Einstein's Masterwork

by John Gribbin

  Hot on the heels of Einstein’s discovery of what he thought was ‘the’ cosmological solution to the equations of the General Theory, the Dutch astronomer Willem de Sitter found another solution – another cosmological model. This was not a realistic description of our Universe because it contained no matter – it described mathematically empty, stationary spacetime. But when mathematicians did the equivalent of sprinkling bits of matter in to de Sitter’s universe to see what would happen, they found a curious thing. It expanded, with space stretching to increase the distances between the particles of matter. And if you imagined a being on one of those ‘test particles’ monitoring light from the other test particles, the equations said that the light would be stretched by the expansion, shifting it from the blue end of the spectrum to the red – a redshift. Nobody saw this as anything more than a mathematical curiosity in 1917.

  The next big step forward came from a Russian mathematician, Alexander Friedman, in 1922. It was Friedman who was the first to realise that it was futile to seek a unique cosmological solution to Einstein’s equations, and that he was dealing with a family of solutions, a whole variety of cosmological models. And instead of forcing those models to keep still by adding a cosmological constant, he let them do their own thing, and expand or contract if they wanted to. But for completeness he also included models with different cosmological constants.

  Three kinds of model discovered by Friedman are particularly important. In one variation on the theme, the model universes expand forever, slowing down because of the gravitational influence of all the matter they contain, but never stopping. These are called ‘open’ models. Another set of models start out expanding, but slow to a halt and then fall back in on themselves. These are called ‘closed’ models. And in between these two varieties there is a special kind of universe which expands ever more slowly and gradually comes almost to a halt, but never re-collapses. These are called ‘flat’ models, because the overall spacetime of such a universe is flat, except for the dents caused by objects like stars.

  Friedman’s work did not attract much attention at the time, partly because he was Russian and cut off from other scientists in those troubled times, and partly because he died in 1925 and was not around to promote it. But in 1927, unaware of Friedman’s work, Georges Lemaître, a Belgian astronomer (who also happened to be an ordained Catholic priest), published a similar analysis of the equations. By then, it had just been established that the Milky Way is just one galaxy in a vast sea of similar objects, and there had been a few measurements of redshifts in the light from some of these other galaxies. Lemaître suggested that this was evidence that the Universe is expanding, and developed the idea that it must therefore have been smaller in the past, with galaxies and stars squeezed together in what he called the ‘cosmic egg’.

  None of this attracted much attention until the American astronomer Edwin Hubble (the man who had proved that there are galaxies beyond the Milky Way), building on the work of Vesto Slipher and assisted by the superb observations made by his colleague Milton Humason, measured the redshifts and distances of many more galaxies at the end of the 1920s and into the 1930s, and came up with Hubble’s law – that the redshift of a galaxy is proportional to its distance. This law works whatever galaxy you are viewing from, and does not mean that we are at the centre of the Universe. Indeed, it means that there is no centre to the Universe! With Lemaître’s cosmic egg idea and the work of many astronomers and physicists (including Gamow) over the next four decades, this Big Bang model became established as a good description of our Universe, matching the Friedman/Lemaître expanding flat model with no cosmological constant. If Einstein had believed what the equations were telling him, he could have predicted this in 1917.

  Up until the late 1990s, improved observations using better telescopes (both optical and radio) and instruments in space seemed to match the simplest ‘Einstein universe’ more and more accurately – the discovery of the cosmic microwave background radiation, a weak hiss of radio noise coming from all directions in space and interpreted as leftover radiation from the Big Bang itself, was particularly telling. The picture that was established was of a Universe that burst out from a superdense state (perhaps a singularity) in an initial phase of rapid expansion called inflation, followed by a gradually slowing expansion matching the flat Friedman models. One intriguing feature is that in order to make spacetime flat, and to account for the way galaxies move within clusters of galaxies, there has to be a lot more matter than we can see in stars and galaxies. To match the understanding of Big Bang physics, this matter cannot just be cold everyday matter, but has to be a kind of stuff not seen on Earth or in the stars. It was dubbed ‘dark matter’, and the search for dark matter is ongoing. Then, at the end of the 20th century, an even more exciting discovery was made.

  With the best telescopes ever available, it was possible to measure redshifts and distances for galaxies very far away across the Universe. It turned out that these galaxies are receding from us, because of the stretching of space, slightly faster than they ‘ought’ to be, according to the simplest version of Hubble’s law.e The explanation wasn’t long in coming. Everything fits together if there is, after all, a small cosmological constant, a kind of springiness of space, affecting the expansion of the Universe. When the Universe was younger and more compact, gravity dominated the expansion, slowing it down in line with Hubble’s law; but as the galaxies have got farther apart and matter has thinned out, the influence of gravity has weakened, while the cosmological constant has stayed the same, so that it is just beginning to overcome gravity and make the Universe expand faster. If this continues, the ultimate fate of the Universe is eternal expansion at an ever faster rate. Einstein’s ‘biggest blunder’ turns out to be a key to understanding the Universe.

