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All physics
of the 19th century and earlier

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is called classical physics.

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Examples are
Newtonian mechanics,

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which we dealt
with this whole term,

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and electricity and magnetism,

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which you will encounter
the next term.

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In the early part
of this century,

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when we learned
about the composition of atoms,

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it became clear that
classical physics did not work

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on the very small scale
of the atoms.

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The size of an atom is only
ten to the minus ten meters.

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If you take 250 million of them
and you line them up,

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that's only one inch.

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In 1911, the English physicist
Rutherford demonstrated

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that almost all the mass
of an atom is concentrated

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in an extreme small volume
at the center of the atom.

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We call that the nucleus,
it's positively charged.

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And there are electrons
which are negatively charged,

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which are in orbits
around the nucleus,

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and the typical distances from
the nucleus to the electrons

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is about 100,000 times larger

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than the size
of the nucleus itself.

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As early as 1920,
Rutherford named the proton,

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and Chadwick discovered
the neutron in 1932,

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for which he received
the Nobel Prize.

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Now, let us imagine that
this lecture hall is an atom.

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And the size of an atom
is defined by the orbits,

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the outer orbits
of the electrons.

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If I scale it properly, now,
in this ratio 100,000 to 1,

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then the size
of the nucleus would be

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even smaller
than a grain of sand.

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And it just so happens

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that yesterday
I went to Plum Island,

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I walked for three hours
on the beach

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and I ended up
with some sand in my pockets.

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And so I will donate
to you one proton; 

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make sure you hold onto it...

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Ooh, this is two protons,
that's too generous.

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So keep it there--
this is one proton.

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And there would be
an electron, then,

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anywhere there, near the walls,
going around like mad in orbit

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and that would then be
a hydrogen atom.

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Just think about
what an atom is.

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An atom is all vacuum.

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You and I are all vacuum.

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You think of yourself as being
something, but we are nothing.

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You can ask yourself
the question,

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If you are all vacuum,

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why is it, then,
that I can move my hand

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not through the other hand, like
a ghost can walk through a wall?

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That's not so easy to answer,

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and in fact, you cannot answer
it with classical physics

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and I will not return
to that today.

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But you are all vacuum.

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According to Maxwell's
equations,

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Maxwell's law of electricity
and magnetism,

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an electron, because of the
attractive force of the proton,

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would spiral into the proton

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in a minute fraction
of a second,

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and so atoms could not exist.

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Now, we know that's not true.

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We know that atoms do exist.

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And so that created
a problem for physics

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and it was the Danish physicist
Niels Bohr

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who in 1913 postulated

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that electrons move around the
nucleus in well-defined orbits

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which are distinctly separated
from each other,

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and that the spiraling-in of
the electrons into the nucleus

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does not occur,

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for the reason
that an electron cannot exist

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in between these allowed orbits.

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It can jump
from one orbit to another,

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but it cannot exist in between.

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Now, Bohr's suggestion
was earth-shaking,

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because it would also imply

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that a planet
that goes around the sun

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cannot orbit the sun
just at any distance.

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You couldn't move it
just a trifle in

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or a trifle farther out.

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It would also require
discrete orbits.

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It would also mean that
if you had a tennis ball

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and you would bounce
the tennis ball up and down,

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that the tennis ball
could not reach

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just any level above the ground,

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but it would only be
discrete levels,

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and that is very much
against our intuition.

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We'd like to think that
when you bounce a tennis ball,

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that it can reach
any level that you want to.

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You give it
just a little bit more energy

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and it will go a little higher.

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That, according
to quantum mechanics,

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would not be possible.

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Now, all this seems
rather bizarre,

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as it goes
against our daily experiences,

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but before we dismiss
the idea of quantization--

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see, the quantization comes in

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when you talk
about discrete orbits--

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you have to realize
that the differences

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in the allowed heights
of the tennis ball

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and the differences

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between the allowed orbits
of the planets around the sun

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would be so
infinitesimally small

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that we may never be able
to measure it.

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In other words, quantum
mechanics really plays no role

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in our macroscopic world.

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Now, atoms are very, very small
compared to tennis balls,

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and the quantization effects
are much larger

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in the sub-microscopic world
of electrons and atoms

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than in our familiar world

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of baseballs,
pots and pans, and planets.

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So before we continue,
I would like to repeat to you

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one of the cornerstones
of quantum mechanics.

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And it says that the electrons
in atoms can only exist

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at well-defined energy levels--
think of them as being orbits--

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around the nucleus, and
they cannot exist in between.

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Now, when I heat a substance,
the electrons in the atoms

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can jump from inner orbits
to allowed outer orbits,

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and when they do so,

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they can leave a hole,
an opening,

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an empty space
in the inner orbits.

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But later on, they can fall back
to fill that opening.

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They can occupy
that place again.

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And when I keep heating
this substance,

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there is some kind of
a musical chair game going on.

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The electrons will go
to outer orbits,

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they may spend there some time

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and then they may fall to
lower orbits, to inner orbits.

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You see here a vase,
a very precious vase,

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and when I pick up this vase,
I have to do work.

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I bring it further away
from the center of the Earth.

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Now, is that energy lost? No.

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I could drop the vase, and it
would pick up kinetic energy.

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I will get that energy back.

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Gravitational
potential energy

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will be converted
to kinetic energy.

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It will crash to pieces,
and it will generate some heat.

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In fact, the breaking itself
of this vase

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would take some energy.

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In a similar way, the energy
that you put into electrons

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when you bring them
to outer orbits

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is retrieved
when the electrons fall back.

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So there is a parallel--

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dropping this vase and getting
your work back that I put in.

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It wouldn't be a nice thing
to do to this 500-year-old vase,

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but as far as I'm concerned,

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perfectly reasonable
to do it with Ohanian,

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so we can let that go,

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and the energy will come out
in the form of heat

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and also in the form
of, perhaps, some noise.

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When electrons fall

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from an outer orbit
back to an inner orbit,

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it's not kinetic energy
that is released,

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but it comes out often
in the form of light,

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electromagnetic radiation.

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Light has energy.

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Einstein formulated
that a light photon,

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the energy of a light photon,
is h times the frequency,

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and h is Planck's constant--
named after Max Planck--

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and h is about 6.6 times 10
to the minus 34 joule-seconds.

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Now we've also seen in 8.01

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that lambda,
the wavelength of light,

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equals the speed of light
divided by the frequency.

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And so if I eliminate the
frequency, I also can write

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that the energy
of a light photon

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equals hc divided by lambda.

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And so you see, the more energy
there is available,

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the smaller the wavelength.

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And the less energy
there is available,

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the longer the wavelength.

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And so if the jump

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from an outer orbit
to an inner orbit is very high,

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then the wavelength
will be shorter

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than when the jump
is relatively small.

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I can make you some kind of an
energy diagram of these jumps.

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And these are energy levels, so
energy goes in this direction,

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but if you want to,
you can think of these

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as the position of how far

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the electrons are away
from the nucleus,

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if you like that,
if it helps you,

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so this will be the electron

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that will be the closest
to the nucleus.

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So these would be allowed
energy levels, allowed orbits.

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And if this electron had jumped
all the way here,

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then it could fall back
at a later moment in time

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and the energy could be so much

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that you couldn't even see
the light.

