The whole history of science has been the gradual realisation that events do not happen in an arbitrary manner, but that they reflect a certain underlying order. (p.122)

This book was a publishing phenomenon when it was published in 1988. Nobody thought a book of abstruse musings about obscure theories of cosmology would sell, but it became a worldwide bestseller, selling more than 10 million copies in 20 years. It was on the London Sunday Times bestseller list for more than five years and was translated into 35 languages by 2001. So successful that Hawking went on to write seven more science books on his own, and co-author a further five.

Accessible As soon as you start reading you realise why. From the start is it written in a clear accessible way and you are soon won over to the frank, sensible, engaging tone of the author. He tells us he is going to explain things in the simplest way possible, with an absolute minimum of maths or equations (in fact, the book famously includes only one equation E = mc²).

Candour He repeatedly tells us that he’s going to explain things in the simplest possible way, and the atmosphere is lightened when Hawking – by common consent one of the great brains of our time – confesses that he has difficulty with this or that aspect of his chosen subject. (‘It is impossible to imagine a four-dimensional space. I personally find it hard enough to visualise three-dimensional space!’) We are not alone in finding it difficult!

Historical easing Also, like most of the cosmology books I’ve read, it takes a deeply historical view of the subject. He doesn’t drop you into the present state of knowledge with its many accompanying debates i.e. at the deep end. Instead he takes you back to the Greeks and slowly, slowly introduces us to their early ideas, showing why they thought what they thought, and how the ideas were slowly disproved or superseded.

A feel for scientific change So, without the reader being consciously aware of the fact, Hawking accustoms us to the basis of scientific enquiry, the fundamental idea that knowledge changes, and from two causes: from new objective observations, often the result of new technologies (like the invention of the telescope which enabled Galileo to make his observations) but more often from new ideas and theories being worked out, published and debated.

Hawking’s own contributions There’s also the non-trivial fact that, from the mid-1960s onwards, Hawking himself has made a steadily growing contribution to some of the fields he’s describing. At these points in the story, it ceases to be an objective history and turns into a first-person account of the problems as he saw them, and how he overcame them to develop new theories. It is quite exciting to look over his shoulder as he explains how and why he came up with the new ideas that made him famous. There are also hints that he might have trodden on a few people’s toes in the process, for those who like their science gossipy.

Thus it is that Hawking starts nice and slow with the ancient Greeks, with Aristotle and Ptolemy and diagrams showing the sun and other planets orbiting round the earth. Then we are introduced to Copernicus, who first suggested the planets orbit round the sun, and so on. With baby steps he takes you through the 19th century idea of the heat death of the universe, on to the discovery of the structure of the atom at the turn of the century, and then gently introduces you to Einstein’s special theory of relativity of 1905. (The special theory of relativity doesn’t take account of gravity, the general theory of relativity of 1915, does, take account of gravity).

Chapter 1 Our Picture of the Universe (pp.1-13)

Aristotle thinks earth is stationary. Calculates size of the earth. Ptolemy. Copernicus. In 1609 Galileo starts observing Jupiter using the recently invented telescope. Kepler suggests the planets move in ellipses not perfect circles. 1687 Isaac newton publishes Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) ‘probably the most important single work ever published in the physical sciences’, among many other things postulating a law of universal gravity. One implication of Newton’s theory is that the universe is vastly bigger than previously conceived.

In 1823 Heinrich Olbers posited his paradox which is, if the universe is infinite, the night sky out to be as bright as daylight because the light from infinite suns would reach us. Either it is not infinite or it has some kind of limit, possibly in time i.e. a beginning. The possible beginning or end of the universe were discussed by Immanuel Kant in his obscure work A Critique of Pure Reason  (1781). Various other figures debated variations on this theme until in 1929 Edwin Hubble made the landmark observation that, wherever you look, distant galaxies are moving away from us i.e. the universe is expanding. Working backwards from this observation led physicists to speculate that the universe was once infinitely small and infinitely dense, in a state known as a singularity, which must have exploded in an event known as the big bang.

He explains what a scientific theory is:

A theory is just a model of the universe, or a restricted part of it, and a set of rules that relate quantities in the model to observations that we make… A theory is a good theory if it satisfies two requirements: it must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations.

A theory is always provisional. The more evidence proving it, the stronger it gets. But it only takes one good negative observation to disprove a theory.

Today scientists describe the universe in terms of two basic partial theories – the general theory of relativity and quantum mechanics. They are the great intellectual achievements of the first half of this century.

But they are inconsistent with each other. One of the major endeavours of modern physics is to try and unite them in a quantum theory of gravity.

Chapter 2 Space and Time (pp.15-34)

Aristotle thought everything in the universe was naturally at rest. Newton disproved this with his first law – whenever a body is not acted on by any force it will keep on moving in a straight line at the same speed. Newton’s second law stats that, When a body is acted on by a force it will accelerate or change its speed at a rate that is proportional to the force. Newton’s law of gravity states that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. But like Aristotle, Newton believed all the events he described took place in a kind of big static arena named absolute space, and that time was an absolute constant. The speed of light was also realised to be a constant. In 1676 Danish astronomer Ole Christensen estimated the speed of light to be 140,000 miles per second. We now know it is 186,000 miles per second. In the 1860s James Clerk Maxwell unified the disparate theories which had been applied to magnetism and electricity.

