The fundamental building blocks of the natural world, and three of the four fundamental forces of nature: the strong nuclear force, carried by gluons; the weak nuclear force, carried by W and Z bosons; and the electromagnetic force, carried by photons.
The fourth and final fundamental force is the most familiar – gravity. It is so weak that its effects on the subatomic world are invisible even in our most high-precision experiments, like those at HERA. If this statement seems a little mystifying, particularly if you’ve ever fallen off a ladder, then park it in your memory for a while; we’ll get back to gravity later when we discuss the shape of planets and galaxies.
These four particles, four forces and the Higgs boson appear to be all that is needed to make a water molecule, a honeybee, a human being, or planet Earth. This is a dazzlingly elegant and simple structure. For some reason, Nature didn’t adopt this economical scheme but instead made two further copies of the family of up quarks, down quarks, electrons and electron neutrinos. These two extra families are identical to the first family in every way except that they are more massive, possibly because they interact with Higgs particles in a different way. The existence of the three families of particle is another of the great mysteries, and discovering why Nature appears to have been unduly profligate is one of the most important goals of twenty-first-century particle physics. She won’t have been unduly profligate, of course! We know that three families is the minimum number to accommodate a process known as CP violation, which is needed to explain why, if the Universe started out with equal amounts of matter and anti-matter, there is matter left over in the Universe today to make stars and people. But that’s not an answer to the ‘Why?’ question, and it would be nice to know if the existence of planets, stars and galaxies is down to more than blind luck.
With these extra families, there are twelve fundamental particles of matter, four different sorts of force-carrying particle and the Higgs particle. That’s it, as far as we know – although I wouldn’t be surprised if some more pop up at the Large Hadron Collider over the next few years. This is fuelled by the fact that we already have good evidence from many independent astronomical observations that there is another form of matter in the Universe known as dark matter. There is five times more dark matter than ‘normal’ matter in the Universe by mass, and the dark matter cannot be made up out of the twelve particles that we’ve seen in experiments at particle accelerators such as HERA or the LHC. The collection of fundamental building blocks, circa 2015, is shown in the illustration opposite.
This isn’t intended to be a complete course on particle physics, much as I’d like to deliver that; rather, it is a chapter about shapes and patterns in Nature and what they reveal about the way in which the Universe works. Having said that, if you’ll allow me one last foray into particle physics, the story of the discovery of the quarks inside the proton and neutron is a very beautiful example of the way physicists notice patterns and attempt to explain them. The remarkable thing is that quarks were predicted before they were discovered experimentally.
Two baryon ‘super-multiplets’ showing the quark content of each baryon.
The theoretical prediction that building blocks exist beneath the level of protons and neutrons was made by Murray Gell-Mann and George Zweig in 1964. It was based on a pattern in the subatomic particles known at the time. By the early 1960s, an inelegant, profligate and seemingly ever-expanding list of subatomic building blocks had been discovered. The proton and neutron are part of a whole family of particles known as baryons; there are Lambdas, Sigmas, Deltas, Cascades and a host of others. There is also a family of particles known as mesons: Pions, Kaons, Rho and so on. There are thirteen different types of Lambda particle alone, nine Sigmas and eight Kaons. Particle physics was looking increasingly like a subatomic branch of botany. Then Gell-Mann and Zweig noticed a beautiful pattern. The particles could be arranged according to their observed properties in geometrical patterns. Two such patterns are shown in the illustration (left). Today, these are known as ‘super-multiplets’.
As Kepler suspected when he considered the six-fold symmetry of snowflakes, patterns in nature are often a clue that there is a deeper underlying structure. The patterns may or may not be easy to recognise – Gell-Mann received the Nobel Prize in Physics in 1969 for noticing the pattern amongst the particles – but they are the Rosetta Stone that allows Nature’s language to be deciphered. In this case, the pattern in the particles suggested to Gell-Mann and Zweig that the baryons are all constructed out of three smaller building blocks, that Gell-Mann called quarks. When they first recognised the pattern, they included three quarks in their scheme: up, down and strange. The different baryons on the lower planes of the super-multiples are the possible three-fold combinations of the three building blocks. A dding a fourth quark – charm – constructs the higher layers. The quark constituents of the particles are shown in the illustration opposite: for example the Delta++ contains three up quarks.
