A little while ago I was asked to suggest the year in which I believed the quantum theory was first properly established. There are some obvious candidates. In his famous ‘act of desperation’, the venerable physicist Max Planck first inserted quantum ideas into the formulation of his radiation law in 1900, and introduced a new constant of nature: Planck’s constant h. In 1905, Albert Einstein borrowed Planck’s ideas to explain the phenomenon of photoelectricity. He went further, making the outrageous suggestion that light could be considered to consist of bundles or quanta of energy, whose energy is calculable as h multiplied by the frequency of the light. In 1913, Niels Bohr shoehorned quantum concepts into his theory of the atom, along the way introducing the notion of a quantum jump.
But Einstein’s light-quantum hypothesis is an odd mix. By their nature, quanta of light are particulate (we would later call them photons), yet frequency is a characteristic property of waves, implying the rather absurd notion that light is somehow both wave and particle. In 1923, Louis de Broglie wondered if such quantum wave-particle ‘duality’ might extend to sub-atomic particles like electrons. The floodgates opened. Werner Heisenberg formulated matrix mechanics in June 1925, and Erwin Schrödinger formulated wave mechanics in January 1926, introducing the notion of a quantum wavefunction. Schrödinger later showed that matrix and wave mechanics are very different mathematical expressions of the same underlying theory. Later in 1926, Max Born cut the Gordian knot tying cause to effect, thereby ‘solving’ the riddle posed by quantum jumping by abandoning causality and determinism in favour of a purely probabilistic interpretation of the wavefunction. We could no longer say: when I do this, that will happen. In the quantum domain we could only say: when I do this, that may happen with a certain probability.
In my answer to the opening question, I acknowledged that there are arguments in favour of all these moments in quantum history. But for me, the quantum theory was only properly established as such in 1927, following Heisenberg’s discovery of the uncertainty principle, Bohr’s attempt to interpret what quantum theory means, and the insistence, by Bohr, Heisenberg, and Born, that the theory should be considered complete.
Incompatible Conceptions
This was also a pivotal moment in the history of science. Einstein had grown increasingly uneasy about the implications of the quantum theory whose foundations he had laid in 1905. As far as he was concerned, there were two possible conceptions of the wavefunction. In conception I, the wavefunction does not describe an individual electron (for example), but rather a cloud or ensemble of many electrons. In other words, the quantum theory does not provide a complete description of individual particles and events, only statistical outcomes averaged over many particles and events. Probabilities derived from the wavefunction then represent the probabilities of finding one electron among many. Within the ensemble there is a certain probability that we will find an electron ‘here’, at this particular point in space and time.
In Einstein’s conception II, the wavefunction describes a single electron and the theory is assumed to be complete, but now we have a problem. Like surf on a beach, a wavefunction can become extended or distributed in space – it can be ‘non-local’. And yet, when we make a measurement, it must somehow ‘collapse’ to a single, localised point, to register that the electron is ‘here’. Einstein said: ‘But the interpretation that [the wavefunction] expresses the probability that a particular particle lands at a given point assumes a very peculiar mechanism of action at a distance, which prevents the wave, which is continuously distributed in space, from acting in two places [at once]’.
Einstein thought that such action at a distance violated the postulates of his own special theory of relativity: no action can be transmitted from one place to another at speeds faster than light. And yet the collapse of the wavefunction must be instantaneous, everywhere the wavefunction reaches, all at once. He was unequivocal. Conception II could not stand, so the quantum theory could not be complete.
He presented these arguments at the fifth Solvay conference, held in Brussels in October 1927. Bohr was nonplussed. As far as he was concerned, according to his interpretation the wavefunction does not describe anything at all – it is purely symbolic, a mathematical device that enables the accurate calculation of probabilities, and nothing more. Symbols do not exert action, peculiar or otherwise. Einstein was being too literal in both his conceptions of the wavefunction.
The two joined in debate. This was primarily concerned with the interpretation of quantum theory, but was in truth concerned with the purpose of science itself. Is the ultimate purpose of science merely the accurate description of phenomena, whether we can understand the description or not? Or is its ultimate purpose the ultimate, (and meaningful) truth of things? Bohr and his colleagues were in a hurry, insistent on closure; on finality. Einstein urged patience, confident that quantum theory was not – could not – be the final word.