In 1905 Einstein published his theory of relativity. It is derived not from observation but from Einstein working through in his head the consequences and shortcomings of the existing theories. Newton had posited a privileged observer, someone outside the universe who was watching it as if a play on a stage. From this privileged position a number of elements appeared constant, such as time.

Einstein imagines a universe in which there is no privileged outside point of view. We are all inside the universe and all moving. The theory threw up a number of consequences. One is that energy is equal to mass times the speed of light squared, or E = mc². Another is that nothing may travel faster than the speed of light. Another is that, as an object approaches the speed of light its mass increases. One of its most disruptive ideas is that time is relative. Different observes, travelling at different speeds, will see a beam of light travel take different times to travel a fixed distance. Since Einstein has made it axiomatic that the speed of light is fixed, and we know the distance travelled by the light is fixed, then time itself must appear different to different observers. Time is something that can change, like the other three dimensions. Thus time can be added to the existing three dimensions to create space-time.

The special theory of relativity was successful in explaining how the speed of light appears the same to all observers, and describing what happens to things when they move close to the speed of light. But it was inconsistent with Newton’s theory of gravity which says objects attract each other with a force related to the distance between them. If you move on of the objects the force exerted on the other object changes immediately. This cannot be if nothing can travel faster than the speed of light, as the special theory of relativity postulates. Einstein spent the ten or so years from 1905 onwards attempting to solve this difficulty. Finally, in 1915, he published the general theory of relativity.

The revolutionary basis of this theory is that space is not flat, a consistent  continuum or Newtonian stage within which events happen and forces interact in a sensible way. Space-time is curved or warped by the distribution of mass or energy within it, and gravity is a function of this curvature. Thus the earth is not orbiting around the sun in a circle, it is following a straight line in warped space.

The mass of the sun curves space-time in such a way that although the earth follows a straight line in four-dimensional pace-time, it appears to us to move along a circular orbit in three-dimensional space. (p.30)

In fact, at a planetary level Einstein’s maths is only slightly different from Newton’s but it predicts a slight difference in the orbit of Mercury which observations have gone on to prove. Also, the general theory predicts that light will bend, following a straight line but through space that is warped or curved by gravity. Thus the light from a distant star on the far side of the sun will bend as it passes close to the sun due to the curvature in space-time caused by the sun’s mass. And it was an expedition to West Africa in 1919 to observe an eclipse, which showed that light from distant stars did in fact bend slightly as it passed the sun, which helped confirm Einstein’s theory.

Newton’s laws of motion put an end to the idea of absolute position in space. The theory of relativity gets rid of absolute time.

Hence the thought experiment popularised by a thousand science fiction books that astronauts who set off in a space ship which gets anywhere near the speed of light will experience a time which is slower than the people they leave behind on earth.

In the theory of relativity there is no unique absolute time, but instead each individual has his own personal measure of time that depends on where he is and how he is moving. (p.33)

Obviously, since most of us are on planet earth, moving at more or less the same speed, everyone’s personal ‘times’ coincide. Anyway, the key central implication of Einstein’s general theory of relativity is this:

Before 1915, space and time were thought of as a fixed arena in which events took place, but which was not affected by what happened in it. This was true even of the special theory of relativity. Bodies moved, forces attracted and repelled, but time and space simply continued, unaffected. It was natural to think that space and time went on forever.

the situation, however, is quite different in the general theory of relativity. Space and time are now dynamic quantities. : when a body moves, or a force acts, it affects the curvature of space and time – and in turn the structure of space-time affects the way in which bodies move and forces act. Space and time not only affect but also are affected by everything that happens in the universe. (p.33)

This view of the universe as dynamic and interacting, by demolishing the old eternal static view, opened the door to a host of new ways of conceiving how the universe might have begun and might end.

Chapter 3 The Expanding Universe (pp.35-51)

Our modern picture of the universe dates to 1924 when American astronomer Edwin Hubble demonstrated that ours is not the only galaxy. We now know the universe is home to some hundred million galaxies, each containing some hundred thousand million stars. We live in a galaxy that is about one hundred thousand light-years across and is slowly rotating. Hubble set about cataloguing the movement of other galaxies and in 1929 published his results which showed that they are all moving away from us, and that, the further away a galaxy is, the faster it is moving.

The discovery that the universe is expanding was one of the great intellectual revolutions of the twentieth century. (p.39)

From Newton onwards there was a universal assumption that the universe was infinite and static. Even Einstein invented a force he called ‘the cosmological constant’ in order to counter the attractive power of gravity and preserve the model of a static universe. It was left to Russian physicist Alexander Friedmann to seriously calculate what the universe would look like if it was expanding.

In 1965 two technicians, Arno Penzias and Robert Wilson, working at Bell Telephone Laboratories discovered a continuous hum of background radiation coming from all parts of the sky. This echoed the theoretical work being done by two physicists, Bob Dicke and Jim Peebles, who were working on a suggestion made by George Gamow that the early universe would have been hot and dense. They posited that we should still be able to see the light from this earliest phase but that it would, because the redshifting, appear as radiation. Penzias and Wilson were awarded the Nobel Prize in 1987.

