The Hot Big Bang:
A Point-Form Summary.
This section of the course notes, and the associated PowerPoint presentation, makes the following critical points:
by combining the distance of a particular galaxy with its apparent recession velocity, we can calculate the time 'since it was where we are now' -- that is, since the moment of creation at which all the material was packed together at unimaginably high density. This calculation will give the same estimate of the 'Hubble age' (or 'expansion age') no matter which galaxy we use, and Hubble estimated the age of the universe in this way
Hubble's answer was about 2 billion years, which was too small by a factor of 5-10 because his distance determinations were wrong (as we know now). But the calculation was correct in principle
at first, his estimates agreed with geological estimates of the age of the Earth, but later it was realised that the Earth was yet older. For a time, this led to a near-abandonment of the 'big bang' model for the 'Steady State' model in which the universe is largely unchanging over infinite time. (This model requires the slow continuous creation of matter to compensate for the dilution caused by the expansion.)
the 'big bang' is a name given derisively, but one which has caught on -- unfotunately, since it suggests that the expansion needed to be hot to 'make it happen' (like a bomb) and that it features fragments driven outward into pre-existing empty space. Neither of these is correct: the expansion did not need to be driven by heat; and there never was (and is not now) any 'outside' to the universe
although heat is not necessry for the expansion, it still might have been hot in the early phases. Gamow speculated that it might have been, and that the dense hot phases would have allowed thermonuclear reactions for a time, until the expansion quenched them. In this way, he hoped that he could account for the existence of the heavy elements in the universe
he realized quickly that this does not work, although it yields small amounts of the lightest elements (including helium). But he had the wit to realize that if the universe did indeed start out hot, we should now be surrounded by a 'bath' of low energy photons left over from the early intensely hot epoch>
long forgotten, this notion was revived in the 1960s and a search was being mounted (using radio telescopes) at just about the time that it was serendipitously found by two astronomers not actually looking for it. They won the Nobel prize for their discovery of the Cosmic Microwave Background Radiation (CMBR)
the universe is now filled with this low-energy leftover radiation, but it is of little conequence except insofar as we can study it to learn about the earliest stages of the big bang. But in those early stages, the intense radiation would have had a more important dynamical effect than ordinary matter, and at the very early stages, light was everything -- just as in so many creation stories and myths. (Think of the book of Genesis)
Associated Readings from the Text.Please look at: Chapter 20, pages 641-645. Chapter 23, pages 702-712.The `Expansion Age' of the Universe.As we have seen, Hubble's observations immediately implied an age for the universe by telling us how much time had passed since the universe was in some very dense early state, which we take to define the moment of its origin. (I will justify that in a bit.) The argument is simple, and goes as follows: We see a remote galaxy some distance away (say, 30 million light years). We assume that all the atoms within that galaxy were once all very close to our own atoms, at a time when everything was densely packed together. We discover that this galaxy is receding from us at some high speed, say one thousand kilometers per second. We assume that the material it consists of always been moving at roughly this speed. (Technically, that is not correct. Presumably it started out moving somewhat faster, and has slowed a little under the influence of gravity over the billions of years. A small correction can be made for this effect.) We remember the general rule that the distance a moving object covers is given by the product of its speed and the time it has been travelling. (If you drive at 80 km/hr for 2 hours, you cover 80 x 2 = 160 kilometers.) You can rearrange that relationship to deduce that the time which has elapsed since the expansion began is given by the distance covered divided by the velocity at which the galaxy is moving. This gives us an estimate of the expansion age of the universe (also known as the Hubble time). In the example I gave, a galaxy moving at 1000 km/sec would take abou t ten billion years to reach a distance of 30 million light years. The interesting thing about the age we derive is that it is plausible in the sense that it is of the same order as the ages of the oldest known stars. This did not have to be the case: if, for instance, the universe had formed in some other way so that the expansion was really telling us nothing about its age, then quite a different number might have arisen. The fairly good agreement gives us some reason to hope that our interpretation is correct, and that the oldest stars were indeed formed shortly after the Big Bang