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

Chemistry is the science of changes in matter. (p.37)

At just under 150 pages long, A Journey Into the Land of the Chemical Elements is intended as a novel and imaginative introduction to the 118 or so chemical elements which are the basic components of chemistry, and which, for the past 100 years or so, have been laid out in the grid arrangement known as the periodic table.

The periodic table explained

Just to refresh your memory, it’s called the periodic table because it is arranged into rows called ‘periods’. These are numbered 1 to 7 down the left-hand side.

What is a period? The ‘period number’ of an element signifies ‘the highest energy level an electron in that element occupies (in the unexcited state)’. To put it another way, the ‘period number’ of an element is its number of atomic orbitals. An orbital is the number of orbital positions an electron can take around the nucleus. Think of it like the orbit of the earth round the sun.

For each element there is a limited number of these ‘orbits’ which electrons can take up. Hydrogen, in row one, can only have one electron because it only has one possible orbital for an electron to take up around its nucleus. All the elements in row 2 have two orbitals for their electrons, and so on.

Sodium, for instance, sits in the third period, which means a sodium atom typically has electrons in the first three energy levels. Moving down the table, periods are longer because it takes more electrons to fill the larger and more complex outer levels.

The columns of the table are arranged into ‘groups’ from 1 to 18 along the top. Elements that occupy the same column or group have the same number of electrons in their outer orbital. These outer electrons are called ‘valence electrons’. The electrons in the outer orbital are the first ones to be involved in chemical bonds with other elements; they are relatively easy to dislodge, the ones in the lower orbitals progressively harder.

Elements with identical ‘valance electron configurations’ tend to behave in a similar fashion chemically. For example, all the elements in group or column 18 are gases which are slow to interact with other chemicals and so are known as the inert gases – helium, neon etc. Atkins describes the amazing achievement of the Scottish chemist William Ramsey in discovering almost all the inert gases in the 1890s.

Although there are 18 columns, the actual number of electrons in the outer orbital only goes up to 8. Take nitrogen in row 2 column 15. Nitrogen has the atomic number seven. The atomic number means there are seven electrons in a neutral atom of nitrogen. How many electrons are in its outer orbital? Although nitrogen is in the fifteenth column, that column is actually labelled ‘5A’. 5 represents the number of electrons in the outer orbital. So all this tells you that nitrogen has seven electrons in two orbitals around the nucleus, two in the first orbital and five in the second (2-5).

 

The Periodic Table. Karl Tate © LiveScience.com

Note that each element has two numbers in its cell. The one at the top is the atomic number. This is the number of protons in the nucleus of the element. Note how the atomic number increases in a regular, linear manner, from 1 for hydrogen at the top left, to 118 for Oganesson at the bottom right. After number 83, bismuth, all the elements are radioactive.

(N.B. When Atkins’s book was published in 1995 the table stopped at number 109, Meitnerium. As I write this, 24 years later, it has been extended to number 118, Oganesson. These later elements have been created in minute quantities in laboratories and some of them only exist for a few moments.)

Beneath the element name is the atomic weight. This is the mass of a given atom, measured on a scale in which the hydrogen atom has the weight of one. Because most of the mass in an atom is in the nucleus, and each proton and neutron has an atomic weight near one, the atomic weight is very nearly equal to the number of protons and neutrons in the nucleus.

Note the freestanding pair of rows at the bottom, coloured in purple and orange. These are the lanthanides and actinides. We’ll come to them in a moment.

Not only are the elements arranged into periods and groups but they are also categorised into groupings according to their qualities. In this diagram (taken from LiveScience.com) the different groupings are colour-coded. The groupings are, moving from left to right:

Alkali metals The alkali metals make up most of Group 1, the table’s first column. Shiny and soft enough to cut with a knife, these metals start with lithium (Li) and end with francium (Fr), among the rarest elements on earth: Atkins tells us that at any one moment there are only seventeen atoms of francium on the entire planet. The alkali metals are extremely reactive and burst into flame or even explode on contact with water, so chemists store them in oils or inert gases. Hydrogen, with its single electron, also lives in Group 1, but is considered a non-metal.

