Einstein on the Run Read online

  WAVE/PARTICLE DUALITY AND ATOMIC STRUCTURE

  Two years later, after further reflection and publication on the subject, at the Salzburg meeting of German scientists in 1909, Einstein – instead of speaking on relativity as everyone had expected – gave his keynote address on ‘The nature and con-stitution of radiation’. It included this astonishingly prescient statement:

  It cannot be denied that there exists a large group of radiation-related facts which show that light possesses certain fundamental properties which can much more easily be understood from the standpoint of Newtonian emission theory [i.e. light corpuscles/quanta] than from the standpoint of the wave theory. . . .

  It is my opinion that the next phase in the development of theoretical physics will bring us a theory of light that can be interpreted as a kind of fusion of the wave and the [particle] theory. . . . [The] wave structure and [the] quantum structure . . . are not to be considered incompatible.

  The Salzburg speech was ‘one of the landmarks in the development of theoretical physics’, said Wolfgang Pauli, another pioneer of quantum mechanics, on Einstein’s seventieth birthday in 1949. It was the first announcement of the disturbing idea of wave/particle duality.

  Soon after this, Einstein shifted his attention to general relativity for the next five years, though of course he continued to think about quantum theory. He had no role at all in the next important quantum development, which came from Bohr, who was working in Rutherford’s University of Manchester laboratory on the structure of the atom.

  In 1911, Rutherford had discovered the atomic nucleus and conceived the solar-system model of the atom, in which an electron was thought to orbit the nucleus like a planet around the Sun, held in place not by gravity but by an electrostatic force acting between the positively charged nucleus and the negatively charged electron. This was a familiar enough concept from nineteenth-century physics. But, appealing though Rutherford’s picture was, it did not explain atomic spectra, which had been documented over many decades. The colours of fireworks illustrate the visible emission spectra of different chemical elements and compounds, as does a sodium or neon street light. Yet, Rutherford’s model did not account for why atoms of different elements emit and absorb electromagnetic radiation at specific frequencies/wavelengths, creating sharp bright and dark lines in the electromagnetic spectrum as characteristic of a given element as a fingerprint is of a human individual.

  According to the Rutherford–Bohr proposal of 1913, the existence of spectra implied that the electrons in an atom could occupy only particular orbits, not continuously varying orbits. Then emission of light – a bright spectral line – would occur when an electron fell from one fixed orbit to another lower-energy orbit nearer the nucleus, thus decreasing its energy and emitting the balance of its initial energy as radiation of a characteristic frequency. Absorption of light – a dark spectral line – would entail the reverse of this process, with an electron jumping to a higher-energy orbit further away from the nucleus.

  In order to explain these fixed orbits, Bohr, like Planck before him in 1900, was obliged to add a crucial postulate of his own: that the electron orbits of Rutherford’s atom were quantised. The angular momentum (and hence the velocity and energy) of an orbiting electron could take only certain values, Bohr speculated. These values were whole-number multiples of a constant based on Planck’s constant, which appears in Planck’s equation connecting energy and frequency. On this basis Bohr successfully constructed a model of a one-electron hydrogen atom with orbital energy levels that accounted for the experimentally observable spectrum of hydrogen. In 1916, Einstein called this Bohr model a ‘revelation’.

  However, the Rutherford–Bohr model had two major weaknesses. First, it offered no convincing explanation for the stability of atoms. According to Maxwell’s equations, electrons, being accelerated charged objects, must radiate energy and quickly spiral into the nucleus. Bohr’s quantum postulate forbade such an atomic collapse by simple theoretical fiat. Second, although the electron orbits themselves were quantised, the radiation emitted and absorbed by the electrons was observed in the form of (continuous) waves. Even if one accepted this discrete/con-tinuous contradiction, how could an electron ‘know’ when it left one orbit at what frequency it should immediately begin radiating before it had ‘arrived’ at its next orbit? How did it ‘know’ to which orbit it was going? What really occurred during the electron’s transition? At this early stage of the quantum theory Bohr had no confidence in quantised light (he was one of the last physicists to take Einstein’s photons seriously in the 1920s) – only in quantised electron orbits. In the end, Bohr’s model of the atom blended nineteenth-century and quantum physics imaginatively, even brilliantly (as a Nobel prize for Bohr soon confirmed), but without fully satisfying anyone.

