Video Transcript
We may have heard the fact that our
universe is expanding, that too, at an ever-accelerating rate. In other words, our universe is
getting bigger faster and faster. But the question is, how do we know
this. What evidence do we have regarding
this fact? In this video, we will be learning
about redshift. But in order to do this, we first
need to learn about absorption spectra.
One way that we measure the
chemical compositions of distant stars, as well as distant galaxies, is by
collecting the light coming from them and passing it through a prism. This way, the light from the star,
initially white, ends up splitting into all the colours of the rainbow. Now, in this particular spectrum,
we can see the longer wavelengths down the right end and the shorter wavelengths
down the left end. Where, of course, we use the Greek
letter 𝜆 to represent the wavelength of light.
Now, interestingly, in this
spectrum of light that we’ve gathered from the star, we don’t see a complete
spectrum. In fact, we can see some black
bands here, here, here, and here in this diagram. These bands are caused because even
though the star itself emits white light, or in other words, all possible
wavelengths of visible light, there are certain chemicals in the star itself, for
example in the atmosphere of the star, that absorb very specific wavelengths of
light. So, even though the star is
emitting white light, some wavelengths of light get absorbed, and so they don’t
reach us at Earth. Therefore, at the positions of
those wavelengths of light, we see black bands.
So, we said that there are
chemicals in this star that absorb some light. Now, these chemicals are most
commonly just hydrogen gas or helium gas. But there are other possible
elements that the star could contain that would absorb different kinds of light. But interestingly, each element has
its own signature in terms of what wavelength of light it absorbs. And so, based on this fact, if we
can work out which wavelengths of light each element absorbs, then we can look at
the spectrum coming from a star or from a galaxy and work out what elements are
present in that star or galaxy.
Now, this is all well and good
theoretically speaking, but practically, it gets a little bit more complicated. It turns out that when we conduct
experiments in a laboratory to try and figure out which wavelengths of light a
particular element absorbs. So, let’s say, for argument’s sake,
we took a sample of hydrogen and we found that hydrogen absorbed these particular
wavelengths of light. Now, we’re not saying that this is
necessarily the absorption spectrum of hydrogen, but we’re saying, for argument’s
sake, let’s imagine that it was. So, if we figure out in the
laboratory that these are the wavelengths that hydrogen absorbs, then that means
that if we see black lines in the spectrum from a star or a galaxy at these
particular positions, then we can be confident that the star or galaxy in question
contains hydrogen.
However, in many cases, what we end
up seeing is that in the spectrum from the star or the galaxy, we see the same
pattern of black lines in the spectrum but that each spectral line has been shifted
towards the right side of this diagram, or towards the red end of the spectrum. In other words, towards a longer
wavelength. Now, this phenomenon, this shifting
of the spectral lines, is known as redshift because each spectral line has shifted
to the red end of the spectrum.
What this means in practice is that
the hydrogen in our laboratory on Earth absorbs this particular wavelength for
example and the hydrogen in the star or the galaxy absorbs the same wavelength but
then all of the light gets redshifted, shifted towards the right, as it comes
towards Earth. And the spectral lines get shifted
too. Because, remember, longer
wavelengths are to the right of this diagram and shorter wavelengths are to the
left. And this is true for each one of
the spectral lines. Each one of them is redshifted.
So, why does redshift occur? Well, to answer this question, we
first need to think about how we’re actually gathering the light from the distant
star in this case. So, let’s say we’ve got the distant
star here and we’ve got the Earth here with all its scientists and all its
telescopes and all its cameras. So, we know that the star emits
white light in all directions. And we know that this is a
combination of all wavelengths of visible light. For simplicity, though we’re just
going to be thinking about one of these wavelengths that the star emits.
So, let specifically think right
down the middle of the spectrum. Let’s think about some of the green
light that the star emits. And we’re specifically thinking
about the light emitted in the direction of the Earth. Now, of course, we have to note
that these wavelengths and star sizes and Earth sizes are not drawn to scale
here. But anyway, so, we see that the
distant star is emitting green light towards the Earth, as well as all of the
wavelengths of light. But like we said earlier, we’re
only focusing on the green light here.