Alkaline-earth metals The alkaline-earth metals make up Group 2 of the periodic table, from beryllium (Be) through radium (Ra). Each of these elements has two electrons in its outermost energy level, which makes the alkaline earths reactive enough that they’re rarely found in pure form in nature. But they’re not as reactive as the alkali metals. Their chemical reactions typically occur more slowly and produce less heat compared to the alkali metals.

Lanthanides The third group is much too long to fit into the third column, so it is broken out and flipped sideways to become the top row of what Atkins calls ‘the Southern Island’ that floats at the bottom of the table. This is the lanthanides, elements 57 through 71, lanthanum (La) to lutetium (Lu). The elements in this group have a silvery white color and tarnish on contact with air.

Actinides The actinides line forms the bottom row of the Southern Island and comprise elements 89, actinium (Ac) to 103, lawrencium (Lr). Of these elements, only thorium (Th) and uranium (U) occur naturally on earth in substantial amounts. All are radioactive. The actinides and the lanthanides together form a group called the inner transition metals.

Transition metals Returning to the main body of the table, the remainder of Groups 3 through 12 represent the rest of the transition metals. Hard but malleable, shiny, and possessing good conductivity, these elements are what you normally associate with the word metal. This is the location of many of the best known metals, including gold, silver, iron and platinum.

Post-transition metals Ahead of the jump into the non-metal world, shared characteristics aren’t neatly divided along vertical group lines. The post-transition metals are aluminum (Al), gallium (Ga), indium (In), thallium (Tl), tin (Sn), lead (Pb) and bismuth (Bi), and they span Group 13 to Group 17. These elements have some of the classic characteristics of the transition metals, but they tend to be softer and conduct more poorly than other transition metals. Many periodic tables will feature a highlighted ‘staircase’ line below the diagonal connecting boron with astatine. The post-transition metals cluster to the lower left of this line. Atkins points out that all the elements beyond bismuth (row 6, column 15) are radioactive. Here be skull-and-crossbones warning signs.

Metalloids The metalloids are boron (B), silicon (Si), germanium (Ge), arsenic (As), antimony (Sb), tellurium (Te) and polonium (Po). They form the staircase that represents the gradual transition from metals to non-metals. These elements sometimes behave as semiconductors (B, Si, Ge) rather than as conductors. Metalloids are also called ‘semi-metals’ or ‘poor metals’.

Non-metals Everything else to the upper right of the staircase (plus hydrogen (H), stranded way back in Group 1) is a non-metal. These include the crucial elements for life on earth, carbon (C), nitrogen (N), phosphorus (P), oxygen (O), sulfur (S) and selenium (Se).

Halogens The top four elements of Group 17, from fluorine (F) through astatine (At), represent one of two subsets of the non-metals. The halogens are quite chemically reactive and tend to pair up with alkali metals to produce various types of salt. Common salt is a marriage between the alkali metal sodium and the halogen chlorine.

Noble gases Colorless, odourless and almost completely non-reactive, the inert, or noble gases round out the table in Group 18. The low boiling point of helium makes it a useful refrigerant when exceptionally low temperatures are required; most of them give off a colourful display when electric current is passed through them, hence the generic name of neon lights, invented in 1910 by Georges Claude.

The metaphor of the Periodic Kingdom

In fact the summary I’ve given above isn’t at all how Atkins’s book sounds. It is the way I have had to make notes to myself to understand the table.

Atkins’ book is far from being so clear and straightforward. The Periodic Kingdom is dominated by the central conceit that Atkins treats the periodic table as if it were an actual country. His book is not a comprehensive encyclopedia of biochemistry, mineralogy and industrial chemistry; it is a light-hearted ‘traveller’s guide’ (p.27) to the table which he never refers to as a table, but as a kingdom, complete with its own geography, layout, mountain peaks and ravines, and surrounded by a sea of nothingness.

