Quantum
Page 30
After a few brief words of welcome from Lorentz as president of the scientific committee and chair of the conference, the task of opening the proceedings fell to William L. Bragg, professor of physics at Manchester University. Now 37, Bragg was only 25 when he was awarded the Nobel Prize for physics in 1915, together with his father, William H. Bragg, for pioneering the use of X-rays to investigate the structure of crystals. He was the obvious choice to report on the latest data concerning the reflection of X-rays by crystals and how these results led to a better understanding of atomic structure. After Bragg’s presentation, Lorentz invited questions and contributions from the floor. The agenda had been organised to allow ample time after each report for a thorough discussion. With Lorentz using his command of English, German and French to help those less fluent, Bragg, Heisenberg, Dirac, Born, de Broglie, and the old Dutch master himself were among those who took part in the discussion before the first session came to an end and everyone adjourned for lunch.
In the afternoon session, the American Arthur Compton reported on the failure of the electromagnetic theory of radiation to explain either the photoelectric effect or the increase in the wavelength of X-rays when they are scattered by electrons. Although awarded a share of the 1927 Nobel Prize only a few weeks earlier, genuine modesty prevented him from referring to this last phenomenon as the Compton effect, as it was universally known. Where James Clerk Maxwell’s great nineteenth-century theory failed, Einstein’s light-quantum, newly rebranded as the ‘photon’, succeeded in uniting theory and experiment. The reports presented by Bragg and Compton were intended to facilitate the discussion of theoretical concepts. At the end of the first day all the leading players had spoken bar one, Einstein.
After a leisurely reception on Tuesday morning at the Free University of Brussels, everyone reconvened in the afternoon to hear Louis de Broglie’s paper on ‘The new dynamics of quanta’. Speaking in French, de Broglie began by outlining his own contribution, the extension of wave-particle duality to matter, and how Schrödinger ingeniously developed it into wave mechanics. Then, treading carefully by conceding that Born’s idea contained a great deal of truth, he offered an alternative to the probabilistic interpretation of Schrödinger’s wave function.
In the ‘pilot wave theory’, as de Broglie later called it, an electron really exists both as a particle and a wave, in contrast to the Copenhagen interpretation where an electron behaves like either a particle or a wave depending on the type of experiment performed. Both particles and waves exist simultaneously, de Broglie argued, with the particle, akin to a surfer, riding a wave. The waves leading or ‘piloting’ the particles from one place to another were physically real rather than Born’s abstract waves of probability. With Bohr and his associates determined to assert the primacy of the Copenhagen interpretation and Schrödinger still doggedly wanting to promote his views on wave mechanics, de Broglie’s pilot wave proposal came under attack. Looking for support from the one man who might sway the neutrals, de Broglie was disappointed when Einstein remained silent.
On Wednesday, 26 October, the proponents of the two rival versions of quantum mechanics addressed the conference. During the morning session, Heisenberg and Born gave a joint report. It was divided into four broad sections: the mathematical formalism; the physical interpretation; the uncertainty principle; and the applications of quantum mechanics.
The presentation, like the writing of the report, was a double act. Born, the senior man, delivered the introduction and sections I and II before handing over to Heisenberg. ‘quantum mechanics,’ they began, ‘is based on the intuition that the essential difference between atomic physics and classical physics is the occurrence of discontinuities.’14 Then came the metaphorical tipping of their hats to colleagues sitting only feet away as they pointed out that quantum mechanics was essentially ‘a direct continuation of the quantum theory founded by Planck, Einstein, and Bohr’.15
After an exposition of matrix mechanics, the Dirac-Jordan transformation theory, and the probability interpretation, they turned to the uncertainty principle and the ‘actual meaning of Planck’s constant h’.16 It was nothing less, they maintained, than the ‘universal measure of the indeterminacy that enters the laws of nature through the dualism of waves and corpuscles’. In effect, if there were no wave-particle duality of matter and radiation there would be no Planck’s constant and no quantum mechanics. In conclusion, they made the provocative statement that ‘we consider quantum mechanics to be a closed theory, whose fundamental physical and mathematical assumptions are no longer susceptible of any modification’.17
Closure implied that no future developments would ever alter any of the fundamental features of the theory. Any such claim to the completeness and finality of quantum mechanics was something that Einstein could not accept. For him quantum mechanics was indeed an impressive achievement but not yet the real thing. Refusing to take the bait, Einstein took no part in the discussion that followed the report. Nor did any one else raise objections, as only Born, Dirac, Lorentz and Bohr spoke.