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It could be ultraviolet,

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and this jump may
still be ultraviolet,

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but now this jump, which is
a little less energy,

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that may be in the blue part
of our spectrum.

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So we may see this
as blue light.

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And this one, which is
a little less than this,

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this energy may generate,

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this jump may generate
green light.

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And the jump from here to here,
which is even less,

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may generate red light.

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And a jump from here to here,
which iseven less,

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may again be invisible,
so this may be infrared.

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And so as the electrons fall

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from outer orbits
to inner orbits,

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you expect very discrete
energies to come out,

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very discrete wavelengths,

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and these wavelengths that you
would see correspond, then,

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to these allowed transitions
between these energy levels.

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So if we could look at that
light and sort it out by color,

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we would, in a way, see
these energy levels.

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Now, you have
in your little envelope

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a piece of plastic,
which we call a grating,

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and the grating has the ability

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to decompose the light
in colors,

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which we call a spectrum,

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and we're going to shortly use
that grating

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to look at light from helium
and light from neon.

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But before we do that,
I'd like to hand out--

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as a souvenir to a few people,
randomly picked--

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something
that they can also use.

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It's not as good
as your grating, though,

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but it's also nice.

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You will see a more spectacular
result, but not as clean.

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It's not as clean.

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All right, one for you,
one for you,

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one for you and one for you.

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And you want one-- I can tell
that-- and you want one.

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And here, for you, for you.

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Oh, no, this side hasn't
had anything.

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I've got to walk
all the way over now.

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So this is really for children's
parties, which I'm handing out.

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Oh, George Costa, you want one,
of course.

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Professor Costa wants one--
I couldn't bypass him.

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And you want one, okay,
and you want one.

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So, by all means,
use your grating,

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but then, at the very end,

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you can always use
these little spectacles,

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which don't work nearly as well,
but, uh... this kind of thing.

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I'm going to light here

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this bulb, this light,
which has helium in it,

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and what you're going to see
with your grating,

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if you hold
your grating properly--

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you may have to rotate
it 90 degrees;

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you will see how that works
when you try it--

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you're going to see
very, very sharp, narrow lines

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at various colors.

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I want you to realize
that the reason

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why you see
very sharp, narrow lines

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is only because my light source
are very sharp, narrow line.

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If you use it on something

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that is not
a very sharp, narrow line,

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then you're not going to see
through that grating

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very sharp, narrow lines.

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So don't confuse the lines
that are on the grating

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with the line source
that I have here.

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Now, when you look through
your grating very shortly,

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you will see, on both sides,
the wonderful lines.

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It's a mirror image,

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and we will discuss it
in a little bit more detail,

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but before you look
through your grating,

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I first want you to simply look
at it without the grating,

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because then it is
even more spectacular

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when you use the grating.

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Because you have no clue,
when you don't use the grating,

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what kind of colors
are hidden there.

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And the colors
that you are going to see

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are these electron levels.

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So I am going to make it dark.

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And I will turn this on.

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And this one, I believe,
is helium.

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I have a grating here.

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So we have to rotate it
so that you see vertical lines

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on either side.

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You may have to rotate it
90 degrees, no more.

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And if you look closely--

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for instance, look on
the right side of the light--

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you'll see a distinct blue line,
a few blue lines, green,

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very nice bright yellow one,
and you see red.

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And if you go further
to the right, you see a repeat.

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It's a little fainter,
but you see a repeat of that.

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That's not important right now; 

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I just want you to see that this
light, which you have no idea

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that it comes out
in very discrete wavelengths,

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very discrete frequencies,

288
00:14:38 --> 00:14:44
and they correspond to these
jumps from allowed energy levels

289
00:14:43 --> 00:14:49
to other allowed energy levels,
but there is nothing in between.

290
00:14:46 --> 00:14:52
And when you look on the left
side, you'll see a mirror image

291
00:14:50 --> 00:14:56
of what you see
on the right side.

292
00:14:51 --> 00:14:57
Now, neon... excuse me, helium
has only two electrons.

293
00:14:54 --> 00:15:00
I'm now going to put in the neon
bulb and that makes it richer,

294
00:15:01 --> 00:15:07
for reasons that neon
has ten electrons,

295
00:15:04 --> 00:15:10
so you have many more orbits,
so many more ways

296
00:15:08 --> 00:15:14
that the electrons can play
musical chair.

297
00:15:12 --> 00:15:18
 

298
00:15:16 --> 00:15:22
A lot of lines in the red--
I'm not blocking you, I hope--

299
00:15:19 --> 00:15:25
a lot of lines in the red,

300
00:15:21 --> 00:15:27
and some beautiful lines
in the yellow.

301
00:15:23 --> 00:15:29
I see some in the green,

302
00:15:24 --> 00:15:30
I don't see much in the blue...
a little bit in the blue.

303
00:15:28 --> 00:15:34
But the key thing is,
I want you to see

304
00:15:30 --> 00:15:36
that these lines are discrete.

305
00:15:32 --> 00:15:38
It is not just any wavelength
that can be generated;

306
00:15:36 --> 00:15:42
it's only the allowed orbits,
the musical game

307
00:15:42 --> 00:15:48
when the electrons jump
from one orbit to another,

308
00:15:48 --> 00:15:54
and that gives you
this unique discrete spectrum.

309
00:15:50 --> 00:15:56
 

310
00:15:59 --> 00:16:05
Now, these light spectra
were known

311
00:16:00 --> 00:16:06
long before Bohr came
with his daring ideas,

312
00:16:04 --> 00:16:10
but before quantum mechanics,

313
00:16:06 --> 00:16:12
these lines were
a great mystery,

314
00:16:08 --> 00:16:14
but they no longer are.

315
00:16:11 --> 00:16:17
I suggest you use this grating

316
00:16:14 --> 00:16:20
and use it
when you are outside at night; 

317
00:16:17 --> 00:16:23
look at some streetlights,

318
00:16:18 --> 00:16:24
particularly sodium lamps
and mercury lamps.

319
00:16:22 --> 00:16:28
And, of course, the neon lamps
are quite spectacular,

320
00:16:24 --> 00:16:30
but keep in mind, you will not
see very nice straight lines

321
00:16:28 --> 00:16:34
unless your light source itself

322
00:16:30 --> 00:16:36
is a very nice straight,
narrow light source.

323
00:16:34 --> 00:16:40
Now, quantum mechanics took
a big leap in the '20s,

324
00:16:40 --> 00:16:46
and it would be
impossible for me

325
00:16:42 --> 00:16:48
in the available amount of time

326
00:16:44 --> 00:16:50
to do justice
to all the basic concepts.

327
00:16:47 --> 00:16:53
However, I will discuss
some consequences

328
00:16:51 --> 00:16:57
that are rather nonintuitive.

329
00:16:56 --> 00:17:02
Prior to quantum mechanics,

330
00:16:57 --> 00:17:03
there was a long-standing battle
between physicists

331
00:16:59 --> 00:17:05
whether light consists
of particles

332
00:17:02 --> 00:17:08
or whether they are waves.

333
00:17:04 --> 00:17:10
Newton believed strongly
that they're particles,

334
00:17:10 --> 00:17:16
and the Dutchman Huygens
believed that they were waves.

