The Book of Universes by John D. Barrow (2011)

This book is twice as long and half as good as Barrow’s earlier primer, The Origin of the Universe.

In that short book Barrow focused on the key ideas of modern cosmology – introducing them to us in ascending order of complexity, and as simply as possible. He managed to make mind-boggling ideas and demanding physics very accessible.

This book – although it presumably has the merit of being more up to date (published in 2011 as against 1994) – is an expansion of the earlier one, an attempt to be much more comprehensive, but which, in the process, tends to make the whole subject more confusing.

The basic premise of both books is that, since Einstein’s theory of relativity was developed in the 1910s, cosmologists and astronomers and astrophysicists have:

  1. shown that the mathematical formulae in which Einstein’s theories are described need not be restricted to the universe as it has traditionally been conceived; in fact they can apply just as effectively to a wide variety of theoretical universes – and the professionals have, for the past hundred years, developed a bewildering array of possible universes to test Einstein’s insights to the limit
  2. made a series of discoveries about our actual universe, the most important of which is that a) it is expanding b) it probably originated in a big bang about 14 billion years ago, and c) in the first few milliseconds after the bang it probably underwent a period of super-accelerated expansion known as the ‘inflation’ which may, or may not, have introduced all kinds of irregularities into ‘our’ universe, and may even have created a multitude of other universes, of which ours is just one

If you combine a hundred years of theorising with a hundred years of observations, you come up with thousands of theories and models.

In The Origin of the Universe Barrow stuck to the core story, explaining just as much of each theory as is necessary to help the reader – if not understand – then at least grasp their significance. I can write the paragraphs above because of the clarity with which The Origin of the Universe explained it.

In The Book of Universes, on the other hand, Barrow’s aim is much more comprehensive and digressive. He is setting out to list and describe every single model and theory of the universe which has been created in the past century.

He introduces the description of each model with a thumbnail sketch of its inventor. This ought to help, but it doesn’t because the inventors generally turn out to be polymaths who also made major contributions to all kinds of other areas of science. Being told a list of Paul Dirac’s other major contributions to 20th century science is not a good way for preparing your mind to then try and understand his one intervention on universe-modelling (which turned, in any case, out to be impractical and lead nowhere).

Another drawback of the ‘comprehensive’ approach is that a lot of these models have been rejected or barely saw the light of day before being disproved or – more complicatedly – were initially disproved but contained aspects or insights which turned out to be useful forty years later, and were subsequently recycled into revised models. It gets a bit challenging to try and hold all this in your mind.

In The Origin of the Universe Barrow sticks to what you could call the canonical line of models, each of which represented the central line of speculation, even if some ended up being disproved (like Hoyle and Gold and Bondi’s model of the steady state universe). Given that all of this material is pretty mind-bending, and some of it can only be described in advanced mathematical formulae, less is definitely more. I found The Book of Universes simply had too many universes, explained too quickly, and lost amid a lot of biographical bumpf summarising people’s careers or who knew who or contributed to who’s theory. Too much information.

One last drawback of the comprehensive approach is that quite important points – which are given space to breathe and sink in in The Origin of the Universe are lost in the flood of facts in The Book of Universes.

I’m particularly thinking of Einstein’s notion of the cosmological constant which was not strictly necessary to his formulations of relativity, but which Einstein invented and put into them solely in order to counteract the force of gravity and ensure his equations reflected the commonly held view that the universe was in a permanent steady state.

This was a mistake and Einstein is often quoted as admitting it was the biggest mistake of his career. In 1965 scientists discovered the cosmic background radiation which proved that the universe began in an inconceivably intense explosion, that the universe was therefore expanding and that the explosive, outward-propelling force of this bang was enough to counteract the contracting force of the gravity of all the matter in the universe without any need for a hypothetical cosmological constant.

I understand this (if I do) because in The Origin of the Universe it is given prominence and carefully explained. By contrast, in The Book of Universes it was almost lost in the flood of information and it was only because I’d read the earlier book that I grasped its importance.

The Book of Universes

Barrow gives a brisk recap of cosmology from the Sumerians and Egyptians, through the ancient Greeks’ establishment of the system named after Ptolemy in which the earth is the centre of the solar system, on through the revisions of Copernicus and Galileo which placed the sun firmly at the centre of the solar system, on to the three laws of Isaac Newton which showed how the forces which govern the solar system (and more distant bodies) operate.

There is then a passage on the models of the universe generated by the growing understanding of heat and energy acquired by Victorian physicists, which led to one of the most powerful models of the universe, the ‘heat death’ model popularised by Lord Kelvin in the 1850s, in which, in the far future, the universe evolves to a state of complete homegeneity, where no region is hotter than any other and therefore there is no thermodynamic activity, no life, just a low buzzing noise everywhere.

But this is all happens in the first 50 pages and is just preliminary throat-clearing before Barrow gets to the weird and wonderful worlds envisioned by modern cosmology i.e. from Einstein onwards.

