The Expanding Universe:
A Point-Form Summary.
This section of the course notes, and the associated PowerPoint presentation, makes the following critical points:
Hubble extended his study of the nature and distances of the galaxies to include what we knew of their motions (as determined from the Doppler shifts measured in their spectra). He discovered that the galaxies are almost all rushing away from us, with velocities that are proportionally larger for the more remote galaxies. This is a uniform expansion, and we describe the correlation of velocity with distance as obeying a 'Hubble law'
although a uniform expansion of this sort gives us the impression that we are at the centre, this is not the case. In fact, a uniform expansion (or contraction) is the only motion allowed which gives every observer, no matter their location, the impression of Hubble expansion away from them. The requirement that all observers have essentially the same view of the universe is the ultimate 'Copernican argument' (that we are in no way special, and is enshrined in the Cosmological Principle which is the basic tenet of modern cosmology
the expansion really only dominates on large scales. Within a gravitationally bound system, like our Solar System, our galaxy, and even the Local Group of galaxies, there is no net expansion: gravity dominates. But on sufficiently large scales, the expansion dominates
for many centuries, the prevailing belief of astronomers was that the universe was infinite in extent and in time, with stars sprinkled here and there in ways which were uniform when averaged over sufficiently large scales. There were two problems with this: first, in such a universe the night sky would look as bright as the face of the sun (Olbers' paradox is that it does not); second, such a universe would be unstable and would led to the collapsing together of all stars everywhere at once (as Einstein demonstrated)
both of these problems are solved by recognizing that the universe is in a dynamic state of motion -- the Hubble expansion -- and has a finite age since some creation event in the measurable past. This solves Olbers paradox because we have not yet had time to see the light of stars that lie very far away, and the Doppler shift reduces the intensity to negligibility anyway. The instability might have led (but did not lead) Einstein to predict that the universe had to be in a dynamic state of some sort. Instead, he built in a fictitious repulsion, effective only at large distances, to explain why the galaxies could be hovering (as he thought) in a delicate balance
when the Hubble expansion was discovered, Einstein discarded his 'cosmological constant' (the fictitious repulsion), but in fact it has had a recent resurgence owing to the discovery that the universal expansion is actually accelerating. The effect is not exactly as Einstein intended it, but he may have been right all along to include this term
Associated Readings from the Text.Please look at: Chapter 20, pages 632-645. Chapter 22, pages 693-696.Hubble's Discovery.By about 1930, Hubble had determined the distances to quite a number of galaxies, and from a study of their spectra was able to determine their radial velocities as well (the speeds with which they seem to moving towards or away from us). Naturally enough, as a good scientist, he wanted to see if these independent properties were related, so he did the natural thing of plotting one quantity against the other. What he found was the following: most galaxies seem to be moving away from us, with the more remote ones moving more rapidly than those near us. In fact, Hubble showed that the recession velocity is proportional to distance: if one galaxy is twice as far away, it is moving with twice the speed. This is the expansion of the universe, and the law which describes it (velocity = constant x distance) is known as the Hubble law. I will explore this a bit later, but please note the immediate implication: if you run the present behaviour `backwards' in your mind, you can see that it implies that at some time in the finite past, the universe was more densely packed. Hubble's discovery implied a finite and determinable age for the origin of the universe. Before considering any further interpretation of this amazing observation, let us look at Hubble's original data for a moment. (See page 637 of the text.) What you notice right away is that some of the nearby galaxies actually have negative velocities - that is, they are approaching us. (This is true for the Andromeda galaxy, for instance.) It is only when you look farther out that the general pattern becomes apparent. Within the Local Group, which is a gravitationally bound system, the galaxies are not separating. But on large scales, things seem to be flying apart. The second point is that we seem to be at the centre of this expansion! Right away, this should worry you, on the sort of Neo-Copernican grounds we considered before. Why should we be in such a preferred location, apparently at the very center of the expanding universe? The answer, as we will see, is that we