Their debate took the form of a series of challenges which began outside the conference room. Einstein peppered Bohr with thought experiments devised to reveal confusions or contradictions that be believed were inherent in quantum theory. Their exchanges went on like a game of chess. ‘Einstein all the time with new examples... Bohr from out of philosophical smoke clouds constantly searching for the tools to crush one example after the other. Einstein like a jack-in-the-box: jumping out fresh every morning…’ But Bohr could not be outmanoeuvred.
But Einstein remained stubbornly unmoved. They re-joined debate at the next Solvay conference in 1930, where Einstein described his latest and most ingenious thought experiment. ‘At the next meeting with Einstein at the Solvay Conference in 1930,’ Bohr wrote some years later, ‘our discussions took quite a dramatic turn’.
The Photon Box
Suppose, said Einstein, we build an apparatus consisting of a box which contains a clock connected to a shutter. The shutter covers a small hole in the side of the box. We fill the box with photons and weigh it. At a predetermined and precisely known time, the clock triggers the shutter to open for a very short time interval sufficient to allow a single photon to escape from the box. The shutter closes. We re-weigh the box and, from the mass difference and Einstein’s special theory of relativity (in the form energy = mass times the speed of light squared) we determine the precise energy of the photon that escaped. By this means, we have measured precisely the energy and the time of release of a photon from the box.
It seems there is no point of principle – no inescapable law of physics – that denies us access to unlimited precision in our measurements of both energy and time. But these quantities are governed by a version of Heisenberg’s uncertainty principle. According to this principle, unlimited precision in time is supposed to come with infinite uncertainty in energy, and vice versa. Einstein wanted to know: what’s going on?
Bohr’s immediate reaction was described by his colleague Léon Rosenfeld: ‘It was quite a shock for Bohr… he did not see the solution at once. 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. I shall never forget the vision of the two antagonists leaving the club [of the Fondation Universitaire]: Einstein a tall majestic figure, walking quietly, with a somewhat ironical smile, and Bohr trotting near him, very excited…’.
Bohr experienced a sleepless night, searching for the flaw in Einstein’s argument that he was convinced must exist. ‘This argument amounted to a serious challenge and gave rise to a thorough examination of the whole problem’, Bohr later wrote. By breakfast the following morning he had his answer. He worked out that the clock was the culprit.
On the blackboard Bohr produced a rough, pseudo-realistic sketch of the apparatus that would be required to make the measurements in the way Einstein had described them. In this sketch the whole box is imagined to be suspended by a spring and fitted with a pointer so that its position can be read on a scale affixed to the support. A small weight is added to align the pointer with the zero reading on the scale. The clock mechanism is shown inside the box, connected to the shutter.
Bohr accepted that the mass difference could serve as a suitable proxy for the energy of the photon, but not the assumption that it could be determined unproblematically by weighing. To bring the box back to its initial position after the loss of its photon, Bohr proposed adding a sequence of smaller and smaller weights until the pointer was returned to within a small distance of its original setting. To realign the pointer exactly (with unlimited precision) would require an unknown small residual weight, representing a classical uncertainty. Precise alignment might require a very long time, and some considerable patience.
Let the time spent fiddling with the box be told by a clock fixed to the wall of the laboratory. During the fiddling, the box bounces up and down against the acceleration due to gravity. Now comes Bohr’s coup de grâce. According to Einstein’s general theory of relativity, this motion introduces time dilation effects. As the clock inside the box moves upwards against gravity, the time it keeps slows down. As it moves downwards, the time it keeps speeds up. The very act of weighing a clock effectively changes the way it keeps time. The more the box jiggles up and down (the longer the reweighing procedure) the greater the likely disagreement between the clock inside the box and the clock on the laboratory wall. Bohr derived this difference by assuming a ‘weak-field’ limit of general relativity.
Bohr was then able to show that the product of the uncertainties in energy and time for the photon box apparatus cannot be greater than Planck’s constant h, in accordance with the uncertainty principle. This was hailed as a triumph for Bohr. Bohr had used Einstein’s own general theory of relativity against him.
But Bohr was never comfortable with his rebuttal. The ‘time’ in Bohr’s analysis refers to an uncertainty in the reweighing time, whereas Einstein’s ‘time’ refers to the moment of release of the photon. Perhaps most objectionable was the sleight-of-hand that Bohr had employed: to demonstrate the validity of the energy-time uncertainty relation Bohr had assumed the validity of its position-momentum counterpart. Although most physicists accepted Bohr’s answer as brilliant and definitive, he fretted over it for the rest of his life. A rough sketch of the apparatus was on his blackboard the day he died in 1962. Einstein conceded that Bohr’s response was ‘free of contradictions’, but he accused it of ‘a certain unreasonableness’. He remained unconvinced.