itself. Notice that this age determination does not work for galaxies which do not participate fully in the expansion. For instance, we saw that the Andromeda galaxy is actually approaching us, so its behaviour tells us nothing about the age of the universe. But for more remote galaxies, a reasonable estimate can be derived. You should also note that you will get the same answer for any galaxy that participates in the observed expansion since the Hubble law tells us that velocity is proportional to distance. A galaxy twice as far away is moving twice as fast, and our calculation will yield the same answer. (In a sense, the galaxy got twice as far away in the available time because it started off moving twice as fast, and has continued to do so!) This consistency follows immediately from the fact that the expansion is uniform, and is consistent with our assumption that all the matter in the visible universe was `packed together' in a tiny volume of unimaginably high density at the very earliest stages. Hubble recognized the way these calculations could be done and interpreted, and worked out an expansion age for the universe. What did he find?Hubble's Answer.Hubble deduced that the universe was about 1.8 billion years old. You should immediate object to such a number, because we already know from radioactive age dating that the Earth, the moon, and the meteoroids are older than that. How can the universe contain any objects older than itself? But interestingly, in Hubble's day the oldest rocks on Earth were thought to be only about 2 billion years old, and the apparent agreement was often referred to in approving terms. Unfortunately this agreement did not persist. At about the time of the Second World War, geological age-dating techniques improved to such an extent that the low ages were shown to be incorrect. This worrying inconsistency actually led some astronomers, led by Fred Hoyle, to abandon the big bang model and to suggest that the universe, while appearing to expand, might in fact be infinite in age and not to change significantly in appearance as time passes. This model, the `Steady State', needed to propose that new atoms would spontaneously appear in the middle of empty space to make up for the fact that the expanding universe would otherwise lead to a continuous decline in the density of material. A lot of other astronomers objected to that on the grounds that it requires material to appear out of nothing, in violation of the Conservation of Mass and Energy, but in fact the Big Bang model does this as well. The difference is that the Big Bang assumes that all the mass and energy in the universe came into existence at one time, rather than in dribs and drabs! (By the way, Hoyle is the man who gave the name `Big Bang' to the cosmological model I have been describing, with the origin a finite, determinable time ago. He did not mean the name to be taken seriously, and indeed meant it in sarcastic and derogatory terms since he did not believe in the model. But the name has stuck, although it is not a good one for reasons I will describe in a moment.) The problem with the age derived from Hubble's observations was resolved in the 1950s, after the opening of the great 200-inch reflector at Mt. Palomar. New observations in the Andromeda galaxy and other nearby systems revealed that Hubble had made some mistakes - quite forgiveably, given the technology at his disposal - in determining galaxy distances. These were corrected, with the result that a new, much larger age was deduced.Why Not the Big Bang?As I said, the name `Big Bang' is not a good one. Why not? To answer that, let me ask you what the name conjurs up. For most of you, it implies a big lump of matter which explodes like a bomb into a surrounding pre-existing space, so that chunks come flying out like the pieces of shrapnel from an exploding grenade. It probably also makes you visualise something exploding outwards simply because of some intense inner pressure. (Perhaps, for instance, you visualise the lump of material as being extemely hot, like a bomb within which an explosion has just been ignited -- an explosion which is, after all, caused by nothing more than the intense energy released by a vigorous chemical reaction.) This is all quite wrong, for a number of reasons: The material does not fly out into preexisting space. There is no space `outside'. The universe was, at the time of the Big Bang, completely filled with matter at high density. In the expansion, new space appears between the chunks of material - they do not travel out into a waiting void. It may be possible for you to visualise an infinite universe at high density, because this avoids the question of an `outside.' In due course, however, I am going to ask you to visualise a finite universe which has no outside! (I will return to this point in a bit.) The material did not need to be hot to trigger the expansion. Instead, the universe merely came into existence with the expansion as part of it. If the universe was hot in the past (as indeed we will see it was), that was merely an interesting circumstance but not at all necessary to the expansion. The universe could have come into existence cold, if the creation event had made it