Hence, from start to finish of the book, Atkins uses metaphors from landscape and exploration to describe the kingdom, talking about ‘the Western desert’, ‘the Southern Shore’ and so on. Here’s a characteristic sentence:

The general disposition of the land is one of metals in the west, giving way, as you travel eastward, to a varied landscape of nonmetals, which terminates in largely inert elements at the eastern shoreline. (p.9)

I guess the idea is to help us memorise the table by describing its characteristics and the changes in atomic weight, physical character, alkalinity, reactivity and so on of the various elements, in terms of geography. Presumably he thinks it’s easier to remember geography than raw information. His approach certainly gives rise to striking analogies:

North of the mainland, situated rather like Iceland off the northwestern edge of Europe, lies a single, isolated region – hydrogen. This simple but gifted element is an essential outpost of the kingdom, for despite its simplicity it is rich in chemical personality. It is also the most abundant element in the universe and the fuel of the stars. (p.9)

Above all the extended metaphor (the periodic table imagined as a country) frees Atkins not to have to lay out the subject in either a technical nor a chronological order but to take a pleasant stroll across the landscape, pointing out interesting features and making a wide variety of linkages, pointing out the secret patterns and subterranean connections between elements in the same ‘regions’ of the table.

There are quite a few of these, for example the way iron can easily form alliances with the metals close to it such as cobalt, nickel and manganese to produce steel. Or the way the march of civilisation progressed from ‘east’ to ‘west’ through the metals, i.e. moving from copper, to iron and steel, each representing a new level of culture and technology.

The kingdom metaphor also allows him to get straight to core facts about each element without getting tangled in pedantic introductions: thus we learn there would be no life without nitrogen which is a key building block of all proteins, not to mention the DNA molecule; or that sodium and potassium (both alkali metals) are vital in the functioning of brain and nervous system cells.

And hence the generally light-hearted, whimsical tone allows him to make fanciful connections: calcium is a key ingredient in the bones of endoskeletons and the shells of exoskeletons, compacted dead shells made chalk, but in another format made the limestone which the Romans and others ground up to make the mortar which held their houses together.

Then there is magnesium. I didn’t think magnesium was particularly special, but learned from Atkins that a single magnesium atom is at the heart of the chlorophyll molecule, and:

Without chlorophyll, the world would be a damp warm rock instead of the softly green haven of life that we know, for chlorophyll holds its magnesium eye to the sun and captures the energy of sunlight, in the first step of photosynthesis. (p.16)

You see how the writing is aspiring to an evocative, poetic quality- a deliberate antidote to the dry and factual way chemistry was taught to us at school. He means to convey the sense of wonder, the strange patterns and secret linkages underlying these wonderful entities. I liked it when he tells us that life is about capturing, storing and deploying energy.

Life is a controlled unwinding of energy.

Or about how phosphorus, in the form of adenosine triphosphate (ATP) is a perfect vector for the deployment of energy, common to all living cells. Hence the importance of phosphates as fertiliser to grow the plants we need to survive. Arsenic is such an effective poison because it is a neighbour of phosphorus, shares some of its qualities, and so inserts itself into chemical reactions usually carried out by phosphorus but blocking them, nulling them, killing the host organism.

All the facts I explained in the first half of this post (mostly cribbed from the LiveScience.com website) are not reached or explained until about page 100 of this 150-page-long book. Personally, I felt I needed them earlier. As soon as I looked at the big diagram of the table he gives right at the end of the book I became intrigued by the layout and the numbers and couldn’t wait for him to get round to explaining them, which is why I went on the internet to find out more, more quickly, and why Istarted my review with a factual summary.

And eventually, the very extended conceit of ‘the kingdom’ gets rather tiresome. Whether intentional or not, the continual references to ‘the kingdom’ begin to sound Biblical and pretentious.

Now the kingdom is virtually fully formed. It rises above the sea of nonbeing and will remain substantially the same almost forever. The kingdom was formed in and among the stars.. (p.75)

The chapter on the scientists who first isolated the elements and began sketching out the table continues the metaphor by referring to them as ‘cartographers’, and the kingdom as made of islands and archipelagos.

As an assistant professor of chemistry at the University of Jena, [Johann Döbereiner] noticed that reports of some of the kingdom’s islands – reports brought back by their chemical explorers – suggested a brotherhood of sorts between the regions. (p.79)

For me, the obsessive use of the geographical metaphor teeters on the border between being useful, and becoming irritating. He introduces me to the names of the great pioneers – I was particularly interested in Dalton, Michael Faraday, Humphrey Davy (who isolated a bunch of elements in the early 1800s) and then William Ramsey – but I had to go to Wikipedia to really understand their achievements.

