Why String Theory? Page 7
Everything said above involves deep, powerful and true statements. However the mathematics of this is rather abstract and I am not going to elaborate further. Instead, having considered geometric and gauge symmetries, I want to consider a final topic: symmetries that are almost but not quite symmetries.
This refers to the fact that there exist certain discrete operations that are possible, and under which the laws of physics must clearly and obviously not change – were it not for the fact that experiment tells us they do indeed change. The best example of these is called parity. Parity is the operation that interchanges left and right. The distinction between left and right is a conventional one. I drive on the left in the United Kingdom but in the United States people drive on the right. This is not a reflection of deep cultural or linguistic differences. A choice had to be made; no choice was intrinsically preferable; different choices were made in different places.
The distinction between left and right is so obviously conventional that it is striking that nature, in the form of the laws of physics, does actually distinguish between left and right. What does this mean? Write down the laws of physics in one particular coordinate system, using coordinates x, y and z. Now exchange x with ‘minus x’, thereby exchanging the meaning of left and right.15 The laws of physics change form, and the equations take a different form. After the operation, the old laws, applied in the new coordinate system, do not work: they make definite predictions for experimental measurements, and these predictions are wrong.
For a long time, there was no awareness that this could be possible. Experience with electromagnetism did not help as parity is a good symmetry of electromagnetism. The possibility that parity symmetry may be violated in nature was realised as a theoretical possibility in 1956 by the Sino-American pair Tsung-Dao Lee and Chen-Ning Yang. Their suggestion was followed by rapid experimental confirmation by Chien-Shiung Wu in 1957. The observation of parity violation came as a shock, and it led to the almost immediate award of the Nobel Prize to Lee and Yang. The fact that parity is not a symmetry of nature was one of the first clues to understanding the full form of the weak interactions. In contrast, the laws of the gravitational, strong and electromagnetic interactions do respect parity, and they take the same form under the interchange of left and right.
The classification and application of symmetries has then played several major roles in twentieth century physics. Geometric symmetries underlie both special and general relativity. Particular ‘internal’ symmetries, called gauge symmetries, set the nature of the strong, weak and electromagnetic forces. Discrete almost-symmetries, such as parity, determine the finer structure of particle interactions.
We now move from the minutiae of particles to the largest scales in physics.
3.6 THE UNIVERSE WAS YOUNG, SMOOTH AND HOT, BUT IS NOW OLD, COLD AND WRINKLY
The heavens, it was thought, endure from everlasting to everlasting. So it seemed to our ancestors, and so it seems to us. So it also is, on any timescale that we either live by or are biologically sensitive to. Our universe does not change on the timescale of old people – a hundred years – or old civilisations – a thousand years. If Ur the Cro-Magnon had developed general relativity and satellite astronomy, he would have measured the same universe, with the same parameters, as ourselves. Even restricting to the Milky Way, over the last hundred thousand years the sun would have moved through only one part in two thousand of its orbit around the galactic centre.
However, on very long timescales we do now know that the universe has in fact aged. We may not know its future, but we do know its past. It has an age, and its complexion and appearance have changed with time. The universe used to be younger. The universe used to be smoother, and the universe used to be hotter.
What do we know about the universe? First, it is not just big, but Big. We – the collective noun for all those who have ever reflected on our place in the cosmos – have always known this. It took us a long time though to realise just how large the visible universe is. Let us allow ourselves to race through history to the point where we can assume the earth goes round the sun at a distance of ninety-three million miles, or a hundred and fifty million kilometres.16 This is a great distance, but it is small compared to what is to come. We look at the night sky and see stars. How far away are they? How can we work out this distance?
One clue is that the stars do not appear to change their relative position throughout the course of the year, even though during this period the earth has changed its position relative to the sun by around two hundred million miles. Perspective normally depends on our locus of view, and is only unaltered for objects far off in the distance. The apparent positions of the apple tree and the rose bush differ when viewed from the living room or the garden shed – but the distant mountains look exactly the same. Between winter and summer, our viewing platform for the stars moves by a distance of two hundred million miles, yet the relative arrangement of the constellations remains the same. For this to happen, the stars must be as distant from our solar system as the mountains are from the garden.
For this reason, the stars were historically called fixed – thus contrasting them with the wandering stars, the planets. Despite the name, the fixed stars are not truly fixed. The stellar positions do change, ever so slightly, when viewed in summer and in winter. The change is not large. It is at the level of one thousandth of a degree or smaller, roughly equivalent to the width of your finger viewed from several miles away. This change is, however, measurable, and is called parallax. Once it is measured, trigonometry and knowledge of the earth-sun distance then determine the distance to the given star. Proportionately closer objects have proportionately larger parallaxes. Parallax gives its name to the distance unit of a parsec: one parsec is the distance from earth of an object with a parallax of exactly one arc-second, where one arc-second is three-thousand-six-hundredth of a degree.