How can the universe be expanding? Imagine blowing up a balloon with dots (or little galaxies) drawn on it: they all move apart from each other and the further apart they are, the larger the distance becomes; but there is no centre to the balloon. Similarly the universe is expanding but not into anything. There is no outside. If you set out to travel to the edge you would find no edge but instead find yourself flying round the periphery and end up back where you began.

There are three possible states of a dynamic universe. Either 1. it will expand against the contracting force of gravity until the initial outward propulsive force is exhausted and gravity begins to win; it will stop expanding, and start to contract. Or 2. it is expanding so fast that the attractive, contracting force of gravity never wins, so the universe expands forever and matter never has time to clump together into stars and planets. Or 3. it is expanding at just the right speed to escape collapsing back in on itself, but but so fast as to make the creation of matter impossible. This is called the critical divide. Physicists now believe the universe is expanding at just around the value of the critical divide, though whether it is just under or just above (i.e. the universe will eventually cease expanding, or not) is not known.

Dark matter We can calculate the mass of all the stars and galaxies in the universe and it is a mystery that our total is only about a hundredth of the mass that must exist to explain the gravitational behaviour of stars and galaxies. In other words, there must a lot of ‘dark matter’ which we cannot currently detect in order for the universe to be shaped the way it is.

So we don’t know what the likely future of the universe is (endless expansion or eventual contraction) but all the Friedmann models do predict that the universe began in an infinitely dense, infinitely compact, infinitely hot state – the singularity.

Because mathematics cannot really handle infinite numbers, this means that the general theory of relativity… predicts that there is a point in the universe where the theory itself breaks down… In fact, all our theories of science are formulated on the assumption that space-time is smooth and nearly flat, so they break down at the big bang singularity, where the curvature of space-time is infinite. (p.46)

Opposition to the theory came from Hermann Bondi, Thomas Gold and Fred Hoyle who formulated the steady state theory of the universe i.e. it has always been and always will be. All that is needed to explain the slow expansion is the appearance of new particles to keep it filled up, but the rate is very low (about one new particle per cubic kilometre per year). They published it in 1948 and worked through all its implications for the next few decades, but it was killed off as a theory by the 1965 observations of the cosmic background radiation.

He then explains the process whereby he elected to do a PhD expanding Roger Penrose’s work on how a dying star would collapse under its own weight to a very small size. The collaboration resulted in a joint 1970 paper which proved that there must have been a big bang, provided only that the theory of general relativity is correct, and the universe contains as much matter as we observe.

If the universe really did start out as something unimaginably small then, from the 1970s onwards, physicists turned their investigations to what happens to matter at microscopic levels.

Chapter 4 The Uncertainty Principle (pp.53-61)

1900 German scientist Max Planck suggests that light, x-rays and other waves can only be emitted at an arbitrary wave, in packets he called quanta. He theorised that the higher the frequency of the wave, the more energy would be required. This would tend to restrict the emission of high frequency waves. In 1926 Werner Heisenberg expanded on these insights to produce his Uncertainty Principle. In order to locate a particle in order to measure its position and velocity you need to shine a light on it. One has to use at least one quantum of energy. However, exposing the particle to this quantum will disturb the velocity of the particle.

In other words, the more accurately you try to measure the position of the particle, the less accurately you can measure its speed, and vice versa. (p.55)

Heisenberg showed that the uncertainty in the position of the particle times the uncertainty in its velocity times the mass of the particle can never be smaller than a certain quantity, which is known as Planck’s constant. For the rest of the 1920s Heisenberg, Erwin Schrödinger and Paul Dirac reformulated mechanics into a new theory titled quantum mechanics. In this theory particles no longer have separate well-defined positions and velocities, instead they have a general quantum state which is a combination of position and velocity.

Quantum mechanics introduces an unavoidable element of unpredictability or randomness into science. (p.56)

Also, particles can no longer be relied on to be particles. As a result of Planck and Heisenberg’s insights, particles have to be thought of as sometimes behaving like waves, sometimes like particles. In 1913 Niels Bohr had suggested that electrons circle round a nucleus at certain fixed points, and that it takes energy to dislodge them from these optimum orbits. Quantum theory helped explain Bohr’s theory by conceptualising the circling electrons not as particles but as waves. If electrons are waves, as they circle the nucleus, their wave lengths would cancel each other out unless they are perfect numbers. The frequency of the waves have to be able to circle the nucleus in perfect integers. This defines the height of the orbits electrons can take.

Chapter 5 Elementary Particles and Forces of Nature (pp.63-79)

A chapter devoted to the story of how we’ve come to understand the world of sub-atomic particles. Starting (as usual) with Aristotle and then fast-forwarding through Galton, Einstein’s paper on Brownian motion, J.J. Thomson’s discovery of electrons, and, in 1911, Ernest Rutherford’s demonstration that atoms are made up of tiny positively charged nucleus around which a number of tiny positively charged particles, electrons, orbit. Rutherford thought the nuclei contained ‘protons’, which have a positive charge and balance out the negative charge of the electrons. In 1932 James Chadwick discovered the nucleus contains neutrons, same mass as the proton but no charge.

