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Language: en
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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 redshifted
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 I'll
represent them with a 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 1G 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 Edge 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 a
mission 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
photons 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
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the misconception is to think that
because photons are redshifted 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 know because your body is held
together by electromagnetic forces but
what if we could turn off the
electromagnetic force 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
redshifting 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
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