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In January 1999, Scientific American published a group of articles proclaiming a revolution in cosmology, discussing how some new astronomical observations had smashed our view of the universe. As usual in cosmology, it was obvious that something interesting was going on, but it all seemed very complicated.
I figured I knew a bit about this stuff but it took a little while to disentangle. It turned out to be both simple and surprising.
Put very briefly, some new observations didn't quite fit with existing theory. If the observations stood (and of course there was question of this), there are two ways of fixing up the theory, but whichever route you take, common sense is liable to be quite affronted!
Now, several years later, the observations seem to be generally accepted, and a consensus seems to be emerging on what to do about them. And indeed, as promised, common sense is indeed most seriously affronted!
So here is my note. I have not updated it much since I am more interested in how the obervations make us re-examine our theories than I am in the results of that re-examination. Or put another way, what makes science so interesting for me is the process whereby we know stuff, rather than what we end up knowing. And this is a classic example of that process.
It may also be worth noticing as we go that science is not based on facts, in fact there are hardly any facts available; we work mostly with observations that ony become meaningful when interpreted in the light of theory. Again, this is a classic example!
The observations in question are from a survey of a particular class of supernova events called Type IA Supernovae. The observations suggest that very distant supernovae of this type are 25% less bright than expected. Big deal? Well, as it turns out, yes!
Before we consider the implications of these observations in detail, lets prepare the ground by reviewing some of the science that will turn out to be relevent.
The Universe is expanding and Hubble's law describes how fast. It says that any two points in space are separating at a speed proportional to their distance apart.
This was a huge surprise to everyone, Einstein included, in the early part of this century. There had never been the slightest suspicion that the universe was anything but unchanging! Now this expansion is practically an assumption in today's astronomy. In the next few paragraphs I will tease out the different strands of observation and theory that underlie this widespread acceptance.
The light radiated by hot gases can be spread out by a spectrometer, just like sunlight through a prism. Different frequencies are spread to different positions in the spectrum. Each gas, because of its particular atomic structure, radiates and absorbs light at different frequencies; this results in a pattern of light and dark lines scattered over the spectrum, characteristic of each gas. These patterns can be recognised by comparison with reference patterns established in the laboratory.
At the turn of the century, this was already a well-established lab technique for analysing the components of gases.
Believing stars were gaseous, it was natural to try to apply this technique to starlight. The basic observations are done using a telescope and a spectrometer.
From the patterns of lines found in the spectrum of a star one can disentangle the principal gases the star is made of, and in what proportions. In point of fact, this is how the element helium was first detected. (And there are all sorts of other good stuff hidden these spectra: would you believe the star's surface temperature? and the rate a star spins?)
If you classify nearby stars using these characteristics, you also find it is not totally random; you find a lot of stars falling into the same groups sharing similar chemistry. So we can classify stars by spectral analysis.
At first sight there is very little physics in this, so far. It is mostly observation and comparison with observations made in the lab. But those observations, of lines in spectra, are only interesting because of the interpretation we have overlaid on them.
But improvement in recognition of individuals, whether stars or whales, usually leads to new ways of looking at data, and then to new uses of that data.
One group of stars in particular that could be recognised in this way became known as the Cepheid variable (CV) stars. The brightness of individual CV stars varies in a very regular cycle, and it was soon noticed that stars with similar periods had similar spectral characteristics. But there were a stack of variable stars whose spectra didn't fit..until it was realised that some of them had Cepheid characteristics but with the spectral lines shifted over towards the red end of the spectrum. Whatever the cause of the red shift this made a lot more stars recognisable as CV stars.
It seemed reasonable to assume that similar types of stars behaved in similar ways. and therefore, amongst other things, that similar Cepheid stars were of similar maximum brightness.
If you know how bright something really is, and you measure how bright it appears, then you can work out how distant it must be. Very very roughly!
The CV stars provided the first useful set of milestones across the universe. You find stars with the right spectral type, and measure their apparent brightness and period. From the period you get their absolute brightness and then comparing apparent and absolute brightness you deduce their distance.
For the first time some very rough maps of the universe could be made. It became clear, to general surprise, that stars were collected in galaxies and that the galaxies were seperated by vast distances.
It is typical of science that scientists are always graphing stuff. An obvious thing to graph was that red-shift against the newly available distances. Bingo, it looked like there was a relationship - the further away, the more the shift! And Hubble suggested it was linear - twice as far, twice as much red-shift. Bizarre!
Bizarre, but useful. This immediately gave a new set of standard candles, in addition to the Cepheids. You don't need variable stars, you can use any stars with a recognisable spectral type, simply by measuring their red-shift, and computing their distance from Hubble's Law. (You don't actually need to use stars of recognisable spectral characteristics, but it simplifies the task of deciding which lines are red-shifted from where)
Thus the red shift, even without an explanation, was useful in extending our techniques for measuring the universe. And no new science yet, merely observations and a useful tool. But we can see the beginnings of a question. The relation between redshift and distance, at this stage, was not much more that a fact of observation. But it was undeniably an awkward fact. Why are they related? What is the connection?