In 1965 quarks were discovered by Murray Gell-Mann. In fact scientists went on to discover six types, up, down, strange, charmed, bottom and top quarks. A proton or neutron is made up of three quarks.

He explains the quality of spin. Some particles have to be spin twice to return to their original appearance. They have spin 1/2. All the matter we can see in the universe has the spin 1/2. Particles of spin 0, 1, and 2 give rise to the forces between the particles.

Pauli’s exclusionary principle: two similar particles cannot exist in the same state, they cannot have the same position and the same velocity. The exclusionary principle is vital since it explains why the universe isn’t a big soup of primeval particles. The particles must be distinct and separate.

In 1928 Paul Dirac explained why the electron must rotate twice to return to its original position. He also predicted the existence of the positron to balance the electron. In 1932 the positron was discovered and Dirac was awarded a Nobel Prize.

Force carrying particles can be divided into four categories according to the strength of the force they carry and the particles with which they interact.

1. Gravitational force, the weakest of the four forces by a long way.
2. The electromagnetic force interacts with electrically charged particles like electrons and quarks.
3. The weak nuclear force, responsible for radioactivity. In findings published in 1967 Abdus Salam and Steven Weinberg suggested that in addition to the photon there are three other spin-1 particles known collectively as massive vector bosons. Initially disbelieved, experiments proved them right and they collected the Nobel Prize in 1979. In 1983 the team at CERN proved the existence of the three particles, and the leaders of this team also won the Nobel Prize.
4. The strong nuclear force holds quarks together in the proton and neutron, and holds the protons and neutrons together in the nucleus. This force is believed to be carried by another spin-1 particle, the gluon. They have a property named ‘confinement’ which is that you can’t have a quark of a single colour, the number of quarks bound together must cancel each other out.

The idea behind the search for a Grand Unified Theory is that, at high enough temperature, all the particles would behave in the same way, i.e. the laws governing the four forces would merge into one law.

Most of the matter on earth is made up of protons and neutrons, which are in turn made of quarks. Why is there this preponderance of quarks and not an equal number of anti-quarks?

Hawking introduces us to the notion that all the laws of physics obey three separate symmetries known as C, P and T. In 1956 two American physicists suggested that the weak force does not obey symmetry C. Hawking then goes on to explain more about the obedience or lack of obedience to the rules of symmetry of particles at very high temperatures, to explain why quarks and matter would outbalance anti-quarks and anti-matter at the big bang in a way which, frankly, I didn’t understand.

Chapter 6 Black Holes (pp.81-97)

In a sense, all the preceding has been just preparation, just a primer to help us understand the topic which Hawking spent the 1970s studying and which made his name – black holes.

The term black hole was coined by John Wheeler in 1969. Hawking explains the development of ideas about what happens when a star dies. When a star is burning, the radiation of energy in the forms of heat and light counteracts the gravity of its mass. When it runs out of fuel, gravity takes over and the star collapses in on itself. The young Indian physicist Subrahmanyan Chandrasekhar calculated that a cold star with a mass of more than one and a half times the mass of our sin would not be able to support itself against its own gravity and contract to become a ‘white dwarf’ with a radius of a few thousand miles and a density of hundreds of tones per square inch.

The Russian Lev Davidovich Landau speculated that the same sized star might end up in a different state. Chandrasekhar had used Pauli’s exclusionary principle as applied to electrons i.e. calculated the smallest densest state the mass could reach assuming no electron can be in the place of any other electron. Landau calculated on the basis of the exclusionary principle repulsion operative between neutrons and protons. Hence his model is known as the ‘neutron star’, which would have a radius of only ten miles or so and a density of hundreds of millions of tonnes per cubic inch.

(In an interesting aside Hawking tells us that physics was railroaded by the vast Manhattan Project to build an atomic bomb, and then to build a hydrogen bomb, throughout the 1940s and 50s. This tended to sideline large-scale physics about the universe. It was only the development of a) modern telescopes and b) computer power, that revived interest in astronomy.)

A black hole is what you get when the gravity of a collapsing star becomes so high that it prevents light from escaping its gravitational field. Hawking and Penrose showed that at the centre of a black hole must be a singularity of infinite density and space-time curvature.

In 1967 the study of black holes was revolutionised by Werner Israel. He showed that, according to general relativity, all non-rotating black holes must be very simple and perfectly symmetrical.

Hawking then explains several variations on this theory put forward by Roger Penrose, Roy Kerr, Brandon Carter who proved that a hole would have an axis of symmetry. Hawking himself confirmed this idea. In 1973 David Robinson proved that a black hole had to have ‘a Kerr solution’. In other words, no matter how they start out, all black holes end up looking the same, a belief summed up in the pithy phrase, ‘A black hole has no hair’.

What is striking about all this is that it was pure speculation, derived entirely from mathematical models without a shred of evidence from astronomy.