The particle on the base of the pyramid in the illustration (left) known as the Omega-minus, is of particular historical interest because its existence was predicted by Gell-Mann at a meeting at CERN in 1962, based solely on the pattern of the base of the pyramid. It was subsequently discovered at the Brookhaven National Laboratory in the United States in 1964. When a theory predicts the existence of something new that is subsequently discovered, we can have particular confidence that we are on the right track.
We’ve met three of the four fundamental forces of nature; the strong and weak nuclear forces and electromagnetism, and the twelve building blocks of nature. We will now turn to the final, weakest and most familiar force – gravity – and investigate it by thinking about the size and shape of the objects it sculpts. These are not tiny things like subatomic particles, or small things like snowflakes, but very much larger structures: planets, stars and galaxies.
Why is the Earth a sphere?
This picture of Earth is known as the Blue Marble. It was taken on 7 December 1972 by the crew of Apollo 17 during their journey to the Moon. Close to the winter solstice, Antarctica is a continent of permanent light, and Madagascar, the island of lemurs, takes centre stage. Ochre deserts set against blue oceans, green hues hinting at life.
On 5 December 2012, NASA released the Black Marble, an image of the Americas at night. Now we see a civilisation on the planet; the lights herald the dawn of the Anthropocene – the age of human dominance. What do you see in these images? What is the most basic property of Earth? Alexei Leonov, on completing the first human spacewalk on 18 March 1965, had an answer.
‘I never knew what the word round meant until I saw Earth from space.’
Alexei Leonov, Voskhod 2, Soyuz 19/ASTP
Seen from space, the Earth is a near-perfect sphere. All the planets in the Solar System, all the large moons and the Sun itself share this property, as does every star in the Universe. Why? If lots of different objects share a common feature, there must be an explanation. To make progress, let’s think about what could affect the shape of a planet, moon or star. It can’t be much to do with their composition because planets are made of different stuff to stars. The Earth is made up of heavy chemical elements such as iron, oxygen, silicon and carbon. The Sun, on the other hand, is primarily hydrogen and helium; it’s a giant ball of plasma with no solid surface. Giant planets such as Jupiter have more in common with stars than with Earth, at least in terms of their composition. They too are primarily composed of hydrogen and helium. Stars and planets are united, however, by the force that formed them and holds them together – gravity. So to understand why they are all spherical, we should explore the nature of the gravitational force further.
Soviet astronaut Alexei Leonov taking Man’s first steps into space on 18 March 1965.
Defying gravity
For most of the time Tarragona is a quiet Mediterranean port on the northeastern coast of Spain, but each September it explodes into vivid, violent colour as teams compete against gravity in the T
arragona Castells competition. Castells are human towers, reaching ten people high and involving an intricate mix of strength, balance, strategy and teamwork to be built up to the top. Each team begins by forming the foundations of the tower, with up to two hundred people creating the pinya. Once the foundation is in place, a variety of human geometries are used to build as high as possible, with each level taking shape before the next is added. The most successful team is the Castellers de Vilafranca, having won the Tarragona competition eight times since 1972. A mass of green shirts acting in unison flows from one level to the next, with higher levels consisting of fewer people, until two children form a final stable platform for the exaneta – the castellar who ascends daringly to the summit; since low mass, agility – and perhaps a lack of fear – are called for, the exaneta will be as young as 6 or 7 years old. This is what the crowds have come to see. Towers give way, human buildings come tumbling down, falls softened by the elbows, knees, heads and shoulders, colliding and crashing, usually delivering only bruises, bumps and the occasional lost tooth. Serious injuries are very rare.