In some of these models the universe expands indefinitely, in others it will reach a peak expansion before contracting back towards a Big Crunch. Some models envision a static universe, in others it rotates like a top, while other models are totally chaotic without any rules or order.

Some universes are smooth and regular, others characterised by clumps and lumps. Some are shaken by cosmic tides, some oscillate. Some allow time travel into the past, while others threaten to allow an infinite number of things to happen in a finite period. Some end with another big bang, some don’t end at all. And in only a few of them do the conditions arise for intelligent life to evolve.

The Book of Universes then goes on, in 12 chapters, to discuss – by my count – getting on for a hundred types or models of hypothetical universes, as conceived and worked out by mathematicians, physicists, astrophysicists and cosmologists from Einstein’s time right up to the date of publication, 2011.

A list of names

Barrow namechecks and briefly explains the models of the universe developed by the following (I am undertaking this exercise partly to remind myself of everyone mentioned, partly to indicate to you the overwhelming number of names and ideas the reader is bombarded with):

  • Aristotle
  • Ptolemy
  • Copernicus
  • Giovanni Riccioli
  • Tycho Brahe
  • Isaac Newton
  • Thomas Wright (1771-86)
  • Immanuel Kant (1724-1804)
  • Pierre Laplace (1749-1827) devised what became the standard Victorian model of the universe
  • Alfred Russel Wallace (1823-1913) discussed the physical conditions of a universe necessary for life to evolve in it
  • Lord Kelvin (1824-1907) material falls into the central region of the universe and coalesce with other stars to maintain power output over immense periods
  • Rudolf Clausius (1822-88) coined the word ‘entropy’ in 1865 to describe the inevitable progress from ordered to disordered states
  • William Jevons (1835-82) believed the second law of thermodynamics implies that universe must have had a beginning
  • Pierre Duhem (1961-1916) Catholic physicist accepted the notion of entropy but denied that it implied the universe ever had a beginning
  • Samuel Tolver Preson (1844-1917) English engineer and physicist, suggested the universe is so vast that different ‘patches’ might experience different rates of entropy
  • Ludwig Boltzmann and Ernst Zermelo suggested the universe is infinite and is already in a state of thermal equilibrium, but just with random fluctuations away from uniformity, and our galaxy is one of those fluctuations
  • Albert Einstein (1879-1955) his discoveries were based on insights, not maths: thus he saw the problem with Newtonian physics is that it privileges an objective outside observer of all the events in the universe; one of Einstein’s insights was to abolish the idea of a privileged point of view and emphasise that everyone is involved in the universe’s dynamic interactions; thus gravity does not pass through a clear, fixed thing called space; gravity bends space.

The American physicist John Wheeler once encapsulated Einstein’s theory in two sentences:

Matter tells space how to curve. Space tells matter how to move. (quoted on page 52)

  • Marcel Grossmann provided the mathematical underpinning for Einstein’s insights
  • Willem de Sitter (1872-1934) inventor of, among other things, the de Sitter effect which represents the effect of the curvature of spacetime, as predicted by general relativity, on a vector carried along with an orbiting body – de Sitter’s universe gets bigger and bigger for ever but never had a zero point; but then de Sitter’s model contains no matter
  • Vesto Slipher (1875-1969) astronomer who discovered the red shifting of distant galaxies in 1912, the first ever empirical evidence for the expansion of the galaxy
  • Alexander Friedmann (1888-1925) Russian mathematician who produced purely mathematical solutions to Einstein’s equation, devising models where the universe started out of nothing and expanded a) fast enough to escape the gravity exerted by its own contents and so will expand forever or b) will eventually succumb to the gravity of its own contents, stop expanding and contract back towards a big crunch. He also speculated that this process (expansion and contraction) could happen an infinite number of times, creating a cyclic series of bangs, expansions and contractions, then another bang etc
A graphic of the oscillating or cyclic universe (from Discovery magazine)

A graphic of the oscillating or cyclic universe (from Discovery magazine)