  Einstein saw this, and saw he could connect Planck’s radiation law of 1900 with Bohr’s atomic energy levels of 1913 using his light quanta. In 1916–17, having completed general relativity, he published three papers using the quantum concept. His new idea was that atoms, in addition to emitting light spontaneously, could be forced or stimulated by light to emit light, in the process moving from a high-energy state to a lower-energy state. The effect would be that one light quantum would stimulate an atom and two quanta would emerge, resulting in light amplification. The laser – the word is an acronym standing for ‘light amplification by stimulated emission of radiation’ – eventually grew from this idea. ‘Einstein was the first to recognise clearly, from basic thermodynamics, that if photons can be absorbed by atoms and lift them to higher energy states, then it is necessary that light can also force an atom to give up its energy and drop to a lower level. One photon hits the atom, and two come out,’ wrote Charles Townes, one of the inventors of the laser in the 1950s. Einstein himself told his old friend Besso in 1916: ‘With this, the light quanta are as good as certain.’ But in his published paper he noted that his theory of stimulated emission had a failing: that it ‘leaves the time and direction of the elementary process to “chance”’. Here was a hint of Einstein’s coming dislike of quantum mechanics because of its random, probability-based foundation.

  However, before we finally reach that great debate, there was still another prescient proposal from Einstein arising from light quanta. In 1924, he received a paper from an unknown physicist in India, Satyendra Nath Bose, entitled ‘Planck’s Law and the Light Quantum Hypothesis’. It derived Planck’s radiation law not from classical electrodynamics but by regarding radiation as a gas composed of light quanta and then applying a statistical approach based on the fact that large numbers of photons – unlike, say, electrons – are permitted by nature to occupy exactly the same quantum state. Bose asked Einstein for help in getting his article published. Einstein immediately read it, translated it into German and recommended it to a journal – and then himself wrote two papers inspired by it, in which he applied Bose’s approach to atoms. The results were called Bose–Einstein statistics and gave rise to a concept of a class of elementary particles now known as bosons. In 1925, Einstein predicted that bosons, given the right conditions at very low temperature, could condense into a new state of matter. In 1995, Bose–Einstein condensates were at last produced in the laboratory, fully seventy years after Einstein’s prediction.

  With Bose–Einstein statistics we come to the end of the ‘old’ quantum theory and the beginning of quantum mechanics. It was also the end of Einstein’s central role in quantum theory; after 1926 he became a critic of, rather than a contributor to, quantum physics.

  DEBATING QUANTUM MECHANICS

  His criticisms turned out to be fundamental and fascinating. ‘Were it not for Einstein’s challenge, the development of quantum physics would have been much slower,’ admitted Bohr in 1962. Bohr and Einstein were the most persistent protagonists in this debate for some ten years, but at various times Einstein challenged just about every pioneering contributor to quantum mechanics. For example, in 1924 he told Born humor
ously: ‘I find the idea quite intolerable that an electron exposed to radiation should choose of its own free will, not only its moment to jump off, but also its direction. In that case, I would rather be a cobbler, or even an employee in a gaming-house, than a physicist.’ And in 1948, he remarked bluntly to Born: ‘if one abandons the assumption that what exists in different parts of space has its own, independent, real existence, then I simply cannot see what it is that physics is meant to describe’.

  Modern quantum theory abandons exactly this assumption. In answer to Einstein’s well-known poser, ‘Does the moon really exist only when you look at it?’, the physicist David Peat answered: ‘Einstein’s moon really exists. It is linked to us through non-local correlations but does not depend upon us for its actual being in the world. On the other hand, what we call the moon’s reality, or the electron’s existence, depends to some extent upon the contexts we create in thought, theories, language and experiments.’