Atkins speculates that some day we might find another bunch or set of elements, which might even form an entire new ‘continent’, though it is unlikely. This use of a metaphor is sort of useful for spatially imagining how this might happen, but I quickly got bored of him calling this possible set of new discoveries ‘Atlantis’, and of the poetic language as a whole.

Is the kingdom eternal, or will it slip beneath the waves? There is a good chance that one day – in a few years, or a few hundred years at most – Atlantis will be found, which will be an intellectual achievement but probably not one of great practical significance…

A likely (but not certain) scenario is that in that distant time, perhaps 10100 years into the future, all matter will have decayed into radiation, it is even possible to imagine the process. Gradually the peaks and dales of the kingdom will slip away and Mount Iron will rise higher, as elements collapse into its lazy, low-energy form. Provided that matter does not decay into radiation first (which is one possibility), the kingdom will become a lonely pinnacle, with iron the only protuberance from the sea of nonbeing… (p.77)

And I felt the tone sometimes bordered on the patronising.

The second chemical squabble is in the far North, and concerns the location of the offshore Northern Island of hydrogen. To those who do not like offshore islands, there is the problem of where to put it on the mainland. This is the war of the Big-Endians versus the Little-Endians. Big-Endians want to tow the island ashore to form a new Northwestern Cape, immediately north of lithium and beryllium and across from the Northeastern Cape of helium… (p.90)

Hard core chemistry

Unfortunately, none of these imaginative metaphors can help when you come to chapter 9, an unexpectedly brutal bombardment of uncompromising hard core information about the quantum mechanics underlying the structure of the elements.

In quick succession this introduces us to a blizzard of ideas: orbitals, energy levels, Pauli’s law of exclusion, and then the three imaginary lobes of orbitals.

As I understood it, the Pauli exclusion principle states that no two electrons can inhabit a particular orbital or ‘layer’ or shell. But what complicates the picture is that these orbitals come in three lobes conceived as lying along imaginary x, y and z axes. This overlapped with the information that there are four types of orbitals – s, p, d and f orbitals. In addition, there are three p-orbitals, five d-orbitals, seven f-orbitals. And the two lobes of a p-orbital are on either side of an imaginary plane cutting through the nucleus, there are two such planes in a d-orbital and three in an f-orbital.

After pages of amiable waffle about kingdoms and Atlantis, this was like being smacked in the face with a wet towel. Even rereading the chapter three times, I still found it impossible to process and understand this information.

I understand Atkins when he says it is the nature of the orbitals, and which lobes they lie along, which dictates an element’s place in the table, but he lost me when he said a number of electrons lie inside the nucleus – which is the opposite of everything I was ever taught – and then when described the way electrons fly across or through the nucleus, something to do with the processes of ‘shielding’ and ‘penetration’.

The conspiracy of shielding and penetration ensure that the 2s-orbital is somewhat lower in energy than the p-orbitals of the same rank. By extension, where other types of orbitals are possible, ns- and np-orbitals both lie lower in energy than nd-orbitals, and nd-orbitals in turn have lower energy than nf-orbitals. An s-orbital has no nodal plane, and electrons can be found at the nucleus. A p-orbital has one plane, and the electron is excluded from the nucleus. A d-orbital has two intersecting planes, and the exclusion of the electron is greater. An f-orbital has three planes, and the exclusion is correspondingly greater still. (p.118)

Note how all the chummy metaphors of kingdoms and deserts and mountains have disappeared. This is the hard-core quantum mechanical basis of the elements, and at least part of the reason it is so difficult to understand is because he has made the weird decision to throw half a dozen complex ideas at the reader at the same time. I read the chapter three times, still didn’t get it, and eventually wanted to cry with frustration.

This online lecture gives you a flavour of the subject, although it doesn’t mention ‘lobes’ or penetration or shielding.

In the next chapter, Atkins, briskly assuming  his readers have processed and understood all of this information, goes on to combine the stuff about lobes and orbitals with a passage from earlier in the book, where he had introduced the concept of ions, cations, and anions:

  • ion an atom or molecule with a net electric charge due to the loss or gain of one or more electrons
  • cation a positively charged ion
  • anion a negatively charged ion

He had also explained the concept of electron affinity

The electron affinity (Eea) of an atom or molecule is defined as the amount of energy released or spent when an electron is added to a neutral atom or molecule in the gaseous state to form a negative ion.