  • Arthur Eddington (1882-1944) most distinguished astrophysicist of the 1920s
  • George Lemaître (1894-1966) first to combine an expanding universe interpretation of Einstein’s equations with the latest data about redshifting, and show that the universe of Einstein’s equations would be very sensitive to small changes – his model is close to Eddington’s so that it is often called the Eddington-Lemaître universe: it is expanding, curved and finite but doesn’t have a beginning
  • Edwin Hubble (1889-1953) provided solid evidence of the redshifting (moving away) of distant galaxies, a main plank in the whole theory of a big bang, inventor of Hubble’s Law:
    • Objects observed in deep space – extragalactic space, 10 megaparsecs (Mpc) or more – are found to have a redshift, interpreted as a relative velocity away from Earth
    • This Doppler shift-measured velocity of various galaxies receding from the Earth is approximately proportional to their distance from the Earth for galaxies up to a few hundred megaparsecs away
  • Richard Tolman (1881-1948) took Friedmann’s idea of an oscillating universe and showed that the increased entropy of each universe would accumulate, meaning that each successive ‘bounce’ would get bigger; he also investigated what ‘lumpy’ universes would look like where matter is not evenly spaced but clumped: some parts of the universe might reach a maximum and start contracting while others wouldn’t; some parts might have had a big bang origin, others might not have
  • Arthur Milne (1896-1950) showed that the tension between the outward exploding force posited by Einstein’s cosmological constant and the gravitational contraction could actually be described using just Newtonian mathematics: ‘Milne’s universe is the simplest possible universe with the assumption that the universe s uniform in space and isotropic’, a ‘rational’ and consistent geometry of space – Milne labelled the assumption of Einsteinian physics that the universe is the same in all places the Cosmological Principle
  • Edmund Fournier d’Albe (1868-1933) posited that the universe has a hierarchical structure from atoms to the solar system and beyond
  • Carl Charlier (1862-1934) introduced a mathematical description of a never-ending hierarchy of clusters
  • Karl Schwarzschild (1873-1916) suggested  that the geometry of the universe is not flat as Euclid had taught, but might be curved as in the non-Euclidean geometries developed by mathematicians Riemann, Gauss, Bolyai and Lobachevski in the early 19th century
  • Franz Selety (1893-1933) devised a model for an infinitely large hierarchical universe which contained an infinite mass of clustered stars filling the whole of space, yet with a zero average density and no special centre
  • Edward Kasner (1878-1955) a mathematician interested solely in finding mathematical solutions to Einstein’s equations, Kasner came up with a new idea, that the universe might expand at different rates in different directions, in some parts it might shrink, changing shape to look like a vast pancake
  • Paul Dirac (1902-84) developed a Large Number Hypothesis that the really large numbers which are taken as constants in Einstein’s and other astrophysics equations are linked at a deep undiscovered level, among other things abandoning the idea that gravity is a constant: soon disproved
  • Pascual Jordan (1902-80) suggested a slight variation of Einstein’s theory which accounted for a varying constant of gravitation as through it were a new source of energy and gravitation
  • Robert Dicke (1916-97) developed an alternative theory of gravitation
  • Nathan Rosen (1909-995) young assistant to Einstein in America with whom he authored a paper in 1936 describing a universe which expands but has the symmetry of a cylinder, a theory which predicted the universe would be washed over by gravitational waves
  • Ernst Straus (1922-83) another young assistant to Einstein with whom he developed a new model, an expanding universe like those of Friedman and Lemaître but which had spherical holes removed like the bubbles in an Aero, each hole with a mass at its centre equal to the matter which had been excavated to create the hole
  • Eugene Lifschitz (1915-85) in 1946 showed that very small differences in the uniformity of matter in the early universe would tend to increase, an explanation of how the clumpy universe we live in evolved from an almost but not quite uniform distribution of matter – as we have come to understand that something like this did happen, Lifshitz’s calculations have come to be seen as a landmark
  • Kurt Gödel (1906-1978) posited a rotating universe which didn’t expand and, in theory, permitted time travel!
  • Hermann Bondi, Thomas Gold and Fred Hoyle collaborated on the steady state theory of a universe which is growing but remains essentially the same, fed by the creation of new matter out of nothing
  • George Gamow (1904-68)
  • Ralph Alpher and Robert Herman in 1948 showed that the ratio of the matter density of the universe to the cube of the temperature of any heat radiation present from its hot beginning is constant if the expansion is uniform and isotropic – they calculated the current radiation temperature should be 5 degrees Kelvin – ‘one of the most momentous predictions ever made in science’
  • Abraham Taub (1911-99) made a study of all the universes that are the same everywhere in space but can expand at different rates in different directions
  • Charles Misner (b.1932) suggested ‘chaotic cosmology’ i.e. that no matter how chaotic the starting conditions, Einstein’s equations prove that any universe will inevitably become homogenous and isotropic – disproved by the smoothness of the background radiation. Misner then suggested the Mixmaster universe, the  most complicated interpretation of the Einstein equations in which the universe expands at different rates in different directions and the gravitational waves generated by one direction interferes with all the others, with infinite complexity
  • Hannes Alfvén devised a matter-antimatter cosmology
  • Alan Guth (b.1947) in 1981 proposed a theory of ‘inflation’, that milliseconds after the big bang the universe underwent a swift process of hyper-expansion: inflation answers at a stroke a number of technical problems prompted by conventional big bang theory; but had the unforeseen implication that, though our region is smooth, parts of the universe beyond our light horizon might have grown from other areas of inflated singularity and have completely different qualities
  • Andrei Linde (b.1948) extrapolated that the inflationary regions might create sub-regions in  which further inflation might take place, so that a potentially infinite series of new universes spawn new universes in an ‘endlessly bifurcating multiverse’. We happen to be living in one of these bubbles which has lasted long enough for the heavy elements and therefore life to develop; who knows what’s happening in the other bubbles?
  • Ted Harrison (1919-2007) British cosmologist speculated that super-intelligent life forms might be able to develop and control baby universe, guiding the process of inflation so as to promote the constants require for just the right speed of growth to allow stars, planets and life forms to evolve. Maybe they’ve done it already. Maybe we are the result of their experiments.
  • Nick Bostrom (b.1973) Swedish philosopher: if universes can be created and developed like this then they will proliferate until the odds are that we are living in a ‘created’ universe and, maybe, are ourselves simulations in a kind of multiverse computer simulation

