It was me, waiting for me,
Hoping for something more,
Me, seeing me this time,
Hoping for something else.
Ian Curtis, New Dawn Fades,
Unknown Pleasures
Let us begin in the spirit of taking small steps with a brief summary of the known fundamental laws of nature.
THE RULES OF THE GAME
Attempting to describe the laws that govern the existence of everything from galaxies to human beings in a single paragraph of a book of a TV series might seem overly ambitious. It is at one level; otherwise everyone would complete physics, chemistry and biology degree courses in an afternoon. What we can do, however, is to outline the known fundamental laws in a concise and accurate way, so let us do that.
There are twelve known particles of matter, listed on here. They are arranged into three families, or generations. You are made out of particles in the first generation alone. Up quarks and down quarks bind together to make protons and neutrons, which in turn bind together to form your atomic nuclei. Your atoms are composed of electrons bound to those nuclei. Molecules, such as water and DNA, are built up out of collections of atoms bound together. That’s all there is to you; three fundamental particles arranged into patterns. Particles called gauge bosons carry the forces of nature. There are four known fundamental forces: the strong and weak nuclear forces, electromagnetism and gravity. Gravity is missing from the figure here, and we’ll get to that in a moment. The other three forces are represented in the fourth column. To see how this all works, let’s focus on the familiar electromagnetic force. Imagine an electron bound to the atomic nucleus of one of your atoms. How does that binding happen? The most fundamental description we have is that the electron can emit a photon, which you can think of as a particle of light. That photon can be absorbed by one of the quarks inside the nucleus, and this emission and absorption acts to assert a force between the electron and the quark. There is a vast number of ways in which the electrons and the quarks inside the nucleus can emit and absorb photons, and these all combine to keep the electron firmly glued to the nucleus. A similar picture can be applied to the quarks themselves. They also interact via the strong nuclear force by emitting and absorbing force-carrying particles called gluons. The strong nuclear force is the strongest known force (the clue is in the name) and binds the quarks together very tightly indeed. This is why the nucleus is significantly smaller and denser than the atom. Only quarks and gluons feel the strong nuclear force. Finally, there is the weak nuclear force. This is mediated by the exchange of the W and Z bosons. All known particles of matter feel the weak nuclear force but it is extremely weak relative to the other two, which is why its action is unfamiliar, but not unimportant. The Sun would not shine without the weak nuclear force, which allows protons to convert into neutrons, or more precisely up quarks into down quarks, which has the same result. This is the first step in the nuclear burning of hydrogen into helium, the source of the Sun’s energy. During the conversion of a proton into a neutron, an anti-electron neutrino is produced along with an electron. The neutrino is the remaining particle in the first generation we haven’t discussed yet. Because neutrinos only interact via the weak nuclear force, we are oblivious to them in everyday life. This is fortunate, because there are approximately sixty billion per square centimetre per second passing through your head from the nuclear reactions in the Sun. If the weak force were a little stronger, you’d get a hell of a headache. Actually, you wouldn’t because you wouldn’t exist, and this foreshadows the subject of the fine-tuning of the laws of nature we will undertake later in this chapter. The one remaining type of particle is the Higgs Boson, on its own in the fifth column. Empty space isn’t empty, but is jammed full of Higgs particles. All the known particles apart from the photon and the gluons, which are massless, interact with the Higgs particles, zigzagging through space and acquiring mass in the process. This is the counter-intuitive picture that was confirmed by the discovery of the Higgs Boson at CERN’s Large Hadron Collider in 2012.
What really interests
me is whether God had any choice
in the creation of
the world.
Albert Einstein
Two further generations of matter particles have been discovered. They are identical to the first generation except that the particles are more massive because they interact with Higgs particles more strongly. The muon, for example, is a more massive version of the familiar electron. The reason for their existence is unknown.
This is all there is in terms of the description of the fundamental ingredients of the universe. There are almost certainly other particles out there somewhere – the dark matter that dominates over normal matter in the universe by a factor of 5 to 1 is probably in the form of a new type of particle which we may discover at the Large Hadron Collider or a future particle accelerator. The evidence for dark matter is very strong and comes from astronomical observations of galaxy rotation speeds, galaxy formation models and the cosmic microwave background radiation that we met in Chapter 1 and will meet again later in this chapter. But because we don’t know what form the dark matter takes, we are not able to incorporate it into our list.
