WEBVTT

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MARKUS KLUTE: Welcome back
to 8.20 Special Relativity.

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In this section, we'll
talk about waves.

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You have all seen waves.

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You know what a wave
is in principle.

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You might have had an
opportunity to surf on a wave

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just like the one behind me.

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What we want to do here is
be more quantitative and more

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precise in the
definitions, and also

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look at different
sorts of waves.

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I find this Wikipedia article
here quite interesting.

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It starts with saying
that, in physics, a wave is

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an oscillation accompanied
by the transfer of energy

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that travels through
space or mass.

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It continues then talking about
the various types of waves,

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and it makes a distinction
between mechanical waves, which

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travels through a
medium or substance,

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and the deformation
of the substance

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is reversed by restoring force.

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In contrast, there's
electromagnetic waves,

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which we have just seen
in the previous section.

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They do not require
a medium, and that

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is topic of the next section
as we continue the discussion

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of special relativity.

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Here, the electromagnetic
waves consist

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of an oscillation of
electrical and magnetic fields,

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which are generated
through charged particles.

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Things that don't
require a medium,

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they can travel
through a vacuum,

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but an electromagnetic
wave can also

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travel through a
medium like water

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or anything else
you come up with.

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It doesn't stop there really,
because the concept of waves

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are really everywhere
in physics.

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Specifically, when
you start studying

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quantum mechanics and the
behavior of particles,

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those are described by waves.

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Really exciting
recent results are

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those of the discovery of
gravitational waves, which

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are vibrations or movement
of a gravitational field.

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Also those don't
require a medium.

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They travel through vacuum.

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When we look at waves, we can
start characterizing them,

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and one primary sort
of characterization

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is the polarization of a
wave, meaning whether or not

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the oscillation itself
happens in a transverse way

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with respect to the
direction of movement,

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or longitudinal to the
direction of movement.

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Mechanical waves can be
transverse and longitudinal,

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polarized, or have transverse
and longitudinal components.

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Electromagnetic waves in free
space are transverse only.

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So here's a picture of
a wave, sine or cosine,

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and we can start with
the characterization.

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One aspect is the amplitude.

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How big is, for
example, the water wave?

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How big is the
maximum strength of

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the electric or magnetic field?

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That's the amplitude.

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Waves propagate and
they have a velocity.

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That is a characterization.

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The length of the
wave, the wavelength,

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is another way to
characterize them.

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In physics, it's always
important to understand

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the units of the
object we discuss.

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Here, just as a
reminder, the velocity

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given in meter per second.

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The frequency of your waves.

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So how often do we find a
trough, for a wave for example,

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per second.

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The frequency 1 over second.

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The wavelength is in meters.

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We can continue with
the characterization

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and be a little
bit more complete.

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We can start from the
medium, the period,

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the polarization, transverse and
longitudinal, the wavelength,

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frequency, velocity,
or even how much energy

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is being carried by the wave.

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When we compare waves and
look at their properties,

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we have to consider
the phase of the waves.

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So where do, for example,
two waves line up,

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the difference in phase
between two waves,

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and some waves can interfere.

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So if you have two
waves which interfere

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and they are out of phase, like
the one drawn in this picture,

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the resulting wave
has amplitude 0.

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This is called
destructive interference.

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You can have constructive
interference.

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For example, when those
two waves are aligned,

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there's no phase difference,
and then the amplitudes

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you simply add.

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The situation can
be more complicated.

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When we study the
speed of a wave,

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there are a number
of considerations.

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The first one is that
the speed of a wave

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depends on the medium
in which it travels.

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And the study of the
speed or the velocity

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dependent on the
medium is part of what

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we will discuss in
the discussion of

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whether or not there is a
medium responsible for carrying

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electromagnetic waves.

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The source.

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So for electromagnetic waves,
you have a charged particle.

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Does the speed of the source
change the speed of the wave?

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The answer is no.

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It changes the wavelength
or the frequency,

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but the velocity is not changed,
and you find this, for example,

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in sound waves in
the Doppler effect.

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When you listen to
a police car, you

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hear that the frequency changes
depending on whether or not

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the police car is coming towards
you or driving away from you.

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That is called the
Doppler effect.

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That does not change the
velocity of sounds in air.

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That's independent.

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When your medium is moving,
that changes the velocity,

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and so here you have to add
the velocities of the medium.

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So for light, as
a summary, light

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is an electromagnetic
wave which is

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moving in vacuum with
speed C, and that

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is independent of the source.

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But you can ask, in which frame.

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In which frame is that the
velocity of light, and what

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is the medium, and that
is really the discussion

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we want to carry on from here.

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At the time, when Einstein
developed special relativity,

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there was still a discussion
going on whether or not

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electromagnetic waves are
of the nature of a particle

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or of the nature of a wave
and whether or not that

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wave moves in a medium,
which was called ether.

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So we can then experimentally
determine this.

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We can look at various
properties of our waves

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and ask whether or not this is
consistent with the hypothesis

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that this is a particle,
this is a wave in ether,

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maybe both, maybe neither.

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And we can then fill
a table like this one

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here and answer the question.

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So this is, again,
an opportunity

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for you to stop the video
and think through this

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and try to answer the
individual questions.

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I do this here for you.

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One characteristic of
light, at least when

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there is no heavy
masses involved,

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is that it travels
in a straight line.

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That is certainly consistent
with light being a particle,

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but it's also consistent
with it being a wave.

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So the answer is
both are correct.

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Interference and
diffraction pattern.

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That's rather difficult to
describe for a particle model,

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but waves, as we just
saw, can interfere,

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and there can be diffraction.

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Polarization.

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What does it mean for a
particle to be polarized,

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but waves can be polarized.

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We have just seen transverse
and longitudinal polarization.

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Light velocity depend
on the velocity

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of the source velocity.

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For particles, it
doesn't seem to hold.

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For waves, this does.

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And then, the last,
is the speed of light

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greater in air than in water.

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That's true for a wave.

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For particles, you
might argue this one,

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but I put a no in
this table here,

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which means that in our
discussion up to this point,

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clearly the hypothesis of a
wave for light and ether holds.

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You'll see in the next sections
that there is aspects of light

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where the discussion will not
hold like this, especially

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for the ether hypothesis.