Einstein on the Run Read online

  The deflection of light by Earth’s gravity would be far too small to measure, Einstein realised. But deflection might be measurable, he reasoned, when light from distant stars passed close to a massive body like the Sun. Furthermore, the equivalence principle dictated that the light emitted from the Sun should feel the drag of solar gravity too. Its energy must therefore fall slightly, which meant that its frequency must fall and therefore its wavelength must get longer (since light’s velocity must remain constant, and the velocity of a wave equals its frequency multiplied by its wavelength). So light from atoms in the surface of the Sun, as compared with light emitted by the same atoms in interstellar space, should be shifted towards the red – longer wavelength – end of the visible spectrum when observed on Earth. The deflection of starlight by the Sun and the red shift of solar radiation were therefore possible tests of relativity.

  But in order to introduce gravity into relativity, a major problem confronted Einstein in trying to apply the equivalence principle to the flat space-time visualised by Minkowski. The problem can be perceived, at least dimly, from a paradox about a simple merry-go-round that bothered Einstein. When a merry-go-round is at rest, its circumference is equal to π times its diameter. But when it spins, its circumference travels faster than its interior. According to relativity, the circumference should therefore shrink more than the interior (since space contraction increases with velocity), which must distort the shape of the merry-go-round and make the circumference less than π times the diameter. The result is that the surface is no longer flat; space is curved. Euclid’s geometry, based on flat surfaces and straight light rays, no longer applies. Einstein is said to have had a nice analogy for this curvature, which he gave to his young son, when the boy asked his father why he was so famous: ‘When a blind beetle crawls over the surface of a curved branch, it doesn’t notice that the track it has covered is indeed curved. I was lucky enough to notice what the beetle didn’t notice.’

  In the mid-nineteenth century, the mathematician Bernhard Riemann had invented a geometry of curved space in which, said Einstein, ‘space was deprived of its rigidity, and the possibility of its partaking in physical events was recognised’. Now Einstein – initially with the help of his mathematician friend Grossmann but after he moved to Berlin in 1914 almost entirely alone – used Riemann’s geometry to create a new geometry of curved space-time. ‘His idea was that mass and energy would warp space-time in some manner yet to be determined,’ explained Hawking. Gravity would no longer be an interaction of bodies through a law of forces; it would be a field effect that emerged from the way in which mass curved space. When a marble is propelled across a flat, smooth trampoline on which sits a large and heavy ball, the marble follows a curved path around the depression caused by the ball. In the Newtonian view, a gravitational force emanates from the ball and somehow compels the marble to move in a curve. But according to general relativity it is the curvature of space – or rather space-time – that is responsible; there is no mysterious force. ‘Matter tells space-time how to curve, and curved space tells matter how to move’ – to quote a well-known summary of Einstein’s general theory of relativity by the physicist John Archibald Wheeler.

  The light ‘corpuscles’ in a light ray from a distant star grazing the Sun on its way to our eyes could be interpreted like marbles moving past a ball. In 1911, before he had mastered curved space-time, Einstein had calculated the expected deflection of starlight on the basis of Newton’s law of gravitation. In 1915, however, having completed general relativity, he recalculated the deflection as twice the size of his 1911 calculation based on Newton. If the magnitude of the actual deflection were to be measured by astronomers, it would test which gravitational theory was correct: Newton’s or Einstein’s. ‘The examination of the correctness or otherwise of this deduction is a problem of the greatest importance, the early solution of which is to be expected of astronomers,’ wrote Einstein in his introduction to relativity in 1916. It was to be British astronomers who would answer his challenge, in 1919, and launch Einstein as a new star visible across planet Earth.

  [T]he English have behaved much more nobly than our colleagues here. . . . How magnificent their attitude has been towards me and relativity theory in comparison! . . . I can only say: Hats off to the fellows!