Isn’t ‘affinity’ a really bad word to describe this? ‘Affinity’ usually means ‘a natural liking for and understanding of someone or something’. If it is the amount of energy released, why don’t they call it something useful like the ‘energy release’? I felt the same about the terms ‘cation’ and ‘anion’ – that they had been deliberately coined to mystify and confuse. I kept having to stop and look up what they meant since the name is absolutely no use whatsoever.

And the electronvolt – ‘An electronvolt (eV) is the amount of kinetic energy gained or lost by a single electron accelerating from rest through an electric potential difference of one volt in vacuum.’

Combining the not-very-easily understandable material about electron volts with the incomprehensible stuff about orbitals means that the final 30 pages or so of The Periodic Kingdom is thirty pages of this sort of thing:

Take sodium: it has a single electron outside a compact, noble-gaslike core (its structure is [Ne]3s¹). The first electron is quite easy to remove (its removal requires an investment of 5.1 eV), but removal of the second, which has come from the core that lies close to the nucleus, requires an enormous energy – nearly ten times as much, in fact (47.3 eV). (p.130)

This reminds me of the comparable moment in John Allen Paulos’s book Innumeracy where I ceased to follow the argument. After rereading the passage where I stumbled and fell I eventually realised it was because Paulos had introduced three or so important facts about probability theory very, very quickly, without fully explaining them or letting them bed in – and then had spun a fancy variation on them…. leaving me standing gaping on the shore.

Same thing happens here. I almost but don’t quite understand what [Ne]3s¹ means, and almost but don’t quite grasp the scale of electronvolts, so when he goes on to say that releasing the second electron requires ten times as much energy, of course I understand the words, but I cannot quite grasp why it should be so because I have not understood the first two premises.

As with Paulos, the author has gone too fast. These are not simple ideas you can whistle through and expect your readers to lap up. These are very, very difficult ideas most readers will be completely unused to.

I felt the sub-atomic structure chapter should almost have been written twice, approached from entirely different points of view. Even the diagrams were no use because I didn’t understand what they were illustrating because I didn’t understand his swift introduction of half a dozen impenetrable concepts in half a page.

Once through, briskly, is simply not enough. The more I tried to reread the chapter, the more the words started to float in front of my eyes and my brain began to hurt. It is packed with sentences like these:

Now imagine a 2 p-electron… (an electron that occupies a 2 p-orbital). Such an electron is banished from the nucleus on account of the existence of the nodal plane. This electron is more completely shielded from the pull of the nucleus, and so it is not gripped as tightly.In other words, because of the interplay of shielding and penetration, a 2 s-orbital has a lower energy (an electron in it is gripped more tightly) than a 2 p-orbital… Thus the third and final electron of lithium enters the 2 s-orbital, and its overall structure is 1s²2s¹. (p.118)

I very nearly understand what some of these words meant, but the cumulative impact of sentences like these was like being punched to the ground and then given a good kicking. And when the last thirty pages went on to add the subtleties of electronvoltages and micro-electric charges into the mix, to produce ever-more complex explanations for the sub-atomic interactivity of different elements, I gave up.

Summary

The first 90 or so pages of The Periodic Kingdom do manage to give you a feel for the size and shape and underlying patterns of the periodic table. Although it eventually becomes irritating, the ruling metaphor of seeing the whole place as a country with different regions and terrains works – up to a point – to explain or suggest the patterns of size, weight, reactivity and so on underlying the elements.

When he introduced ions was when he first lost me, but I stumbled on through the entertaining trivia and titbits surrounding the chemistry pioneers who first isolated and named many of the elements and the first tentative attempts to create a table for another thirty pages or so.

But the chapter about the sub-atomic structure of chemical elements comprehensively lost me. I was already staggering, and this finished me off.

If Atkins’s aim was to explain the basics of chemistry to an educated layman, then the book was, for me, a complete failure. I sort of quarter understood the orbitals, lobes, nodes section but anything less than 100% understanding means you won’t be able to follow him to the next level of complexity.

As with the Paulos book, I don’t think I failed because I am stupid – I think that, on both occasions, the author failed to understand how challenging his subject matter is, and introduced a flurry of concepts far too quickly, at far too advanced a level.

