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[Music]
the first piece of evidence that showed
our universe is expanding
came in the light from distant galaxies
if you look at the spectrum of the sun
you see these dark lines and we see
those same lines
in the spectra from galaxies except
they're shifted
to longer wavelengths towards the red
end of the spectrum
so we say their light is red-shifted
now the usual explanation for this
redshift is that as the light is
traveling through expanding space
the photons themselves become stretched
so short wavelengths get longer and this
is known as cosmological redshift the
explanation is fairly intuitively
satisfying and most people go on without
giving it a second thought
but the problem is if you do give it a
second thought you think
well if expanding space can stretch
something like a photon something that's
so incredibly tiny does it also stretch
atoms and molecules is expanding
space stretching stars and galaxies
and what about you are you expanding
with the universe
to answer these questions we've got to
take a closer look at what it really
means to
redshift physicists actually talk about
three different types of redshift
doppler redshift where observers moving
relative to one another
measure photons to have different
wavelengths gravitational redshift where
observers at different locations in a
gravitational field
measure different wavelengths and
cosmological redshift where observers
exchanging photons over
vast cosmological distances in an
expanding universe
measure different wavelengths these
three cases
appear very different and they're
governed by different equations
so how does each redshift actually occur
let's start with a photon in a
gravitational field
there is this famous experiment
conducted in 1959 by pound and rebka
sending photons up and down a 22 meter
tower at harvard
now they used gamma rays but all
represent them with visible light
they found that photons detected at the
top of the tower
were redshifted relative to the source
by the exact amount
predicted by general relativity which
is a tiny amount i'm dramatically
exaggerating the effect just so you can
see it
now where along the photons path does
this redshift take place
well it seems to happen continuously the
photon loses
a little bit of energy each millimeter
it climbs
up that tower meaning that the photon in
the middle of the tower
would appear green now according to
einstein's equivalence principle
being at rest on earth's surface is
indistinguishable from being
in a rocket in deep space accelerating
up at one
g so we could do the same experiment
in a rocket ship and we should get the
same result
if we send blue photons from the back of
the rocket
they should be red when they reach the
front and in the middle of the ship they
would appear
green this is exactly what we saw at
rest in a gravitational field so
the equivalence principle holds now
imagine
there are a line of external observers
just
hanging out in space at rest relative to
each other
and they can all see into the rocket
let's also say the rocket is initially
at rest
and the thrusters are switched on the
instant the photon
is released now since both observers are
at rest at this moment
they will both measure the photon as
having the exact same wavelength
it's blue but what about when the photon
reaches the middle of the rocket
well we know someone inside will see it
as green
but what about a stationary observer
outside
well to them the photon has just been
moving through ordinary flat
space-time so it must look blue
just as blue as it was when it was
emitted
so what's the deal how can the same
photon
look green and blue at the same time
has the equivalence principle been
violated the answer
is no it matters a lot to this
measurement
who is doing the observation consider
this
after the photon is emitted the rocket
accelerates it's
speeding up so by the time the photon
reaches the middle of the rocket
everyone inside is now moving at high
velocity
relative to the source when the light
was emitted and relative to the
observers outside the rocket
so it makes sense that the photon as
measured inside will look different
it'll be
redshifted this is the doppler redshift
because
the observer in the middle of the ship
is moving very quickly away from the
source
by the time the photon makes it to the
top of the rocket well the rocket will
be going even
faster and this is why it appears red
but to a stationary observer outside
well it still
looks blue this thought experiment
shows us that wavelength and energy are
not intrinsic properties
of photons they are properties of the
photon observer system
now let's recreate the harvard tower
experiment
observers in the building see the photon
redshifted as it climbs
but here's a question for you what would
a free-falling observer
see well they would be just like
the stationary observers in space
watching the rocket accelerate up
the physics of these two situations are
identical so
they would measure no redshift to them
the photon would look blue the whole
time
what i want to show is that there aren't
actually three different types of
redshifts there is
only one we've seen that the
gravitational redshift can
equivalently be seen as a doppler red
shift when we do the same analysis
in an accelerating rocket ship so what
about
cosmological redshift well for this we
have to zoom
way out past our solar system
the milky way galaxy our local cluster
of galaxies
we want to zoom so far out that the
galaxies in the observable universe
are like molecules in a fluid the
cosmic fluid at this scale we can treat
the whole universe as being
smooth and uniform cosmologists say it
is homogeneous
and just as you don't notice the
individual molecules in a cup of water
at this scale we don't notice the
individual galaxies in the cosmic fluid
and the cosmic fluid looks the same in
every direction
there is no preferred orientation it's
said to be
isotropic now what you'll notice is that
the cosmic fluid is
spreading out it doesn't matter where
you look
you see the same thing things moving
apart
the density of the cosmic fluid is
decreasing
over time and this is the basic property
of an expanding universe
we can draw some coordinates on the
universe we could pick
any different coordinate system we like
but one way it's often done
is to make a coordinate system that
expands with the cosmic fluid
so there will be certain observers whose
coordinates
don't change over time and these are
known as
co-moving observers they are at rest
with respect to the cosmic fluid
by the way on earth we are not a
co-moving observer our galaxy is moving
at 600 kilometers per second
relative to the cosmic microwave
background radiation
now let's pick two co-moving observers a
large distance apart
and have them exchange a photon its
wavelength will be stretched by the
amount the universe has expanded
during the photons journey this is the
standard picture of cosmological
redshift
but now consider a bunch of other
co-moving observers along the path of
this photon
each one absorbs the photon and
instantaneously emits another
identical to the one they measured now
each successive observer
will measure a slightly longer
wavelength than the observer before them
the photons stretching out just as you'd
expect in an expanding universe
but the reason they would give for this
redshift would be different
to each observer their neighboring
co-moving observers
would appear to be moving away from them
in locally flat space time
so they would attribute the increase in
wavelength to the doppler shift
just due to the relative motion between
them the
entirety of the cosmological redshift
then
can equivalently be thought of as the
result of a long
series of doppler shifts
what we've seen is redshifting is not
something that happens to a photon
itself instead it depends on what's
happening to observers at the point of
emission
and absorption of that photon and
because of this
there are actually not three different
types of redshift there's only one
described by a single underlying
mathematical framework
they only look different depending on
your frame of reference
now it can be convenient to talk about
expanding space when you have
two co-moving observers exchanging a
photon over vast distances in
an expanding universe then the photon's
wavelength is just
stretched by the amount the universe
expanded during its journey
that's nice and simple but you can
equally well describe the redshift by
a long chain of doppler shifts no
expanding space required
[Music]
the misconception is to think that
because photons are red-shifted as they
travel across the universe
that means expanding space is pulling on
things
and stretching things apart that's not
how it works space
is not like that so let's come back to
the central question of this video which
is
do you expand with the universe the
answer
is no because on the scale of people
the universe is not homogeneous i mean
matter is condensed down into objects in
the earth
and the universe is not isotropic
looking up looks decidedly different
from
looking down the basic assumptions we
made
about our expanding universe just don't
apply here
i mean the local space-time curvature is
dominated by
the earth so what if we took you out
into deep space
the middle of nowhere then would you
expand
still no because your body is held
together by
electromagnetic forces but what if we
could turn off
the electromagnetic force so your body
is just a jumble of particles that don't
interact
well in that case over time you
would expand but only because our
universe is now dominated by dark energy
so the take-home message of this video
is that red-shifting photons don't mean
that space is expanding and pulling on
everything stretching things apart
so molecules are not expanding and
neither are stars
and neither are galaxies and neither are
you
except for very extraordinary
circumstances
that tells you it's recording here we go
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