  Letter from Einstein to Fritz Haber, March 1921

  Despite Einstein’s deep admiration for English physics, his theory experienced a surprisingly indifferent reception in England following its publication in Germany: as special relativity in 1905, followed by general relativity in 1915–16. Hardly any English mathematicians and physicists adopted it in the period 1905–19; as Rutherford remarked as late as 1932, ‘The theory of relativity by Einstein, quite apart from any question of its validity, cannot but be regarded as a magnificent work of art.’ Even their German opposite numbers viewed general relativity more with awe than comprehension. Einstein’s friend Born decided never to attempt any work in the field. ‘The foundation of general relativity appeared to me then, and it still does, the greatest feat of human thinking about Nature, the most amazing combination of philosophical penetration, physical intuition and mathematical skill,’ Born recalled in 1955 on the fiftieth anniversary of special relativity, looking back on his bemused reaction in 1915. ‘But its connections with experience were slender.’ In a presumably unconscious echo of Rutherford, Born concluded: ‘It appealed to me like a great work of art, to be enjoyed and admired from a distance.’

  Less surprisingly, all English thinkers in the humanities were baffled by Einstein’s theory. To them, ‘Einstein had really offended against common sense, the limited yardstick with which men measure the exterior world,’ observed Einstein’s English biographer, Ronald Clark.

  RELATIVITY AT OXFORD AND CAMBRIDGE

  At the University of Oxford, for instance, as late as 1919, Einstein’s theory was openly considered to be wrong on technical grounds by the Waynflete Professor of Metaphysical Philosophy, J. A. Smith. He said as much in a tense public debate in Oxford with Lindemann, Dr Lee’s Professor of Experimental Philosophy (i.e. physics). After Smith had spoken, a second Oxford philosopher, H. W. B. Joseph, announced that he agreed with Smith’s conclusion, though on purely philosophical rather than technical grounds, apparently based on his own unshakeable faith that the space we inhabit must be Euclidean. No wonder that Lindemann had recently been appointed professor with a remit to rescue physical science at Oxford from the doldrums. It was then dominated by Greats (the Oxford term for classical studies), as epitomised by the approach to relativity of these two philosophers, and also by a story later recalled by Lindemann. When once he happened to express his misgivings about the inferior position of science in Oxford to the wife of the warden of All Souls College, she assured him that ‘he should not worry because a man who had got a first-class degree in classics and philosophy could get up science in a fortnight’!

  One of the members of the audience for this 1919 Oxford debate, Roy Harrod, described it four decades later in delicious and devastating detail in his memoir of Lindemann, The Prof. At the time, Harrod was a mere undergraduate in humanities, whose tutor happened to be Joseph; in later years, he would become a distinguished colleague of Lindemann and Einstein at Christ Church. His memoir expressed undisguised scorn for Smith, who discussed certain mathematical equations and physical assumptions. ‘How came it that this distinguished purveyor of Greats wisdom, himself neither a mathematician nor a physicist, supposed that he could find, not on the plane of philosophy, but on the plane of physics itself, a technical error in the assumptions behind a theory that had been minutely scrutinised for some time by the greatest minds in the world?’ As for Harrod’s tutor Joseph, ‘he did not show the slightest sign of his ever having seriously tried to understand either what the theoretical considerations were, or what the experimental results had been, that had led these distinguished physicists to the need to expound these tiresome theories of the relativity of space and time�
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  Nevertheless, Harrod honestly admitted that Lindemann – himself a recent convert to relativity – struggled, and largely failed, to win the debate, despite some support from scientists in the audience. ‘It was a hot-house Oxford product’, to which Lindemann, as an Oxford newcomer, had no access. At one point, he was reduced to telling Joseph with an ironic facial expression (perhaps regarding Joseph’s Euclidean convictions), ‘Well, if you really suppose that you have private inspiration enabling you to know that . . .’ – and leaving this provocation dangling in the charged atmosphere of the debating chamber. ‘The Prof really never got to grips with his argument; he did not know how to do so; none of the real points of interest in relation to relativity had been touched on; the whole game must have seemed to him to be perfectly futile.’