Looking really closely I realise it is on the same page (page 111) that Atkins introduces the concepts of energy levels, orbitals, the fact that there are three two-lobed orbitals, and the vital existence of nodal planes. On the same page! Why the rush?

An interesting and seemingly trivial feature of a p-orbital, but a feature on which the structure of the kingdom will later be seen to hinge, is that the electron will never be found on the imaginary plane passing through the nucleus and dividing the two lobes of the orbital. This plane is called a nodal plane. An s-orbital does not have such a nodal plane, and the electron it describes may be found at the nucleus. Every p-orbital has a nodal plane of this kind, and therefore an electron that occupies a p-orbital will never be found at the nucleus. (p.111)

Do you understand that? Because if you don’t, you won’t understand the last 40 or so pages of the book, because this is the ‘feature on which the structure of the kingdom will later be seen to hinge’.

I struggled through the final 40 pages weeping tears of frustration, and flushed with anger at having the thing explained to me so badly. Exactly how I felt during my chemistry lessons at school forty years ago.


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Reviews of other science books

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Psychology

A Brief History of Time: From the Big Bang to Black Holes by Stephen Hawking (1988)

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 –

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

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

Reviews of other science books

Cosmology

The environment

Human evolution

Genetics and life

  • What Is Life? How Chemistry Becomes Biology by Addy Pross (2012)
  • The Diversity of Life by Edward O. Wilson (1992)
  • The Double Helix by James Watson (1968)

Maths

Particle physics

Psychology

The Origin of the Universe by John D. Barrow (1994)

In the beginning, the universe was an inferno of radiation, too hot for any atoms to survive. In the first few minutes, it cooled enough for the nuclei of the lighter elements to form. Only millions of years later would the cosmos be cool enough for whole atoms to appear, followed soon by simple molecules, and after billions of years by the complex sequence of events that saw the condensation of material into stars and galaxies. Then, with the appearance of stable planetary environments, the complicated products of biochemistry were nurtured, by processes we still do not understand. (The Origin of the Universe, p.xi)

In the late 1980s and into the 1990s science writing became fashionable and popular. A new generation of science writers poured forth a wave of books popularising all aspects of science. The ones I remember fell into two broad categories, evolution and astrophysics. Authors such as Stephen Jay Gould and Edward O. Wilson, Richard Dawkins and Steve Jones (evolution and genetics) and Paul Davies, John Gribbin, John Polkinghorne and, most famously of all, Stephen Hawking, (cosmology and astrophysics) not only wrote best-selling books but cropped up as guests on radio shows and even presented their own TV series.

Early in the 1990s the literary agent John Brockman created a series titled Science Masters in which he commissioned experts across a wide range of the sciences to write short, jargon-free and maths-light introductions to their fields.

This is astrophysicist John D. Barrow’s contribution to the series, a short, clear and mind-blowing introduction to current theory about how our universe began.

The Origin of the Universe

Billions It is now thought the universe is about 13.7 billion years old, the solar system is 4.57 billion years old and the earth is 4.54 billion years old. The oldest surface rocks anywhere on earth are in northwestern Canada near the Great Slave Lake, and are 4.03 billion years. The oldest fossilised bacteria date from 3.48 billion years ago.

Visible universe The visible universe is the part of the universe which light has had time to cross and reach us. If the universe is indeed 13.7 billion years old, and nothing can travel faster than the speed of light (299,792,458 metres per second) then there is, in effect, a ‘horizon’ to what we can see. We can only see the part of the universe which is about 13.7 billion years old. Whether there is any universe beyond our light horizon, and what it looks like, is something we can only speculate about.

Steady state Until the early 20th century philosophers and scientists thought the universe was fixed, static and stable. Even Einstein put into his theory of relativity a factor he named ‘the cosmological constant’, which wasn’t strictly needed, solely in order to make the universe appear static and so conform to contemporary thinking. The idea of this constant was to counteract the attractive force of gravity, in order to ensure his steady state version of the universe didn’t collapse into a big crunch.

Alexander Friedmann It was a young mathematician, Alexander Friedmann, who looked closely at Einstein’s formulae and showed that the cosmological constant was not necessary, not if the universe was expanding; in this case, no hypothetical repelling force would be needed, just the sheer speed of outward expansion. Einstein eventually conceded that including the constant in the formulae of relativity had been a major mistake.

