Why String Theory? Page 3
We are all human. We measure distances in metres and time in seconds. It is not a coincidence that the acceleration due to gravity, measured in these units, has a numerical value of ten metres per second per second – not a thousand, and not a thousandth. Metres and seconds are units that are adapted to us, which is why our most familiar force is characterised by a number not too different from one when measured in these units.
From our own scales, there are two ways to go: up and up, or down and down. As we go up, we increase the distance scale. The metre becomes the kilometre and we step beyond the scales of living organisms. These scales belong to geography and geology, and they are associated with a profound if prehistoric discovery: the earth is not flat but round.2 The evidence for this is simple: as ships sail to distant ports, they disappear beyond sight over the horizon. First the body of the ship disappears, and finally the masts. This effect is due to the curvature of the earth. Attempting to see a distant ship is like attempting to see over a hill. From the distance at which a ship disappears, it is possible to estimate the radius of the earth. Indeed, already in the third century BC the Greek scholar Eratosthenes – using a different method – made an accurate measurement of the diameter of the earth. The sphericity and size of the earth is the first major result in astronomy. Islands, countries and seas have distance scales ranging from kilometres to thousands of kilometres, and it is these scales that are used to characterise the geography of earth. For example, the distance to the centre of the earth is around six thousand kilometres, and the tectonic plates on which the surface of the earth is supported are thousands of kilometres across.
Larger distances are not elegantly described in terms of kilometres. The distance from the earth to the moon is around three hundred and eighty thousand kilometres. The distance from the earth to the sun is around one hundred and fifty million kilometres, while the distance to the next star is around forty thousand billion kilometres. The numbers become clunky, and do nothing to develop intuition. There is a more natural kind of unit: light units. These involve the distances travelled by light in either seconds, minutes or years. Light travels at approximately three hundred thousand kilometres a second. One light second corresponds to a distance of three hundred thousand kilometres while one light year corresponds to a little over four thousand billion kilometres. Within the solar system, the sun is a mere eight light minutes from earth, and the earth just over one light second from the moon. The planetary denizens of the solar system – Uranus, Mars, Venus and Jupiter – took their names from the Roman deities; now they are simply the domestic avatars of planetary science.
The next step is from one star to many: as light minutes become light years, we move from our own sun to all other stars, and the scale of the galaxy is reached. Galaxies are a collection of stars, some very much like the sun and others less so. This collection numbers around a hundred billion stars in total. These all circle an enormously heavy black hole at the centre of the galaxy, in the same way that the planets circle our sun. The size of our galaxy is such that it takes light around one hundred thousand years to cross it, and such that a galactic year, the time taken for the sun to rotate around the galaxy back to its current location, is two hundred and twenty-five million years. By now these distance scales, the scales of galactic astronomy, are so large that we have no real human conception of them. We can state them, we can calculate with them, but we cannot feel them.
For one science even this distance is parochial. That science is cosmology, the study of the whole universe. A cosmologist asked to discuss galactic dynamics is like a national politician asked about the church fête: the event is rather parochial for those with eyes on grander matters. Cosmologists concern themselves not with thousands of light years but billions, and not with single galaxies but the statistical properties of thousands: how far apart are galaxies on average, and how do they cluster together?
Coming up from human scales, the scales attained in cosmology represent the largest distances in science. There are no bigger scales known, and we literally cannot see any further. There is a finite amount of time since the Big Bang, and in this period light has only had the opportunity to travel a certain finite, albeit large, distance. Light is what we can see, and light travels further and faster than anything else.
This ends the upwards journey. Before asking where string theory fits in, we also want to trace distances downwards, from the scales of humans down to the smallest known scales. It turns out, surprisingly, that the science of the very largest distances is closely related to the science of the very smallest. As for the far left and far right in politics, the principles that apply at the extremes turn out to be remarkably similar to one another.
We started the upwards journey on the human scale, the scale of metres, and we return here for the downwards journey. This scale is shared by other large mammals and is the largest of the biological scales – even the biggest of the dinosaurs was never more than tens of metres in length. The reason for this is gravity: the bigger you are, the more energy is required to move muscles against gravity. The largest mammal today is the blue whale, which only achieves its size by mitigating these effects through the buoyancy of a watery home.
The large animals are merely the most biologically visible, sitting at the top of the digestive ladder of who eats whom. As we come down in distances by a factor of a hundred, we start measuring lengths in centimetres and millimetres. This is still the scale of biology, but it is the scale of a different kind of biology: ants and other insects live here. Why is this a different kind of biology? This is because, as mentioned above, clever ants and clever insects would develop science in a very different order to us. They experience the world differently, and the differences are entirely due to size. Where horses can only splash, insects such as pond skaters can actually walk on water. This is so because they are small enough that the surface tension of water can dominate the effects of gravity. Unlike elephants, small insects can be picked up and blown away in the wind, and they can fall great distances without harm. An ant weighs one hundredth of a gram and a human one hundred kilograms. The gravitational force on an ant is almost a billion times weaker than that on a human, and gravity plays a proportionately smaller part in the entomological environment.