Although the arrival of Einstein and his theory of relativity marks a decisive break with the tradition of Newtonian physics, and comes at page 47 of this 300-page book, it seemed to me the really decisive break comes on page 198 with the publication Alan Guth’s theory of inflation.

Up till the Guth breakthrough, astrophysicists and astronomers appear to have focused their energy on the universe we inhabit. There were theoretical digressions into fantasies about other worlds and alternative universes but they appear to have been personal foibles and everyone agreed they were diversions from the main story.

However, the idea of inflation, while it solved half a dozen problems caused by the idea of a big bang, seems to have spawned a literally fantastic series of theories and speculations.

Throughout the twentieth century, cosmologists grew used to studying the different types of universe that emerged from Einstein’s equations, but they expected that some special principle, or starting state, would pick out one that best described the actual universe. Now, unexpectedly, we find that there might be room for many, perhaps all, of these possible universes somewhere in the multiverse. (p.254)

This is a really massive shift and it is marked by a shift in the tone and approach of Barrow’s book. Up till this point it had jogged along at a brisk rate namechecking a steady stream of mathematicians, physicists and explaining how their successive models of the universe followed on from or varied from each other.

Now this procedure comes to a grinding halt while Barrow enters a realm of speculation. He discusses the notion that the universe we live in might be a fake, evolved from a long sequence of fakes, created and moulded by super-intelligences for their own purposes.

Each of us might be mannequins acting out experiments, observed by these super-intelligences. In which case what value would human life have? What would be the definition of free will?

Maybe the discrepancies we observe in some of the laws of the universe have been planted there as clues by higher intelligences? Or maybe, over vast periods of time, and countless iterations of new universes, the laws they first created for this universe where living intelligences could evolve have slipped, revealing the fact that the whole thing is a facade.

These super-intelligences would, of course, have computers and technology far in advance of ours etc. I felt like I had wandered into a prose version of The Matrix and, indeed, Barrow apologises for straying into areas normally associated with science fiction (p.241).

Imagine living in a universe where nothing is original. Everything is a fake. No ideas are ever new. There is no novelty, no originality. Nothing is ever done for the first time and nothing will ever be done for the last time… (p.244)

And so on. During this 15-page-long fantasy the handy sequence of physicists comes to an end as he introduces us to contemporary philosophers and ethicists who are paid to think about the problem of being a simulated being inside a simulated reality.

Take Robin Hanson (b.1959), a research associate at the Future of Humanity Institute of Oxford University who, apparently, advises us all that we ought to behave so as to prolong our existence in the simulation or, hopefully, ensure we get recreated in future iterations of the simulation.

Are these people mad? I felt like I’d been transported into an episode of The Outer Limits or was back with my schoolfriend Paul, lying in a summer field getting stoned and wondering whether dandelions were a form of alien life that were just biding their time till they could take over the world. Why not, man?

I suppose Barrow has to include this material, and explain the nature of the anthropic principle (p.250), and go on to a digression about the search for extra-terrestrial life (p.248), and discuss the ‘replication paradox’ (in an infinite universe there will be infinite copies of you and me in which we perform an infinite number of variations on our lives: what would happen if you came face to face with one of your ‘copies?? p.246) – because these are, in their way, theories – if very fantastical theories – about the nature of the universe and he his stated aim is to be completely comprehensive.

The anthropic principle Observations of the universe must be compatible with the conscious and intelligent life that observes it. The universe is the way it is, because it has to be the way it is in order for life forms like us to evolve enough to understand it.

Still, it was a relief when he returned from vague and diffuse philosophical speculation to the more solid territory of specific physical theories for the last forty or so pages of the book. But it was very noticeable that, as he came up to date, the theories were less and less attached to individuals: modern research is carried out by large groups. And he increasingly is describing the swirl of ideas in which cosmologists work, which often don’t have or need specific names attached. And this change is denoted, in the texture of the prose, by an increase in the passive voice, the voice in which science papers are written: ‘it was observed that…’, ‘it was expected that…’, and so on.