Black holes are one of only a fairly small number of cases in the history of science in which a theory was developed in great detail as a mathematical model before there was any evidence from observations that it was correct. (p.92)

Hawking then goes on to list the best evidence we have for black holes, which is surprisingly thin. Since they are by nature invisible black holes can only be deduced by their supposed affect on nearby stars or systems. Given that black holes were at the centre of Hawking’s career, and are the focus of these two chapters, it is striking that there is, even now, very little direct empirical evidence for their existence.

(Eerily, as I finished reading A Brief History of Time, the announcement was made on 10 April 2019 that the first ever image has been generated of a black hole –

• First ever black hole image released)

Theory predicts that other stars which stray close to a black hole would have clouds of gas attracted towards it. As this matter falls into the black hole it will a) be stripped down to basic sub-atomic particles b) make the hole spin. Spinning would make the hole acquire a magnetic field. The magnetic field would shoot jets of particles out into space along the axis of rotation of the hole. These jets should be visible to our telescopes.

First ever image of a black hole, captured the Event Horizon Telescope (EHT). The hole is 40 billion km across, and 500 million trillion km away

Chapter 7 Black Holes Ain’t So Black (pp.99-113)

Black holes are not really black after all. They glow like a hot body, and the smaller they are, the hotter they glow. Again, Hawking shares with us the evolution of his thinking on this subject, for example how he was motivated in writing a 1971 paper about black holes and entropy at least partly in irritation against another researcher who he felt had misinterpreted his earlier results.

Anyway, it all resulted in his 1973 paper which showed that a black hole ought to emit particles and radiation as if it were a hot body with a temperature that depends only on the black hole’s mass.

The reasoning goes thus: quantum mechanics tells us that all of space is fizzing with particles and anti-particles popping into existence, cancelling each other out, and disappearing. At the border of the event horizon, particles and anti-particles will be popping into existence as everywhere else. But a proportion of the anti-particles in each pair will be sucked inside the event horizon, so that they cannot annihilate their partners, leaving the positive particles to ping off into space. Thus, black holes should emit a steady stream of radiation!

If black holes really are absorbing negative particles as described above, then their negative energy will result in negative mass, as per Einstein’s most famous equation, E = mc² which shows that the lower the energy, the lower the mass. In other words, if Hawking is correct about black holes emitting radiation, then black holes must be shrinking.

Gamma ray evidence suggests that there might be 300 black holes in every cubic light year of the universe. Hawking then goes on to estimate the odds of detecting a black hole a) in steady existence b) reaching its final state and blowing up. Alternatively we could look for flashes of light across the sky, since on entering the earth’s atmosphere gamma rays break up into pairs of electrons and positrons. No clear sightings have been made so far.

(Threaded throughout the chapter has been the notion that black holes might come in two types: one which resulted from the collapse of stars, as described above. And others which have been around since the start of the universe as a function of the irregularities of the big bang.)

Summary: Hawking ends this chapter by claiming that his ‘discovery’ that radiation can be emitted from black holes was ‘the first example of a prediction that depended in an essential way on both the great theories of this century, general relativity and quantum mechanics’. I.e. it is not only an interesting ‘discovery’ in its own right, but a pioneering example of synthesising the two theories.

Chapter 8 The Origin and Fate of the Universe (pp.115-141)

This is the longest chapter in the book and I found it the hardest to follow. I think this is because it is where he makes the big pitch for His Theory, for what’s come to be known as the Hartle-Hawking state. Let Wikipedia explain:

Hartle and Hawking suggest that if we could travel backwards in time towards the beginning of the Universe, we would note that quite near what might otherwise have been the beginning, time gives way to space such that at first there is only space and no time. Beginnings are entities that have to do with time; because time did not exist before the Big Bang, the concept of a beginning of the Universe is meaningless. According to the Hartle-Hawking proposal, the Universe has no origin as we would understand it: the Universe was a singularity in both space and time, pre-Big Bang. Thus, the Hartle–Hawking state Universe has no beginning, but it is not the steady state Universe of Hoyle; it simply has no initial boundaries in time or space. (Hartle-Hawking state Wikipedia article)

To get to this point Hawking begins by recapping the traditional view of the ‘hot big bang’, i.e. the almost instantaneous emergence of matter from a state of infinite mass, energy and density and temperature.

This is the view first put forward by Gamow and Alpher in 1948, which predicted there would still be very low-level background radiation left over from the bang – which was then proved with the discovery of the cosmic background radiation in 1965.

Hawking gives a picture of the complete cycle of the creation of the universe through the first generation of stars which go supernova blowing out into space the heavier particles which then go into second generation stars or clouds of gas and solidify into things like planet earth.