These distances are clearly large. It is apparent that such minuscule angular changes, when viewed from points separated by two hundred million miles, can only hold if stars are at enormous distances. To measure these distances, the light units introduced in chapter 2 are used. The distance from London to New York is one-sixtieth of a light second, the distance from the earth to the moon is around one light second, the distance from us to the sun is eight light minutes, and the distance to the nearest star Proxima Centauri is four light years – or twenty million million miles. Indeed one parsec equals three and a quarter light years, and an object whose apparent angle changes from summer to winter by only one thousandth of a degree is at a distance of ten light years from earth.
Using these techniques, the distances to nearby stars can be measured, up to a range of approximately one thousand light years. Beyond that, stars are so far away that their positions remain fixed even to our most sensitive telescopes. Parallax is still only the first rung on the cosmic distance ladder. The progression through the rungs to measure distances to objects further away requires several clever tricks. This book is not the place for the full details, but all of these tricks rely on the notion of a Standard Candle.
What is a Standard Candle? You go to the supermarket to purchase twelve identical sixty watt bulbs. Plugged in to sockets, each emits a fixed amount of energy per second. Every second, a hand placed five centimetres, or ten centimetres, or one metre away from the bulb will receive a definite amount of energy. The amount of energy received is determined only by the wattage of the bulb and the distance of the hand from it. If we know the distance, we can work out the energy the hand will receive.
We can then turn this around. By measuring the energy received each second, we can determine our distance from the bulb. For a supply of identical bulbs, it is not even necessary to know the wattage. We take one bulb, find a metre rule and lightmeter, and plug the bulb into a socket. Measuring at a known distance, we obtain a calibrated graph of intensity against distance. Once this is done, we can discard the metre rule: our graph now provides the means of measurement. U
sing this graph, we can measure the distance to any other Standard Candle bulb purely by measuring the intensity of the arriving light.
The cosmic distance ladder is climbed by reaching from one Standard Candle to another. The only difference is that the Standard Candles used are provided not by the supermarket but by the universe. Starting with nearby objects, the overlapping distance ranges of each Standard Candle eventually take us out to the furthest ends of the universe.
The first Standard Candles are numerous and nearby. Their intensities are calibrated against direct distance measurements via parallax. Using this calibration, the measurable distances can be extended outwards, which in turn allow the determination of the distances to the next Standard Candles, and so on in a chain which spreads out across the visible universe.
The Standard Candles come in various forms. At short distances dim but numerous sources, such as Cepheid variable stars, can be used. At the largest distances, bright but rare objects, such as type IA supernovae, are needed. In all cases the Standard Candles are believed to burn with a fixed intrinsic brightness: by measuring the light received, we can measure the distance to the Standard Candle. By measuring the distance to the Standard Candle, we can also measure distances to everything close to it – for example, to all other stars within the same galaxy. The upshot is a network of distance measurements stretching out across the universe.17
These distance measurements reveal something striking. Everything is moving away from us, and the further away objects are, the more rapidly they are receding. As we go forward in time, the distance separating us from any distant galaxy is continuously increasing. Looking around, we see in all directions the cosmos withdrawing from us.
How do we tell? How do we know whether a faraway galaxy, a billion light years away, is approaching or receding? We cannot, after all, visit it. We tell the same way we tell that a distant ambulance is approaching or receding. An ambulance siren emits a note at a fixed intrinsic pitch, and we are alerted to the ambulance by the siren. The pitch we hear, however, depends on the motion of the ambulance. If the ambulance is coming towards us, the pitch increases as the signals pile up with the added velocity of the ambulance. As the ambulance pulls away, the pitch falls as the gap between notes reaching us increases. Even without seeing it, we can tell from the pitch of its note whether the ambulance approaches or departs.
The same principle applies for distant galaxies. The cosmic siren comes not from sound, which cannot travel through the vacuum of deep space, but from light. Quantum transitions between the atomic energy levels of hydrogen emit light at universal frequencies set by the laws of quantum mechanics. This light shines out across the cosmos, eventually reaching us and our telescopes. As the light originates from particular known transitions within the hydrogen atom, its intrinsic frequency is set. If the arriving light is at a higher frequency than the intrinsic one, the emitting object is moving towards us. If the arriving light is at a lower frequency, the emitting object is moving away.