Now, if the star is not moving
relative to the Earth, then the Earth would just pick up green wavelength light
coming towards it. Now, to make our next point more
clearly, what we’re going to do is to draw our diagram from this perspective. Imagine placing our eyeball
here. And additionally, if we imagine
some more of the green light being emitted in another direction, then what we’re
going to do is to label all the peaks of the light emitted by the star with a
line. And so, what we’re going to see are
concentric circles around the star where each circle is an outward spreading peak of
green light. So, let’s do that. Let’s modify our diagram now.
So, here’s what the diagram looks
like once we’ve shifted our perspective. Looks pretty similar but we’re
looking at it from above now, remember. And as well as this, we said that
we would label every peak of green light coming from the star with a line. And these lines form concentric
circles, or more accurately concentric spheres. Because, remember, the star emits
light in all directions.
But anyway, so, let’s now imagine
that the time it takes for one peak of the green light to move to where the next
peak is, because, remember, this light is spreading outwards, let’s say that this
time is one second. So, what we’re actually saying is
that the period of this light is one second. Now, of course, the period of green
light is not actually one second, but we’re just saying that for argument’s sake
here, just to make our numbers simpler and our life easier.
So, what we’re actually saying,
once again to recap, is that our green light is spreading outwards at a rate of one
peak per second, or one complete cycle of green light per second. Now, if we just think about the
light moving towards the Earth, then what this means in practice is that if the star
is not moving relative to the Earth, then the Earth will receive one peak every
second. In other words, at this point in
time, the Earth is receiving this peak. One second later, it will receive
this peak. Two seconds later, it will receive
this peak, and so on and so forth.
And so, that’s all well and
good. The star is emitting green light at
a rate of one cycle per second and the Earth is receiving green light at a rate of
one cycle per second. However, let’s now imagine what
would happen if the star is moving away from Earth. So, at this point in time, the star
emits green light outwards. And then, we can imagine what would
happen one second later. We can imagine that the green light
that we just saw being emitted spreads outward about the point at which the star was
centred when that light was emitted. But then, at this point the star
itself has moved slightly. The new centre of the star is
here. Because, remember, we’re saying
that the star is now moving away from Earth.
And so, at this point, the star
emits a peak of light again. Because, remember, it’s one second
later. But this time the light emitted is
centred about the current centre of the star. And so, now, we can think about
what happens one second after this point in time. The original peak of light that we
saw being emitted is still going to spread outwards. And it’s going to continue
spreading outwards about the centre of the star when the light was emitted. And the same is true for this peak
of light. It’s going to spread outwards but
about the centre of the star when the light was emitted. So, one second later the star’s
centre has shifted yet again. And in fact, the whole star itself
has shifted. And it emits light at this point
again.
So, what we’re now seeing is not a
pattern of concentric circles with their centres aligned, but rather each circle
representing the peak of light emitted is centred about the point at which the star
was when that light wave was emitted. And in practice, what this means is
that the distance between peaks on the left-hand side of the star as we’ve drawn it
is much shorter than before.
If there was an observer standing
here, then they would receive a peak of light at a time interval shorter than one
second. In other words, they might receive
a peak of light every half a second, say. Whereas any observer on this side
of the star, such as for example our Earth, will receive a peak of light at a time
interval of greater than one second. In other words, it will be more
than one second between when the Earth receives this peak and when it receives this
peak. And that is all due to the motion
of the star away from Earth.
Now, up until this point, we’ve
been drawing these peaks as green to represent green light. Because we said earlier that green
light was equivalent to one cycle of light every second, just for argument’s
sake. However, from the point of view of
the observer, such as the Earth, we’re receiving one cycle of light at a time
interval of more than one second. And as we can visibly see, the
distance between two peaks, which in other words is the wavelength of this light,
has increased. There is a larger gap between
peaks, and so the wavelength is larger.
