by Peter Coles
The ripples in the early Universe were produced by a kind of sound wave. When the Universe was very hot, with a temperature of several thousand degrees, it was ringing with sound waves travelling backwards and forwards. The surface of the Sun is at a similar temperature and is vibrating in a similar way. Because of its poor resolution COBE was able to detect only those ripples that have a very long wavelength. These represent sound waves of very low pitch, the bass notes of creation. The information contained in these waves is important but not very detailed; their sound is rather dull.
25. Simulation of structure formation. Starting from almost smooth initial conditions, modern supercomputers can be used to evolve a simulated chunk of the Universe forward in time. In this example, performed by the Virgo Consortium, we can see hierarchical clustering develop as the Universe expands by a factor of 4. The dense knots seen in the last frame form galaxies and galaxy clusters, while the filamentary structure is strongly reminiscent of that seen in the galaxy surveys.
On the other hand, the Universe should also produce sound of higher pitch and this is much more interesting. Sound waves travel with a particular speed. In air, for example, this is around 300 metres per second. In the early Universe the sound speed is much greater, approaching the speed of light. By the time the microwave background is produced the Universe is about 300,000 years old. In the time up to then since the Big Bang, which is presumably when the sound waves were excited in the first place, they can have travelled only about 300,000 light years. Oscillations with this wavelength produce a characteristic ‘note’, like the fundamental tone of a musical instrument. It is no coincidence that superclusters of galaxies are roughly of this size; they result from this resounding cosmic fanfare.
The characteristic wavelength of the early Universe should reveal itself in the pattern of hot and cold spots on the microwave sky, but because the wavelength is quite short it appears as a much finer scale than can be resolved by COBE. In fact, the angular size of the spots it produces is around one degree. Since COBE, therefore, there has been a race to develop instruments capable of detecting not just the fundamental tone of the Universe but also its higher harmonics. By a detailed analysis of the sound of creation, it is hoped to answer many of the major questions facing modern cosmology. The spectrum of sound contains information about how much mass there is, whether there is a cosmological constant, what the Hubble constant is, whether space is curved, and perhaps even whether inflation happened or not.
Two major experiments, the NASA-led MAP mission to be launched in 2001 and the European Space Agency’s Planck Surveyor to be launched a few years later, will make detailed maps of the pattern of ripples on the sky with very high resolution. If the interpretation of these structures is correct, we should have definite answers very soon. The sense of anticipation is palpable.
In the mean time, there are very strong hints as to how things will pan out. Two important balloon-borne experiments, BOOMERANG and MAXIMA, have mapped little bits of the sky with only slightly poorer resolution than MAP and Planck will. These experiments have not yielded definitive answers, but they do indicate that the geometry of the Universe is flat. The argument is simple. We know the characteristic wavelength of the sounds producing the measured features. We know how far away these waves are observed (about 15 billion light years). We can therefore work out what angle they should occupy on the sky if the Universe is flat. If the Universe is open the angle will be smaller than it would be in a flat Universe; if it is closed the angle will be larger. The results imply flatness. Together with the acceleration I talked about in the previous chapter, this measurement also provides strong evidence for a cosmological constant. The only way we know of having a flat yet accelerating cosmos is if there is vacuum energy.
26. BOOMERANG. The picture shows this experiment about to be launched on a balloon in Antarctica. The experimental payload is perched on the vehicle to the right. The flight path of this balloon took it around the South Pole, making use of circulating winds to return it near the point of launch. Antarctica is very dry, making it the best place on Earth for microwave background experiments, but it is still better to get out into space if possible.
The picture emerging from structure studies seems to be in line with the other strands I have discussed, but we still don’t know how the Universe contrived to be the way it is. The answer to this deeper puzzle will rely on deeper understandings of the nature of matter, space, and time. I’ll discuss these in the next chapter.
27. The flatness of space. The top panel here shows the fine-scale pattern of temperature fluctuations measured by BOOMERANG. Below are simulated patterns that take into account the expected angular size of these fluctuations in closed, flat, and open cosmologies. The best match is with a flat Universe (centre). This strong indication has added impetus to the future experiments MAP and the Planck Surveyor that will map the whole sky with this resolution.
Chapter 8
A theory of everything?
The modern era of physics began with two revolutions that took place in the early years of the twentieth century. One of them involved the introduction of relativity, and it played a major role in the development of cosmology throughout this century. The other major upheaval was the birth of quantum mechanics. By contrast, the implications of quantum physics for cosmology are still far from understood.