  There’s more. The cosmological constant is a form of energy, sometimes called ‘dark energy’. The springiness of space contains energy, just as an ordinary compressed spring contains energy. And as Einstein taught us, energy is equivalent to mass. So this dark energy contributes to making spacetime flat. In fact, it is the dominant form of mass in the Universe. Using data from a satellite known as Planck, in honour of the founding father of quantum physics, in 2013 astronomers were able to announce a superbly detailed breakdown of the material content of the Universe. Just 4.9 per cent of the mass of the Universe (less than one twentieth) is in the form of what we think of as ordinary matter, the stuff we are made of and the stuff stars and planets are made of. Exactly 26.8 per cent of the mass of the Universe, more than five times the amount of everyday matter, is in the form of the stillmysterious dark matter. More than two-thirds, 68.3 per cent, of the Universe is in the form of the cosmological constant, aka dark energy. And the Universe is 13.8 billion years old. This astonishingly precise description of the entire Universe rests securely on the foundation of the General Theory of Relativity – a legacy which Einstein could never have dreamed of when he was grappling with the cosmological equations under conditions of extreme privation in Berlin in the second half of the First World War.

  Footnotes

  a But there is a modern counterpart, known as string theory.

  b It actually took two years to analyse all the data, so the final results came out in 1978.

  c Don’t worry about the bizarre units. Astronomers can’t actually measure the change in one second, but derive this from observations made over much longer intervals. What matters is the close agreement between the two numbers.

  d My World Line, Viking, New York, 1970. Gamow was a good storyteller, although he sometimes exaggerated for effect. But this is the original (and only) source for one of Einstein’s most widely-quoted remarks.

  e In some ways, it is better to think of this as us receding from distant galaxies faster than we are receding from nearby galaxies.

  5

  The Icon of Science

  Personal problems; Fame; A last quantum hurrah; Exile; Spooky action at a distance; The final yearsr />
  To pick up the threads of Einstein’s personal story, remember that he was alone in Berlin, starting a new life, when the First World War broke out. He had complete freedom to work as he wished, but nobody, at first, to look after the domestic side of things. This became increasingly important as the Allied blockade began its attempt to starve Germany into submission. It was in these circumstances, which became increasingly difficult as the war progressed, that Einstein completed his masterwork. And he only survived the war thanks to the support he soon received from his cousin Elsa.

  Einstein, as I have mentioned, worked obsessively, slept only when he was exhausted, forgot to eat and neglected personal hygiene. He completed his General Theory in 1915 and almost immediately moved on to the cosmological implications. As if that were not enough, in 1916 he made another major contribution to quantum physics, using the methods of statistical mechanics (harking back to his early interest) to explain the behaviour of electrons ‘jumping’ between energy levels in atoms. This behaviour produces the lines in spectra which are the characteristic fingerprints of different elements (used, among many other things, to measure redshifts of galaxies in the expanding Universe). In explaining the nature of these jumps, Einstein derived the equation for black-body radiation – Planck’s formula – in a new way, and also laid the foundations for an investigation of the way atoms could be stimulated into the emission of radiation. Einstein had returned to the puzzle of how light interacts with matter armed now with the model of the atom as a tiny central nucleus surrounded by a cloud of electrons, developed by the Dane Niels Bohr from the experimental work of the New Zealander Ernest Rutherford. Using the idea that electrons ‘jump’ from one energy level to another inside the atom as they emit or absorb light quanta (photons), he discovered how suitably energised atoms could, in principle, be made to release a pulse of light quanta all with the same wavelength, at the same time, as an energetic beam of pure light.

  This became, decades later, the foundation of laser physics; the acronym ‘laser’ stands for Light Amplification by Stimulated Emission of Radiation. All this work was completed in 1916, but published in the Physikalische Zeitschrift in 1917, in a paper which also introduced the idea that photons – particles of light – carry momentum, just like everyday objects such as cricket balls. The effort, coming on top of the race to complete the General Theory before he was beaten to it, and combined with his self-neglect, nearly killed him. But all the while, Elsa was there, providing increasingly important support as the conditions in wartime Berlin deteriorated.

  Personal problems

  One reason why Einstein flung himself back into his work in the summer of 1916 was the continuing deterioration of his relationship with Mileva. He had visited Switzerland at Easter, chiefly to see his sons, but refused to have any contact with his estranged wife. This understandably angered Hans Albert, then twelve years old, and their father parted from the boys on bad terms. Mileva herself became ill, undergoing some sort of breakdown, which Einstein dismissed as either faked or psychosomatic, and still refused to see her. He wrote to his friend Besso, who tried to act as a go-between, that: ‘She leads a worry-free life, has her two precious boys with her, lives in a fabulous neighbourhood, does what she likes with her time, and innocently stands by as the guiltless party.’ (Which, to be fair, she was.) His reaction to outside problems was always to immerse himself in his work, which he did to such effect that he soon became seriously ill.

  Everything we need to know about Einstein’s state of health in 1917 has been summed up by a friend of his, Janos Plesch, who was also a physician:

  As his mind knows no limits, so his body follows no set rules … he sleeps until he is wakened; he stays awake until he is told to go to bed; he will go hungry until he is given something to eat; and he eats until he is stopped.1

  The person who did the telling, of course, was Elsa, assisted by her two grown-up daughters (Ilse was twenty in 1917; Margot was eighteen).