are not at the centre. It is possible to have a universe in which every observer, no matter where they are, will see the same kind of behaviour.The Cosmological Principle.Modern cosmology (the study of the cosmos, the whole universe) believes so deeply in the neo-Copernican argument - a statement that there is nothing particularly special about our location - that it has enshrined it as a fundamental principle, called the Cosmological Principle. The formal statement of this is that, on sufficiently large scales, every observer will see essentially the same sort of structure and dynamical behaviour in the universe. (The qualification about the need for `sufficiently large scales' is obvious. Not every observer will live in a city identical to Kingston, on a planet just like the Earth. But we are saying that every randomly-chosen big region, perhaps a hundred million light years across, will contain similar numbers and kinds of galaxies, and the observed behaviour will look the same as within every other big region, all over the whole universe.) It is worth pointing out that this cannot be rigorously proven. There are regions of the universe we have not yet seen because not enough time has passed since the universe came into existence for light to have reached us from there. Moreover, if the universe is infinite in extent, there are regions we will never see. The Cosmological Principle is, in a very real sense, an article of faith rather than a strictly scientific statement. It is the ultimate neo-Copernican assumption that we are merely one among many of the possible vantage points, and that there is nothing special about us. Of course, we can test the Cosmological Principle in various limited ways. We can, for instance, ask if the galaxies seem to be distributed fairly uniformly `on sufficiently large scales,' and ask whether any motions we see are consistent with the Principle. But these are merely consistency checks: they cannot prove it.Uniform Expansion.Let us consider some numbers. (Look at the diagram of Hubble's original data.) I hasten to point out that Hubble was wrong about the distances - in general, he underestimated all distances rather badly, for a number of technical reasons - but the systematic effect is still the same. You will see, for instance, that Hubble found a galaxy at a distance of a million parsecs (about three million light years) to be receding at a speed of about 500 km/sec, while one at twice this distance would be moving at twice the speed (one thousand km/sec). Modern astronomical measurements have changed the distance estimates, but the behaviour is the same. This kind of expansion, with a rate which is proportional to distance, is known as a uniform expansion. This may puzzle you. You might think that a uniform expansion would be one in which everything is moving away from you with exactly the same speed, regardless of distance. But a uniform expansion is one in which every observer, no matter where placed, sees the same pattern. Indeed it is possible to show that uniform expansion is the only behaviour which is consistent with the Cosmological Principle. (The expansion rate could be fast, or slow, or zero, or even negative - a universal contraction - but it would still have to obey the Hubble law.) To understand this, visualise an infinitely large flat rubber sheet like a chessboard. Put yourself, a pawn, on one of the white squares and imagine an infinite number of pawns on all the other white squares. Now imagine stretching the rubber chessboard uniformly in all directions. As the rubber sheet enlarges, the distance between you and a nearby pawn will grow, but the distance between you and remote pawns will grow even faster, in proportion. If you start one inch from a `near neighbour' pawn and one foot from a distant neighbour, when you later find yourself two inches from the near neighbour you will be two feet from the distant neighbour. (Try this with some ink marks on a rubber band!) Moreover, this sort of behaviour will be seen by every single pawn on the infinite chess board.Opportunities Missed.The interesting dynamical behaviour of the universe - its apparently uniform expansion - could have been predicted by a sufficiently far-seeing and imaginative astronomer who thought seriously about what the universe was believed to be like a century or more ago. In those days, most scientists believed that the universe had to be infinite in extent. (It is hard to imagine anything else: how could there be an end to the universe? What would lie beyond?) The cosmological assumption, or an early equivalent of it, suggested that the universe should be full of stars everywhere. (In modern terms, we talk about the stars being gathered together into galaxies rather than uniformly distributed, but the galaxies are scattered throughout the universe, so the effect is the same.) And there seemed to be no reason for the stars (or galaxies) to be moving in any systematic way, so the universe was visualised as being static, with the stars (and galaxies) maintaining roughly the same positions as time