And this means that we will no
longer receive this light as green light. We might receive it as a
long-wavelength light such as yellow light for example, or even red light if this
shift in wavelength is extreme. And so, that is why redshift
occurs. It occurs when there’s relative
motion between the source of light, in this case the star, and the receiver of
light, in this case the Earth. Redshift specifically occurs when
the source is moving away from the receiver or the receiver is moving away from the
source.
The flip side of this is that if we
had an observer on the other side such that the star, or the source of light, was
moving towards the observer, then the wavelength of light shrinks. And this is known as blueshift. In other words, then, if a source
of light is either moving towards you or you are moving towards the source, then the
light you receive will be blueshifted. Whereas if the relative motion
between the source and the observer is that they are moving away from each other,
then the light you receive will be redshifted.
And interestingly, from comparing
these two diagrams, we can even see that if the source is moving relatively slowly,
then the change in wavelength is not massive. Whereas if the source is moving
really quickly, in other words covering a large distance per unit time, then the
shift in wavelength is large. In other words, then, the faster
the source is moving away from the observer, the larger the redshift.
Now, as it turns out, when we look
at most of the galaxies in the sky, we see that the light coming from them is
redshifted. In other words, we find the
spectrum of light coming from them, and we realise that, for example, a certain
galaxy might contain the same pattern of absorption lines as hydrogen’s absorption
spectrum, but that each of these spectral lines have been shifted to the red end of
the spectrum.
And we see that this is true for
the majority of galaxies that we look in in our universe. Only a very small proportion of
galaxies are blueshifted. So, what this is telling us is that
the majority of galaxies in our universe are moving away from us. And what’s even more interesting is
that the galaxies that are further away from us are moving away from us even
faster. Because the light from the further
galaxies is redshifted more.
Now, Earth is not in a special
position. It’s not like everything is moving
away from us specifically. It turns out that all galaxies are
moving away from each other. But because we are on Earth, it
seems like everything is moving away from us specifically. But anyway, so, all galaxies are
moving away from each other on average. And what’s more is that further
galaxies are moving away from us faster than nearer galaxies. And so, what this tells us is that
the universe is expanding. This must be true because all
galaxies seem to be moving away from Earth as well as away from each other. And so, the universe is getting
bigger.
But more interestingly, like we
said earlier, further galaxies are moving away faster than nearer galaxies. And this means that the expansion
of the universe is accelerating. It’s getting faster. It seems like the larger of the
universe gets, the faster it is expanding. Now, there is actually a
mathematical relationship that we can apply here which links the speed of the source
of light to how much the light coming from it is redshifted.
The equation that we’re looking for
is this one here. This one tells us that 𝜆 subscript
source, that’s the wavelength of, let’s say, a particular spectral line in the
spectrum of light coming from a star or a galaxy. Minus 𝜆 sub Earth, which is the
wavelength of that same spectral line when taken on Earth, or in other words when
stationary relative to the observer. Divided by that same value of 𝜆
Earth. Is equal to 𝑉 divided by 𝐶, where
𝑉 is the speed at which the source, let’s say a star or a galaxy, is moving away
from the observer, which usually is the Earth. And 𝐶 is the speed of light.
So, in practice, then, let’s say
that this is the spectrum for hydrogen taken on Earth because this means that the
hydrogen is stationary relative to the observer. And we see the same spectral lines,
the spectral lines for hydrogen, in the spectrum from a distant star. So, we know that this distance star
must contain hydrogen, but we see that each one of these spectral lines is
redshifted.
Based on this redshift, we can
figure out the velocity at which the star is moving away from Earth. And to do this, we find 𝜆
subscript source for a particular spectral line, for example, minus 𝜆 subscript
Earth, the wavelength of that same spectral line when taken in a spectrum stationary
relative to the observer. Divided by that same value of 𝜆
sub Earth. And when we find that fraction, it
is equal to 𝑉, the speed at which the source is moving away from the observer,
divided by 𝐶, the speed of light. So, now that if we’ve understood
what redshift is and taken a look at this equation here, let’s attempt an example
question.