  Even at the University of Cambridge – the home of Newton, Maxwell, Sir J. J. Thomson and (later) Rutherford – the initial response to Einstein’s theory was not much more perceptive. When Rutherford was told in 1910 by the German physicist (and future fellow Nobel laureate) Wilhelm Wien that ‘No Anglo-Saxon can understand relativity!’, he laughingly replied: ‘No! They have too much sense.’ According to Masters of Theory: Cambridge and the Rise of Mathematical Physics by the historian Andrew Warwick, ‘In Cambridge during the period 1905 to 1920, Einstein’s work was, by turns, ignored, reinterpreted, rejected, and, finally, accepted and taught to undergraduates’ – eventually under the leadership of an astronomer, Sir Arthur Eddington, rather than a physicist.

  Indeed, only one British physicist is known to have corresponded directly with Einstein about relativity before 1919: G. F. C. Searle, a demonstrator in experimental physics at the Cavendish Laboratory in Cambridge and a regular pre-war visitor to German physicists. In 1907, Einstein sent Searle a copy of his 1905 paper on special relativity from his position at the Patent Office in Bern. When Searle eventually replied in 1909, after a period of illness, he confessed to Einstein: ‘I have not been able so far to gain any really clear idea as to the principles involved or as to their meaning and those to whom I have spoken in England about the subject seem to have the same feeling.’

  One of Searle’s unnamed advisers was probably the Cambridge-educated James Jeans, who gave no particular importance to Einstein’s relativity in his book The Mathematical Theory of Electricity and Magnetism, published in 1908. Another was likely to have been a mathematician, Ebenezer Cunningham, also Cambridge educated, who published The Principle of Relativity in 1914. In this book Cunningham alluded to Einstein’s theory as follows, though without mentioning Einstein’s name: ‘The principle of relativity then does not deny the existence of an aethereal medium; that is only the interpretation of an individual. What it does do is to emphasise the insufficiency of the existing conceptions of the aether, and to set up a criterion by which suggestions as to the nature of the aether may be examined.’ At this time Cunningham and his fellow British physicists strongly objected to Einstein’s attempt, from 1905 onwards, to abandon the revered aether/ether: a concept first postulated by Aristotle as a fifth element composing the heavenly realm, along with earth, fire, water and air.

  The chief stumbling-block in these English reactions to relativity between 1905 and 1919 was that English physicists, following the discovery of electromagnetic waves by Hertz in 1888 and of the electron by Thomson in 1897, had chosen to adopt an exclusively electronic theory of matter (known as the ETM), accompanied by a firm belief in the existence of the ether. In Hertz’s emphatic words: ‘Take electricity out of the world, and light vanishes; take the luminiferous ether out of the world, and electric and magnetic forces can no longer travel through space.’ Aether and Matter, an influential work published in 1900 by Cunningham’s teacher, Joseph Larmor, Lucasian Professor of Mathematics at Cambridge (the chair once held by Newton), argued that matter was electrically constituted and contracted minutely in its direction of motion through the ether according to the relativistic theory of Hendrik Lorentz. When another of Larmor’s students, G. H. Livens, published The Theory of Electricity in 1918, he included a short section on ‘Relativity’, but did not associate the concept especially with the name of Einstein! In fact, Livens opened with the comment that ‘the whole electrodynamic properties of matter can be explained on the basis of a stationary aether and electrons’ – that is, using Larmor’s ETM, not involving relativity.

