Triple Life

In the last few years of the 19th century the world of the physicist began to undergo a revolution that ultimately affected much else beside physics. The discovery of the electron by Thomson, and of radioactivity by Becquerel, opened the attack on the mysteries of the atom which, through the genius of Rutherford, led within fifteen years to the nuclear model and Bohr’s quantum theory of the hydrogen atom. The quantum theory itself had been adumbrated by Planck at the very end of the century, and only five years previously Röntgen had discovered X-rays, which were to give important insights into atomic theory and to expose the paradoxes of the quantum. To see Schrödinger’s achievement in perspective we must appreciate the nature of these paradoxes, for if they had not been argued over in their manifestation by X-rays and light it is most unlikely that his great advance – a genuine paradigm-shift – would have aroused so little opposition.

Some eighty years earlier the work of Young and Fresnel had undermined the belief, to which Newton gave authority, that light consisted of particles. By Planck’s time the alternative wave model was universally accepted, with formidable support from experiment and theory, but by about 1905 this model in its turn was under attack from two quarters. Einstein had shown that Planck’s ideas demanded the co-existence of waves and particles in light, while in Cambridge Thomson, at this time unaware of the patents clerk in Zürich, could point to experiments that indicated the same for X-rays. The following twenty years of research and anxious discussion only strengthened the evidence both for waves and for photons, their associated particles, without resolving the question of how the same beam of light could behave sometimes as one and sometimes as the other, according to which experiment it took part in. It seemed to some, though the idea found no general favour, that the waves served to guide the photons which then interacted with matter to produce the manifold effects of light and X-rays. But how a photon decided at which point on an extended wave-front to make its appearance remained mysterious (and still does).

Meanwhile Bohr had developed his theory of the hydrogen atom, that miniature solar system which in popular art has become the icon of physical science. Entirely successful in describing one electron circulating round a nucleus, it failed for atoms that had more than one electron, though Bohr and others found inspiration in it to explain the periodic table of the elements and put order into the vast complexity of their characteristic spectra. Nevertheless, the theory was clearly only a makeshift, the forerunner of some more generally applicable conception. It was Louis de Broglie’s doctoral dissertation of 1923 which in Schrödinger’s hands made this dream a reality. De Broglie suggested that the duality of wave and particle might apply as well to electrons and other assumed particles as to light which, in its time, had been as firmly assumed to be waves. His deduction of the relationships between the characteristic features of waves (frequency and wavelength) and of particles (energy and momentum) was accepted by his examiners as the masterly exposition of an ingenious fantasy.

Only in the winter of 1925 was this work published fully, and read by Schrödinger who recognised a connection with an earlier, at that time unfruitful, idea of his own. Stimulated to feverish activity, he developed de Broglie’s conception into a remarkably complete and elegant mathematical formulation which goes by the name of Wave Mechanics, being summed up in Schrödinger’s equation and the rules for applying it to the solution of physical problems. Having satisfied himself that it reproduced the successful results of Bohr’s theory, and was consistent with a theory of Heisenberg’s, parallel to his own but much more abstruse, he left it to others to explore further applications.

Within a few years it became clear that wave mechanics was going to succeed not only with atoms but with chemical compounds and metals. The development of mathematical methods to cope with ever more difficult problems has occupied many of the best physicists since then and, with the advent of powerful computers, systems of considerable complexity have been analysed and tested against experiment, with such success that disagreements are taken as evidence of poor experimentation, false assumptions about the model to be analysed, or simply mathematical errors – never as an indication of the failure of quantum mechanics, which has taken its place among the great systems of Newton, Maxwell and Einstein as one of the foundations of our understanding of the material world.

This achievement is justification enough for compiling as definitive as possible an account of the life of its author. But it must be added that it is almost the sole justification, for there is little else in Schrödinger’s life and works that singles him out for special treatment. At this moment of triumph he was 38 years old, unusually late for so radical an innovation. His previous publications, though sound enough to raise him up the academic ladder to a chair in Zürich, would hardly have won him the succession to Planck’s chair in Berlin. Indeed, but for his wave mechanics one could have imagined him settling into the role of elder statesman – scholar, distinguished expositor, writing elegant papers on difficult but not highly topical subjects. In fact this is rather what happened, but in the limelight, rather than the shadows where his peccadilloes, private and public, would have passed unnoticed.

The reward of fame, however, is that his irregular private life occupies a considerable fraction of this book. Professor Moore faithfully records Schrödinger’s diligent pursuit of alluring women and adolescent girls, with only a few restrained criticisms of the impropriety. Schrödinger was vain of his erotic skills and one must (putting envy aside) accept his own assessment, for his discarded mistresses seem to have held him in affection long afterwards.Nevertheless, the limitations imposed by the fragmentary evidence of letters and a scientist’s proper regard for truth have the effect that the tales of pursuit, capture and disillusion make a rather tedious narrative.

As a politically naive hedonist he was unfitted for heroic opposition to the Nazis whom he despised; his equivocations earned him accusations of cowardice from friends in England who had worked hard to find him a congenial refuge, and from Jewish colleagues, including Einstein, who expected better of a civilised gentile. With the end of the war, after Schrödinger had settled in De Valera’s Dublin Institute of Advanced Studies, he was able to renew correspondence with Einstein, and an unhappy episode came to an end.

Schrödinger’s reluctance to enter the rich research field made accessible by his wave mechanics greatly reduced his scientific influence during the Thirties when he might have been a leader. Insofar as he was caught up in the philosophical debates on the duality which was now seen to afflict material particles as well as light, his contribution was reactionary. While recognising, with Einstein and de Broglie among others, that the theory was wholly successful as a computational tool, he joined them in resisting the challenge to the classical assumption of determinacy. The standard view, promoted by Bohr and his numerous followers, is that the wave model enables one to calculate the probability of a given initial state of affairs leading to any chosen outcome: but the actual outcome is not uniquely determined, and is even beyond the powers of physics to determine. The most one can say is that in many repetitions of the same experiment each possible outcome will occur with an average frequency that accords with the calculated probability, but which one it will be next time remains a mystery until it actually occurs.

It is not surprising that physicists, accustomed to strict determinacy, as of the planets in their orbits, had trouble assimilating so radical a break, which is compounded if one has a suspicion that the transition from probability (the wave picture) to certainty (observation of a particle, or its effects) is no mere function of inanimate matter, but demands the participation of a conscious observer. Of all those intimately involved in the development of the new physics, the one who must have seemed, to those who knew him, most open to persuasion on the interrelation of mind and matter was surely Schrödinger with his professed attachment to Indian mystical doctrines. Yet where Bohr the Western sceptic led, the devotee of Vedanta shrank from following. Thus he distanced himself both from the philosophically indifferent, but enthusiastic exploiters of the new technique and from the philosophers to whom a new insight brought more anguish than satisfaction in their search for resolution of a fundamental conflict.

After the war, in Dublin, he attempted a grand unification of the forces of Nature, in the footsteps of Einstein and Eddington, but like them he found no way through the maze and abandoned his efforts in disappointment. Amid all this evidence of failure one peculiar success stands out – his little book What is life? Not much of it is original, and he commits one or two basic errors into which a physicist should not have fallen, especially one who understood thermodynamics as he did. Yet it appeared, in 1944, at a time when many young scientists were wondering where to turn when released from military work, and aroused their interest in what looked a promising research line – applying physical methods to determining the structure and behaviour of genes and other constituents of the living organism. Among them were Francis Crick and Maurice Wilkins, and one cannot doubt that Schrödinger’s little, flawed classic was an instigator of one of the most significant scientific advances of the century.