In a casual aside, he gives his version of the origin of life on earth:

The earth was initially very hot and without an atmosphere. In the course of time it cooled and acquired an atmosphere from the emission of gases from the rocks. This early atmosphere was not one in which we could have survived. It contained no oxygen, but a lot of other gases that are poisonous to us, such as hydrogen sulfide. There are, however, other primitive forms of life that can flourish under such conditions. It is thought that they developed in the oceans, possibly as a result of chance combinations of atoms into large structures, called macromolecules, which were capable of assembling other atoms in the ocean into similar structures. They would thus have reproduced themselves and multiplied. In some cases there would have been errors in the reproduction. Mostly these errors would have been such that the new macromolecule could not reproduce itself and eventually would have been destroyed. However, a few of the errors would have produced new macromolecules that were even better at reproducing themselves. They would have therefore had an advantage and would have tended to replace the original macromolecules. In this way a process of evolution was started that led to the development of more and more complicated, self-reproducing organisms. The first primitive forms of life consumed various materials, including hydrogen sulfide, and released oxygen. This gradually changed the atmosphere to the composition that it has today and allowed the development of higher forms of life such as fish, reptiles, mammals, and ultimately the human race. (p.121)

(It’s ironic that he discusses the issue so matter-of-factly, demonstrating that, for him at least, the matter is fairly cut and dried and not worth lingering over. Because, of course, for scientists who’ve devoted their lives to the origins-of-life question it is far from over. It’s a good example of the way that every specialist thinks that their specialism is the most important subject in the world, the subject that will finally answer the Great Questions of Life whereas a) most people have never heard about the issues b) wouldn’t understand them and c) don’t care.)

Hawking goes on to describe chaotic boundary conditions and describe the strong and the weak anthropic principles. He then explains the theory proposed by Alan Guth of inflation i.e. the universe, in the first milliseconds after the big bang, underwent a process of enormous hyper-growth, before calming down again to normal exponential expansion. Hawking describes it rather differently from Barrow and Davies. He emphasises that, to start with, in a state of hypertemperature and immense density, the four forces we know about and the spacetime dimensions were all fused into one. They would be in ‘symmetry’. Only as the early universe cooled would it have undergone a ‘phase transition’ and the symmetry between forces been broken.

If the temperature fell below the phase transition temperature without symmetry being broken then the universe would have a surplus of energy and it is this which would have cause the super-propulsion of the inflationary stage. The inflation theory:

• would allow for light to pass from one end of the (tiny) universe to the other and explains why all regions of the universe appear to have the same properties
• explain why the rate of expansion of the universe is close to the critical rate required to make it expand for billions of years (and us to evolve)
• would explain why there is so much matter in the universe

Hawking then gets involved in the narrative explaining how he and others pointed out flaws in Guth’s inflationary model, namely that the phase transition at the end of the inflation ended in ‘bubble’s which expanded to join up. But Hawking and others pointed out that the bubbles were expanding so fat they could never join up. In 1981 the Russian Andre Linde proposed that the bubble problem would be solved if  a) the symmetry broke slowly and b) the bubbles were so big that our region of the universe is all contained within a single bubble. Hawking disagreed, saying Linde’s bubbles would each have to be bigger than the universe for the maths to work out, and counter-proposing that the symmetry broke everywhere at the same time, resulting in the uniform universe we see today. Nonetheless Linde’s model became known as the ‘new inflationary model’, although Hawking considers it invalid.

[In these pages we get a strong whiff of cordite. Hawking is describing controversies and debates he has been closely involved in and therefore takes a strongly partisan view, bending over backwards to be fair to colleagues, but nonetheless sticking to his guns. In this chapter you get a strong feeling for what controversy and debate within this community must feel like.)

Hawking prefers the ‘chaotic inflationary model’ put forward by Linde in 1983, in which there is no phase transition or supercooling, but which relies on quantum fluctuations.

At this point he introduces four ideas which are each challenging and which, taken together, mark the most difficult and confusing part of the book.

First he says that, since Einstein’s laws of relativity break down at the moment of the singularity, we can only hope to understand the earliest moments of the universe in terms of quantum mechanics.

Second, he says he’s going to use a particular formulation of quantum mechanics, namely Richard Feynman’s idea of ‘a sum over histories’. I think this means that Feynman said that in quantum mechanics we can never know precisely which route a particle takes, the best we can do is work out all the possible routes and assign them probabilities, which can then be handled mathematically.

Third, he immediately points out that working with Feynman’s sum over histories approach requires the use of ‘imaginary’ time, which he then goes on to explain.

To avoid the technical difficulties with Feynman’s sum over histories, one must use imaginary time. (p.134)

And then he points out that, in order to use imaginary time, we must use Euclidean space-time instead of ‘real’ space-time.

All this happens on page 134 and was too much for me to understand. On page 135 he then adds in Einstein’s idea that the gravitational field us represented by curved space-time.

It is now that he pulls all these ideas together to assert that, whereas in the classical theory of gravity, which is based on real space-time there are only two ways the universe can behave – either it has existed infinitely or it had a beginning in a singularity at a finite point in time; in the quantum theory of gravity, which uses Euclidean space-time, in which the time direction is on the same footing as directions in space it is possible:

for space-time to be finite in extent and yet to have no singularities that formed a boundary or edge.

In Hawking’s theory the universe would be finite in duration but not have a boundary in time because time would merge with the other three dimensions, all of which cease to exist during and just after a singularity. Working backwards in time, the universe shrinks but it doesn’t shrink, as a cone does, to a single distinct point – instead it has a smooth round bottom with no distinct beginning.