Edwin Hubble In what Barrow calls ‘the greatest discovery of twentieth century science’, the American astronomer Edwin Hubble in the 1920s discovered that distant galaxies are moving away from us, and the further away they are, the faster they are moving, which became known as Hubble’s Law. He established this by noticing the ‘red-shifting’ of frequencies denoting detectable elements in these galaxies i.e. their light frequencies had been altered downwards, as light (and sound and all waves are) when something is moving away from the observer.

Critical divide An argument against the steady-state theory of the universe is that, over time, the gravity of all the objects in it would pull everything together and it would all collapse into one massive clump. Only an initial throwing out of material could counter-act the affect of all that gravity.

So how fast is the universe expanding? Imagine a rate, x. Below that speed, the effect of gravity will eventually overcome the outward acceleration, the universe will slow down, stop expanding and start to contract. Significantly above this speed, x, and the universe would continue flying apart in all directions so quickly that gas clouds, stars, galaxies and planets would never be formed.

As far as we know, the actual acceleration of the universe hovers just around this rate, x – just fast enough to prevent the universe from collapsing, but not too fast for it to be impossible for matter to form. Just the right speed to create the kind of universe we see around us. The name for this threshold is the critical divide.

Starstuff Stars are condensations of matter large enough to create at their centre nuclear reactions. These reactions burn hydrogen into helium for a long, sedate period, as our sun is doing. At the end of their lives stars undergo a crisis, an explosive period of rapid change during which helium is transformed into carbon nitrogen, oxygen, silicon, phosphorus and many of the other, heavier elements. When the ailing star finally explodes as a supernova these elements disperse into space and ultimately find their way into clouds of gas which condense as planets.

Thus every plant, animal and person alive on earth is made out of chemical elements forged in the unthinkable heat of dying stars – which is what Joni Mitchell meant when she sang, ‘We are stardust’.

Heat death A theory that the universe will continue expanding and matter become so attenuated that there are no heat or dynamic inequalities left to fuel thermal reactions i.e. matter ends up smoothly spread throughout space with no reactions happening anywhere. Thermodynamic equilibrium reached at a universal very low temperature. The idea was formulated by William Thomson, Lord Kelvin, in the 1850s who extrapolated from Victorian knowledge of mechanics and heat. 170 years later, updated versions of heat death remain a viable theory for the very long-term future of the universe.

Steady state The ‘steady state’ theory of the universe was developed by astrophysicists Thomas Gold, Hermann Bondi and Fred Hoyle in 1948. They theorised that. although the universe appeared to be expanding it had always existed, the expansion being caused by a steady rate of creation of new matter. This theory was disproved in the mid-1960s by the confirmation of background radiation

Background radiation theorised In the 1940s George Gamow and assistants Alpher and Herman theorised that, if the universe began in a hot dense state way back, there should be evidence, namely a constant layer of background radiation everywhere which, they calculated, would be 5 degrees above absolute zero.

Background radiation proved In the 1960s researchers at Bell Laboratories, calibrating a sensitive radio antenna, noticed a constant background interference to their efforts which seemed to be coming from every direction of the sky. A team from Princeton interpreted this as the expected background radiation and measured it at 2.5 degrees Kelvin. It is called ‘cosmic microwave background radiation’ and is one of the strong proofs for the Big Bang theory. The uniformity of the background radiation was confirmed by observations from NASA’s Cosmic Background Explorer satellite in the early 1990s.

Empty universe There is very little material in the universe. If all the stars and galaxies in the universe were smoothed out into a sea of atoms, there would only be about one atom per cubic meter of space.

Inflation This is a theory developed in 1979 by theoretical physicist Alan Guth – the idea is that the universe didn’t arise from a singularity which exploded and grew at a steady state but instead, in the first milliseconds, underwent a period of hyper-growth, which then calmed back down to ‘normal’ expansion.

The theory has been elaborated and generated numerous variants but is widely accepted because it explains many aspects of the universe we see today – from its large-scale structure to the way it explains how minute quantum fluctuations in this initial microscopic inflationary region, once magnified to cosmic size, became the seeds for the growth of structure in the Universe.