  • Edward Tryon (b.1940) American particle physicist speculated that the entire universe might be a virtual fluctuation from the quantum vacuum, governed by the Heisenberg Uncertainty Principle that limits our simultaneous knowledge of the position and momentum, or the time of occurrence and energy, of anything in Nature.
  • George Ellis (b.1939) created a catalogue of ‘topologies’ or shapes which the universe might have
  • Dmitri Sokolov and Victor Shvartsman in 1974 worked out what the practical results would be for astronomers if we lived in a strange shaped universe, for example a vast doughnut shape
  • Yakob Zeldovich and Andrei Starobinsky in 1984 further explored the likelihood of various types of ‘wraparound’ universes, predicting the fluctuations in the cosmic background radiation which might confirm such a shape
  • 1967 the Wheeler-De Witt equation – a first attempt to combine Einstein’s equations of general relativity with the Schrödinger equation that describes how the quantum wave function changes with space and time
  • the ‘no boundary’ proposal – in 1982 Stephen Hawking and James Hartle used ‘an elegant formulation of quantum  mechanics introduced by Richard Feynman to calculate the probability that the universe would be found to be in a particular state. What is interesting is that in this theory time is not important; time is a quality that emerges only when the universe is big enough for quantum effects to become negligible; the universe doesn’t technically have a beginning because the nearer you approach to it, time disappears, becoming part of four-dimensional space. This ‘no boundary’ state is the centrepiece of Hawking’s bestselling book A Brief History of Time (1988). According to Barrow, the Hartle-Hawking model was eventually shown to lead to a universe that was infinitely large and empty i.e. not our one.
The Hartle-Hawking no boundary Hartle and Hawking No-Boundary Proposal

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

  • In 1986 Barrow proposed a universe with a past but no beginning because all the paths through time and space would be very large closed loops
  • In 1997 Richard Gott and Li-Xin Li took the eternal inflationary universe postulated above and speculated that some of the branches loop back on themselves, giving birth to themselves
The self-creating universe of J.Richard Gott III and Li-Xin Li

The self-creating universe of J.Richard Gott III and Li-Xin Li

  • In 2001 Justin Khoury, Burt Ovrut, Paul Steinhardt and Neil Turok proposed a variation of the cyclic universe which incorporated strong theory and they called the ‘ekpyrotic’ universe, epkyrotic denoting the fiery flame into which each universe plunges only to be born again in a big bang. The new idea they introduced is that two three-dimensional universes may approach each other by moving through the additional dimensions posited by strong theory. When they collide they set off another big bang. These 3-D universes are called ‘braneworlds’, short for membrane, because they will be very thin
  • If a universe existing in a ‘bubble’ in another dimension ‘close’ to ours had ever impacted on our universe, some calculations indicate it would leave marks in the cosmic background radiation, a stripey effect.
  • In 1998 Andy Albrecht, João Maguijo and Barrow explored what might have happened if the speed of light, the most famous of cosmological constants, had in fact decreased in the first few milliseconds after the bang? There is now an entire suite of theories known as ‘Varying Speed of Light’ cosmologies.
  • Modern ‘String Theory’ only functions if it assumes quite a few more dimensions than the three we are used to. In fact some string theories require there to be more than one dimension of time. If there are really ten or 11 dimensions then, possibly, the ‘constants’ all physicists have taken for granted are only partial aspects of constants which exist in higher dimensions. Possibly, they might change, effectively undermining all of physics.
  • The Lambda-CDM model is a cosmological model in which the universe contains three major components: 1. a cosmological constant denoted by Lambda (Greek Λ) and associated with dark energy; 2. the postulated cold dark matter (abbreviated CDM); 3. ordinary matter. It is frequently referred to as the standard model of Big Bang cosmology because it is the simplest model that provides a reasonably good account of the following properties of the cosmos:
    • the existence and structure of the cosmic microwave background
    • the large-scale structure in the distribution of galaxies
    • the abundances of hydrogen (including deuterium), helium, and lithium
    • the accelerating expansion of the universe observed in the light from distant galaxies and supernovae

He ends with a summary of our existing knowledge, and indicates the deep puzzles which remain, not least the true nature of the ‘dark matter’ which is required to make sense of the expanding universe model. And he ends the whole book with a pithy soundbite. Speaking about the ongoing acceptance of models which posit a ‘multiverse’, in which all manner of other universes may be in existence, but beyond the horizon of where can see, he says:

Copernicus taught us that our planet was not at the centre of the universe. Now we may have to accept that even our universe is not at the centre of the Universe.


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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

The Perfect Theory by Pedro G. Ferreira (2014)

On page three of this book, astrophysicist Pedro G. Ferreira explains that part of what enthralled him as a student studying the theory of relativity was the personalities and people behind the ideas.