It is a hard empirical fact that these sirens of distant galaxies, reaching earth, are all received at lower frequencies than the intrinsic frequency, and the more distant the original galaxy, the lower the arrival frequency. The consequence is that all faraway galaxies are receding, and the further they are, the more rapid the recession.18
The most distant objects we see are currently separated from us by around forty-five billion light years – and growing. If they are moving away into the future, then in the past they must have been closer. The equations of general relativity can be used to wind the clock back. As we do so, the distance to far-off galaxies steadily reduces. Going back in time, as objects move together the universe becomes more crowded and more dense. All that we can see today was in the past confined to a smaller volume. Extrapolating the equations naively, we find that approximately fifteen billion years ago everything was on top of everything else. The final few seconds of this extrapolation are conventionally called the Big Bang.19 According to Einstein’s equations of general relativity, as we return to the point of ‘zero time’ the density of matter becomes larger and larger and eventually, according to the mathematics, infinite at time zero. This infinity implies either the mystical attainment of the eternal Tao of nothingness or that the equations of general relativity have moved beyond their regime of validity. It is unclear precisely when this would occur – one millionth of a second after ‘zero time’, a thousandth of a second after ‘zero time’ – but it is clear that the early universe was both far smaller and far denser than the present one.
This contraction has another effect. It is true but not obvious that the universe itself has a temperature. This is not a trick sentence based on double meanings. It means precisely what it says. If you go out into deep space, far away from any stars or galaxies, and place a thermometer there, it will measure a temperature. That temperature is minus 271 degrees Celsius, or 2.73 degrees above absolute zero. Such a temperature is a little parky, but there are places colder: for example the magnets inside the Large Hadron Collider.
The early universe was a crowded place. While the current universe is a bit chilly, as we go back in time, all the light, all the energy and all the matter we see today was squashed into a smaller and smaller volume. The result of squashing so much energy into so small a region is to make the universe hotter. The further we go back in time, the hotter the temperature of this oven becomes. When the universe was a tenth of the current size, its temperature was ten times its present value, and when the universe was a hundredth of its current size, the temperature was a hundred times the present value – or approximately room temperature. When the universe was one second old, its temperature was ten billion degrees.
The early universe was not just much hotter than the present one. It was also much smoother. A defining feature of the cosmos is that it is clumpy. Under the action of gravity, matter has clumped together to form structured objects such as the earth or the galaxy. Matter is not distributed equally: the density of the earth is much denser than the space touching onto the upper atmosphere, which is in turn much denser than at a typical place in the galaxy.
This clumpiness is visible on many different scales. Tiny grains of dust came together to form planets and stars. Planets and stars make up solar systems. The different solar systems are grouped into galaxies, which in turn join with other galaxies into galactic clusters and superclusters. Each of these groupings looks like a concentration of matter surrounded by emptiness. The earth is much denser than the solar system, and the solar system is much denser than the galaxy as a whole. However, even a spot halfway between here and the nearest star, a cold and inhospitable place if ever there was one, is busy and bustling compared to true deep space. True, deep, empty space cannot be found near this or any other galaxy. It lies out in the great voids between galaxies and galaxy clusters. In these voids, not only is there no one to hear you scream, but there is nothing to scream with. A cubic metre of galactic space contains approximately one million hydrogen atoms worth of matter. In a deep void, the same cubic metre contains only around one lonely hydrogen atom. To obtain matter sufficient to make one grain of sand, it would be necessary to trawl a region of deep space a thousand miles by a thousand miles by a thousand miles.
And for all this, nature is never spent. The voids are only the counterparts to massive overdensities. Gravity brings stuff together, and the gravitational force operates on a principle beloved of both hedge fund managers and the evangelist Matthew:
‘For unto every one that hath shall be given, and he shall have abundance: but from him that hath not shall be taken away even that which he hath.’ [Matthew 25:29]
More attracts more. Moving forward in time, matter has been brought together. The clumpiness of the universe has only grown with time, and it is growing steadily as we move to the future.
A more unequal future requires a more equal past. As we run the history of the universe in reverse, the allocations of matter become more proportionate. H
omogeneity replaces clumpiness. First go the megaclusters of galaxies, then the smaller galaxy groups, then the galaxies themselves and finally even the stars that make them. The face of the universe becomes smoother and smoother as blemishes disappear and warts become dimples.
How do we know this? Remarkably, there is one direct snapshot of the young universe. This snapshot is called the Cosmic Microwave Background (CMB). It consists of light that was emitted when the universe was four hundred thousand years old, and which since then has travelled to us unimpeded. Having neither scattered nor interacted during its journey, it arrives to us now as a pristine image of the universe then. As the name suggests, it represents a continuous background of light at microwave frequencies, which can be measured by any suitable detector. After first mistaking their signal for the effects of bird poo, the microwave background was detected in 1967 by Arno Penzias and Robert Wilson using a distinctive horn-shaped antenna. Penzias and Wilson did not work for a university. They were instead employees of the American industrial superpower Bell Telephone Laboratories during its gilded age, when its employees won seven Nobel Prizes for a variety of fundamental discoveries.