The inflation is currently thought to have taken place from 10−36 seconds after the conjectured Big Bang singularity to sometime between 10−33 or 10−32 seconds after.

Chaotic inflationary universe Proposed by Soviet physicist Andrei Linde in 1983, this is the idea that multiple distinct sections of the very early universe might have experienced inflation at different rates and so have produced a kind of cluster of universes, like bubbles in a bubble bath, except that these bubbles would have to be at least nine billion light years in size in order to produce stable stars. Possibly the conditions in each of the universes created by chaotic inflation could be quite different.

Eternal inflation A logical extension of chaotic inflation is that you not only have multiple regions which undergo inflation at the same time, but you might have sub-regions which undergo inflation at different times – possibly one after the other, in other words maybe there never was a beginning, but this process of successive creations and hyper-inflations has been going on forever and is still going on but beyond our light horizon (which, as mentioned above, only reaches to about 13.7 billion light years away).

Time Is time a fixed and static quality which creates a kind of theatre, an external frame of reference, in which the events of the universe take place, as in the Newtonian view? Or, as per Einstein, is time itself part of the universe, inseparable from the stuff of the universe and can be bent and distorted by forces in the universe? This is why Einstein used the expression ‘spacetime’?

The quantum universe Right back at the very beginning, at 10−43 seconds, the size of the visible universe was smaller than its quantum wavelength — so its entire contents would have been subject to the uncertainty which is the characteristic of quantum physics.

Time is affected by a quantum view of the big bang because, when the universe was still shrunk to a microscopic size, the quantum uncertainty which applied to it might be interpreted as meaning there was no time. That time only ‘crystallised’ out as a separate ‘dimension’ once the universe had expanded to a size where quantum uncertainty no longer dictated.

Some critics of the big bang theory ask, ‘What was there before the big bang?’ to which exponents conventionally reply that there was no ‘before’. Time as we experience it ceased to exist and became part of the initial hyper-energy field.

This quantum interpretation suggests that there in fact was no ‘big bang’ because there was literally no time when it happened.

Traditional visualisations of the big bang show an inverted cone, at the top is the big universe we live in and as you go back in time it narrows to a point – the starting point. Imagine, instead, something more like a round-bottomed sack: there’s a general expansion upwards and outwards but if you penetrate back to the bottom of the sack there is no ‘start’ point.

This theory was most fully worked out by Stephen Hawking and James Hartle.

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

Wormholes The book ends with speculations about the possibility that ‘wormholes’ existed in the first few milliseconds, tubes connecting otherwise distant parts of the exploding ball of universe. I understood the pictures of these but couldn’t understand the problems in the quantum theory of the origin which they set out to solve.

And the final section emphasises that everything cosmologists work on relates to the visible universe. It may be that the special conditions of the visible universe which we know about, are only one set of starting conditions which apply to other areas of the universe beyond our knowledge or to other universes. We will never know.

Thoughts

Barrow is an extremely clear and patient explainer. He avoids formulae. Between his prose and the many illustrations I understood most of what he was trying to say, though a number of concepts eluded me.

But the ultimate thing that comes over is his scepticism. Barrow summarises recent attempts to define laws governing the conditions prevailing at the start of the universe by, briefly describing the theories of James Hartle and Stephen Hawking, Alex Vilenkin, and Roger Penrose. But he does so only to go on to emphasise that they are all ‘highly speculative’. They are ‘ideas for ideas’ (p.135).

By the end of the book you get the idea that a very great deal of cosmology is either speculative, or highly speculative. But then half way through he says it’s a distinguishing characteristic of physicists that they can’t stop tinkering – with data, with theories, with ideas and speculations.

So beyond the facts and then the details of the theories he describes, it is insight into this quality in the discipline itself, this restless exploration of new ideas and speculations relating to some of the hardest-to-think-about areas of human knowledge, which is the final flavour the reader is left with.


Related links

Reviews of other science books

Cosmology

The environment

Human evolution

Genetics and life

  • What Is Life? How Chemistry Becomes Biology by Addy Pross (2012)
  • The Diversity of Life by Edward O. Wilson (1992)
  • The Double Helix by James Watson (1968)

Maths

Particle physics

Psychology

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