In 1936, London moved to the Institut Henri Poincaré in Paris. It had become evident that liquid helium had two different phases and, below 2.19 K, it defied all classical expectations for the behavior of a liquid. From the very beginning, London was convinced that the transition to the superfluid phase could not be understood as an order–disorder transition.

In the fall of 1937, he attended the Congress for the Centenary of van der Waals at Amsterdam, where he was impressed by Joseph Mayer's attempt to formulate a statistical theory of condensation for real gases. In the same Congress, Uhlenbeck retracted his criticism of the Bose– Einstein condensation which he had expressed in his thesis of 1925. In 1924, Bose (and later Einstein, after receiving Bose's paper) had discovered that, below a certain temperature, an ideal gas of integer electron spin will start condensing and that, with each condensing atom, there will be an increased probability that the next atom will find itself in the condensed state. This condensation was a purely quantum mechanical effect which was derived from the kind of statistics the atoms obeyed.

Upon London's return to Paris, he started working frantically and discovered a ‘crazy thing’ – as he duly informed Heinz London who was now at Bristol University. He proposed that the onset of superfluidity could be regarded as being the start of this peculiar condensation, since helium is a gas obeying Bose–Einstein statistics. His initial calculations gave results that were surprisingly close to the experimentally measured values.

In March 1953, the Royal Dutch Academy of Sciences informed Fritz London that it had awarded him the prestigious Lorentz Medal. The only other recipients were Max Planck, Peter Debye, Arnold Sommerfeld and Hendrick Kramers. In July of that year, London attended a ceremony at Leiden to receive the Medal. At the end of his short speech, Fritz London talked for the first and last time about himself publicly. ‘During most of my life I have been so fortunate that I could do the things which my own nature drove me to do. It is embarassing to earn so much respect for just doing this. Yet, it is a great satisfaction for me to receive this particular sign of recognition, because it tells me that the work which was done, apparently by an internal necessity, has been found to be of some objective value’.

Some?

Surely it was a show of humility demanded under the circumstances, I thought when I first read that speech a few years ago. But, after reading and rereading his papers and books, going through his notebooks, doing most of the calculations to understand the missing steps, examining more than 3000 letters in his own and his correspondents' archives, talking to his family, friends and colleagues, I came to realize that Fritz London was not being humble that day at Leiden. He truly meant some. As I slowly realized that, the man whose work so deeply intrigued me, shrank into much smaller dimensions. And happily he become a very real person to me.

I have decided to write a scientific biography of Fritz London for many reasons.

Like the great majority of Jews living in Germany, Fritz and Edith London did not read the signs of the ominous events that culminated with the formation of the Nazi Government in 1933 and the decrees it issued during its first six months in power. London was obliged to resign and soon afterwards Lindemann offered him a research fellowship at Oxford University, UK.

Lindemann was very keen to set up a group to study low temperature physics. He had brought Simon, Mendelssohn and Kurti to Oxford, and, in 1934, London's brother Heinz joined them. A couple of months after Heinz's arrival, the two brothers worked out the electrodynamics of the superconductors and offered a theoretical schema for the explanation of superconductivity – twenty-two years after the phenomenon was first discovered. In 1933, Meissner and Ochsenfeld discovered that, in contrast to all expectations, superconductors were diamagnetic. In view of this result, the Londons considered the expulsion of the magnetic field, rather than the infinite conductivity, to be the fundamental characteristic of superconductors and proceeded to formulate their equations. Hence, the vantage point for superconductivity shifted and what was considered, for over twenty years, to be a phenomenon of infinite conductivity came to be regarded, primarily, as a case of diamagnetism at very low temperatures. Their theory was not a microscopic theory but explained the phenomenon in terms of the dynamics of the electrons. Even though the scientific community reacted favorably to their theory, Max von Laue had many objections to it.

After the unhappy years in Oxford and the hopeful years in Paris, North Carolina, USA, was a melancholy place. At Duke University, the very private London was lonely and scientifically isolated. He was not associated, even peripherally, with the atom bomb project, and he was far away from where the action took place after the end of the war.