335
00:17:14 --> 00:17:20
And it seemed like, in 1801,

336
00:17:16 --> 00:17:22
that a conclusive experiment
was done by Young,

337
00:17:19 --> 00:17:25
which demonstrated unambiguously
that light was waves; 

338
00:17:25 --> 00:17:31
Huygens was right.

339
00:17:26 --> 00:17:32
But as time went on,
discomfort was growing,

340
00:17:31 --> 00:17:37
as there were also experiments

341
00:17:32 --> 00:17:38
that showed rather conclusively
that light really was particles.

342
00:17:37 --> 00:17:43
And it was one of the great
victories of quantum mechanics

343
00:17:40 --> 00:17:46
that it showed
that light is both.

344
00:17:43 --> 00:17:49
At times it behaves like waves

345
00:17:46 --> 00:17:52
and at other times,
it behaves like particles;

346
00:17:48 --> 00:17:54
it all depends on
how you do your experiment.

347
00:17:52 --> 00:17:58
In 1923, Louis de Broglie made
the daring suggestion

348
00:18:01 --> 00:18:07
that a particle can behave
like a wave,

349
00:18:05 --> 00:18:11
and he specified, he was very
specific, that the wavelength--

350
00:18:10 --> 00:18:16
which nowadays is called
de Broglie wavelength--

351
00:18:14 --> 00:18:20
is h, Max Planck's constant,

352
00:18:16 --> 00:18:22
divided by the momentum
of that particle

353
00:18:19 --> 00:18:25
and the momentum is the mass of
the particle times the velocity,

354
00:18:22 --> 00:18:28
as we have seen in 8.01.

355
00:18:27 --> 00:18:33
If the momentum is higher,
then the wavelength is shorter.

356
00:18:32 --> 00:18:38
A baseball will have
a very high momentum,

357
00:18:34 --> 00:18:40
with a ridiculously low...
short wavelength.

358
00:18:39 --> 00:18:45
Now, one of
the startling consequences

359
00:18:42 --> 00:18:48
is that protons and electrons,

360
00:18:44 --> 00:18:50
which everyone of that time
considered particles,

361
00:18:48 --> 00:18:54
can then also be considered
as being waves.

362
00:18:51 --> 00:18:57
And in 1926, the Austrian
physicist Schrodinger

363
00:18:55 --> 00:19:01
drove the nail in the coffin
with his famous equation--

364
00:18:59 --> 00:19:05
Schrodinger's equation,
it's called now--

365
00:19:02 --> 00:19:08
which is the ground pillar
of quantum mechanics

366
00:19:04 --> 00:19:10
and it unifies the wave and the
particle character of matter.

367
00:19:11 --> 00:19:17
Returning to my baseball,

368
00:19:14 --> 00:19:20
take a mass of the baseball
of, say, half a kilogram

369
00:19:18 --> 00:19:24
and give it a speed
of 100 miles per hour.

370
00:19:21 --> 00:19:27
Calculate the wavelength
that you would find,

371
00:19:25 --> 00:19:31
according to quantum mechanics.

372
00:19:26 --> 00:19:32
That wavelength
is so absurdly small,

373
00:19:31 --> 00:19:37
it is 20 orders
of magnitude smaller

374
00:19:33 --> 00:19:39
than the radius of an electron,
so it is completely meaningless.

375
00:19:38 --> 00:19:44
So quantum mechanics plays
no role in our macroscopic world

376
00:19:42 --> 00:19:48
of pots and pans and baseballs.

377
00:19:45 --> 00:19:51
But now take an electron.

378
00:19:47 --> 00:19:53
You take the mass
of the electron,

379
00:19:49 --> 00:19:55
10 to the minus 30 kilograms.

380
00:19:50 --> 00:19:56
And you give the electron

381
00:19:52 --> 00:19:58
a speed of, say,
1,000 meters per second.

382
00:19:54 --> 00:20:00
Now you get a wavelength which
is comparable to the wavelength

383
00:19:58 --> 00:20:04
of visible light, red light.

384
00:20:00 --> 00:20:06
And now it's something
that becomes very meaningful,

385
00:20:03 --> 00:20:09
something that can be measured.

386
00:20:08 --> 00:20:14
Now, you may argue, "Gee,
what difference does it make?

387
00:20:11 --> 00:20:17
"Who cares
whether something is a wave

388
00:20:14 --> 00:20:20
or whether something
is a particle?"

389
00:20:16 --> 00:20:22
Well, it makes
a huge difference,

390
00:20:19 --> 00:20:25
because waves have crests
and they have valleys,

391
00:20:23 --> 00:20:29
and so if you take two sources
of waves, either water waves--

392
00:20:27 --> 00:20:33
two sources, tapping up and down
on the water--

393
00:20:29 --> 00:20:35
or you can take
two sound sources,

394
00:20:32 --> 00:20:38
then there are certain locations
on the surface of the water

395
00:20:36 --> 00:20:42
where the crest of one wave

396
00:20:38 --> 00:20:44
arrives at the same time
as the valley of the other,

397
00:20:42 --> 00:20:48
and so they cancel
each other out.

398
00:20:43 --> 00:20:49
There is nothing,
there is no motion of the water.

399
00:20:46 --> 00:20:52
We call that
destructive interference.

400
00:20:48 --> 00:20:54
Of course,
there are other places

401
00:20:51 --> 00:20:57
where there is
constructive interference,

402
00:20:53 --> 00:20:59
where they support each other.

403
00:20:55 --> 00:21:01
Now, if particles
can do that, too...

404
00:20:58 --> 00:21:04
That is very hard to imagine--

405
00:20:59 --> 00:21:05
how can one particle
with another particle

406
00:21:04 --> 00:21:10
interfere and vanish, that the
two particles no longer exist?

407
00:21:09 --> 00:21:15
So if, indeed,
particles are waves,

408
00:21:12 --> 00:21:18
you should be able
to demonstrate that

409
00:21:14 --> 00:21:20
by having the interference
pattern of two particles,

410
00:21:18 --> 00:21:24
like the water waves,

411
00:21:19 --> 00:21:25
and make--
at certain locations in space--

412
00:21:21 --> 00:21:27
those particles disappear,
which turn out to be possible.

413
00:21:24 --> 00:21:30
But that's
a very nonintuitive idea.

414
00:21:29 --> 00:21:35
So we think of it
too classically when we say,

415
00:21:31 --> 00:21:37
"Well, two particles
cannot disappear."

416
00:21:34 --> 00:21:40
But in quantum mechanics,

417
00:21:35 --> 00:21:41
you can think in waves
if you want to,

418
00:21:37 --> 00:21:43
and then you have no problems
with the interference pattern

419
00:21:40 --> 00:21:46
and the destructive interference
at certain locations.

420
00:21:44 --> 00:21:50
Now, there are
other remarkable consequences

421
00:21:46 --> 00:21:52
of quantum mechanics
in classical mechanics.

422
00:21:51 --> 00:21:57
If you and I are clever enough,

423
00:21:55 --> 00:22:01
you think that
we should be able to determine

424
00:21:58 --> 00:22:04
the position of an object
to any accuracy that we require,

425
00:22:03 --> 00:22:09
and at the same time
determine also its momentum

426
00:22:07 --> 00:22:13
at any accuracy that we require.

427
00:22:09 --> 00:22:15
It's just a matter
of how clever we are.