I felt that I had entered a completely new universe of ideas populated by the most fascinating characters. (p.xiii)

This is the approach he takes in the 14 chapters and 250 pages of this book which skip lightly over the technicalities of the theory in order to give us an account of the drama behind the discovery of the theory. Ferreira describes relativity’s slow acceptance and spread among the community of theoretical physicists, many of whom went on to unravel unexpected consequences from his equations which Einstein hadn’t anticipated (and often fiercely opposed). He shows how the theory was eclipsed in the middle years of the century by the more fashionable theory of quantum physics, then underwent a resurgence from the 1960s onwards, until Ferreira brings the story right up to date with predictions that we are trembling on the brink of major new, relativity-inspired, discoveries.

This book isn’t about the theory of relativity so much as the story of how it was devised, received, tested, studied and expanded, and by whom. It is ‘the biography of general relativity’ (p.xv).

Thus the narrative eschews maths and scientific formulae to focus on a narrative with plenty of human colour and characters. For example, early explanations of the theory are dovetailed with accounts of Einstein’s opposition to the Great War and the political attitudes of Sir Arthur Eddington, his chief promoter in Britain, who was a Quaker. A typically vivid and grabby opening sentence of a new section reads:

While Einstein was working on his theory of general relativity, Alexander Friedmann was bombing Austria. (p.31)

Some reviews I’ve read say that – following Stephen Hawking’s example in his A Brief History of Time (1988) – there isn’t a single equation in the book, but that isn’t quite true; there’s one on page 72:

2 + 2 = 4

is the only equation in the book – which I suspect is a joke. For the most part the ideas are explained through the kind of fairly simple-to-describe thought experiments (Gedankenexperimenten) which led Einstein to his insights in the first place – simple except that they are taking place against an impossibly sophisticated background of astrophysical knowledge, maths theories, weird geometry and complex equations.

Timeline

In 1905 Albert Einstein wrote a number of short papers based on thought experiments he had been carrying out in his free time at his undemanding day job working in the Berne Patent Office. The key ones aimed to integrate Newtonian mechanics with James Clerk Maxwell’s force of electromagnetism. His breakthrough was ‘seeing’ that space and time are not fixed entities but can, under certain circumstances, bend and curve. (It is fascinating to learn that Einstein’s insights came through thought experiments, thinking through certain, fairly simple, scenarios and working through the consequences – only then trying to find the mathematical formulas which would express essentially mental concepts. Only years later was any of it subjected to experimental proof.)

The book gives a powerful sense of the rivalry and jostling between different specialisms. It’s interesting to learn that pure mathematicians often looked down on physicists; they thought physicists too ready to bodge together solutions, whereas mathematicians always strive for elegance and beauty in the equations. Physicists, for their part, suspect the mathematicians of coming up with evermore exotic and sometimes bizarre formulas, which bear little or no relation to the ‘reality’ which physicists have to work with.

So the short or ‘special’ theory of relativity – focusing on mechanics and electromagnetism – was complete by around 1907. But Einstein was acutely aware that it didn’t integrate gravity into his model of the universe. It would take Einstein another ten years to integrate gravity into his theory which, as a result, is known as the general theory of relativity.

Ferreira explains how he was helped by his friend, the mathematician Marcel Grossman, who introduced him to the realm of non-Euclidean mathematics devised by Bernhard Riemann. This is typical of how the book proceeds: by showing us the importance of personal contacts, exchanges, dialogue between scientists in different specialities.

For example, Ferreira explains that the ‘Hilbert program’ was the attempt by David Hilbert to give an unshakable theoretical foundation to all mathematics. Einstein visited Hilbert at the university of Göttingen in 1915, because his general theory still lacked complete mathematical provenance. He had intuited a way to integrate gravity into his special theory – but didn’t have the maths to prove it. Eventually, by the end of 1915, in a process Ferreira describes as Einstein dropping some of his ‘intuitions’ in order to ‘follow the maths’, Einstein completed his general theory of relativity, expressed as a set of equations which became known as the ‘Einstein field equations’.

In fact the field equations were ‘a mess’. A set of ten equations of ten functions of the geometry of space and time, all nonlinearly tangled and intertwined, so that solving any one function by itself was impossible. The theory argued that what we perceive as gravity is nothing more than objects moving in the geometry of spacetime. Massive objects affect the geometry, curving space and time.

Almost before he had published the theory (in an elegantly compact three-page paper) other physicists, mathematicians, astronomers and scientists had begun to take the equations and work through their implications, sometimes with results which Einstein himself strongly disapproved of. One of the most interesting themes in the book is the way that Einstein himself resisted the implications of his own theory.

For example, Einstein assumed, on the classical model, that matter was spread evenly through the universe; but mathematicians pointed out that, if so, Einstein’s equations suggested that at some point the universe would start to evolve i.e. large clumps of matter would be attracted to each other; nothing would stay still; potentially, the entire universe could end up collapsing in on itself. Einstein bent over backwards to exclude this ‘evolving universe’ scenario from his theory by introducing a ‘cosmological constant’ into it, a notional force which pushed back against gravity’s tendency to collapse everything: between the attraction of gravity and the repellent force of the ‘cosmological constant’, the universe is held in stasis. Or so he claimed.