The iconic Blue Marble – Earth as seen from Apollo 17 on 7 December 1972.
The Black Marble. Released by NASA on 5 December 2012. This image, taken 40 years after the Blue Marble, shows the presence of human civilisation through the illuminated city lights.
‘Força, equilibri, valor i seny’
(Strength, balance, courage and common sense)
The teams in action building the Castells, human towers that defy gravity – and fear!
It is obvious why people fall to the ground if they lose their balance: gravity. But how precisely do objects behave under the influence of gravity? We have two theoretical frameworks, both of which are still in use, depending on what we wish to calculate. Here we see an idea central to the success of science; there are no absolute truths! Usefulness is the figure of merit; if a theory can be used to make predictions that agree with experiment in certain circumstances, then as long as we understand the restrictions, we can continue to use the theory. The first theory of gravity was written down by Isaac Newton in 1687 in his Philosophiae Naturalis Principia Mathematica – the mathematical principles of natural philosophy, inspired at least in part by the work of our curious companion, Johannes Kepler.
A more precise description of gravity was published in 1915 by Albert Einstein. Newton’s theory doesn’t have anything to say about the mechanism by which gravity acts between objects, but it does allow us to calculate the gravitational force between any objects, anywhere in the Universe. Einstein’s more accurate Theory of General Relativity provides an explanation for the force of gravity. Space and time are distorted by the presence of matter and energy, and objects travel in straight lines through this curved and distorted spacetime. Because of the distortion, it appears to us as if the objects are being acted upon by a force, which we call gravity. But in Einstein’s picture there isn’t a force; there is curved spacetime and the rule that everything travels in a straight line through it. We will encounter spacetime in much more detail in Chapter Two.
To answer the question about spherical planets, we don’t need Einstein’s elegant but significantly more mathematically challenging Theory of General Relativity. It is a sledgehammer to crack a nut. We’ll therefore confine ourselves to Newton’s simpler theory; General Relativity would give the same answer. Here is Newton’s Law of Universal Gravitation:
F = G m M / r2
In words, this equation says that there is a force between all objects, F, which is equal to the product of their masses, m and M, and inversely proportional to the square of their distance apart, r. If you double the distance between two objects, the gravitational force between them falls by a factor of 4. G is known as Newton’s Constant, and it tells us the strength of the gravitational force. If we measure mass in kilograms, distance in metres and wish to know the gravitational force in Newtons, then G = 6.6738 x 10-11 m3 kg-1s-2.
Newton’s Gravitational Constant is one of the fundamental physical constants. It describes a property of our Universe that can be measured, but not derived from some deeper principle, as far as we know. One of the great unsolved questions in physics is why Newton’s gravitational constant is so small, which is equivalent to asking why the gravitational force between objects is so weak. Comparing the strengths of forces is not entirely straightforward, because they change in strength depending on the energy scale at which you probe them; very close to the Big Bang, at what is known as the Planck temperature – 1.417 x 1032 degrees Celsius – we have good reason to think that all four forces had the same strength. To describe physics at such temperatures we require a quantum theory of gravity, which we don’t currently possess in detail. But at the energies we encounter in everyday life, gravity is around forty orders of magnitude weaker than the electromagnetic force; that’s 1 followed by 40 zeroes. This smallness seems absurd, and demands an explanation. Physicists speculate about extra spatial dimensions in the Universe and other exotic ideas, but as yet we have no experimental evidence to point the way. One possibility is that the constants of nature were randomly selected at the Big Bang, in which case they are simply a set of incalculable fundamental numbers that define what sort of Universe we happen to live in. Or maybe we will one day possess a theory that is able to explain why the fundamental numbers take on the values they do.
It is through missions such as that of the lunar module in July 1969 that we learn about the relationship between Earth and the Moon and the formation of the planets.