428
00:22:12 --> 00:22:18
Simultaneously,
the object is right there

429
00:22:16 --> 00:22:22
and that is its mass
and that is its speed.

430
00:22:19 --> 00:22:25
However, the German physicist
Heisenberg realized in 1927

431
00:22:26 --> 00:22:32
that a consequence
of quantum mechanics is

432
00:22:29 --> 00:22:35
that this is not possible.

433
00:22:32 --> 00:22:38
Strange as it may sound to you,
Heisenberg stated

434
00:22:35 --> 00:22:41
that the position
and the momentum of an object

435
00:22:39 --> 00:22:45
cannot be measured very
accurately at the same time.

436
00:22:43 --> 00:22:49
And I will read to you

437
00:22:46 --> 00:22:52
Heisenberg's uncertainty
principle, the way we know it.

438
00:22:50 --> 00:22:56
It says, "The very concept
of exact position of an object

439
00:22:55 --> 00:23:01
"and its exact momentum,
together,

440
00:22:58 --> 00:23:04
have no meaning in nature."

441
00:23:02 --> 00:23:08
It's a profound
nonclassical idea,

442
00:23:03 --> 00:23:09
and it is hard for any one
of us-- you and me included--

443
00:23:07 --> 00:23:13
to comprehend.

444
00:23:09 --> 00:23:15
But it is consistent
with all experiments

445
00:23:11 --> 00:23:17
that we can do to date.

446
00:23:12 --> 00:23:18
I want to repeat it,

447
00:23:13 --> 00:23:19
because it's going to be
important of what follows.

448
00:23:17 --> 00:23:23
"The very concept of exact
position of an object

449
00:23:20 --> 00:23:26
"and its exact momentum,
together,

450
00:23:24 --> 00:23:30
have no meaning in nature."

451
00:23:27 --> 00:23:33
What does it mean?

452
00:23:30 --> 00:23:36
First, let me write down

453
00:23:31 --> 00:23:37
Heisenberg's
uncertainty principle.

454
00:23:34 --> 00:23:40
Delta p, which is
the uncertainty in the momentum,

455
00:23:37 --> 00:23:43
multiplied by delta x,

456
00:23:39 --> 00:23:45
which is an uncertainty in
the position of that particle,

457
00:23:43 --> 00:23:49
is larger
or approximately equal

458
00:23:46 --> 00:23:52
to Planck's constant
divided by two pi--

459
00:23:49 --> 00:23:55
for which, in physics,
we call that "h-bar"--

460
00:23:52 --> 00:23:58
and h-bar is approximately 10
to the minus 34 joule-seconds.

461
00:23:59 --> 00:24:05
You see, h is 6.6 times 10
to the minus 34.

462
00:24:03 --> 00:24:09
If you divide that by two pi,

463
00:24:06 --> 00:24:12
you get about 10
to the minus 34.

464
00:24:09 --> 00:24:15
What does this mean, now?

465
00:24:10 --> 00:24:16
What it means

466
00:24:11 --> 00:24:17
that if the position is known
to an accuracy delta x--

467
00:24:16 --> 00:24:22
we'll give you some examples--

468
00:24:18 --> 00:24:24
that the momentum is ill-
determined, is not determined,

469
00:24:25 --> 00:24:31
to the amount delta p,

470
00:24:28 --> 00:24:34
larger or equal
than h-bar divided by delta x.

471
00:24:33 --> 00:24:39
That's what it means.

472
00:24:35 --> 00:24:41
And I'll give you an example

473
00:24:37 --> 00:24:43
which I've chosen
from a book of George Gamow.

474
00:24:42 --> 00:24:48
Gamow wrote a book
which he called

475
00:24:45 --> 00:24:51
Mr. Tompkins in Wonderland.

476
00:24:47 --> 00:24:53
It's about dreams.

477
00:24:49 --> 00:24:55
Mr. Tompkins wants
to understand the quantum world,

478
00:24:53 --> 00:24:59
and there is a professor--

479
00:24:55 --> 00:25:01
you will see a picture
of the professor--

480
00:24:57 --> 00:25:03
who takes him, in his dreams,

481
00:24:58 --> 00:25:04
along the various
remarkable nonintuitive effects

482
00:25:02 --> 00:25:08
of quantum mechanics.

483
00:25:03 --> 00:25:09
And in one of these dreams,

484
00:25:06 --> 00:25:12
the professor suggests
that we make h-bar one.

485
00:25:13 --> 00:25:19
And the professor takes
a triangle in the pool table

486
00:25:16 --> 00:25:22
and he puts the triangle
over one billiard ball,

487
00:25:22 --> 00:25:28
so the billiard ball is
constrained in its position

488
00:25:26 --> 00:25:32
and that delta x is roughly...
say, 30 centimeters, 0.3 meters.

489
00:25:35 --> 00:25:41
That means that the momentum
is not determined,

490
00:25:42 --> 00:25:48
not determined to an approximate
value of one divided by 0.3,

491
00:25:50 --> 00:25:56
is about 3 kilogram-meters
per second.

492
00:25:54 --> 00:26:00
Now, if we give the billiard
ball a mass of one kilogram,

493
00:25:59 --> 00:26:05
then delta p is m delta v,
and so if m is one kilogram,

494
00:26:06 --> 00:26:12
then the speed of that
billiard ball is undetermined,

495
00:26:11 --> 00:26:17
according to Heisenberg's
uncertainty principle,

496
00:26:14 --> 00:26:20
by at least approximately
three meters per second.

497
00:26:18 --> 00:26:24
Three meters per second--
that means seven miles per hour,

498
00:26:22 --> 00:26:28
and so that billiard ball

499
00:26:24 --> 00:26:30
will go around like crazy
in that triangle,

500
00:26:28 --> 00:26:34
and that's exactly
what happens in the dream.

501
00:26:33 --> 00:26:39
And I will show you here
a picture from that book.

502
00:26:41 --> 00:26:47
Mr. Tompkins is
always in pajamas,

503
00:26:43 --> 00:26:49
just to remind you
that it is a dream.

504
00:26:45 --> 00:26:51
And needless to say,

505
00:26:46 --> 00:26:52
the professor is a very old man
and has a very nice beard; 

506
00:26:50 --> 00:26:56
it adds to the prestige.

507
00:26:51 --> 00:26:57
And I will read you
from this book.

508
00:26:53 --> 00:26:59
I will read you a very short
paragraph that deals with this.

509
00:26:57 --> 00:27:03
"So the professor says,

510
00:26:59 --> 00:27:05
"'Look, here, I'm going
to put definite limits

511
00:27:03 --> 00:27:09
"'on the position of this ball

512
00:27:05 --> 00:27:11
by putting it
inside a wooden triangle.'"

513
00:27:08 --> 00:27:14
"As soon as the ball
was placed in the enclosure,

514
00:27:12 --> 00:27:18
"of the whole inside
of the triangle

515
00:27:13 --> 00:27:19
"became filled up
with glittering of ivory.

516
00:27:17 --> 00:27:23
"'You see,' said the professor,

517
00:27:20 --> 00:27:26
"'I defined the position
of the ball

518
00:27:22 --> 00:27:28
"'to the extent of the
dimensions of the triangle.

519
00:27:25 --> 00:27:31
"'This results in considerable
uncertainty in the velocity

520
00:27:30 --> 00:27:36
"'and the ball is moving rapidly
inside the boundary.