Ants and other insects do, however, have eyes, which they use to navigate their world. The next step on our descent is to the largest end of the so-called mesoscopic scale, involving distances comparable to one micrometre, one thousand times smaller than a millimetre. One micrometre is approximately twice the size of the wavelength of visible light. Distances smaller than this cannot, even in principle, be resolved using ordinary light; it would be like attempting to make filigree lace whilst wearing boxing gloves. This scale is the end boundary of biology, inhabited by the smallest living organisms. A single cell is around ten micrometres across, and a single virus around one-fifth of a micrometre in length.
The mesoscopic scale extends down to tens of nanometres. The mesoscale is also the scale of the physics of polymers and liquid crystals. The physics of these distances is one where gravity is entirely negligible and all forces and interactions arise from electromagnetic effects and the distribution of electric charge. It is at this scale that the fictional forces, such as friction, are seen to originate from interactions between the surfaces of two bodies. I use the expression ‘fictional’ not because friction does not exist, but because it does not have an independent existence. ‘Friction’ is a macroscopic name given to the effects of microscopic interactions. These electromagnetic interactions are remarkably strong. One of the easiest ways to understand this is to note that in a sitting position the downwards gravitational pull of the entire earth – all thousand billion billions tons of it – on the bottom is defeated by the short range electromagnetic effects between the chair and the derrière. While these short-range forces are known by many names – ‘stress’, ‘strain’, ‘normal reaction’ and ‘friction’ – each one of these only serves to cap
ture a different macroscopic aspect of the electromagnetic forces of the mesoscale.
As we pass through the mesoscale, we cross the great Rubicon of physics. We start with distances described using classical physics, for which there is no need to introduce quantum mechanics. We end with distances for which there is no longer a good classical description – the world is quantum, and irrevocably quantum. This marks a radical change in how we can think about physics, as an object can no longer have both a well-defined location and a well-defined speed. Quantum mechanics is subsequently needed at all distance scales smaller than this, and it is never again absent from the equations.
The next big step down is to the nanoscale at one-billionth of a metre. Once at the nanoscale, the truth that the world is quantum and not classical is undeniable and encountered everywhere.
The nanoscale is also the scale of atoms. On one level, atoms are tiny. They were traditionally viewed as the fundamental building blocks of matter, and their name comes from the Greek for indivisible – ‘a-tomos’. Atoms are also at a scale so far removed from everyday life that the existence of atoms was not established until the 19th century. Size is however relative, and the atomic scale is simply a staging post on our continuing journey. It is easy to think that as atoms are small, everything within them is equally small. This is not so. Atoms consist of electrons with negative electric charge orbiting a tiny central nucleus, which has positive electric charge and consists of protons and neutrons.
One of the greatest of all conceptual realignments in science was the discovery that the periodic table of elements, and their properties, follows entirely from quantum mechanics applied to protons, neutrons and electrons. The hydrogen atom is the quantum mechanical solution of the system of an electron and a proton. The helium atom is the quantum mechanical solution of the system of two electrons around a nucleus consisting of two protons and two neutrons. The scale of atoms is the scale of chemistry, the science that studies the combination of atoms to form molecules, and the subsequent interactions between atoms, molecules and other molecules. Chemistry is ‘just’ applied quantum mechanics: the ‘chemical bond’ is a name that describes the effects of the solutions of quantum mechanics.
In the hydrogen atom, the proton is a minute central ball of charge while the electron is diffused throughout the atom. Quantum-mechanically, the electron is everywhere. The nucleus, even quantum mechanically, is confined in a tiny central region. Tiny here really does mean tiny. To get a sense of the relative scales, if the hydrogen atom as a whole were blown up to the size of a mountain, the central nucleus would still only be the size of a lightbulb.
The laws of quantum mechanics govern the diffuse, probabilistic motion of the electron around this central lightbulb. What happens within it? The laws of quantum mechanics also govern the far more complicated internal behaviour of the lightbulb. The step from the scale of the atom to the scale of the nucleus brings us to the scales of nuclear physics. Nuclear physics is a science with a glorious infancy in the 1930s and 1940s, a happy maturity in the fifties and sixties, and a long gradual decline since then. The atomic nuclei are made of some number of protons and some number of neutrons. There are many different nuclei, which can be enumerated as a botanist enumerates flowers. These different types of nuclei directly give the diversity of chemical elements. The distinct chemical elements directly correspond to the different numbers of protons that a nucleus can have. The interactions between atoms are determined by physics at the scale of the atom; the distinct types of atom are determined by physics at the scale of the nucleus.
