# Universal Misconceptions #3: Redshifts

We’re talking, once again, about common questions and misconceptions about the expanding universe. If you haven’t already done so, take a look at my posts on the fact that time isn’t expanding and the fact the there’s no center to the expansion.

Today I’d like to talk about redshift. In the 1920’s, Edwin Hubble noticed that the more distant a galaxy was from our own, the more the spectral lines of that galaxy were redshifted. All this means is that rather than measure a spectral feature at, say, a wavelength of 600nm, you might measure it at 620nm. Within a particular galaxy, every single line was shifted by the same fractional amount:
$zequiv frac{Delta lambda}{lambda}$
with $z$ called the “redshift”, $lambda$ is the wavelength that the light should have under laboratory conditions, and $Delta lambda$ is the difference in observed wavelength from the laboratory wavelength. Hubble found that for relatively nearby galaxies, redshift and distance are just linearly proportional to one another. Further away, the relationship gets a bit more complicated mathematically, in part because there are so many possible types of distance.

Under normal conditions, we usually think of redshifts as being caused by the relative motion of the body emitting the photon and the body absorbing it: a Doppler shift. This, incidentally, is how radar detectors work in speed traps, or, using sound waves, why you hear a shift in pitch when a firetruck passes by. One of the most common ideas, and one that even shows up in some introductory physics classes, is that the light from distant galaxies is caused by a Doppler shift. It’s not*.

What’s really going on is that as a photon travels from the source to our telescopes on earth, the universe expands underneath it. If the universe doubles in size, so does the wavelength of the photon.

Here’s the balloon analogy to help makes things clearer:

In other words, what redshift really tells us is not how “fast” a galaxy is moving away from us, but rather, how big the universe is now compared to how big it was when the light was emitted. This picture has a number of implications:

1. Photons lose energy as they travel over cosmological distances. For light, long wavelength means low energy. Consider the light coming to us from the cosmic microwave background. It originates (around 380,000 years after the big bang) at a temperature of about 3000K, comparable to the surface of a relatively cool star. After subsequent expansion of the universe by a factor of 1200 or so, the temperature is now only about 2.7K.

Since photons lose energy as the universe expands, but massive particles don’t lose mass, at some point in the past, there was more energy in the form of photons than in ordinary and dark matter combined. This was back at a redshift of z=3900 — when the universe was about 1/3900th the size it is now.

2. A redshift doesn’t tell you anything about the expansion right now. For a distant galaxy, you only learn about the relative size of the universe when the photon was emitted to today. The universe could be accelerating or decelerating or even stopped at this moment, and you don’t get that directly form the redshift. What you need are lots of redshifts in order to figure out the history of the expansion, and thus the rate of change.
3. If light travels through a bunch of hydrogen clouds on the way from a distant galaxy to us, the galaxy and each of the clouds will each be at a different redshift. The galaxy will be most redshifted (since it is most distant), and so on. The clouds will then absorb only the particular wavelengths of light that correspond to spectral lines. However, since for each cloud there’s a different redshift, this creates a “forest” of absorption:

I sometimes get followup questions about how we know that the redshift really does correspond to cosmological expansion.

That’s a fair question. Here is a partial list of things which are 100% consistent with the view of cosmological redshifts, but would have to be utterly discarded if it were wrong:

• General relativity (since GR predicts a dynamically expanding or contracting universe)
• Gravitational lensing
• Distance estimates from nearby galaxies
• Any and all interpretation of the Cosmic Microwave Background
• The Big Bang model

But let’s suppose you’re one of those people who never liked the Big Bang model anyway and think you’re being subversive by challenging it. (You’re not, by the way.) Before throwing out a model that matches theory and observation perfectly, you’re required to come up with a model that does at least as well.

Good luck with that.

-Dave

* Well, technically it is, but only a little bit. Throughout this series of posts, I’ve been ignoring something called “peculiar motion.” Galaxies really do move around their local environment, but at a speed of only a few hundred kilometers per second. The peculiar motion causes a Doppler shift on top of the cosmological redshift.

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### 9 Responses to Universal Misconceptions #3: Redshifts

1. Tereasa Brainerd says:

So, Dave, when the photons lose energy as the universe expands, where does that energy go?

• dave says:

But for those of you who WEREN’T my cosmology professor/senior research adviser, the answer is that radiation has pressure, which means that it does work as the universe expands. That work has to come from somewhere, and it comes from the internal energy of the photon fluid.

This is the PdV contribution to internal energy.