The mathematical framework used to describe all the known particles and forces other than gravity is known as quantum field theory. It is a series of rules that allows the probability of any particular process occurring to be calculated. The whole thing can be described in one single equation, known as the Standard Model Lagrangian. Here it is:
It takes a lot of work to use this piece of mathematics to make predictions, but the predictions are spectacularly accurate and agree with every experimental measurement ever made in laboratories on Earth. This equation even predicted the existence of the Higgs particle; that’s how good it is. It probably looks like a set of squiggles unless you are a professional physicist, but in fact it isn’t too difficult to interpret, so let’s dig just a little deeper. The 12 matter particles are all hidden away in the symbol Ψj. The Standard Model is a quantum field theory because particles are represented by objects known as quantum fields. There is an electron field, an up quark field, a Higgs field and so on. The particles themselves can be thought of as localised vibrations in these fields, which span the whole of space. Fields will be important for us later, when we’ll want to think about a certain type of field that may have appeared in the very early universe, known as a scalar field. The Higgs field is an example of a scalar field. The mathematical terms between the two Ψjs on the second line describe the forces and how they cause the particles to interact. The forces are also represented by quantum fields. The term – gs Tj · Gµ for example, describes the gluon field that allows the quarks in the Ψj terms to bind together into protons and neutrons. The term gs is known as the strong coupling constant. It is a fundamental property of our universe that encodes the strength of the strong nuclear force. Each of the forces has one of these coupling constants. We will want to discuss these coupling constants later, because they define what our universe is like and what is allowed to exist within it. The last two lines deal with the Higgs Boson. The strength of the interaction between a matter particle and the Higgs field is contained in the yj terms, which are known as Yukawa couplings. These must be inserted to produce the observed masses of the particles of matter. That’s pretty much it.
Here ends our crash course on particle physics. The central point is that there exists a remarkably economical description of everything other than gravity, and it is contained within the Standard Model.
We considered the gravitational force in some detail in Chapter 1. It is described by Einstein’s Theory of General Relativity, which is what physicists call a classical theory. There are no force-carrying particles in Einstein’s theory; instead the force is described in terms of the curvature of spacetime by matter and energy and the response of particles to that curvature. A quantum theory of gravity, which we have already noted will be necessary to describe the first fleeti
ng moments in the history of the universe, would involve the exchange of particles known as gravitons, but as yet nobody has worked out how to construct such a description. This is why Einstein’s theory remains the only fundamental non-quantum theory we have.
For completeness, let’s refresh our memory of Einstein’s Theory of General Relativity:
General Relativity, like the Standard Model, contains a coupling constant encoding the measured strength of gravity: G, Newton’s gravitational constant. The amount of dark energy is inserted by hand, in accord with observations, as was the case for the strengths of the forces and the masses of the particles in the Standard Model.
* * *
THE STANDARD MODEL
The Standard Model of particle physics is a theory that explains the interactions between subatomic particles in the form of the strong, weak and electromagnetic forces. The original theory has been tested experimentally since it was first postulated and has proven extremely robust. In 2013 the Higgs Boson that had been predicted by the theory was discovered using the Large Hadron Collider at CERN.
INSIDE THE ATOM
* * *
General Relativity and the Standard Model are the rules of the game. They contain all our knowledge of the way that nature behaves at the most fundamental level. They also contain almost all the properties of our universe that we think of as fundamental. The speed of light, the strengths of the forces, the masses of the particles (encoded as the strength of their interaction with the Higgs Bosons via the Yukawa couplings) and the amount of dark energy are all in these equations. In principle, any known physical process can be described by them. This is the current state of the art, but it doesn’t mean that we know how everything works and can all retire, by a long shot or well-timed cover drive.
Most games are skin-deep, but cricket goes to the bone.
John Arlott and Fred Trueman
I timed a cover drive properly once when I was 14 years old playing at Hollinwood Cricket Club near Oldham. Front foot, head in line with the ball, sweet sound of the middle, four runs. I know what I have to do, but I never did it quite as well again. Cricket is an art built on simple rules, first codified by the members of the Marylebone Cricket Club on 30 May 1788; a significant date in world history according to historians with good taste. Those original laws still form the basis of the game today. There are 42 of them, and they define the framework within which each game evolves. Yet despite the rigid framework, no two games are ever alike. The temperature and humidity of the air, a light scatter of dew on the grass, the height of grass on the wicket, and hundreds of other factors will subtly shift and change throughout the game. More importantly, the players and umpires are each complex biological systems whose behaviour is far from predictable, with the exception of Geoffrey Boycott. The presence of so many variables makes the number of possible permutations effectively infinite, which is why cricket is the most interesting of human pursuits excluding science, sex and wine tasting.