The world of the quantum
In the world according to quantum theory, every entity has a dual nature. In classical physics two distinct concepts were used to describe distinct natural phenomena: waves and particles. Quantum physics tells us that these concepts do not apply separately to the microscopic world. Things that we previously imagined to be particles can sometimes behave like waves. Phenomena that we previously thought of as waves can sometimes behave like particles. Light behaves like a wave. One can produce interference and diffraction effects using prisms and lenses. Moreover, Maxwell had shown that light was actually described mathematically by an equation called the wave equation: the wave nature of light is therefore predicted by this theory. On the other hand, Max Planck’s work on the radiation emitted by hot bodies had also shown that light could also behave as if it came in discrete packets, which he called quanta. He hesitated to claim that these quanta could be identified with particles. It was in fact Albert Einstein, in the work on the photoelectric effect for which he won the Nobel Prize, who made the step of saying that light was actually made of particles. These particles later became known as photons. But how can something be both a wave and a particle? One has to say that reality cannot be exactly described by either concept, but that it behaves sometimes as if it were a wave and sometimes as if it were a particle.
Imagine a medieval monk returning to his monastery after his first trip to Africa. During his travels he chanced upon a rhinoceros, and is faced with the task of describing it to his incredulous brothers. Since none of them has ever seen anything as strange as a rhino in the flesh, he has to proceed by analogy. The rhinoceros, he says, is in some respects like a dragon and in others like a unicorn. The brothers then have a reasonable picture of what the beast looks like. But neither dragons nor unicorns exist in nature, while the rhinoceros does. It is the same with our quantum world: reality is described neither by idealized waves nor by idealized particles, but these concepts can give some impression of certain aspects of the way things really are.
The idea that energy came in discrete packets (or quanta) was also successfully applied to the simplest of all atoms, the hydrogen atom, by Niels Bohr in 1913 and to other aspects of atomic and nuclear physics. The existence of discrete energy levels in atoms and molecules is fundamental to the field of spectroscopy, which plays a role in fields as diverse as astrophysics and forensic science and was crucial to Hubble’s discovery of the recession of the galaxies.
The uncertain Universe
The acceptance of the quantized nature of energy (and light) was only the start of the revolution that founded modern quantum mechanics
. It was not until the 1920s and the work of Schrödinger and Heisenberg that the dual nature of light as both particle and wave was finally elucidated. For while the existence of photons had become accepted in the previous years, there had been no way to reconcile this with the well-known wave behaviour of light. What emerged in the 1920s was a theory of quantum physics built upon wave mechanics. In Schrödinger’s version of quantum theory, the behaviour of all systems is described in terms of a wavefunction (usually called ψ), which evolves according to an equation called the Schrödinger equation. The wavefunction ψ depends on both space and time. Schrödinger’s equation describes waves that fluctuate in both space and time.
So how does the particle behaviour come in? The answer is that the quantum wavefunction does not describe something like an electromagnetic wave, which one thinks of as a physical thing existing at a point in space and fluctuating in time. The quantum wavefunction describes a ‘probability wave’. Quantum theory asserts that the wavefunction is all one can know about the system: one cannot predict with certainty exactly where the particle will be at a given time, just the probability.
An important aspect of this wave-particle duality is the Uncertainty Principle. This has many repercussions for physics, but the simplest one involves the position of a particle and its speed. Heisenberg’s uncertainty principle states that one cannot know the position and speed of a particle independently of one another. The better you know the position, the worse you know the speed, and vice versa. If you can pinpoint the particle exactly, then its speed is completely unknown. If you know its speed precisely, then the particle could be located anywhere. This principle is quantitative, does not apply only to position and momentum, but also to energy and time and other pairs of quantities that are known as conjugate variables.
It is a particularly important consequence of the energy-time Uncertainty Principle that empty space can give birth to short-lived particles that spring in and out of existence on a timescale controlled by the Uncertainty Principle. This is the reason why particle physicists expect the vacuum to possess energy. In other words, there should be a cosmological constant. The only problem is that they don’t know how to calculate it. The best guesses available are too large by more than 100 orders of magnitude. But the idea of cosmic uncertainty has scored one notable success: it is thought to be the reason for the existence of small primordial density fluctuations that started off the growth of cosmic structure.
A Universe running according to Newtonian physics is deterministic, in the sense that if one knew the positions and velocities of all the particles in a system at a given time then one could predict their behaviour at all subsequent times. Quantum mechanics changed all that, since one of the essential components of this theory is the principle that at a fundamental level, the behaviour of particles is inherently unpredictable, hence the need to resort to calculations of probability.