The Hartle-Hawking no boundary Hartle and Hawking No-Boundary Proposal

Finally Hawking points out that this model of a no-boundary universe derived from a Feynman interpretation of quantum gravity does not give rise to all possible universes, but only to a specific family of universes.

One aspect of these histories of the universe in imaginary time is that none of them include singularities – which would seem to render redundant all the work Hawking had done on black holes in ‘real time’. He gets round this by saying that both models can be valid, but in order to demonstrate different things.

It is simply a matter of which is the more useful description. (p.139)

He winds up the discussion by stating that further calculations based on this model explain the two or three key facts about the universe which all theories must explain i.e. the fact that it is clumped into lumps of matter and not an even soup, the fact that it is expanding, and the fact that the background radiation is minutely uneven in some places suggesting very early irregularities. Tick, tick, tick – the no-boundary proposal is congruent with all of them.

It is a little mind-boggling, as you reach the end of this long and difficult chapter, to reflect that absolutely all of it is pure speculation without a shred of evidence to support it. It is just another elegant way of dealing with the problems thrown up by existing observations and by trying to integrate quantum mechanics with Einsteinian relativity. But whether it is ‘true’ or not, not only is unproveable but also is not really the point.

Chapter 9 The Arrow of Time (pp.143-153)

If Einstein’s theory of general relativity is correct and light always appears to have the same velocity to all observers, no matter what position they’re in or how fast they’re moving, THEN TIME MUST BE FLEXIBLE. Time is not a fixed constant. Every observer carries their own time with them.

Hawking points out that there are three arrows of time:

• the thermodynamic arrow of time which obeys the Second Law of Thermodynamics namely that entropy, or disorder, increases – there are always many more disordered states than ordered ones
• the psychological arrow of time which we all perceive
• the cosmological arrow of time, namely the universe is expanding and not contracting

Briskly, he tells us that the psychological arrow of time is based on the thermodynamic one: entropy increases and our lives experience that and our minds record it. For example, human beings consume food – which is a highly ordered form of energy – and convert it into heat – which is a highly disordered form.

Hawking tells us that he originally thought that, if the universe reach a furthest extent and started to contract, disorder (entropy) would decrease, and everything in the universe would happen backwards. Until Don Page and Raymond Laflamme, in their different ways, proved otherwise.

Now he believes that the contraction would not occur until the universe had been almost completely thinned out and all the stars had died i.e. the universe had become an even soup of basic particles. THEN it would start to contract. And so his current thinking is that there would be little or no thermodynamic arrow of time (all thermodynamic processes having come to an end) and all of this would be happening in a universe in which human beings could not exist. We will never live to see the contraction phase of the universe. If there is a contraction phase.

Chapter 10: The Unification of Physics (pp.155-169)

The general theory of relativity and quantum mechanics both work well for their respective scales (stars and galaxies, sub-atomic particles) but cannot be made to mesh, despite fifty of more years of valiant attempts. Many of the attempts produce infinity in their results, so many infinities that a strategy has been developed called ‘renormalisation’ which gets rid of the infinities, although Hawking conceded is ‘rather dubious mathematically’.

Grand Unified Theories is the term applied to attempts to devise a theory (i.e. a set of mathematical formulae) which will take account of the four big forces we know about: electromagnetism, gravity, the strong nuclear force and the weak nuclear force.

In the mid-1970s some scientists came up with the idea of ‘supergravity’ which postulated a ‘superparticle’, and the other sub-atomic particles variations on the super-particle but with different spins. According to Hawking the calculations necessary to assess this theory would take so long nobody has ever done it.

So he moves onto string theory i.e. the universe isn’t made up of particles but of open or closed ‘strings’, which can join together in different ways to form different particles. However, the problem with string theory is that, because of the mathematical way they are expressed, they require more than four dimensions. A lot more. Hawking mentions anywhere from ten up to 26 dimensions. Where are all these dimensions? Well, strong theory advocates say they exist but are very very small, effectively wrapped up into sub-atomic balls, so that you or I never notice them.

Rather simplistically, Hawking lists the possibilities about a complete unified theory. Either:

1. there really is a grand unified theory which we will someday discover
2. there is no ultimate theory but only an infinite sequence of possibilities which will describe the universe with greater and greater, but finite accuracy
3. there is no theory of the universe at all, and events will always seems to us to occur in a random way

This leads him to repeat the highfalutin’ rhetoric which all physicists drop into at these moments, about the destiny of mankind etc. Discovery of One Grand Unified Theory:

would bring to an end a long and glorious chapter in the history of humanity’s intellectual struggle to understand the universe. But it would also revolutionise the ordinary person’s understanding of the laws that govern the universe. (p.167)

I profoundly disagree with this view. I think it is boilerplate, which is a phrase defined as ‘used in the media to refer to hackneyed or unoriginal writing’.

Because this is not just the kind of phrasing physicists use when referring to the search for GUTs, it’s the same language biologists use when referring to the quest to understand how life derived from inorganic chemicals, it’s the same language the defenders of the large Hadron Collider use to justify spending billions of euros on the search for ever-smaller particles, it’s the language used by the guys who want funding for the Search for Extra-Terrestrial Intelligence), it’s the kind of language used by the scientists bidding for funding for the Human Genome Project.