He made several trips to Europe and he was the main speaker at the first International Conference in Low Temperature Physics in Cambridge in 1946. He enjoyed it immensely, even though he felt that ‘the level of physics was that of 1939’. At the time, London was not sympathetic to Tisza's two-fluid model. Experimental results sent by the Soviet physicists who could not attend the conference, appeared to give credence to Tisza's model, and London changed his mind and adopted it, hoping to show that his proposed mechanism of Bose–Einstein condensation could be the theoretical rationale for the two-fluid model. But there was an additional reason for adopting the model. Lev Landau, the enfant terrible of the Soviet Union, had proceeded along a different path, trying to explain superfluidity by quantum hydrodynamics. This particularly ambitious scheme had its weaknesses, but had to be reckoned with, especially since this author, highly regarded in the West, was ostentatiously ignoring London's work on superconductivity and superfluidity.

In March 1953, London was informed that the Royal Netherlands Academy of Sciences had awarded him the prestigious Lorentz Medal, which was presented every five years.

Eddington's whole intellectual framework was shattered by Dirac's electron equation. The authoritative character of the pronouncements of MTR was hopelessly undermined by the evident falsehood of one of them: that all invariant equations were of tensor form. Relativity had by now become an accepted framework within which both Eddington and this young rising star (Dirac had come to St John's College as an unknown research student in 1923 and was 26 when he discovered the equation) were working. Yet somehow the content of relativity was different from Eddington's original conception.

The second part of this book traces the development of Eddington's ideas from the change of approach brought about by the advent of Dirac's equation to Eddington's attempt at an ordered presentation of his own theory in the first of the two books I have described as constituting the Eddington mystery, Relativity Theory of Protons and Electrons (Eddington 1936), referred to here as RTPE. In this chapter I shall be concerned with the crucial first stage in the development of the theory, for it was at that early stage that the possibility of the calculation of physical constants became apparent to Eddington. It was this that set him off along a path that his contemporaries could not or would not follow.

He came to see the algebraic structures arising from Dirac's original postulation as providing the clue to the union of relativity theory and quantum mechanics. Such a union was devoutly to be wished by many of Eddington's contemporaries in the 1930s.

This chapter is devoted to the one major error in MTR which I have mentioned above. Our knowledge of the external world will, it is argued there, be precisely of the form expressible by the tensor calculus. On p. 49, for example, Eddington says:

That Eddington, in common with all physicists (and most mathematicians who were interested), was so convinced was of the greatest importance on a personal level. When his error was exposed by Dirac's 1928 paper on the electron, it had a profound psychological effect. For Dirac expressed the electron equation, not in tensor form, but in terms of new entities – spinors. Since this is such a key issue for my argument, I make no apology for going into it at some length. In the course of the discussion I shall be able to take up the question, left from Chapter 4, of what exactly a tensor is.

The principle of relativity

In order to understand Eddington's conviction and also to see why it is false, it is necessary first to look more closely at the so-called ‘principle of relativity’ which is mentioned by both Einstein and Eddington but without saying exactly what the principle is.

As well as changes in his life, general relativity brought deep intellectual consequences for Eddington. In this chapter I make a significant step towards understanding the Eddington mystery by tracing the results of his immersion in the elegant theoretical construct of general relativity and his successful confirmation of its predictions. This chapter and the next are two complementary philosophical discussions. The first of these sets out eight features of Eddington's later thought, some acknowledged by him, some only implicit. The second deals at some length with his one major error about general relativity, his assumption of the universal character of tensors. This second argument has a slightly technical aspect, which I have reduced as much as possible. What remains is vital in understanding why Eddington made a mistake the revelation of which in 1928 had such a profound psychological effect on him.

Matter as a construction

With the eclipse expedition behind him Eddington began to publish the many thoughts that his experience in general relativity had produced. It was an amazing explosion of intellectual effort. Some of these publications were explanations of the theory in a more or less technical manner but he also began to write on the philosophical consequences he saw flowing from it. It is dangerous to take Eddington's philosophical writings at face value. When he isolates certain ideas as the important ones for understanding physics it is often because he takes for granted others which are, in fact, more idiosyncratic and more in need of exposition.

Most physicists have no difficulty in seeing physics as a single subject. Yet this view, which was straightforwardly tenable until the end of the nineteenth century, is radically inconsistent with the situation since then. There has been a divorce between the theories of the very small and the large scale. Amongst those worried about this the response has been to search for a ‘theory of everything’. This phrase has many closely related connotations and to determine which, if any, is the correct one is an inspiring and useful task, not least for the unexpected by-products. So far, however, it has proved a task without any successful outcome. In this book I draw attention to an alternative. Unnoticed by many today, Eddington in the 1930s made great strides towards a different solution of the enigma.