  Let us now attempt to summarise in just one paragraph the development of quantum mechanics, a very complex and mathematically sophisticated subject, before returning to Einstein’s critique. In 1924, de Broglie proposed that all matter has a wave associated with it, and this was quickly confirmed for electrons by electron diffraction experiments. In 1926, Schrödinger, in his classic wave equation – aided importantly by Born – replaced the picture of an electron as a particle having a precise position and momentum as it orbits a nucleus with a wave function that predicted stationary waves of electron probability around the nucleus. Schrödinger’s equation enabled physicists to calculate not the location of an electron at any given moment but rather its probability of being at any particular point in space. Hence the atom was no longer at risk of collapse, as in Bohr’s original model, because no electric charge was being accelerated; the electron became a probability wave in the Schrödinger/Born model. Then in 1927, Heisenberg, in his far-reaching uncertainty principle, proved that the position and momentum of any elementary particle such as an electron could never be measured simultaneously with unlimited accuracy. The more an experimenter tries to pin down the position in space, the greater will be the uncertainty in the momentum, and vice versa, because the very act of observing the particle (say, by firing a photon at it) will inevitably disturb its position and momentum. The Heisenberg uncertainty principle states that the uncertainty in the position multiplied by the uncertainty in the momentum will always exceed a constant based on Planck’s constant. Other kinds of uncertainty principle may also be derived, such as one which relates the uncertainty in the energy of a particle to the time interval in which one measures its energy.

  At the Solvay Congress in 1927 and again in 1930, and after, Einstein tried to counter some of these ideas and their profound implications for physical reality with his own ‘thought’ experiments. Here is one of the best known.

  Imagine, said Einstein, a box containing radiation. There is a hole in its side and a shutter to open and close the hole. The box is weighed. Then the shutter is opened for a short time T and one photon is allowed to escape. The box is weighed again. The loss in mass, which must equal the mass of the escaped photon, can be converted to a loss in energy (using E = mc2). And this mass or energy can in principle be determined as accurately as one wishes, hence the uncertainty in the energy of the photon may be zero. The uncertainty in the time for the escape of the photon is finite, just T. This means that the two uncertainties multiplied together may be zero – in contradiction of Heisenberg’s uncertainty principle.

  ‘It was quite a shock for Bohr,’ remembered one of the other physicists at the 1930 Solvay Congress, Léon Rosenfeld. ‘During the whole evening he was extremely unhappy, going from one to the other, and trying to persuade them that it couldn’t be true, that it would be the end of physics if Einstein were right; but he couldn’t produce any refutation.’ Einstein left the meeting, ‘a tall majestic figure, walking quietly, with a somewhat ironical smile, and Bohr trotting near him, very excited’.

  Solvay Congress in Brussels, Belgium, 1927, at which Einstein keenly questioned recent developments in quantum theory by Niels Bohr, Max Born, Louis de Broglie, Werner Heisenberg and Erwin Schrödinger. Einstein sits in the front row (fifth from right), along with Max Planck (second from left), Marie Curie (third from left) and Hendrik Lorentz (fourth from left). In the second row appear Peter Debye (first from left), Paul Dirac (fifth from right), Arthur Compton (fourth from right), de Broglie (third from right), Born (second from right) and Bohr (far right), and in the back row are Paul Ehrenfest (third from left), Schrödinger (sixth from right), Wolfgang Pauli (fourth from right) and Heisenberg (third from right). Surprisingly, this is the only photograph of Einstein with his great friend Born.

  But by the following morning, Bohr had a riposte ready. And it depended on general relativity! He had carefully considered, as Einstein had not, how the measurements of the loss in mass of the box and of the time interval for the shutter’s opening and closing might actually be made by an observer. Bohr imagined hanging the box from a delicate spring balance and attaching the shutter to a clock inside the box. Then he realised that general relativity dictated that the clock must change its rate as it moved very slightly upwards with the escape of the photon – since the clock was being decelerated in a gravitational field. This must introduce an uncertainty into the time interval T. As a consequence, Bohr’s calculations showed, the time-energy uncertainty principle would be obeyed after all.