Each of these, their defenders claim, is the ultimate most important science project, quest and odyssey ever,  and when they find the solution it will for once and all answer the Great Questions which have been tormenting mankind for millennia. Etc. Which is very like all the world’s religions claiming that their God is the only God. So a) there is a pretty obvious clash between all these scientific specialities which each claim to be on the brink of revealing the Great Secret.

But b) what reading this book and John Barrow’s Book of Universes convinces me is that i) we are very far indeed from coming even close to a unified theory of the universe and more importantly ii) if one is ever discovered, it won’t matter.

Imagine for a moment that a new iteration of string theory does manage to harmonise the equations of general relativity and quantum mechanics. How many people in the world are really going to be able to understand that? How many people now, currently, have a really complete grasp of Einsteinian relativity and Heisenbergian quantum uncertainty in their strictest, most mathematical forms? 10,000? 1000,000 earthlings?

If and when the final announcement is made who would notice, who would care, and why would they care? If the final conjunction is made by adapting string theory to 24 dimensions and renormalising all the infinities in order to achieve a multi-dimensional vision of space-time which incorporates both the curvature of gravity and the unpredictable behaviour of sub-atomic particles – would this really

revolutionise the ordinary person’s understanding of the laws that govern the universe?

Chapter 11 Conclusion (pp.171-175)

Recaps the book and asserts that his and James Hartle’s no-boundary model for the origin of the universe is the first to combine classic relativity with Heisenberg uncertainty. Ends with another rhetorical flourish of trumpets which I profoundly disagree with for the reasons given above.

If we do discover a complete theory, it should in time be understandable in broad principle by everyone, not just a few scientists. Then we shall all, philosophers, scientists, and just ordinary people, be able to take part in the discussion of the question of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason. (p.175)

Maybe I’m wrong, but I think this is a hopelessly naive view of human nature and culture. Einstein’s general theory has been around for 104 years, quantum mechanics for 90 years. Even highly educated people understand neither of them, and what Hawking calls ‘just ordinary people’ certainly don’t – and it doesn’t matter. 

Thoughts

Of course the subject matter is difficult to understand, but Hawking makes a very good fist of putting all the ideas into simple words and phrases, avoiding all formulae and equations, and the diagrams help a lot.

My understanding is that A Brief History of Time was the first popular science to put all these ideas before the public in a reasonably accessible way, and so opened the floodgates for countless other science writers, although hardly any of the ideas in it felt new to me since I happen to have just reread the physics books by Barrow and Davies which cover much the same ground and are more up to date.

But my biggest overall impression is how provisional so much of it seems. You struggle through the two challenging chapters about black holes – Hawking’s speciality – and then are casually told that all this debating and arguing over different theories and model-making had gone on before any black holes were ever observed by astronomers. In fact, even when Hawking died, in 2018, no black holes had been conclusively identified. It’s a big shame he didn’t live to see this famous photograph being published and confirmation of at least the existence of the entity he devoted so much time to theorising about.

Related links

• A Brief History Of Time: From Big Bang To Black Holes on Amazon

Reviews of other science books

Chemistry

• The Periodic Kingdom: A Journey Into the Land of the Chemical Elements by Peter Atkins (1995)

Cosmology

• The Perfect Theory by Pedro G. Ferreira (2014)
• The Book of Universes by John D. Barrow (2011)
• The Origin Of The Universe: To the Edge of Space and Time by John D. Barrow (1994)
• The Last Three Minutes: Conjectures about the Ultimate Fate of the Universe by Paul Davies (1994)
• A Brief History of Time: From the Big Bang to Black Holes by Stephen Hawking (1988)
• The Black Cloud by Fred Hoyle (1957)

The Environment

• The Sixth Extinction: An Unnatural History by Elizabeth Kolbert (2014)
• The Sixth Extinction by Richard Leakey and Roger Lewin (1995)

Genetics and life

• Life At The Speed of Light: From the Double Helix to the Dawn of Digital Life by J. Craig Venter (2013)
• What Is Life? How Chemistry Becomes Biology by Addy Pross (2012)
• Seven Clues to the Origin of Life by A.G. Cairns-Smith (1985)
• The Double Helix by James Watson (1968)

Human evolution

• The Origin of Our Species by Chris Stringer (2011)
• Guns, Germs and Steel by Jared Diamond (1997)

Maths

• Alex’s Adventures in Numberland by Alex Bellos (2010)
• Nature’s Numbers: Discovering Order and Pattern in the Universe by Ian Stewart (1995)
• Innumeracy: Mathematical Illiteracy and Its Consequences by John Allen Paulos (1988)
• A Mathematician Reads the Newspaper: Making Sense of the Numbers in the Headlines by John Allen Paulos (1995)

Particle physics

• Atomic by Jim Baggott (2009)

Psychology

• Tips For Trying To Think Less Irrationally
• Irrationality: The Enemy Within by Stuart Sutherland (1992)
• Judgement Under Uncertainty: Heuristics and Biases by Amos Tversky and Daniel Kahneman (1974)