Ferreira explains how the Dutch astronomer Willem de Sitter was sympathetic to Einstein’s (gratuitous) cosmological constant and worked through the equations, initially to support Einstein’s theory, but in so doing discovered that the universe could be supported by the constant alone – but it would contain very little matter, very little of the stars and planets which we seem to see. Einstein admired the maths but abhorred the resulting picture of a relatively empty universe.

In fact this was just the beginning of Einstein’s theory running away from him. The Russian astronomer and mathematician Alexander Friedmann worked through the field equations to prove that the perfectly static universe Einstein wanted to preserve – and had introduced his ‘cosmological constant’ to save – was in fact only one out of many possible scenarios suggested by the field equations – in all the others, the universe had to evolve.

Friedmann explained his findings in his 1922 paper, ‘On the Curvature of Space’, which effectively did away with the need for a cosmological constant. His work and that of the Belgian priest, Georges Lemaître, working separately, strongly suggested that the universe was in fact evolving and changing. They provided the theoretical underpinning for what astronomers had observed and named the ‘de Sitter effect’, namely the observation, made with growing frequency in the 1920s, that the furthest stars and nebulae from earth were undergoing the deepest ‘red shift’ i.e. the light emanating from them was shifted down the spectrum towards red, because they were moving away from us. Even though Einstein himself disapproved of the idea, his theory and the observations it inspired both showed us that the universe is expanding.

If so – does that mean that the universe must have had a definite beginning? When? How? And could the theory shed light on what were just beginning to be known as ‘dwarf stars’? What about the bizarre new concept of ‘black holes’ (originally developed by the German astronomer Karl Schwarzchild, who sent his results to Einstein in 1916, but died later that year)?

What Einstein called ‘the relativity circus’ was well underway – and the rest of the book continues to introduce us to the leading figures of 20th century physics, astrophysics, cosmology and mathematics, giving pen portraits of their personalities and motivations and describing the meetings, discussions, conferences, seminars, experiments, arguments and debates in which the full implications of Einstein’s theory were worked out, argued over, rejected, revived and generally played with for the past 100 years.

We are introduced:

  • To Subrahmanyan Chandrasekhar who proposed a sophisticated solution to the problem of white dwarfs and how stars die – which was rejected out of hand by Eddington and Einstein.
  • To the Soviet physicist Lev Davidovich Landau who proposed that stars shine and burn as a result of the radioactive fission of tremendously dense neutrons at their core (before he was arrested for anti-Stalin activities in 1938).
  • To J. Robert Oppenheimer who read Landau’s paper and used its insights to prove Schwarzchild’s wartime idea that stars collapse into such a dense mass that gravity itself cannot escape, and therefore a bizarre barrier is created around the star from which light, energy, radiation or gravity can emerge – the ‘event horizon’ of a ‘black hole’.

These are the main lines of research and investigation which Ferreira outlines in the first quarter or so of the book up to the start of World War Two. At this point, of course, many leading physicists and mathematicians of all nationalities were roped into the massive research projects run in America and Germany into designing a bomb which could harness the energy of nuclear fusion. This had been thoroughly investigated in theory and in observations of distant galactic phenomena – but never created on earth. Not until August 1945, that is, when the two atom bombs dropped on Japan killed about 200,000 people.

Learnings

Some of the several fascinating things to learn from this mesmerising account are:

  • How often Einstein was wrong and wrong-headed, obstinately refusing to believe the universe evolved and changed, refusing to believe (therefore) that it had an origin in some ‘big bang’, and his refusal to accept the calculations which proved the possibility of black holes.
  • That although a great genius may devise a profound theory, in the world of science he doesn’t ‘own’ it – there is literally no limit to the number of other scientists who can probe and poke and work through and analyse and falsify it – and that the strangeness and weirdness of general relativity made it more liable than most theories to produce unexpected and counter-intuitive results, in the hands of its many epigones.
  • That after early successes, namely:
    • predicting the movement of the planets more accurately than Newton’s classical mechanical theory
    • showing that light really is bent by gravity when this phenomenon was observed and measured during a solar eclipse in 1919
    • inspiring the discovery that the universe is expanding
  • the theory of relativity was increasingly thought of as a generator of bizarre mathematical exotica which had little or no relevance to the real world. We learn that ambitious physicists from the 1930s onwards preferred to choose careers in the other great theoretical breakthrough of the 20th century, quantum physics. Quantum could be tested, experimented with and promised many more practical breakthroughs.