that way, but still expanding. There is no need to seek for (or way we can necessarily identify) a cause of the expansion: it just was. No inner pressure made it start off. These are difficult concepts which require a subtle grasp of some geometrical considerations. Before we explore those aspects further, however, I will deal with the question of the `hotness' of the Big Bang.Gamow's Speculations.In the 1940s, a Russian-American astronomer named George Gamow was wondering where all the heavy elements had come from. He realised that the universe must have been very dense in the early stages, so that all the particles and atoms would have been close together, and he reasoned that if it had also been hot (so that they were all moving around rapidly) then it would have been ideal for thermonuclear reactions. The early universe would, for a brief time, have been like the interior of a star of unimaginably large size: hot and dense! Of course, the nuclear reactions would have died away fairly quickly, because the particles and atoms are being carried apart by the universal expansion. The whole system would quickly cool down, and the interactions between particles would become so infrequent and low in energy that no more reactions would take place. This would limit the kinds and amounts of heavy elements which might be formed, but Gamow hoped that a detailed calculation would prove that the elements we see around us today were built in the very early moments of the existence of the universe. Before continuing, let me tell you that Gamow was wrong about most of this, and soon realised it. No elements heavier than Helium, Lithium, and Beryllium can be made in this way. (In fact, as we now know, all the heavier elements are actually the products of thermonuclear reactions within stars.) But the amazing thing is that he was right about those three light elements. In particular, the universe we see is about one-quarter helium because that is the amount that was built up in about the first three minutes of the Big Bang in exactly the way hypothesised by Gamow. Anyway, before he abandoned a theory which explained all of the elements in this way, he played for a time with a model in which the universe began in a very hot state. (As noted, this did not have to be the case. We could have had a universal expansion anyway.) He then had the wisdom to realise that there would be, even now, a way to test this notion: we should be able to see some of the photons which would have been flying around in the very hot material of which the universe consisted at that time. Since he was speculating that the early universe must have been at a temperature of billions of degrees at these early stages, the radiant energy at that time would have been intense gamma rays. But we would not expect to see leftover gamma rays now. Why not? To understand this, consider the behaviour of photons which were emitted billions of years ago by a chunk of material which was then a moderate distance from us. Such photons are only just reaching us now, because the expansion of the universe has carried the material a long way away in the intervening ten billion years. In other words, the distance the photons had to cover was constantly being stretched even as the photons were on their way! (Imagine driving to Toronto and finding that the 401 Highway was rubber and kept lengthening as you drove, so that you made almost imperceptible progress towards your destination.) This means that we are now receiving the photons which were emitted by the very hot material in the early universe. But the expansion of space has a second important consequence: it means that the photons now arriving have been red-shifted (stretched in wavelength) so that they appear to us to have very long wavelengths and very low energy. There is a further prediction: since the Cosmological Principle tells us that the universe is uniform on the largest scales, we would expect the inflow of leftover photons to be coming from all sides. (The universe in the early days would have been hot `everywhere' in Gamow's model: to the left, right, above, below, front, and back.) So he predicted, as a consequence of his theorising about the origin of the elements, that the universe now should be filled with low-energy photons travelling in all directions and of a predictable energy. This constituted a prediction of what has since come to be called the Cosmic Microwave Background Radiation (CMBR). According to Gamow, we should see - in addition to the light from localised hot lumps like stars and galaxies - a diffuse prevasive radiation with an energy which would have its peak in the microwave part of the spectrum. It would be rather as though we were to find ourselves in an oven at a very low temperature, just a few degrees above absolute zero, with the walls `glowing' with the corresponding photon distribution. (Remember our discussion of `thermal radiators' or `blackbodies' in Physics 015.)Interest Lost and Regained.As I noted, Gamow soon realised that he could not explain the build-up of heavy elements in this way. Moreover, the problems of the timescales (why did the Earth seem to be older than the universe?) led some astronomers to discredit the Big Bang