Awkward facts are surprises. Thinking about them often lead to new understanding, new theories. As we shall see.
However, frequency shifting was a phenomenon already familiar to science though in a completely unrelated field, namely acoustics. Remember about steam trains and their whistles?
The Doppler shift is a shift in frequency due to movement of source or receiver. Basically, the motion forces the usual number of signal waves into a shorter distance,and the receiver senses this as a rise in pitch.The shift is proportional to velocity, down for recession, up for approach. Twice as much shift, twice as much speed. Could there be a connection?
Suppose there is a connection. Suppose the redshift (frequency reduced) is due to the velocity of stars receding (and blueshift for stars approaching). Now we have something more than bizarre. And completely unexpected.
The suggestion is that stars are going away from us at a speed proportional to their distance from us. And twice as much distance, twice as much speed. Furthermore, if our part of space is nothing special then this implies that all stars are going away from each other.
Which is to say that the universe is expanding. And Hubble's Law tells us how fast.
Wow. No way? The universe had always been assumed to be static and unchanging. But in fact, there was nothing in science that required that assumption, nothing in science that was contradicted by the new assumption, and it was a sufficient explanation of known facts. So the idea of an expanding universe was taken seriously, disputed strenuously, revisited frequently, but survives to this day as our best explanation of those redshift observations.
Notice something we didn't really discuss above - namely that to go from apparent brightness to distance implies a law, an equation, for the propagation of light through space. We usually accept an inverse square law for this. But this is worth talking about also. As follows.
We like the inverse square law because we are taught it in school, and it is very familiar. Typically
p = k p0 / d2
where p0 is the brightness (say) at the source, p is the brightness at distance d, and k is a transmission constant of some kind.
It seems to work for heat and light and sound and gravity and indeed anything that radiates. There is a reason for that, and it has nothing to do with physics. It is in the geometry of 3 dimensional space; it even has nothing particularly to do with what is being radiated.
Think of it this way. The area of the surface of a sphere is 4 π r2. Suppose P is the amount of energy that leaves a source at the centre of a sphere. If it radiates evenly in all directions, then the amount of energy per unit area at the surface of a sphere of radius r is P/ (4 π r2). Which is exactly the inverse square law.
Okay? Well, maybe.
That equation for the surface of a sphere. To deduce the formula you use Euclidean geometry. And in particular the Pythagorean theorem about right angled triangles.
There are also, at least conceptually, non-Euclidean spaces,
Non Euclidean? Really? Not easy to think about. The maths handles it very easily and I think future generations will have no more trouble with these ideas than we did with Newton's Laws (which were themselves counter intuitive at the time!) But we can take a few steps.
If you live on a flat plane, and draw a circle and measure the radius and circumference, you get C=2 π R. Of course.
But we live on the surface of the Earth. If you do the same thing on a globe, measure a radius and draw a circle, you will find the circumference is less than expected. This is because the radii are curved and the inner part of the circle does not lie in the plane containing its rim. It's like a dish. Easy to visualise?
Ok, but space could be curved in such a way that you get the effect in three dimensions, where it is now the surface of a sphere which is unexpectedly smaller than you expect. I can almost visualise that, but anyway it seems a logical extension of the idea. Such a space is said to have positive curvature and Pythagorean theorem doesn't work.
The consequences are fun. Because the surface area is smaller than expected, light will be brighter than you would expect from a simple square law; brightness will not fall off with distance as fast as you expect.
Now, imagine doing the same thing on a surface shaped like a saddle. Sit in a saddle and on each side it curves down, while front and back it curves up. You also get this shape between hills that are close together. With the radius a constant length in the surface, draw a circle. In this case the circumference is bigger than the radius suggests. Think of a flat disc and then hammer the outer parts of it until they are thinner than the inner parts. The disc will not sit flat anymore. But it will on a saddle. Most potato chips end up something like this. I can visualise this ok. But in three dimensions, I can't even begin. The maths can handle it though. Such a space is said to have negative curvature. Our flat Euclid space has zero curvature.
Again, we may not be able to visualise it, but we can understand the consequences. Now the surface of a sphere is bigger than the radius suggests, and brightness will fall off faster than an inverse square law.
Notice that there is nothing observationally to deny a non-Euclidean space, one with non-zero curvature. Locally, space can be indistinguishably close to flat - with the effects of curved space only showing at very large scale.
But considerations like the above are disconcerting in science. They suggest that a flat space is really a very special case indeed, that a space has curvature that is neither positive or negative but exactly zero. Zero values are especially provocative in science, one wants to know why. For a positive or a negative curvature one would want to know why it was positive or negative, but the particular value would be of less interest; one a little bigger or a little smaller would be equally acceptable. But a zero value?
How could we ever tell? Locally hereabouts every test that is made shows space is very, very flat. Whatever circle and radius you measure, the value of π comes out exactly as expected. But to do a test over huge regions of space doesn't sound possible. There is no way to measure the circumference of a circle with a radius measured in light years. Is there?