Almost everyone’s attention was elsewhere now, enthralled by the triumph of quantum physics. Most of the talented young physicists were focusing their efforts on pushing the quantum theory further, looking for more spectacular discoveries and applications. Einstein’s general theory of relativity, with all its odd predictions and exotic results, had been elbowed out of the way and sentenced to a trek in the wilderness. (p.65)

  • And so that Einstein, now safely ensconced in the rarefied atmosphere of the Institute for Advanced Studies in Princeton, New Jersey, dedicated the last thirty years of his life (he died in 1955) to an ultimately fruitless quest for a ‘Grand Unified Theory’ which would combine all aspects of physics into one set of equations. He was, in the 1940s and 50s, an increasingly marginal figure – yesterday’s man – while the world hurried on without him. He died before the great revival of his theory in the 1960s which the second part of Ferreira’s book chronicles.

Visualisation

Again and again Ferreira shows how the researchers proceeded – or summarises the differences between their approaches and results – in terms of how they visualised the problem. Thus Schwarzchild’s vision of a relativistic universe described a spacetime that was perfectly symmetric about one point; whereas 40 years later, in 1963, New Zealander Roy Kerr modeled a solution for a spacetime that was symmetric about a line (p.121). A different way of visualising and conceiving the problem, which led to a completely different set of equations, and completely different consequences.

Other scientists take an insight like this, a new vision with accompanying new mathematics, and themselves subject it to further experimental modeling. The Soviet physicists Isaak Khalatnikov and Evgeny Lifshitz took Oppenheimer and Snyder’s 1930s model of a star collapsing – which assumed the shape of the star to be a perfect sphere – and modeled what happened if the star-matter was rough and unequal, like the surface of the earth. In this model, different bits collapsed at different rates, creating a churning of space time and never achieving the perfect collapse into a singularity modeled by Schwarzchild 60 years earlier or by Kerr more recently. This Soviet model was itself disproved by Roger Penrose, who had spent years devising his own diagrams and maths to model spacetime, and submitted a paper in 1965 which proved that ‘the issue of the final state’ always ended in singularities (pp.123-125).

And that is how the field progresses, via new ways of seeing and modeling. One revealing anecdote is how, at a conference in the 1990s on the newly hot topic of ‘dark matter’, one presenter put up a slide listing over one hundred different models for how dark matter exists, is created and works (p.192), all theoretical, derived from different sets of equations or observations, all awaiting proof.

It is not only the complexity of the subject matter which makes this such a daunting field of knowledge – it is the sheer number and variety of theories, ancient and modern, which its practitioners are called on to understand and sift and evaluate and which – as the first half makes plain – even the giants in the field, Einstein and Eddington, could get completely wrong.

The 1960s and since

In Ferreira’s account the 1960s saw a great revival of the theory of general relativity to explain the host of new astronomical phenomena which were being discovered and named – joining black holes and dwarf stars were pulsars, quasars and so on – as well as new theoretical micro-particles, like the Higgs boson. Kip Thorne called the 60s and 70s the Golden Age of Relativity, when the theory provided elegant solutions to problems about black holes, dark energy and dark matter, singularities and the Big Bang.

Over the past forty years or so new theories have arisen which take and transcend general relativity, including string theory (which rose to prominence in the 1980s but has since fallen into unpopularity) and supersymmetry (which invokes up to six extra dimensions in its quest for a total theory), loop quantum theory (where reality is comprised of minute loops of quantum gravity which bind together like chainmail), spin networks (frameworks like a children’s climbing frame, devised by Roger Penrose), Modified Newtonian Dynamics (or MOND) or a new theory to rival Einstein’s named the Tensor-Vector-Scalar theory of gravity (TeVeS).

When Ferreira and colleagues undertook a review of theories of quantum mechanics they discovered there are scores of them, ‘a rich bestiary of gravitational theories’ (p.221).

The great ambition is to incorporate quantum gravity into general relativity in order to produce a grand unified theory of everything. Although clever people bet this would happen before the end of the 20th century, it didn’t. 17 years later, we seem as far away as ever.

Thirty years after Stephen Hawking predicted the end of physics and then unleashed his black hole information paradox on an unsuspecting world, there isn’t an agreed-upon theory of quantum gravity, let alone a complete unified theory of all the fundamental forces. (p.205)

Ferreira draws together various developments in theory at the sub-atomic level to conclude that we may be on the brink of moving beyond Einstein’s vision of a curving spacetime: the real stuff of the universe is, depending on various theories, a bubbling foam of intertwining strings or structures or membranes or loops – but certainly not continuous. Newtonian mechanics still work fine at the gross level of our senses; it is only at extremes that Einstein’s theories need to be evoked. Now Ferreira wonders if it’s time to do the same to Einstein’s theories; to go beyond them at the new extremes of physical reality which are being discovered.

Notes

The deliberate non-technicality of the text is compensated by 18 pages of excellent notes, which give a chatty overview of each of the chapter topics before recommending up-to-the-minute websites for further reading, including the websites and even Facebook groups for specific projects and experiments. And there is also a detailed bibliography of books and articles.

All in all this is an immensely useful overview of the ideas and debates in this field.


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