Note that this is the opposite of what happens with dark energy, which has a negative pressure (tension). In that case, even though you might expect the dark energy to get more diffuse, the extra work done on the dark energy is positive, keeping the overall density of the stuff positive while the universe expands. It also accelerates the expansion.

2. Tereasa Brainerd says:

Well done! You’re doing a great job here. Not to mention I really enjoy being able to say that I knew “way back when”.

• dave says:

Hurray! I passed!

3. Hasanito says:

This could be a silly point but, the figure for the balloon analogy above, seems to show the wavelength to be the same from smaller universe to the larger ones. But you also saying that “if universe doubles in size, so the wavelength”.
The wavelength does seem to get larger but still the same wavelength!

• dave says:

How so? The wavelength scales up with the universe. It stays the same in “comoving length” (based on the gridlines on the balloon), but gets longer in “proper length” (which is what you’d measure using a ruler).

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5. Li Kong says:

The following are the explanations why the discovery of Edwin Hubble does not provide a good evidence that our universe would be expanding currently:

a)Despite many red shifts through telescope from astronomers, it does not provide the proof that this universe could be expanding for the following reasons:

1) The possibility that our universe could be very huge that it would take more than trillion of years to reach the opposite end of the unverse (sphere). The assumption is based upon the following factors: This universe is assumed to be as a shape of sphere with external boundary and all galaxies are assumed to move within the boundary of this universe.

Let’s imagine you stand at one end of the sphere (the universe) to have a full view of all the surrounding movement of galaxies. As all the galaxies were advancing at a high speed from your end to the edge of the sphere that is right opposite from you that form a half complete round, you certainly would visualize that all the galaxies are advancing as if that they are leaving away from you since their movement in speed is a few time faster than your galaxy. As this universe is very huge so much so that it would take a very long time, let’s say, more than a trillion years to reach the point that is right opposite to the point so as to make a half complete turn of this universe. Despite many galaxies have been moving towards the point that is right opposite to the point where you are viewing through telescope, the result would turn up to be many red shifts to have appeared in the universe. As universe is too huge for galaxies to travel from one end to another and only a few have completed a half turn to move than to the starting point of the sphere where you are to the edge of the sphere that is right opposite from you, it turns up that they are many red shifts than blue shifts.

2) The second possibility is that many galaxies might have advanced faster than us and yet many galaxies might have made a complete half turn within the sphere (the universe) and yet the galaxies might not as what we think that they would keep on rotating themselves in a circle. Instead, they might not return to the previous track where they have passed through. These could result that they do not turn back to us.

3) The third possibility is that all the clusters of galaxies could be advancing in the same place and same direction just that most of the galaxies are advancing faster than us as if that their galaxies are moving further away from us. As we are in this tiny world and cannot have the full sight of this universe, we could not reject this possibility since it might be so without our full view of this universe since the astronomers just looked at the sky with a telescope that comes to their conclusion without viewing the universe as a whole. No matter how advance is the technology, it could never be possible to build an advice that could capture the whole view of universe from one end (the earth).

4) The fourth possibility is that majoirty of the galaxies might have made a full complete turn in this universe within the boundary of the universe in many years ago, such as, more than a few thousand years ago. Or in other words, there might be a time in the past in which there were many blue shifts than red. What the astonomers that have seen right now with many red shifts do not reflect the universe might be expanding since there might be a period of times in many years ago that almost all the galaxies have made a complete full turn and it turns up that many galaxies have turned up to be red shifts currently. Or in other words, it would take many years later, such as more than a few thousand years later, in order to have many blue shifts instead of red shifts at that time.

5) The fifth possibility is that universe was created in infinity and that all galaxies are advancing ever since the past. If that is so, it is erroneous to use many red shifts as discovered by astronomers to conclude that the universe is expanding.

There might be other possibilities that you could think of why there are more red shifts than blue shifts and yet it does not come to the conclusion that the universe is expanding. As there are many alternative possibilities, to jump into conclusion that the universe is expanding through many red shifts being discovered is rather a little speculation.

• dave says:

@Li, It’s more than simply a matter of saying “galaxies are redshifted and therefore the universe is expanding.” The relationship between redshift, angular diameter distance (how big objects appear as they get more distant) and luminosity distance (how bright things appear when they get more distant) is a fairly detailed prediction of general relativity. The latter, luminosity distance as a function of redshift, is directly probed by, for example, supernova data. The former (angular diameter distance) is probed by measurements of the cosmic microwave background.

While one could, I suppose, suggest some sort of local bubble or somesuch based on Hubble’s original observations, you certainly can’t do so now. The relationship between prediction and observation is far too precise.