521
00:27:34 --> 00:27:40
"'Can't you stop it?'
asked Mr. Tompkins.

522
00:27:38 --> 00:27:44
"'No, it is
physically impossible.

523
00:27:42 --> 00:27:48
"'Anybody in an enclosed space
possesses a certain motion.

524
00:27:47 --> 00:27:53
"'We physicists call it
zero point motion,

525
00:27:50 --> 00:27:56
"'such as, for example,

526
00:27:52 --> 00:27:58
the motion of electrons
in any atom.'"

527
00:27:57 --> 00:28:03
So here you see
quantum mechanics at work

528
00:28:01 --> 00:28:07
when h-bar is one.

529
00:28:05 --> 00:28:11
This is
a very nonclassical idea,

530
00:28:08 --> 00:28:14
because you and I would think--

531
00:28:11 --> 00:28:17
and we've always dealt
with that in 8.01--

532
00:28:13 --> 00:28:19
that you can take an object
and place it at location "a,"

533
00:28:17 --> 00:28:23
and we say at time t zero
it is at "a"

534
00:28:20 --> 00:28:26
and it has no speed
and we know the mass,

535
00:28:22 --> 00:28:28
so we know both the momentum
and the position

536
00:28:25 --> 00:28:31
to an infinite accuracy.

537
00:28:27 --> 00:28:33
But according to quantum
mechanics, that's not possible.

538
00:28:31 --> 00:28:37
So let's now return to the real
world, where h-bar is not one,

539
00:28:35 --> 00:28:41
but where h-bar is
10 to the minus 34,

540
00:28:37 --> 00:28:43
and let's now put a billiard
ball inside this triangle.

541
00:28:41 --> 00:28:47
Now, delta x is the same,

542
00:28:45 --> 00:28:51
but since h-bar is
10 to the minus 34,

543
00:28:48 --> 00:28:54
delta p is, of course,
10 to the 34 times smaller,

544
00:28:54 --> 00:29:00
and so the velocity is 10
to the 34 times smaller.

545
00:28:57 --> 00:29:03
This undeterminedness...

546
00:29:00 --> 00:29:06
degree to which the velocity
is now undetermined,

547
00:29:03 --> 00:29:09
is so ridiculously small--

548
00:29:05 --> 00:29:11
it is 3 times 10 to the minus
34 meters per second--

549
00:29:09 --> 00:29:15
that if you allowed that ball
to move with that speed,

550
00:29:13 --> 00:29:19
in 100 billion years,

551
00:29:15 --> 00:29:21
it would move only 1/100
of a diameter of an electron,

552
00:29:19 --> 00:29:25
so it's meaningless again.

553
00:29:21 --> 00:29:27
And so again, you see that
quantum mechanics plays no role

554
00:29:24 --> 00:29:30
in our daily macroscopic world

555
00:29:27 --> 00:29:33
of baseballs and basketballs
and billiards and pots and pans.

556
00:29:34 --> 00:29:40
And therefore, it is
completely okay for us to say,

557
00:29:37 --> 00:29:43
"I have a billiard ball
which is at point 'a,'

558
00:29:40 --> 00:29:46
and its mass is one kilogram
and it has no speed."

559
00:29:43 --> 00:29:49
That is completely kosher,
completely acceptable,

560
00:29:47 --> 00:29:53
and quantum mechanics
has no problems with that.

561
00:29:51 --> 00:29:57
Let's now turn to an atom.

562
00:29:56 --> 00:30:02
Take a hydrogen atom.

563
00:29:58 --> 00:30:04
The diameter of a hydrogen atom

564
00:30:00 --> 00:30:06
is about 10
to the minus 10 meters.

565
00:30:04 --> 00:30:10
So the electron is confined

566
00:30:07 --> 00:30:13
to a delta x of about 10
to the minus 10 meters.

567
00:30:12 --> 00:30:18
That means the momentum of that
electron becomes undetermined--

568
00:30:17 --> 00:30:23
according to Heisenberg's
uncertainty principle--

569
00:30:20 --> 00:30:26
to about 10 to the minus 34,
divided by 10 to the minus 10,

570
00:30:26 --> 00:30:32
is about 10 to the minus 24
kilogram-meters per second.

571
00:30:35 --> 00:30:41
What is the mass of an electron?

572
00:30:37 --> 00:30:43
That's about 10
to the minus 30 kilograms.

573
00:30:42 --> 00:30:48
So this, delta p,
is also m delta v.

574
00:30:49 --> 00:30:55
So it means that delta v--

575
00:30:51 --> 00:30:57
that means the velocity
of the electron--

576
00:30:53 --> 00:30:59
is undetermined, according
to Heisenberg's principle,

577
00:30:57 --> 00:31:03
by an amount which is at least
10 to the minus 24,

578
00:31:02 --> 00:31:08
which is this delta p divided
by the mass of the electron,

579
00:31:07 --> 00:31:13
which is 10 to the minus 30.

580
00:31:09 --> 00:31:15
And that is about 10
to the six meters per second--

581
00:31:13 --> 00:31:19
that is one-third of a percent
of the speed of light.

582
00:31:19 --> 00:31:25
So the electron is moving

583
00:31:22 --> 00:31:28
only because of the fact
that it is confined.

584
00:31:25 --> 00:31:31
That's what quantum mechanics
is all about.

585
00:31:27 --> 00:31:33
The electron's motion
is dictated exclusively

586
00:31:31 --> 00:31:37
by quantum mechanics.

587
00:31:33 --> 00:31:39
 

588
00:31:39 --> 00:31:45
I'm going to show you
an experiment

589
00:31:42 --> 00:31:48
in which I want to convey to you

590
00:31:46 --> 00:31:52
how nonintuitive Heisenberg's
uncertainty principle is.

591
00:31:52 --> 00:31:58
I have here a laser beam,

592
00:31:55 --> 00:32:01
and this laser beam is going to
be aimed through a narrow slit--

593
00:32:01 --> 00:32:07
I'll make a drawing,
I'll turn this light off--

594
00:32:06 --> 00:32:12
and that slit,
which is a vertical slit,

595
00:32:10 --> 00:32:16
can be made narrow
and can be made wider.

596
00:32:16 --> 00:32:22
Here is this light beam and here
is this opening, this slit.

597
00:32:24 --> 00:32:30
It's only going to be confined
in this direction,

598
00:32:26 --> 00:32:32
not in this direction.

599
00:32:28 --> 00:32:34
And so
the light will come out here,

600
00:32:36 --> 00:32:42
and then, on a screen, which
is going to be that screen,

601
00:32:39 --> 00:32:45
at large distance capital L,

602
00:32:44 --> 00:32:50
we're going to see
that light spot,

603
00:32:46 --> 00:32:52
due to the light beam
going through the slit

604
00:32:49 --> 00:32:55
and this separation, capital L.

605
00:32:55 --> 00:33:01
I start off
with the slit all the way open

606
00:32:59 --> 00:33:05
and so you're going to see
this light spot like this.

607
00:33:04 --> 00:33:10
And then I'm going to make
the slit narrower and narrower,

608
00:33:07 --> 00:33:13
and as I'm going to cut
into the light beam,

609
00:33:10 --> 00:33:16
what you're going to see
is exactly what you expect.

