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.


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.


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.


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.


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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