  At the beginning of 1917 Einstein suffered a physical and mental collapse. He was only 38 in March that year, but experienced severe stomach pains, which he initially suspected were caused by cancer but which were diagnosed as due to an ulcer. The problem would affect him severely for the next four years, and to a lesser extent for the rest of his life. Over two months, early in 1917, he lost 50 pounds in weight. A slow recovery only really began in the summer of that year, when an apartment in the building where Elsa and her daughters lived became vacant and she was able to move Albert in there to take full-time care of him. He might well not have survived the worst months of 1917, when the Allied blockade was at its most effective and food was tightly rationed, without this support. The relationship was exactly what both of them needed – Einstein needed someone to look after him; Elsa needed someone to look after. As his health improved, in 1918 the question of a divorce emerged once again. Einstein made a generous offer to Mileva. He would pay her 9,000 marks a year, 2,000 of which would be earmarked to go into a fund for the children, and ‘The Nobel Prize – in the event of the divorce and the event that it is bestowed upon me – would be ceded to you’. In 1918, the value of the Prize was 135,000 Swedish kronor, or 225,000 German marks. Even better, the kronor was a stable currency, whereas the mark was already showing signs of collapse. Negotiations over details took months, but the offer was eventually accepted and the divorce became final in February 1919 (ironically, on Valentine’s Day), and he married Elsa in June.

  It was also in 1919 that Einstein became world-famous outside the scientific community, when his light-bending prediction was confirmed by observations of a total eclipse of the Sun. But the public icon that he became looked very different from the dashing, dark-haired young man who had set out on the road to the General Theory in 1905. Illness and wartime privation had turned him into the white-haired professor that became ‘the’ image of a scientist (including Emmett Brown in the Back to the Future movies) until Stephen Hawking came along.

  Fame

  Among other things, as we saw in Chapter 3, the General Theory of Relativity predicts exactly how much spacetime will be curved near a massive object like the Sun, and how light rays (which we are used to thinking of as travelling in straight lines) follow curved paths near the Sun as a result. This bending of light rays would show up from Earth, if we could look past the Sun at stars beyond the Sun, as a tiny sideways shift in the apparent positions of those stars on the sky – if the light from those stars wasn’t overwhelmed by the brightness of the Sun. A total eclipse would occur on 29 May 1919, but there was little prospect of the necessary observations being made while the war raged. The fighting in Europe stopped just in time. In 1919, after the Armistice but before the formal peace treaty ending the war had been signed, a British expedition led by Arthur Eddington was sent to observe a solar eclipse visible from an island off the west coast of Africa; it confirmed the prediction of the General Theory, at least to Eddington’s satisfaction, although in truth the observations were barely adequate. The fact that a German prediction had been confirmed by a British expedition so soon after the cessation of hostilities helped to ensure maximum publicity for the discovery, announced to a joint meeting of the Royal Society and the Royal Astronomical Society in London on 6 November 1919. The size of the ‘shift’ in the positions of the stars in the sky was, as predicted by Einstein, equivalent to the thickness of a matchstick seen at a distance of a little more than half a mile.

  The news, as the headline writers put it, that Isaac Newton’s theory of gravity had been superseded, that space was curved and that light could be bent as it passed by the Sun, made waves around the world and made Einstein famous. The Times, usually more sombre, ran the story under the headline ‘Revolution in Science – New Theory of the Universe – Newtonian Ideas Overthrown’. The New York Times was no less enthusiastic:

  LIGHTS ALL ASKEW IN THE HEAVENS

  Men of Science More or Less

  Agog Over Results of Eclipse

  Observations<
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  EINSTEIN THEORY TRIUMPHS

  Of course, Newtonian theory had not been ‘overturned’. Newton’s theory of gravity still applies in regions of weak gravity, and is the theory that space scientists use, for example, when planning the trajectories of spacecraft visiting the planets of the Solar System. You could do this using the field equations of the General Theory, but you would get exactly the same answer in the ‘weak field approximation’. Einstein’s theory goes beyond Newton’s theory, but contains Newton’s theory within itself. This is something that amateur theorists who delight in trying to find a better theory than Einstein’s seldom appreciate (at least, judging by the mail I receive). Any theory of gravity, space and time that is better than the General Theory will have to include the General Theory within itself, explaining everything that the General Theory explains, including the behaviour of weightless gyros and binary pulsars, and then something more besides.

  One result of Einstein’s new-found fame was that his scientific work began to take a back seat. He had become the iconic figure that, until the Stephen Hawking phenomenon, provided the public with their image of what a great scientist ‘ought’ to be. But he wasn’t finished with science yet. Einstein would make just one more important contribution to the quantum theory, in 1924 when he was 45 years old, and in the 1930s he would initiate a line of thinking which has profound implications today. But between 1919 and 1924, although he continued to carry out what was by his standards routine physics, he enjoyed some of the trappings of his fame, travelled and (especially after the award of the Nobel Prize) began to revel in the role of a kind of father figure to the rising generation of physicists.