Nuclear physics blossomed as a subject in the 1930s, when it was understood that nuclei of one type could turn into nuclei of another type. This could occur through occasional random processes – radioactive decay of either alpha or beta kind, as first identified by Marie and Pierre Curie. It could also occur through human intervention. It thus became apparent that the base metals were not immutable, and the Philosopher’s Stone that had been sought for millennia was realised as a focussed beam of particles powered by a Cockroft-Walton accelerator. It was also clear that a deeper layer of physics underlay the changes between the different nuclei.
This deeper layer of physics remained mysterious for a long time. Nuclei, made of protons and neutrons, were known not to be fundamental objects. Complex nuclei consist of large numbers of both protons and neutrons – a typical nucleus of gold contains seventy-nine protons and one hundred and eighteen neutrons. Atoms and their nuclei therefore joined earth, air, fire and water as non-elemental objects that, on close examination, fall to bits.
However, even single protons or neutrons are composite, rather than elementary, objects. A free neutron, left to itself, will decay on an average timescale of fifteen minutes, leaving a proton behind. If a proton is hit hard enough with another particle, it will also break apart. Protons and neutrons, each with a radius of around one femtometre – one millionth of a nanometre – are the smallest known composite objects in the universe.
The science that deals with distances smaller than this is particle physics. This science describes elementary particles such as the electron – and also the quarks that make up the proton and neutron. There are three quarks required for both a proton and a neutron, held together by the strong force. The name quark is an odd one and comes from a literary indulgence: originally called ‘aces’, the human encyclopedia and Nobel Laureate Murray Gell-Mann gave them the name that stuck after a word from James Joyce’s Finnegan’s Wake. As far as is known, the quarks join the electron as elementary particles with no further substructure.
Particle physics is, as it says on the tin, about the physics of particles. At its most basic level, it involves enumerating the known particles, searching for new ones and determining the laws and rules that govern their interactions. ‘Enumeration and classification’ is by itself no more than taxonomy. The real thrust of the subject, capable of waking its practitioners in the night, lies in the search for the deep truths that organise hundreds and thousands of different observations and measurements into different facets of a single beautiful idea. Particle physics may appear complex, but at heart it is a simple subject for simple minds. It is a simple subject, but not an easy one. Its simplicity is of the kind that lies on the far side of difficulty, confusion and complexity. The journey is difficult, but the view once achieved is magnificent.
The known range of particle physics extends down to around one ten thousandth of the size of the nucleus. It has achieved this by first accelerating particles to high energies and then colliding them. The larger the energy, the smaller the distance scales probed. The most energetic collider in the world is the Large Hadron Collider at CERN outside Geneva, which sets the current experimental frontier.
In a completion of the upwards and downwards journeys, it turns out that physics at these very smallest scales is also crucial for cosmology, and in particular for the distribution of matter throughout the visible universe. In a sense that is not totally inaccurate, the Large Hadron Collider can be said to recreate the conditions that held in the very earliest epoch of the universe.
Over the last few pages, I have described the sciences of many different scales. These are all scales on which experiments can be carried out, and almost all of ‘science’ is contained within one of these scales.
String theory is not the science of any of the above distance scales. It is directly relevant for the more hypothetical regions where one asks: what happens as distances get smaller and smaller? This is a real part of nature, but not a part where it is currently possible to do experiments. It involves extrapolating from what we know to be true to what might be true.
What are the laws of nature that apply at these shorter distance scales? At the smallest scales we can measure, particle physics tells us that the laws of nature are described by the combination of quantum mechanics and special relativity. The only consistent way of combining these is through what is called quantum field theory. We first ask: can these techni
ques apply down to arbitrarily small distances? We know that all previous laws of physics have either broken down or required modification as they have been pushed to smaller distances. Nonetheless, if the experimentally confirmed ideas of particle physics would all also work there, Occam’s razor – the statement that entities should not be multiplied without necessity – could be taken to suggest that there is no pressing need to investigate radically new ideas.3
One motivation for string theory, and one reason why this book exists, is that we know that this is not true. What has worked so far must fail at sufficiently short distances. In fact, the theories that we currently have signal their own demise. As we move continually down in size, there is a distance by which this failure must become manifest – a gaping and obvious hole in our attempts to understand nature. This distance is called the Planck length. This distance is genuinely tiny: one billion billion times smaller than the typical radius of the nucleus. It is as small compared to a nucleus as an atom is compared to the earth. This distance is nonetheless finite, and is a distance scale by which we know that our knowledge of physics must break down.
Why must current physics fail? We shall return to this in more detail in the next two chapters. Here, let me say that particle physics describes quantum particles in a classical spacetime. Spacetime is the fixed classical background against which the quantum interactions of particles take place. However, Einstein taught us that spacetime is actually not fixed – spacetime interacts, both with particles and with itself. The fully sophisticated version of this is general relativity, for which Newtonian gravity is for almost all purposes a good approximation.