model entirely and look at alternatives like the Steady State. For a variety of reasons, then, Gamow's prediction was essentially forgotten for many years. In the 1960s, however, a Princeton physicist named Dicke suggested to a young colleague, a Canadian named Jim Peebles, that he consider what might be the presently-observable consequences of a once-hot Big Bang. Peebles (and a colleague named Dave Wilkinson) quickly realised that there should be an observable photon bath surrounding us, and even began to build a simple piece of equipment to detect it. Unfortunately, they were scooped.Serendipity Again.At about the same time, Penzias and Wilson, working at Bell Labs, were using a large horn-shaped antenna to study various forms of radio radiation. (See page 707 of your text.) They found to their annoyance that no matter how they pointed the antenna they got a continuous static of some background radiation. At first they thought it was man-made interference, perhaps from New York city; then they thought there were technical problems with the antenna. They even removed a pair of pigeons who had made a home in the antenna, and shovelled out pigeon droppings in case they were affecting the performance of the antenna and its electronics. Eventually they realised that the radiation was ubiquitous - but what was it? One of them mentioned the problem at a scientific meeting, and the person they told it to said, ``Well, I know who can answer your question. You'd better call Jim Peebles, at Princeton.'' Of course Peebles knew exactly what the effect was, and there was an historic scientific journal issue some months later in which Penzias and Wilson reported the finding while in a companion paper Peebles and Wilkinson interpreted the result. There is a follow-up: Penzias and Wilson won the Nobel Prize for their discovery (and for their persistence in following it up and not just ignoring it as unexplained `noise'). Peebles, on the other hand, was shut out, although the experiments being started in Princeton would have found this in very short order - and he knew what he was looking for! The detection soon established that the CMBR is indeed all around us, and that it consists of photons of the sort which would be emitted by a thermal radiator at the very low temperature of only three degrees above absolute zero. This is, of course, very close to Gamow's prediction, but Gamow is not given much historical credit for this. (Partly it is because his motivation for proposing it was wrong in the first place. If, a century ago, Joe Bloggs proposed that the surface of Venus is hot because he thinks that is where comets come from when they are spit out of active volcanoes, no one will give him much credit for anticipating the greenhouse-induced high temperatures which prevail on Venus!)Let There Be Light.We know that the universe now contains matter: atoms and particles -- some in the stars, some in the interstellar medium. It also contains radiation: light from the stars, plus a dilute `sea' of photons which are left over from the hot Big Bang. (By the way, there are about 400 microwave photons per cubic centimeter all around you. They are the cause of some of the 'static' you get when your cable TV signal drops out or if you tune it to a non-channel.) But what would the universe have been like in the earlier days? You already know this: the material would have been more densely packed, and so too would have been the photons, with the consequence that they would appear more energetic (since their wavelengths would not yet have been `stretched' by the universal expansion). But there is a remarkable and gripping consequence of this: in the early days, the universe must have been radiation dominated. What does this mean? Well, the universe today is matter-dominated. This means, among other things, that if you sail off in a rocket ship you will follow a trajectory which is determined by the gravitational influence of the lumps of matter which are around you. The omnipresent photons have no real effect on your motions. In a larger context, the rate at which the universal expansion will slow down will be determined by the total gravity of all the matter in the universe, with the energy which is present in the form of radiation having a negligible effect. In the early days, things were different. The very rate of expansion of the universe and all of its dynamical behaviour would have been determined almost completely by the densely-packed radiation itself, with the matter having no effect. (I will not go into the reason for this, which has to do with the fact that matter and radiation obey different `equations of state.') You probably know that many creation stories and myths have, as a central element, the dominance and early appearance of light as a central ingredient. (Think for example of the early verses of Genesis, in the Bible.) In that spirit, I played for you in class a section of the oratorio `The Creation,' by Franz Joseph Haydn. I hope that the great fortissimo which attends the sudden appearance of light reminds you that, in some senses, the creation myths had it right. The universe was light in the first moments. 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.)