The interpretation to be put on this probabilistic approach is open to considerable debate. For example, consider a system in which particles travel in a beam towards two closely separated slits. The wavefunction ψ corresponding to this situation displays an interference pattern because the ‘probability wave’ passes through both slits. If the beam is powerful, it will consist of huge numbers of photons. Statistically the photons should land on a screen behind the slits according to the probability dictated by the wavefunction. Since the slits set up an interference pattern, the screen will show a complicated series of bright and faint bands where the waves sometimes add up in phase and sometimes cancel each other. This seems reasonable, but suppose we turn the beam down in power. This can be done in such a way that there is only one photon at any time travelling through the slits. The arrival of each photon can be detected on the screen. By running the experiment for a reasonably long time one can build up a pattern on the screen. Despite the fact that only one photon at a time is travelling through the apparatus, the screen still shows the pattern of fringes. In some sense each photon must turn into a wave when it leaves the source, travel through both slits, interfering with itself on the way, and then turn back into a photon in order to land in a definite position on the screen.
So what is going on? Clearly each photon lands in a particular place on the screen. At this point we know its position for sure. What does the wavefunction for this particle do at this point? According to one interpretation – the so-called Copenhagen interpretation – the wavefunction collapses so that it is concentrated at a single point. This happens whenever an experiment is performed and a definite result is obtained. But before the outcome is settled nature itself is indeterminate: the photon really doesn’t go through either one of the slits: it is in a ‘mixed’ state. The act of measurement changes the wavefunction and therefore changes reality. This has led many to speculate about the interaction between consciousness and quantum ‘reality’. Is it consciousness that causes the wavefunction to collapse?
A famous illustration of this conundrum is provided by the paradox of Schrödinger’s Cat. Imagine there is a cat inside a sealed room containing a vial of poison. The vial is attached to a device which will break it and poison the cat when a quantum event occurs, for example the emission of an alpha-particle by a lump of radioactive material. If the vial breaks, death is instantaneous. Most of us would accept that the cat is either alive or dead at a given time. But if one takes the Copenhagen interpretation seriously it is somehow both: the wavefunction for the cat comprises a superposition of the two possible states. Only when the room is opened and the state of the cat ‘measured’ does it ‘become’ either alive or dead.
An alternative to the Copenhagen interpretation is that nothing physically changes at all when a measurement is performed. What happens is that the observer’s state of knowledge changes. If one asserts that the wavefunction ψ represents what is known by the observer rather than what is true in reality then there is no problem in having it change when a particle is known to be in a definite state. This view suggests an interpretation of quantum mechanics in which at some level things might be deterministic, but we simply do not know enough to predict.
Yet another view is the Many Worlds interpretation. In this, every time an experiment is performed (e.g. every time a photon passes through the slit device) the universe, as it were, splits into two: in one universe the photon goes through the left-hand slit and in the other it goes through the right-hand slit. If this happens for every photon one ends up with an enormous number of parallel universes. All possible outcomes of all possible experiments occur in this ensemble. But before I head off into a parallel universe, let me resume the thread of the story.
The missing link
I described the standard model of fundamental interactions in Chapter 5. The three forces it incorporates are all described by quantum theories. The fourth of the fundamental interactions is gravity. This has proved extremely resistant to efforts to make it fit into a unified scheme of things. The first step in doing so would involve incorporating quantum physics into the theory of gravity in order to produce a theory of quantum gravity. Despite strenuous efforts, this has not yet been achieved. If this is ever done, the next task will be to unify quantum gravity with a unified theory of the particle interactions.
It is ironic that it is general relativity, which really began the modern era of theoretical physics, that should provide the stumbling block to further progress towards a unified theory of all the forces of nature. In many ways, the force of gravity is extremely weak. Most material bodies are held together by electrical forces between atoms which are many orders of magnitude stronger than the gravitational forces between them. But despite its weakness gravity has a perplexing nature that seems to resist attempts to put it together with quantum theory.
28. A theory of everything. The four forces of Nature we know in our low-energy world are thought to become inextricably unified at higher energy. Turning the clock back on the Big Bang we first expect that electromagnetism and weak interactions merge into an elect
roweak force. At higher energies still, this electroweak force will unite with the strong nuclear force in a Grand Unified Theory (GUT). At higher energies still, gravity may join in to produce a theory of everything. It is this theory, if it exists, that will describe the Big Bang itself.
Einstein’s general theory of relativity is a classical theory, in the sense that Maxwell’s equations of electromagnetism are also classical; they involve entities that are smooth rather than discrete and describe behaviour that is deterministic rather than probabilistic. On the other hand, quantum physics describes a fundamental lumpiness: everything consists of discrete packets or quanta. Likewise, the equations of general relativity allow one to calculate the exact state of the Universe at a given time in the future if sufficient information is given at some time in the past. They are therefore deterministic. The quantum world, on the other hand, is subject to the uncertainty embodied in Heisenberg’s Uncertainty Principle.
Of course, classical electromagnetic theory is perfectly adequate for many purposes, but the theory does break down in certain situations, such as when radiation fields are very strong. For this reason physicists sought (and eventually found) the quantum theory of electromagnetism or quantum electrodynamics (QED). This theory was also made consistent with the special theory of relativity, but does not include general-relativistic effects.