610
00:33:13 --> 00:33:19
You expect
that this light disappears,

611
00:33:16 --> 00:33:22
and when I cut in further,
you see exactly what you expect,

612
00:33:21 --> 00:33:27
that this light disappears.

613
00:33:23 --> 00:33:29
And so the light spot
there on that screen

614
00:33:25 --> 00:33:31
will become narrower
and narrower and narrower.

615
00:33:30 --> 00:33:36
But then there comes a point
that Heisenberg says,

616
00:33:32 --> 00:33:38
"Uh-uh, careful now, because
your delta x, your knowledge,

617
00:33:41 --> 00:33:47
"the accuracy in this direction
where the light goes through

618
00:33:44 --> 00:33:50
"is now so high
that now I'm going to introduce

619
00:33:49 --> 00:33:55
"an uncertainty
in the momentum of that light.

620
00:33:53 --> 00:33:59
"The momentum of that light

621
00:33:54 --> 00:34:00
is now no longer determined
to infinite accuracy."

622
00:33:57 --> 00:34:03
And what that means,
if you start fooling around

623
00:33:59 --> 00:34:05
with the momentum of that light
in the x direction,

624
00:34:03 --> 00:34:09
it no longer
goes through straight

625
00:34:04 --> 00:34:10
but it goes off at an angle,
and I will make you

626
00:34:09 --> 00:34:15
a more quantitative calculation
for that.

627
00:34:12 --> 00:34:18
So let's look at this slit
from above.

628
00:34:16 --> 00:34:22
 

629
00:34:19 --> 00:34:25
Here's the slit, and the slit
has an opening, delta x.

630
00:34:28 --> 00:34:34
And this delta x we're going
to make smaller and smaller,

631
00:34:31 --> 00:34:37
and let us start with a delta x
of about 1/10 of a millimeter,

632
00:34:38 --> 00:34:44
which is 10
to the minus 4 meters.

633
00:34:43 --> 00:34:49
I have light, I know
the wavelength of the light,

634
00:34:47 --> 00:34:53
and I know that lambda
equals h divided by p,

635
00:34:50 --> 00:34:56
according to De Broglie.

636
00:34:52 --> 00:34:58
I know the wavelength,

637
00:34:54 --> 00:35:00
I know h, and so I can calculate
the momentum of that light.

638
00:34:57 --> 00:35:03
I have done that,
take my word for it.

639
00:34:59 --> 00:35:05
It is about 10 to the minus 27
kilogram-meters per second.

640
00:35:05 --> 00:35:11
That's the momentum of
the individual light photons.

641
00:35:09 --> 00:35:15
Think of them as particles,

642
00:35:11 --> 00:35:17
which you can do,
according to de Broglie.

643
00:35:14 --> 00:35:20
So now I have a delta p,

644
00:35:19 --> 00:35:25
the degree to which the momentum
is undetermined,

645
00:35:22 --> 00:35:28
according to Heisenberg,

646
00:35:24 --> 00:35:30
is going to be 10 to the minus
34 divided by delta x--

647
00:35:29 --> 00:35:35
which is 10 to the minus 4,

648
00:35:32 --> 00:35:38
so that is 10
to the minus 30, very small.

649
00:35:37 --> 00:35:43
But the momentum itself
is 10 to the minus 27,

650
00:35:41 --> 00:35:47
so it's only one part
in a thousand.

651
00:35:43 --> 00:35:49
So what will happen?

652
00:35:45 --> 00:35:51
If the light comes
through here...

653
00:35:49 --> 00:35:55
And I now make
a classical argument.

654
00:35:51 --> 00:35:57
I say, "This is
the momentum of the light

655
00:35:54 --> 00:36:00
as it comes straight in."

656
00:35:56 --> 00:36:02
When it has to be squeezed
through this narrow opening,

657
00:35:59 --> 00:36:05
Heisenberg's uncertainty
principle demands

658
00:36:02 --> 00:36:08
that it is going
to be undetermined,

659
00:36:04 --> 00:36:10
the momentum in this direction

660
00:36:06 --> 00:36:12
by roughly 10 to the minus 30,
or more.

661
00:36:09 --> 00:36:15
Remember, it is always
larger or equal.

662
00:36:12 --> 00:36:18
In other words, if I introduce,
for instance,

663
00:36:14 --> 00:36:20
in this direction
or in this direction, delta p,

664
00:36:19 --> 00:36:25
then I would expect

665
00:36:21 --> 00:36:27
that some of that light
goes off in this direction.

666
00:36:26 --> 00:36:32
It is this change in momentum,

667
00:36:28 --> 00:36:34
this undeterminedness
in momentum,

668
00:36:30 --> 00:36:36
that makes it go off at an
angle, only in the x direction.

669
00:36:33 --> 00:36:39
If I have the slit like this,

670
00:36:34 --> 00:36:40
don't expect this to happen
in this direction,

671
00:36:37 --> 00:36:43
because the uncertainty
in the y direction,

672
00:36:41 --> 00:36:47
that's not the problem.

673
00:36:43 --> 00:36:49
Delta y is not very small,
it's delta x that is very small,

674
00:36:46 --> 00:36:52
so it's this direction that's
going to give you trouble.

675
00:36:48 --> 00:36:54
It's only in this direction

676
00:36:50 --> 00:36:56
that you know precisely
where that light goes through.

677
00:36:52 --> 00:36:58
This direction is not the issue.

678
00:36:54 --> 00:37:00
So this angle theta can now
be calculated very roughly.

679
00:36:59 --> 00:37:05
Theta is obviously delta p
divided by p,

680
00:37:02 --> 00:37:08
so theta is very roughly
10 to the minus 3 radians,

681
00:37:07 --> 00:37:13
which is a fifteenth
of a degree,

682
00:37:09 --> 00:37:15
and if you have
at a distance L--

683
00:37:12 --> 00:37:18
if this distance here is L--

684
00:37:15 --> 00:37:21
if you have here a screen,

685
00:37:18 --> 00:37:24
then the spot on this screen...
if I call that x at location L,

686
00:37:23 --> 00:37:29
then x at location L
is obviously theta times L.

687
00:37:28 --> 00:37:34
And if theta is
10 to the minus 3--

688
00:37:30 --> 00:37:36
and let's assume this is
about 10 meters away from us,

689
00:37:34 --> 00:37:40
so L is about 10 meters--

690
00:37:35 --> 00:37:41
then you get 10
to the minus 2 meters.

691
00:37:40 --> 00:37:46
That is one centimeter.

692
00:37:42 --> 00:37:48
One centimeter in this direction

693
00:37:44 --> 00:37:50
and one centimeter in that
direction-- two centimeters.

694
00:37:47 --> 00:37:53
But when I make the slit width
10 times smaller,

695
00:37:51 --> 00:37:57
if I make the slit width
only 1/100 of a millimeter,

696
00:37:55 --> 00:38:01
then this becomes
10 centimeters,

697
00:38:01 --> 00:38:07
because now I know delta x
10 times better,

698
00:38:04 --> 00:38:10
and so delta p is 10 times
more uncertain.

699
00:38:07 --> 00:38:13
So now I expect to see here

700
00:38:10 --> 00:38:16
at least a smear
of 20 centimeters

701
00:38:12 --> 00:38:18
and at least a smear
of 20 centimeters there.