Newton discovered his law of gravity by looking for a simple equation that could describe the apparent complexity of the motions of the planets around the Sun. Kepler’s three empirical laws of planetary motion can be derived from Newton’s Law of Gravitation and his laws of motion. This is why we might describe Newton’s theory as elegant, in line with our discussion of quantum theory earlier in the chapter. Newton discovered a simple equation that is able to describe a wide range of phenomena: the flight of artillery shells on Earth, the orbits of planets around the Sun, the orbits of the moons of Jupiter and Saturn, the motion of stars within galaxies. His was the first truly universal law of Nature to be discovered.
The gravitational force is the sculptor of planets. Our Solar System formed from a cloud of gas and dust, collapsing due to the attractive force of gravity around 4.6 billion years ago.
The answer to our question ‘why is the Earth spherical?’ must be contained within Newton’s equation, because the Earth formed by the action of gravity. The gravitational force is the sculptor of planets. Our solar system formed from a cloud of gas and dust, collapsing due to the attractive force of gravity around 4.6 billion years ago. The Sun formed first, followed by the planets. Let’s fast-forward a few million years to a time when the infant sun is shining in the centre of a planet-less solar system. Circling the young sun are the remains of the cloud of dust and gas out of which the Sun formed, containing all the ingredients to make a planet. This is known as a protoplanetary disc. The fine details of the formation of planets are still a matter of active research, and the mechanisms may be different for rocky planets such as the Earth and gas giants such as Jupiter. For Earth-like planets, random collisions between dust particles can result in the formation of objects of around 1 kilometre in diameter known as planetesimals. These grow larger as they attract smaller lumps of rock and dust by their gravitational pull, increasing their mass, which increases their gravitational pull, attracting more objects, and so on. This is known as runaway accretion, and computer simulations using Newton’s laws suggest that through a series of collisions between these ever-growing planetesimals, a small number of rocky planets emerge from the protoplanetary disc orbiting the young star.
The Moon leaves the shadow of the Earth on 28 September 2015 in Glastonbury, England. This so-called Super Moon – because it is the closest full Moon to the Earth – coincided with a lunar eclipse, which last occurred in 1982.
Models of planetary format
ion can be checked using the telescopic observation of young star systems. In 2014 the ALMA (Atacama Large Millimeter/submillimeter Array) observatory in Chile captured a beautiful image of a planetary system forming inside a protoplanetary disc around HL Tauri, a system less than 100,000 years old and only 450 light years from Earth. A series of bright concentric rings is clearly visible, separated by darker areas. It is thought that these dark gaps are being cleared by embryonic planets orbiting around the star and sweeping up material – they are the shadow of the planetary orbits. It is interesting to note that planetary formation appears to be well advanced in this very young system. This image is perhaps a glimpse of what our Solar System looked like 4.5 billion years ago.
All objects in the Solar System are not spheres. The Martian moon Phobos is a misshapen lump. Smaller still are the asteroids, comets and grains of dust that formed at the same time as the planets.
Comet 67P/Churyumov–Gerasimenko, as photographed by the Rosetta spacecraft from cometary orbit on 2 August 2014.
Rocky planets begin life as small, irregular planetesimals and evolve over time into spheres. To make progress in understanding why, we might make an observation; all objects in the Solar System are not spheres. The picture on here shows the Martian moon, Phobos, which has a radius of approximately 11 kilometres. It is a misshapen lump. Smaller still are the asteroids, comets and grains of dust that formed at the same time as the planets. The picture bottom left shows Comet 67P/Churyumov–Gerasimenko, which is less than 5 kilometres across and is an intriguing dumbbell shape. Analysis of data from the Rosetta spacecraft, in orbit around the comet at the time of writing, has shown that 67P was formed by a low-velocity collision of two larger objects. Perhaps this is a snapshot of the processes that previously resulted in the formation of much larger objects such as planets and moons. Smaller lumps of rock merge together under the influence of gravity, and if there is enough material in the vicinity, as there would have been early in the life of the Solar System, the objects will undergo many such collisions and grow. Why isn’t comet 67P spherical?
Forces of Nature Page 4