passed. Finally, the universe was thought to be infinite in age, since no one could imagine a physical origin (other than divine creation, of course). But there were two lines of evidence that showed that we could not be living in a static, unchanging universe of infinite extent and infinite age uniformly filled with stars or galaxies. On either of these grounds, one might have made a bold prediction about the universe. The names associated with these missed opportunities are the unfamiliar one of Olbers and the familiar one of Einstein.Olbers' Paradox.Why is the sky dark at night? Most people would answer that it is because the sun is close (so provides a lot of light in the day) and the stars are remote (so look very faint). But this does not work in an infinite universe of the sort we have been considering. Let me persuade you of that. For simplicity, consider stars of only one type for the moment - say, all the stars which are just like the sun. A nearby star of that sort will look fairly bright, and when we look out into space we will see some number of such nearby stars, depending on how common they are in space and how big an area we are looking at. (See the attached sketch, and consider `Slab A.') But in the background there will be even more stars of this kind. In a volume of space which is twice as far away, for instance, there will be four times as many stars (`Slab B'). Each of these stars will look four times as faint as each of the stars in Slab A (because the brightness falls off like the inverse-square of the distance), but there are four times as many of them, so we get just as much light from Slab B as we do from Slab A. Obviously this argument can be applied to other slabs too, including an infinite number of slabs extending from here to infinity. In short, individual stars in remote slabs look faint but are so numerous that the total light from each slab is just as great as the light from any other slab. The total light, from all slabs, should be infinite, and the sky should be blazing bright! Actually this is too strong a statement. The light from the very remote stars is not guaranteed to reach us, because eventually there are so many stars that the photons from remote stars run into and are blocked by intervening stars. (This is analogous to what happens when you are deep in the woods: no matter what direction you look, you cannot see out because your line-of-sight inevitably runs into a tree. See the figure on page 718 of your text.) But you can still firmly conclude that the night sky should look as bright as the face of the sun does. It does no good, by the way, to imagine a universe filled with interstellar dust which blocks the light from remote stars. Given infinite time, the dust will heat up and get just as hot as a star - so too would the Earth! - until everything is glowing with the temperature of a star. But there are possible resolutions: If the universe is finite in age, then light from remote stars will not have had time to get here yet, and we will not have run into a problem so far. This hypothesises a special kind of creation, with stars and galaxies coming into existence (`turning on') at the same time everywhere in an infinite universe, and then starting to send out light thereafter. If the universe is expanding uniformly, the problem is solved, because very remote stars and galaxies will be moving so rapidly that the photons they emit are Doppler-shifted to extremely long wavelength and reach us with essentially zero energy, contributing nothing at all to the expected overload of luminosity. In other words, an imaginative astronomer might have tried to explain away Olbers' Paradox by predicting that developments in observational cosmology would point towards (i) a universe of finite age and/or (ii) an expanding universe. In fact, modern cosmology includes both of these elements.Einstein's Missed Opportunity.As you have seen, Einstein was deeply interested in gravity and how it controlled the universe. He asked himself the following question: ``How would an infinite universe, uniformly filled with stars or galaxies at rest, behave?'' To answer this, consider any one galaxy. You might think that it would just sit there forever, since it feels tugs in all directions - those arising from the gravity of all its neighbours. But in fact this situation is quite unstable, and Einstein was able to show that the galaxies would all start rushing together, in a uniform contraction. (Again, there would be no `center' - from the point of view of every galaxy, all others would seem to be rushing towards it.) I should remind you that Einstein did not know about galaxies - no one did, in 1915. He was thinking in terms of stars, but the argument is still the same, and still valid. The problem was that he believed, in the absence of any evidence to the contrary, that there were no large-scale motions in the universe. What he should have done is to say: ``My understanding of gravity tells me that the universe cannot be static. It must be doing something!'' Notice that Einstein would not necessarily have had to