702
00:38:15 --> 00:38:21
So the absurdity is that a
teeny-weeny little light source

703
00:38:19 --> 00:38:25
which in the beginning you
will see as a very small spot...

704
00:38:23 --> 00:38:29
When I make this slit
narrower and narrower,

705
00:38:25 --> 00:38:31
indeed, you will see
that you will lose photons,

706
00:38:28 --> 00:38:34
and you will see this getting
narrower and narrower,

707
00:38:30 --> 00:38:36
and then all of a sudden,
it begins to spread out,

708
00:38:34 --> 00:38:40
and it begins to spread out,

709
00:38:35 --> 00:38:41
and by the time I'm close
to a tenth of a millimeter,

710
00:38:38 --> 00:38:44
the light spot will be yay big.

711
00:38:41 --> 00:38:47
Very nonintuitive.

712
00:38:42 --> 00:38:48
You make the slit smaller,
and the photons spread out.

713
00:38:46 --> 00:38:52
And I want to show
that to you now.

714
00:38:49 --> 00:38:55
I have to make it very dark.

715
00:38:51 --> 00:38:57
 

716
00:38:58 --> 00:39:04
And I need my flashlight,
turn on the laser beam.

717
00:39:01 --> 00:39:07
 

718
00:39:08 --> 00:39:14
There you see it.

719
00:39:11 --> 00:39:17
The slit is now
all the way open.

720
00:39:14 --> 00:39:20
 

721
00:39:19 --> 00:39:25
Yeah, it's all the way open,

722
00:39:20 --> 00:39:26
and I'm going to close
the slit now slowly.

723
00:39:27 --> 00:39:33
And if you look closely,
you will see that the...

724
00:39:33 --> 00:39:39
Let me also get my red laser,
then I can point something out.

725
00:39:36 --> 00:39:42
You will see that the light

726
00:39:40 --> 00:39:46
will get squeezed
in the horizontal direction.

727
00:39:43 --> 00:39:49
You can see already
at the left side,

728
00:39:45 --> 00:39:51
has a very sharp
vertical cut-off,

729
00:39:47 --> 00:39:53
and the right side also.

730
00:39:49 --> 00:39:55
It's getting narrower,
it's getting narrower.

731
00:39:51 --> 00:39:57
Getting narrower,

732
00:39:52 --> 00:39:58
but I'm nowhere nearly
a tenth of a millimeter yet.

733
00:39:55 --> 00:40:01
It's getting clearly narrower.

734
00:39:57 --> 00:40:03
You see, it's getting narrower,
it's getting narrower.

735
00:40:01 --> 00:40:07
If I look here...

736
00:40:02 --> 00:40:08
oh, I'm not yet at the
tenth of a millimeter,

737
00:40:04 --> 00:40:10
but I'm getting there.

738
00:40:05 --> 00:40:11
I'm going slowly, squeezing it.

739
00:40:07 --> 00:40:13
I'm squeezing those photons.

740
00:40:09 --> 00:40:15
Those photons now are forced

741
00:40:10 --> 00:40:16
to go through
an extremely narrow opening

742
00:40:15 --> 00:40:21
and Heisenberg is
very shortly going to jump in

743
00:40:18 --> 00:40:24
and says, "You are going
to pay a price for that.

744
00:40:20 --> 00:40:26
"You know too well where those
photons are in the x direction.

745
00:40:23 --> 00:40:29
"The price you pay--

746
00:40:25 --> 00:40:31
"that nature will now make
the momentum undetermined

747
00:40:29 --> 00:40:35
in the x direction."

748
00:40:31 --> 00:40:37
And you begin to...
you see it now.

749
00:40:33 --> 00:40:39
You really begin to see

750
00:40:34 --> 00:40:40
that the center portion
is widening.

751
00:40:37 --> 00:40:43
Even photons appear.

752
00:40:39 --> 00:40:45
Here, you see some dark lines,

753
00:40:40 --> 00:40:46
which I will not
further discuss today,

754
00:40:43 --> 00:40:49
but notice that the light
is spreading.

755
00:40:47 --> 00:40:53
Of course, when I squeeze this
slit, when I make it narrower,

756
00:40:50 --> 00:40:56
it's obvious that I lose light,

757
00:40:52 --> 00:40:58
because the light
that hits the side of the slit

758
00:40:54 --> 00:41:00
is not going through,

759
00:40:56 --> 00:41:02
so the light intensity
will go down.

760
00:40:57 --> 00:41:03
That's just inevitable.

761
00:40:59 --> 00:41:05
I used fewer photons.

762
00:41:00 --> 00:41:06
But look at this.

763
00:41:02 --> 00:41:08
There are photons here,
there are photons there.

764
00:41:04 --> 00:41:10
It's at least 10 centimeters,
this portion.

765
00:41:06 --> 00:41:12
From here to here is
at least one foot.

766
00:41:09 --> 00:41:15
I squeeze more-- this is more
than half a meter now.

767
00:41:13 --> 00:41:19
I squeeze more-- this is
about one meter already.

768
00:41:17 --> 00:41:23
I squeeze even more.

769
00:41:18 --> 00:41:24
I close the slit now,
and I will open it slowly.

770
00:41:23 --> 00:41:29
 

771
00:41:28 --> 00:41:34
I'm opening it very slowly, and
at the moment that it opens...

772
00:41:32 --> 00:41:38
Look at this! You see this?
 

773
00:41:36 --> 00:41:42
You see this wonderful streak?

774
00:41:38 --> 00:41:44
It looks more like a comet.

775
00:41:39 --> 00:41:45
From here to here is
at least a meter.

776
00:41:41 --> 00:41:47
That's that center portion
of the light.

777
00:41:43 --> 00:41:49
It has spread out,
since the poor light was forced

778
00:41:47 --> 00:41:53
to go through
this very narrow opening.

779
00:41:52 --> 00:41:58
Now I'm opening it
more and more.

780
00:41:56 --> 00:42:02
I'm opening it more,

781
00:41:58 --> 00:42:04
and now, of course,
the reverse is happening.

782
00:42:01 --> 00:42:07
Extremely nonintuitive.

783
00:42:05 --> 00:42:11
 

784
00:42:21 --> 00:42:27
Now, not only have you seen
quantum mechanics at work,

785
00:42:24 --> 00:42:30
in terms of electrons jumping
between orbits,

786
00:42:27 --> 00:42:33
but you now have also seen

787
00:42:28 --> 00:42:34
one other
very interesting consequence

788
00:42:30 --> 00:42:36
of quantum mechanics,

789
00:42:31 --> 00:42:37
which is Heisenberg's
uncertainty principle.

790
00:42:34 --> 00:42:40
Now, the spreading of this light
can very easily be explained

791
00:42:39 --> 00:42:45
without Heisenberg's
uncertainty principle.

792
00:42:42 --> 00:42:48
In fact, it was known,
even in the previous century,

793
00:42:46 --> 00:42:52
to a high degree of accuracy,
why this happens,

794
00:42:50 --> 00:42:56
and the dark lines were
very accurately explained.

795
00:42:55 --> 00:43:01
All I wanted to show

796
00:42:57 --> 00:43:03
is that the spreading of the
light is entirely consistent

797
00:43:01 --> 00:43:07
with Heisenberg's uncertainty
principle, and it better be,

798
00:43:04 --> 00:43:10
because it would
not be possible,

799
00:43:07 --> 00:43:13
it would be inconceivable
that you could do any experiment

800
00:43:11 --> 00:43:17
that would violate Heisenberg's
uncertainty principle.