Knowledge of the laws is therefore insufficient to characterise the infinite magic of the game. This is also true for the universe. The laws of nature define the framework within which things happen, but do not ensure that everything that can happen will happen in a finite universe – that rather obscure ‘finite’ caveat will be important for us later on. Virtually all of science beyond particle physics and theoretical cosmology is concerned with the complex outcomes allowed by the laws rather than the laws themselves, and in a certain sense our solipsistic initial question ‘Why are we here?’ is also a question about outcomes rather than laws. The answer to the question ‘Why did England beat Australia in the great Ashes series of 2005?’ is not to be found in the MCC rule book, and similarly the natural world that emerges from the Standard Model and General Relativity cannot be understood simply by discovering the laws themselves.
It’s worth noting that the laws of nature were not written by the MCC, or even the committee of Yorkshire County Cricket Club. We had to work them out by watching the game of the universe unfold, which makes their discovery even more wonderful. Imagine how many matches would have to be viewed in order to deduce the laws of cricket, including but not restricted to the Duckworth Lewis method? The great achievement of twenty-first-century science is that we’ve managed to work out the laws of nature by doing just this; observing many millions of complex outcomes and working out what the underlying laws are.
The Standard Model, then, cannot be used to describe complex emergent systems such as living things. No biologist would attempt to understand the way that ATP is produced inside cells using the Standard Model Lagrangian and no telecommunications engineer would use it to design an optical fibre. They wouldn’t want to even if they could; you wouldn’t gain any insight into how a car engine works by starting off with a description of its constituent subatomic particles and their interactions. So whilst it is important that we have a detailed model of nature at the level of the known fundamental building blocks, we must also understand how the complexity we observe around us emerges from these simple laws if we are to make progress with our difficult ‘Why?’ question.
NATURE’S FINGERPRINT
On Monday 27 March 1905 at 8.30am, William Jones arrived at Chapman’s Oil and Colour Shop on Deptford High Street ready for a day’s work. Jones normally arrived a few minutes after the shop manager Thomas Farrow had raised the shutters. On this particular Monday, however, the shutters were down. Farrow lived with his wife Anne above the shop, but no matter how hard Jones knocked on their door, there was no response. This was a most unusual start to the day, and his concern increased when a glimpse through a window revealed chairs strewn across the floor of the normally tidy shop. Jones and another local resident forced the door, to be confronted by Farrow lying dead in a pool of blood. Anne had been similarly bludgeoned in her bed, although she clung to life for four more days without regaining consciousness.
Such scenes were not uncommon in Edwardian London. The reason that this crime is of note is because it was the first in the world to use a new technology to catch and convict the killers. On an inner surface of the empty cash box, the police noticed a fingerprint. They already had a suspect: a local man named Alfred Stratton, who was arrested three days later along with his brother Albert. The Strattons’ fingerprints were taken, and a positive match was made between the cash-box print and Alfred Stratton’s right thumb. Although fingerprints were never used before in a murder case, expert witnesses convinced the jury that the complex patterns of the cash-box fingerprint could only belong to Alfred Stratton. The jury took just two hours to find the Stratton brothers guilty of murder, and the pair were sentenced to death by hanging, with justice swiftly dispatched on 23 May.
Take a look at your fingerprints now; there is seemingly endless complexity in the swirls and ridges. Since every human being carries different fingerprints on the hands and the soles of their feet (which aren’t fingerprints, but there isn’t a word for them), the size of database required to characterise every human being’s fingerprints would be colossal. One of the most important properties of nature, however, is that the blueprints for the construction of the natural world are far simpler than the natural world itself. In modern language, there is a tremendous amount of data compression going on. The instructions to create fingerprints are far simpler than the fingerprints themselves, and more than that, the same instructions, run over and over again from slightly different starting points in the embryonic stage of our development, always lead to different fingerprints. This behaviour shouldn’t come as a surprise. The sweep of desert dunes or the patterns in summer clouds are all described by a handful of simple laws governing how sand grains or water droplets behave when agitated by shifting air currents, buffeted by chaotic thermals and winds and re-ordered by the action of the forces of nature. And yet from a simple recipe, complexity emerges.
When you have eliminated
the impossible, whatever
remains, however improbable,
mu
st be the truth.
Sherlock Holmes
The quest to understand how the boundless variety of the natural world emerges from underlying simplicity has been a central theme in philosophical and scientific thought. Plato attempted to cast the world available to our senses as the distorted and imperfect shadow of an underlying reality of perfect forms, accessible through reason alone. The modern expression of Plato’s ethereal dualism was captured eloquently by Galileo, 500 years ago: ‘The book of nature is written in the language of mathematics’. The challenge is not only to discern the underlying mathematical behaviour of the world, but also to work back upwards along the chain of complexity to explain how those forms that Plato would have defined as imperfect arise from the assumed lower-level perfection. A rather beautiful early example of this quest is provided by Galileo’s illustrious contemporary, Johannes Kepler.
A BRIEF HISTORY OF THE SNOWFLAKE
Human Universe Page 17