predict a steadily collapsing universe. What the universe is doing right now depends on what it was doing in the past. Here is an analogy to make the point clear. Suppose I ask you to close your eyes for a moment, and tell you that when you open them you will see an unsupported ball in the air in front of your face. What will you predict it to be doing? There is no single answer. If someone on a ladder just dropped the ball from above you, it will be falling towards the ground, and accelerating as it does so. If someone lying on the floor just threw the ball up in front of you, it may still be moving up, and slowing as it does so, thanks to the Earth's gravity. In the second case, it is possible, though very unlikely, that you opened your eyes just at the instant that the ball came to rest in its upward motion; if so, it is just about to start its fall back down towards the floor. So you could predict any one of these states of motion. All you know for sure is that the ball cannot be continuously hovering at rest, unsupported. In like fashion, Einstein's reasoning could have allowed him to predict an expanding universe (a continuation of an earlier fast expansion, slowing down as time passes thanks to the retarding forces of gravity among all the galaxies), a collapsing universe, or one which is only momentarily at rest.Hubble Anticipated.Remarkably, even at the time Einstein was doing his theorising (he published the General Theory of Relativity in 1915), there was already some evidence which might have led him the right direction. An astronomer named Vesto Slipher, working in Arizona, had by then acquired spectra for about fifteen of the mysterious `spiral nebulae.' Of course, no one knew they were galaxies, but they were clearly unusual, and not just in appearance. Slipher discovered that fully twelve of the fifteen nebulae had rather large velocities of recession. You may remember that stars in the solar neighbourhood have typical velocities of 30 km/sec or so with respect to the sun; well, some of the nebulae had velocities approaching a thousand kilometers per second - and most of these were velocities of recession, indicating that they were rushing away from us. Apparently Einstein did not know of this, which is not surprising given that he was in Germany and Slipher was in Arizona. Remember that this was during the First World War, and that there was almost no modern communication between the two countries. Still, it is interesting to speculate on how Einstein might have responded to news of Slipher's observations. He needs no help from us, of course, since history has proven him brilliantly correct in almost everything he did. But what a coup it would have been to predict a dynamically changing universe!Einstein's Solution.Instead of making such a bold prediction, which he could have done even without knowing of Slipher's work, Einstein built a `fudge factor' into his equations. Essentially, through the inclusion of a term called the `cosmological constant', he hypothesised an extra repulsive force which meant that widely-separated galaxies would repel each other with just the right force to exactly compensate the attractive forces of gravity. At the time, this seemed unmotivated - no one had never speculated about such a force before - and Einstein later regretted it, calling it the biggest blunder of his life. Once Hubble discovered the expansion of the universe, Einstein immediately discarded the cosmological constant as unnecessary. It is therefore a little ironic that it now seems to be making a resurgence! For various reasons, modern cosmology may still need to allow for an extra term in the fundamental equations which describe the behaviour and evolution of the universe. Although the motivation for its inclusion is different than it was in Einstein's day, since we know the universe is not static, the way it arises is still rather as Einstein had supposed. So even his greatest blunder may have contained an important truth. Previous chapter:Next chapter0: Physics 016: The Course Notes, spring 2005. 1: The Properties of the Sun: 2: What Is The Sun Doing? 3: An Introduction to Thermonuclear Fusion. 4: Probing the Deep Interior of the Sun. 5: The Sun in More Detail. 6: An Introduction to the Stars. 7: Stars and Their Distances: 8: The HR Diagram: 9: Questions Arising from the HR Diagram: 10: The Importance of Binary Stars: 11: Implications from Stellar Masses: 12: Late in the Life of the Sun: 13: The Importance of Star Clusters in Understanding Stellar Evolution: 14: The Chandrasekhar Limit: 15: Supernovae: The Deaths of Massive Stars, 16: Pulsars: 17: Novae: 18: An Introduction to Black Holes: 19: Gravity as Geometry: 20: Finishing Off Black Holes: 21: Star Formation: 22: Dust in the Interstellar Medium: 23: Gas in the ISM: 24: The Size and Shape of Our Galaxy: 25: The Discovery of External Galaxies: 26: Galaxies of All Kinds: 27: The Expanding Universe: 28: Quasars and Active Galaxies: 29: The Hot Big Bang: 30: The Geometry of the Universe: 31: Closing Thoughts: Part 1:Part 2:Part 3: |
(Wednesday, 22 April, 2026.)