801
00:43:15 --> 00:43:21
And if this light that you would
see on the screen there,

802
00:43:19 --> 00:43:25
if that light spot would get
narrower and narrower

803
00:43:21 --> 00:43:27
and narrower and narrower
all the time,

804
00:43:24 --> 00:43:30
as we would think classically,
that would have been

805
00:43:26 --> 00:43:32
a violation of Heisenberg's
uncertainty principle,

806
00:43:29 --> 00:43:35
and that is not possible.

807
00:43:32 --> 00:43:38
Now, there is no way in advance

808
00:43:34 --> 00:43:40
to predict
which photons end up where.

809
00:43:41 --> 00:43:47
All you can do
with quantum mechanics

810
00:43:43 --> 00:43:49
is to do the experiment
with lots of photons

811
00:43:47 --> 00:43:53
and then you will get
a certain distribution

812
00:43:49 --> 00:43:55
and the distribution will be
exactly as you saw there.

813
00:43:54 --> 00:44:00
Quantum mechanics
can never predict,

814
00:43:57 --> 00:44:03
on an individual photon,
where it will end up.

815
00:44:01 --> 00:44:07
We saw that bright spot
in the center.

816
00:44:04 --> 00:44:10
So if you did this experiment
with one photon per day--

817
00:44:09 --> 00:44:15
one photon per day
going through this slit--

818
00:44:11 --> 00:44:17
and you had
a photographic plate there,

819
00:44:14 --> 00:44:20
and you would keep it there
for months,

820
00:44:16 --> 00:44:22
and you would develop it,

821
00:44:17 --> 00:44:23
you would see the same pattern
that you see there.

822
00:44:20 --> 00:44:26
This photon arrives today.

823
00:44:21 --> 00:44:27
Here arrives one tomorrow.

824
00:44:23 --> 00:44:29
Here arrives one the day
after tomorrow.

825
00:44:25 --> 00:44:31
Here one the day after that,
the day after that,

826
00:44:28 --> 00:44:34
the day after that,
the day after that,

827
00:44:31 --> 00:44:37
the day after that, the day
after that,

828
00:44:34 --> 00:44:40
and slowly are you
beginning to see

829
00:44:36 --> 00:44:42
that pattern that you saw.

830
00:44:40 --> 00:44:46
So don't think

831
00:44:42 --> 00:44:48
that this interference pattern
that you saw

832
00:44:45 --> 00:44:51
is the result of two photons

833
00:44:46 --> 00:44:52
going through the slit
simultaneously-- not at all.

834
00:44:49 --> 00:44:55
You can do it
with one photon at a time

835
00:44:53 --> 00:44:59
and you would see
exactly the same thing.

836
00:44:58 --> 00:45:04
Now, this idea-- that you
cannot in advance predict

837
00:45:01 --> 00:45:07
what a particular photon
will do--

838
00:45:03 --> 00:45:09
is a very nonclassic idea, and
it rubs us all the wrong way

839
00:45:08 --> 00:45:14
because our classical way
of thinking is--

840
00:45:11 --> 00:45:17
and you are no different from
my own feeling in this respect--

841
00:45:14 --> 00:45:20
that if you do an experiment

842
00:45:16 --> 00:45:22
a hundred times
in a controlled way,

843
00:45:18 --> 00:45:24
you should get a hundred times
exactly the same result.

844
00:45:22 --> 00:45:28
Not so, says quantum mechanics.

845
00:45:24 --> 00:45:30
All that quantum mechanics
will tell you

846
00:45:26 --> 00:45:32
is what the probability is
that something will happen.

847
00:45:30 --> 00:45:36
No guarantees,

848
00:45:32 --> 00:45:38
but it is very good
in predicting probabilities.

849
00:45:35 --> 00:45:41
Now, Einstein had great problems

850
00:45:37 --> 00:45:43
with this idea of not knowing
precisely what would happen,

851
00:45:41 --> 00:45:47
and he had endless discussions
with Bohr and others

852
00:45:44 --> 00:45:50
in which
he tried to convince them

853
00:45:47 --> 00:45:53
that because you couldn't
predict what happened,

854
00:45:49 --> 00:45:55
that something had to be wrong
with quantum mechanics,

855
00:45:51 --> 00:45:57
and Einstein's famous words
were, "God does not throw dice."

856
00:45:58 --> 00:46:04
This was the way,
was his way of saying,

857
00:46:00 --> 00:46:06
"It is ridiculous
that the outcome

858
00:46:02 --> 00:46:08
of a well-controlled
experiment is uncertain."

859
00:46:06 --> 00:46:12
Now, almost nine decades
have gone by

860
00:46:09 --> 00:46:15
since the beginning
of quantum mechanics,

861
00:46:11 --> 00:46:17
and we now know that God-- if
there is one-- does throw dice.

862
00:46:19 --> 00:46:25
However, God is bound to
the rules of quantum mechanics

863
00:46:22 --> 00:46:28
and cannot violate Heisenberg's
uncertainty principle.

864
00:46:26 --> 00:46:32
The light could not go straight
through without spreading

865
00:46:31 --> 00:46:37
when I made the slit as narrow
as I did.

866
00:46:35 --> 00:46:41
So quantum mechanics is
a bizarre world

867
00:46:39 --> 00:46:45
that we rarely experience
in our daily lives,

868
00:46:42 --> 00:46:48
because we are used

869
00:46:43 --> 00:46:49
to basketballs,
baseballs, tennis balls.

870
00:46:45 --> 00:46:51
But yet it is the way
the world ticks,

871
00:46:49 --> 00:46:55
and atoms and molecules
can only exist

872
00:46:51 --> 00:46:57
because of quantum mechanics.

873
00:46:52 --> 00:46:58
That means you and I
can only exist

874
00:46:54 --> 00:47:00
because of quantum mechanics.

875
00:46:57 --> 00:47:03
I hope that this will give you
something to think about,

876
00:47:01 --> 00:47:07
but I warn you in advance,

877
00:47:02 --> 00:47:08
because if you
start thinking about this,

878
00:47:04 --> 00:47:10
it will give you headaches

879
00:47:06 --> 00:47:12
and it will give you
sleepless nights.

880
00:47:07 --> 00:47:13
And it has given mecountless
sleepless nights in the past,

881
00:47:11 --> 00:47:17
and even today, when I think
about the consequences--

882
00:47:14 --> 00:47:20
the bizarre consequences
of quantum mechanics--

883
00:47:17 --> 00:47:23
I still cannot comprehend it,
I still cannot digest it

884
00:47:20 --> 00:47:26
and I still have headaches
and sleepless nights.

885
00:47:24 --> 00:47:30
But it may be necessary to go
through these sleepless nights

886
00:47:27 --> 00:47:33
if you want to eventually evolve

887
00:47:29 --> 00:47:35
as an independent
thinking scientist,

888
00:47:32 --> 00:47:38
and I hope
that someday all of you will.

889
00:47:35 --> 00:47:41
Thank you.

890
00:47:37 --> 00:47:43
(class applauds )

891
00:47:40 --> 00:47:46
 

892
00:48:00 --> 00:48:06