Well yes amazingly enough, there is! For example, suppose you have a recognisable type of star with lots of examples in local galaxies that always have the same absolute brightness. A standard candle as mentioned earlier. Suppose also that you can find your candle in a far distant galaxy. The red shift gives you the distance, the distance and apparent brightness give you the absolute brightness. Is this the same as the absolute brightness for your local examples? If so, over that scale of distance, space is still flat. If not, something has to give. Either the Hubble distance is wrong, or the inverse square law is wrong.
Turns out that for the furthest away galaxies in which we can still resolve individual stars, (which really isn't very far in astronomical terms) space is flat. We need a new brighter standard candle that is visible over much larger distances. And that is where things stood until late in 1998.
Okay, now to the present day. Most standard candles are too faint to be individually resolvable at very large distances. But some supernovae are extremely bright; these are single stars exploding with a flare of light comparable to the entire brightness of the galaxy they are in.
There are some theoretical grounds for believing that in Type IA supernova the maximum brightness and the rate at which it fades away are related. Recognise the type of the supernova, observe its decay rate and you have its absolute brightness. Compare this with the observed brightness and you get the distance. Seems to work for local galaxies.
In a typical galaxy you get maybe one of these every 300 years. But watch a thousand galaxies, and they turn up monthly or better. Of course, astronomers immediately recognised the chance to improve their maps of the distance reaches of space, and embarked on a survey of this supernova. You photograph the same area of sky a few weeks apart, which contains thousands of galaxies, and go look again where there are differences.
And they collected lots of data. They measured apparent brightness, decay rate, redshift etc. From the first two, they computed distance (inverse square law), and redrew their maps of galactic distribution. And then the fun started.
Refining the value of the Hubble constant is still an ongoing concern, with little data at large distances. This redshift data was immediately plugged into the Hubble equation. And guess what? The redshift distance was different from the square-law distance. At the distance indicated by the Hubble equation, the supernovae should be 25% brighter than actually observed. A big enough discrepancy to raise eyebrows. And give rise to lots of thinking.
There are all sorts of messy practical considerations, like maybe the observations are distorted by gas and dust or maybe the supernovas aren't good standard candles, or whatever. Of course it's possible and there is a ton of research looking at this. But something like this also prompts science to re-evaluate theory as well as data. Suppose the observations are good. What are the implications?
The supernovae are fainter than expected. Either Hubble underestimates the distance, or light fades with distance faster than the inverse square law suggests.
Suppose the first possibility, that Hubble underestimates the distance for far away galaxies. This is the same as overestimating the redshift, the same as overestimating the velocity. But far away means distant in time also. This suggests that the galaxies were moving more slowly in the past than they are now.
Initially Hubble's Law proposed that the universe is not static but expanding. We have hardly got used to that idea only to find that now it is suggesting that the expansion is accelerating?
Suppose on the other hand that the problem lies with the square-law assumption. The discussion above about curved space suggests one possibility - that at the large-scale, space has negative curvature..
We are very strongly attached to the idea of flat euclidean space, it even may be that we cannot think otherwise. But negative curvature would explain the observations very nicely.
Either way, the existing theories can be saved, which is reasonable as they serve well within their proper limits; but we can only do this by accepting radical revisions to our understanding of the world we live in. And it's all based on simple ideas and concepts. Science truly is simple! Where things get complicated is in the technology we need to gather ever more detailed data.
Firstly, typical of science, the constant (H) in Hubble's Law - V=H x D - as estimated by Hubble, was hundreds of times bigger than the number now accepted. Which is to say that in a very real sense the data could not have justified the proposal of Hubble's Law; the effect was actually too small for it to be reliably measured at that time. But the concept was persuasive, counter-intuitive though it was; the theory was very quickly accepted and is still being calibrated more and more finely.
Secondly, using the red-shift as a yardstick for the universe is a good example of how observation is never just observation. There are very few facts, but always models and expectations and ideas about how things work that inform our interpretation of what we see. For example, the idea that stars of the same spectral type are similar in other ways. This is typical of the way we think about things but was quite unsupported at that time by any astrophysical theory! Indeed, the theory of stellar evolution was considerably stimulated by the need to think some more about that assumption.
Thirdly of course is the question of what is really happening here? The consensus seems to be hardening in favour of an accelerating expansion of the universe. The observations may have a completely different explanation. Perhaps for example these supernovae do not radiate equally in all directions. Who knows? We have few theories and no good ones. But the question will not go just away, and we know that challenges to our knowledge and understanding lead to fun new ideas and even more interesting challenges to that knowledge and understanding.
It may even be that the observations will eventually turn out to be wrong, an artifact of instrumentation. But the questions raised and the possibilities suggested have nonetheless deepened our understanding of what it is we know, and how we know it, and suggest new ways of examining and questioning what we thought we knew.
And that is the real point of all this. The purpose of science is not to find the right explanation. I don't know what that could mean. The goal is more pragmatic than that, to find an explanation that is sufficient for today, that can mesh with what we think we know, or that forces us to change that mesh in order to accomodate the newcomer.