This is the version of Einstein’s photon box experiment that has entered into quantum folklore. But it is not the whole story.
Foreshadowing Entanglement
Einstein soon redirected the argument, if indeed he had ever urged it in the form Bohr would later recount in 1949. His colleague Paul Ehrenfest explained Einstein’s new challenge to him in 1931. It aimed at something much deeper than the uncertainty principle. ‘Einstein told me that he had not doubted the uncertainty relation for a long time and that therefore the “movable light-flash box”... was ABSOLUTELY not designed against [it]’. In his response, Bohr had not addressed Einstein’s main point.
To work Einstein’s new thought experiment, Ehrenfest wrote Bohr, set both the internal clock and the laboratory clock to zero and arrange for the shutter to release the photon at a specific time, say 1000 hours. Weigh the box with the photon inside for 500 hours, then screw it to a rigid frame. Fix a mirror half a light year away from the box (remember, this is a thought experiment) in such a position as to reflect the released photon back to the laboratory. At 1500 hours, when the photon is well on its way towards the mirror, choose whether you want to measure either the time at which the photon left the box or its frequency.
If you opt for time, open the box, which is still rigidly fixed, and compare the readings of the internal and external clocks. This will enable you to take account of the fluctuations in the internal clock’s rate during the 500 hours of weighing and so establish the exact time of release. Alternatively, free the box from the frame and weigh it again for another 500 hours. You will now have precise measures of the mass of the box both before and after the departure of the photon, from which you can deduce its energy from the mass difference. The frequency is then obtained by dividing the energy by Planck’s constant h.
Suppose you choose to measure the precise time of release by comparing the clocks. To conform to the demands of the uncertainty principle, the energy and hence frequency of the distant photon must therefore be uncertain. Let’s further suppose that the frequency lies in the visible region. The uncertainty in frequency means we can’t pin down its colour.
But what if you choose instead to re-weigh the box and measure the precise frequency of the photon? We find that the photon is blue. The bite of the argument is that the photon must somehow adjust its frequency, precisely blue or fuzzily uncertain and washed out, according to the experimenter’s choice of measurement while it is in flight to and from the mirror. Quantum theory seems to demand that a photon too distant from the apparatus from which it came to be reached by any kind of signal travelling at the speed of light must nonetheless respond instantly to the experimenter’s manipulations of it. This is shocking behaviour, without precedent in the entire history of physics, which Einstein thought needed only to be exposed to make all good physicists reject the theory that allowed it.
Einstein’s new argument did not concern contradictions or detailed measurements or the nature of light quanta, but rather the crazy consequence that the separated photon had to take on one or another property depending on whether the experimenter thought to compare the clocks or re-weigh the box. And the choice could be delayed for up to a year, the time it takes for the released photon to make its round-trip journey. It would seem that the photon and its box remain mysteriously connected, their fates somehow tied together, no matter how far apart they are. Some four years later Schrödinger would coin a term for this mysterious connection. He called it entanglement. Einstein could not make the concession. Entanglement would rub out separate, individual objects, essential traits of an acceptable world picture.
In his account of their debate in 1949, Bohr acknowledged Einstein’s 1931 redirection of the photon-box argument and conceded that it ‘might seem to enhance the paradoxes beyond the possibilities of logical solution’. That would have turned up the dramatic tension a few more degrees! To relax it, Bohr issued a decree: a mathematically consistent formalism can be convicted of inadequacy only by showing that its consequences disagree with experience or do not exhaust the possibilities of observation. And a verdict: ‘Einstein’s argumentation could be directed to neither of these ends’.
But Einstein’s 1931 adaptation of the photon box experiment contained the seeds of another, even more powerful challenge to the authority of quantum theory and Bohr’s interpretation, which he formulated in 1935 with his Princeton colleagues Boris Podolsky and Nathan Rosen. Bohr would be quite unprepared for Einstein’s next move.
Jim Baggott is an award-winning science writer and co-author with John Heilbron of Quantum Drama: From the Bohr-Einstein Debate to the Riddle of Entanglement, published by Oxford University Press.