It is half a century since I first succumbed to the Eddingtonian magic – I paraphrase Thomas Mann's phrase to try to do justice to my youthful if uncritical absorption in Relativity Theory of Protons and Electrons, which Eddington had published five years or so earlier, in 1936. I had already enjoyed his authoritative Mathematical Theory of Relativity with no more difficulty than that produced by the complex mathematical techniques which were new to me. Looking back on it, it surprises me that I could take in without a qualm so many of the unorthodox philosophical views in that book. But Relativity Theory of Protons and Electrons was a different matter. Another clutch of mathematical techniques was not enough to obscure a radically new position.

I conclude the first part of this book by carrying the story up to 1928, to the lightning flash in Eddington's mind produced by Dirac's paper on the wave equation of the electron. Setting out the context and Eddington's thinking about it is a very different matter for quantum mechanics and relativity. Both theories are commonly expressed in austere mathematical language. In the case of relativity the basic ideas behind the mathematics are now well understood and can be set out with little complication. These ideas were mostly already clear to Eddington. But for quantum mechanics the mathematics, yoked to the wealth of experimental results, drove the development of the theory at a breakneck speed, mostly without anyone pausing for deeper understanding. It is indeed only in the last decade that it has become generally accepted that quantum mechanics still lacks any coherent interpretation. To explain Eddington's context it is therefore necessary to say something about the mathematical formalism. It is true, as will become clear, that Eddington was a little more sceptical than most, but by and large the mathematics drove him as it did those directly working in the theory.

I begin, then, with a description of that part of the early (pre-1925) history of quantum mechanics that was in Eddington's mind in 1923. Then I explain what happened in 1925–6 and Eddington's reaction to it. The chapter concludes with Dirac's relativistic wave equation of 1928 and Eddington's further reaction to that.

The old quantum theory

What is now called the old quantum theory arose at the turn of the century. Two related experimental contradictions with classical physics played important roles in this.

The task ahead

If one tries to view the problem situation faced by Eddington from his point of view, it breaks into three parts. The expectation was that these three would prove connected in some way when the problem was solved. The first part of the problem is to make some connexion between 136 as a number of algebraic elements and 1/136 as related to (though by 1936 Eddington was aware that it was not equal to) e2/ħc. As I said in the last chapter, the fine-structure constant occurs in many different contexts. Ideally, if it is to be related to algebraic structures, it should be possible to use any of these contexts with the principle of identification to establish the relation. Eddington chose, naturally enough, the occurrence of α as a coefficient in Dirac's equation of the hydrogen atom. Hitherto I have been speaking only of Dirac's equation for the free electron; that is the simplest case. But, as will have been clear from Dirac's explanation quoted in Chapter 6, his work was inspired – like so much work in both the old and new quantum theories – by difficulties in explaining the hydrogen spectrum fully. The way in which the equation for the free electron was modified to take account of the electrostatic force between proton and electron was well known, if not at all understood, in the quantum wave mechanics of Schrödinger. Dirac took it over without question and Eddington followed Dirac. No-one has since questioned this method of introducing an electric force, so I shall do no more now than to remark that it is a little mysterious.

This book is an attempt to unravel a mystery about the writing of two scientific books by Sir Arthur Eddington, his Relativity Theory of Protons and Electrons of 1936 and his posthumous Fundamental Theory, published ten years later. It is an appropriate time to attempt this, for nearly half a century has elapsed since Eddington's death. There is also a more important reason for this book. The ideas that Eddington thought were behind his books – and it will become clear to what extent these are truly the ideas behind them – were addressed to one specific problem. In the first half of the twentieth century, and certainly from 1926 onwards, physics became rather absurdly divided into two disparate parts. By 1916 general relativity had built a theory of gravitation on top of the successes of the special theory of 1905. It was highly successful on the large scale, notably in astronomy. This whole way of thinking about the world had nothing in common with that of the quantum theory, one form of which started at the turn of the century. Despite its crudity it had considerable success in explaining small scale phenomena. 1926 saw its replacement by a more refined approach but still one totally at variance with that of general relativity. Almost every assumption behind one approach was inconsistent with the other. Eddington was not the only scientist to be concerned about this ridiculous situation. As time has gone on, however, and physics has remained in the same unsatisfactory state, the consensus has been that it is almost indecent to mention the fact.