  On this occasion Einstein was vanquished, and it appears that after 1930 he accepted that quantum mechanics was internally consistent. In 1931, he nominated Schrödinger and Heisenberg to the Swedish Academy for a joint Nobel prize as the founders of ‘wave, or quantum, mechanics’ (note the uncertainty in the name). ‘In my opinion, this theory contains without doubt a piece of the ultimate truth,’ Einstein explained. In 1932 Heisenberg received the prize, and in 1933 so did Schrödinger, along with Dirac.

  Yet we know that Einstein was far from satisfied with quantum mechanics, as he made abundantly clear for the rest of his life. This was his ultimate summary verdict:

  The conviction prevails that the experimentally assured duality of nature (corpuscular and wave structure) can be realised only by . . . a weakening of the concept of reality. I think that such a far-reaching theoretical renunciation is not for the present justified by our actual knowledge, and that one should not desist from pursuing to the end the path of the relativistic field theory.

  Einstein’s comment was written in 1952. During the previous three and a half decades, since the publication of general relativity in 1916, Einstein had been relentlessly pursuing, in an increasingly solitary search, his own path towards such a field theory based on relativity, hopefully more fundamental than the new quantum mechanics.

  UNIFIED FIELD THEORY

  In 1925, Einstein explicitly employed a new term, ‘unified field theory’, in the title of one of his publications. ‘Ten more papers appeared in which the term is used in the title, but Einstein had dealt with the topic already in half a dozen publications before 1925,’ according to The Cambridge Companion to Einstein. ‘In total he wrote more than 40 technical papers on the subject. This work represents roughly a fourth of his overall oeuvre of original research articles, and about half of his scientific production published after 1920.’

  One of these papers, ‘On the Unified Field Theory’, produced a sensational flurry of world attention in 1929. ‘Einstein on verge of great discovery; resents intrusion’ ran a headline in the New York Times on 4 November 1928. Ten days later, the newspaper declared: ‘Einstein reticent on new work; will not “count unlaid eggs”.’ Soon, to escape all the attention and concentrate on his work, Einstein left Berlin and went into hiding; he stayed alone in a friend’s house throughout the winter, cooking for himself, ‘like the hermits of old’ as he wrote to Besso. On 10 January 1929, when Planck at last delivered Einstein’s new paper to the Prussian Academy in Berlin on Einstein’s behalf, there was
feverish interest from the world’s press. Einstein was said to have solved the ‘riddle of the universe’. Telegrams came from all over the world requesting information and 100 journalists were held at bay by the academy until the publication of the six-page paper on 30 January. A delay of three weeks between delivery and publication was routine for a scientific paper, but given the unheard-of public speculation about its content the academy decided to up the usual print run to 1,000 copies. This instantly sold out and three further printings of 1,000 copies each were hastily arranged – a record for the academy’s proceedings.

  On 3 and 4 February, the New York Times and The Times in London carried a full-page article by Einstein, ‘The New Field Theory’, which discussed mainly relativity but then attempted to explain his latest idea of ‘distant parallelism’ (which he would soon quietly abandon). The New York Herald Tribune went one better and printed a translation of Einstein’s entire scientific paper, including all the mathematics. But the most extraordinary response, surely, came when the six pages of Einstein’s paper were pasted up side by side in the windows of Selfridges department store in London for the benefit of shoppers and passers-by. ‘Large crowds gather around to read it!’ an amazed and amused Eddington wrote to Einstein in a letter on 11 February.

  Maybe the crowds had some dim inkling of Einstein’s ambition, even if very few among them could comprehend his mathe-matics. As he apparently once told a former student (the astronomer Fritz Zwicky), the aim of his search was ‘to obtain a formula that will account in one breath for Newton’s falling apple, the transmission of light and radio waves, the stars, and the composition of matter’. The key concept, he thought, had to be the field, which had proved so fruitful in both Maxwell’s equations, which had unified electricity, magnetism and radiation, and in general relativity.