  Yet, this Cambridge-based theory of the whole mass of the atom as being electromagnetic in origin plainly failed to incorporate the non-electrical force of gravity. This failure induced gradually increasing doubts among the followers of the ETM, including Cunningham. ‘Quietly obeying the law of the inverse square, [gravitation] heeded not the bustle and excitement of the new physics of the atom, but remained, independent and inevitable, a constant challenge to rash claimants to the key of the universe,’ Cunningham eventually felt obliged to concede in the leading scientific journal, Nature, in December 1919 – after the experimental verification of Einstein’s general relativity, which of course included both light and gravity and also rejected the existence of the ether. ‘The electrical theory seemed on the way to explain every property of matter yet known, except the one most universal of them all. It could trace to its origins the difference between copper and glass, but not the common fact of their weight; and now the aether began silently to steal away,’ Cunningham confessed. (Persistent experimental attempts to demonstrate the ether’s existence, beginning with the classic experiment of two American physicists, Albert Michelson and Edward Morley, in 1887, and continuing in the period 1902–5 and after, always failed to detect it, although this experimental fact played little, if any, direct role in Einstein’s development of relativity.)

  ENTER ARTHUR EDDINGTON

  The 1919 sea-change in English attitude towards Einstein’s theory had its origins in the depths of the First World War, in June 1916, when Einstein sent a copy of his newly published summary of general relativity, spelling out some of its cosmological implications, from Berlin to Willem de Sitter, professor of astronomy at the University of Leiden in the politically neutral Netherlands. De Sitter was a foreign correspondent of the Royal Astronomical Society in England, who wished to maintain wartime scientific contacts between England and Germany. He passed on Einstein’s copy to the secretary of the Society, Eddington, who was Plumian Professor of Astronomy and Experimental Philosophy at Cambridge. An excited Eddington, despite his minimal knowledge of German, and without any direct contact with Einstein, invited de Sitter to write three expository articles, which Eddington published in the Monthly Notices of the Royal Astronomical Society in 1916–17: the first technical introduction to general relativity for English scientists written in English. These articles whetted their appetite for Eddington’s own, highly mathematical, Report on the Relativity Theory of Gravitation, commissioned by the Physical Society and published in 1918. ‘The long train of events set in motion by de Sitter and continued by Eddington was to have repercussions quite as formidable in their own way as the bloody battles being waged on the Western front,’ commented Clark in his Einstein biography.

  Einstein with astronomer Sir Arthur Eddington at the Cambridge Observatory, 1930. Eddington led the British solar eclipse observations in 1919, which confirmed Einstein’s general theory of relativity and made him internationally famous.

  Why did Eddington respond favourably to Einstein’s theory – unlike his mathematician and physicist colleagues at Cambridge, such as Cunningham, Jeans, Larmor and Searle? There appear to have been several reasons for Eddington’s exceptionalism.

  He shared the mathematical education typical of Cambridge in the early Edwardian period, where he was an undergraduate from 1902 to 1905. However, unlike the majority of students, Eddington also studied differential geometry under his tutor Robert Herman, its acknowledged master at Cambridge. This discipline enabled Eddington to penetrate the mathematics of general relativity with much greater confidence than his Cambridge contemporaries.

  Mo
re important, though, was Eddington’s chosen field of study. Rather than the electromagnetic theory studied by Larmor et al., astronomy and cosmology were what appealed to Eddington. After graduating from Cambridge, and a brief, unsuccessful encounter with experimental electronics in the Cavendish Laboratory, he moved in 1906 to the Royal Greenwich Observatory as chief assistant to the Astronomer Royal – Sir Frank Dyson, from 1910 – before returning to Cambridge as Plumian Professor in 1913.

  Astronomers and cosmologists, unlike experimental physicists, were certain to be attracted to general relativity. In the first place, their field was directly affected by the theory’s astronomical predictions, such as the deflection of starlight by the gravity of the Sun. Second, the business of positional astronomy did not require the ether. Indeed, Eddington’s first book, Stellar Movements and the Structure of the Universe, published in 1914, did not refer to the ether. ‘Unlike the case of British electromagnetic theory, therefore, the ether could be abandoned, or simply ignored, in astronomy, without devaluing the professional practice of the discipline and without requiring any retraining on the part of the astronomers,’ wrote Warwick. As a result: