down the
intensity of the source of electrons, you

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stop noticing that the electrons start
arriving at point x at discreet points in

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time. So, you see a flash and then nothing
for a while and then another flash,

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nothing for a while and so on. And as you turn
down the intensity, the flashes don't get

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any, any less intense. What changes is the
frequency with what you see with the

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flashes. So, again what we have to say is
that, you know that would seem to tell us

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that these electrons are really particles.
You know what they are, they are particles

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with, you know these charge particles and,
and you know as you turn down the

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electron, intensity of the electron
source. The fewer and fewer electrons

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going out per unit time and as they go out
and they are not through you know they're

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deflected through the edges of these
slits. They randomly show up at some

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point x. And the, the probability that you
see in electron here depends upon, you

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know, you turned down the intensity of the
source you see them less and less

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frequently but they arrive as discreet
objects as discreet lumps. And so, you can

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talk about ah, the probability of
detecting the, the electron at point x,

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you know, you can call it as intensity
i(x). And so, now, we would, you know,

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given that, given that they are like
discreet particles or bullets, what kind of

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behavior would be expect. And so, again,
if he, if he open only slit one,

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the intensity as a function of x looks
like this. If you open only slit two, the

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intensity of the function of x. The
probability that we see, see in electron

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looks like this. And, since, since
electrons are behaving like particles like

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bullets, you would imagine that if both
slits are open, you should see this curve

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which is i12 which is sum of i1 and i2.
But in fact, what you end up seeing is

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this interference pattern like we did in
the case of [inaudible]. I12 is not equal

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to i1. + i2. And that's the strange thing
about quantum mechanics. So how could it

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be if electrons are traveling, if they
are, if they are like particles, if they

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are discrete objects, discrete you know,
indestructible objects, how could it be

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that when both slits are open, you do not
get to see the sum of these two curves as

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the probability of, of the electron ending
up at x. You could say, well, let's reason

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about this a little more carefully and
say, well, clearly the electron was fired

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through the source. It went through the
source, it called deflected. And then it

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either went through slit one or through
slit two. And if it went through slit one,

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it ended up at x with probability equal to
i1(x). If it went through slit two it

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ended up at x with probability i2(x).
Surely, if both slits were open. It should

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end up with x with probability i1 + i2(x).
Because after all if it went through slit

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one, why should it matter to it whether
slit two was open or not. And now, the

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answer is we don't know but, but when you
do the experiment, you get to see the

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interference battle. Now, in quantum
mechanics, we have a way of explaining

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this. What we can do is we can say, well,
actually, there's an amplitude which,

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which the electrons gets up at one and
ends up at x. And that amplitude is a1(x).

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And actually the, the, the probability
that we detect the proton at point x. I(x)

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is actually the square of a1(x). And
similarly, there's an amplitude with which

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it goes through slit two and ends up at x.
And if only slit two is open, i2(x) is

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just the square of this amplitude. And
similarly, if both slits are open, then

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a1,2 is a1. + a2. So that the amplitude
with which the photon ends up at x is just

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a1(x) + a2(x). And of course the
probability that you've detect before turn

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down is a12(x) squared. This is just like
the [inaudible] case where we have the

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height of the water wave and the intensity
is the square of the height of the water

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wave except that there's no height here.
So what is this amplitude? Well, we don't

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know but this is how nature behaves. The
electrons behave as to there was some

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amplitude with which it ends up at x and
this amplitude can be positive or negative

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leading to this kind of interference
battle. That's the funny thing about

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quantum mechanics. That's how electrons
and protons behave. So, let's summarize

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what we've learned. So, we did this double
slit experiment three times in three

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different settings. First, we considered
it. It was a source of particles or

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bullets which we think of as bullets. Then
we repeated this experiment with waves,

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with water waves. And finally, we repeated
it with quantum objects like with

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elementary particles like photons,
electrons. So, of course, in the case of

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bullets, we have discreet objects that
come, you know, bullets come as discreet

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chunks ah, as UNS. In the case of waves,
the energy arrives not as discrete objects

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but it's, it's continuous. And as we saw
in the case of protons and electrons, they

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behave discreetly. They arrive in discreet
chunks which we think off as electrons or

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photons which are particles of light so
discreet. In the case of bullets, we

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talked about the probability of arrival
at x. In the case of waves, we measured

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the intensity or energy. In the case of
electrons or photons, well again we

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measure the probability of arrival. Which
we said is proportional to the intensity.

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In the case of bullets, when we have both
slits open, we saw no interference. In

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this case of waves, we saw interference.
In the case of protons and electrons, we

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again, have interference and this is the
funny thing. So, even though photons and

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electrons arrive as discreet entities and
we think they should have gone through

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either slit one or slit two, we do get the
interference pattern and this is part of

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the mystery. This is where we have this
strange behavior quantum mechanically. In

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the case of bullets, when both slits are
open, n12 is n1 + n2. In the case of waves

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i12 was not equal to i1 + i2 but what we had was
that each one to the height of the wave

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did add. And the intensity was the square
of the height. In the case of photons or

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electrons, again, we had, i12 is not equal
to i1 + i2. The probabilities did not add

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00:10:01,001 --> 00:10:09,005
but then we, we came up with this notion
of an amplitude which is just some

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00:10:09,005 --> 00:10:19,002
inverted notion and said, a1,2 is equal to
a1 + a2. And that the intensity or

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00:10:19,002 --> 00:10:26,003
probability is just the square of a, and
actually put the square inside absolute

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00:10:26,003 --> 00:10:32,005
values because in fact, the amplitude can
also be a complex number not just positive

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and negative.