An astronomer looks at the
absorption lines in the spectrum of light coming from a distant galaxy. He identifies the absorption lines
of hydrogen, which makes up most of the galaxy. He then compares these lines to the
same absorption lines from a laboratory sample. His results are shown in the
diagram. How is the galaxy moving in
relation to Earth?
Okay, so, what we’ve been told in
this question is that the scientist has two spectra to compare. One is an absorption spectrum taken
from a sample of hydrogen in the laboratory. And the other is the spectrum taken
from a distant galaxy. Now, we’ve been told that the
astronomer identifies the absorption lines of hydrogen in the spectrum from the
distant galaxy. And we can see that this is true
because these are the absorption lines of hydrogen as seen in the laboratory. And we see the same pattern of
absorption lines in the spectrum from the galaxy, except that each spectral line has
been shifted towards the right slightly, or towards the red end of the spectrum.
In other words, then, the
wavelength of each hydrogen spectral line in the spectrum from the galaxy is longer
than the wavelength of that same spectral line in the spectrum from the hydrogen
taken in the laboratory. Now, let’s recall that the reason
for this is that in the laboratory, of course, the hydrogen is not moving relative
to the Earth. And so, we find a particular set of
wavelengths that represent the spectral lines of hydrogen. However, in the spectrum from the
galaxy, each spectral line is shifted in wavelength because the galaxy is moving
relative to Earth.
And we can recall that if this here
is the Earth, and this here is the distant galaxy, and if the Earth and the galaxy
are not moving relative to each other, then the light emitted by the galaxy will be
received by Earth with the same time period, or in other words, the same amount of
time between peaks, as when the light was emitted by the galaxy itself. But if we’ve got the Earth here,
and we’ve got the galaxy initially here, and the galaxy is moving away from Earth,
then we can see that as the galaxy moves away, the wavelength of light received by
Earth will be longer than if the galaxy was stationary relative to Earth.
And that’s exactly what we’re
seeing in the two spectra. Each spectral line is shifted to
the red end of the spectrum towards the right. And so, the wavelength of each
spectral line has increased. The reason for this is because the
light has been redshifted. And this occurs because the galaxy
is moving away from Earth. And therefore, the light reaching
Earth has a stretched wavelength. And hence, we’ve found the answer
to our question. We can say that the galaxy is
moving away from Earth.
Okay, so, now that we’ve had a look
at an example question, let’s summarise what we’ve talked about in this lesson. We firstly saw that redshift is the
shifting of light to the red end of the spectrum, or towards longer wavelengths,
when the source of light is moving away from the observer. Or, of course, when the observer is
moving away from the source. Basically, the relative motion
between the two must be that they are moving apart from each other.
Next, we saw that there’s an
equation which links the amount of redshift, represented by this fraction on the
left-hand side, to the velocity at which the source of light is moving away from the
observer. And we saw that 𝜆 subscript source
represents the wavelength of, for example, a spectral line in the spectrum of light
from the source. And 𝜆 subscript observer is the
wavelength of that same spectral line in a spectrum taken from something that was
stationary relative to the observer.
However, it doesn’t have to apply
to spectral lines. If we know, for example, that a
specific wavelength of light in a stationary source is shifted to another wavelength
in a moving source, then we can still calculate the velocity of the source relative
to the observer using this equation. Where, of course, 𝐶 is the speed
of light.
And finally, we saw that redshift
provided the first real evidence for the expansion of the universe. This is because we observe that
light coming from almost all galaxies was redshifted. And this suggested that all of
those galaxies were moving away from us, but also away from each other. And therefore, the universe is
expanding. And even more interestingly, it
seems like the further galaxies are from us, the faster they are moving away from
us. And this means that the expansion
of the universe is accelerating. In other words, the larger the
universe gets, the faster it expands.