Paul Ehrenfest, sensing Einstein’s disbelief at the boldness of the Born-Heisenberg assertion that quantum mechanics was a closed theory, scribbled a note and passed it to him: ‘Don’t laugh! There is a special section in purgatory for professors of quantum theory, where they will be obliged to listen to lectures on classical physics ten hours every day.’18 ‘I laugh only at their naiveté’, Einstein replied. ‘Who knows who would have the [last] laugh in a few years?’
After lunch it was Schrödinger who took centre stage as he delivered his report in English on wave mechanics. ‘Under this name at present two theories are being carried on, which are indeed closely related but not identical’, he said.19 There was really only one theory, but it was effectively split in two. One part concerned waves in ordinary, everyday three-dimensional space, while the other required a highly abstract multi-dimensional space. The problem, Schrödinger explained, was that for anything other than a moving electron this was a wave that existed in a space with more than three dimensions. Whereas the single electron of the hydrogen atom could be accommodated in a three-dimensional space, helium with two electrons needed six dimensions. Nevertheless, Schrödinger argued that this multi-dimensional space, known as configuration space, was only a mathematical tool and ultimately whatever was being described, be it many electrons colliding or orbiting the nucleus of an atom, the process took place in space and time. ‘In truth, however, a complete unification of the two conceptions has not yet been achieved’, he admitted, before going on to outline both.20
Although physicists found it easier to use wave mechanics, no leading theorist agreed with Schrödinger’s interpretation of the wave function of a particle as representing the cloud-like distribution of its charge and mass. Undeterred by the widespread acceptance of Born’s alternative probability interpretation, Schrödinger highlighted his own and questioned the accepted notion of the ‘quantum jump’.
From the moment he received the invitation to speak in Brussels, Schrödinger was acutely aware of the possibility of a clash with the ‘matricians’. The discussion began with Bohr asking if a remark about ‘difficulties’ later in Schrödinger’s report implied that a result he had stated earlier was incorrect. Schrödinger dealt with Bohr’s inquiry comfortably, only to find Born challenging the correctness of another calculation. Somewhat annoyed, he said it was ‘perfectly correct and rigorous and that this objection by Mr Born is unfounded’.21
After a couple of others had spoken, it was Heisenberg’s turn: ‘Mr Schrödinger says at the end of his report that the discussion he has given reinforces the hope that when our knowledge will be deeper it will be possible to explain and to understand in three dimensions the results provided by the multi-dimensional theory. I see nothing in Mr Schrödinger’s calculations that would justify this hope.’22 Schrödinger argued that his ‘hope of achieving a three-dimensional conception is not quite utopian’.23 A few minutes later the discussion ended and
brought to a close the first part of the proceedings, the presentation of the commissioned reports.
When it was already too late to change the dates, it was discovered that the Académie des Sciences in Paris had chosen Thursday, 27 October to mark the centenary of the death of the French physicist Augustin Fresnel. It was decided that the Solvay meeting would be suspended for a day and a half to allow those wishing to attend the ceremonial event to do so and return for the climax of the conference, a wide-ranging general discussion spread over the last two sessions. Lorentz, Einstein, Bohr, Born, Pauli, Heisenberg and de Broglie were among the twenty who travelled to Paris to honour a kindred spirit.
Amid the distraction of German, French and English voices all seeking permission from Lorentz to speak next, Paul Ehrenfest suddenly got up and walked over to the blackboard and wrote: ‘The Lord did there confound the languages of all the earth.’ As he returned to his chair there was laughter as his colleagues realised that Ehrenfest was not just referring to the biblical Tower of Babel. The first session of the general discussion began on Friday afternoon, 28 October, with Lorentz making some introductory remarks as he tried to focus minds on the issues of causality, determinism, and probability. Were quantum events caused or not? Or as he put it: ‘Could one not maintain determinism by making it an article of faith? Must one necessarily elevate indeterminism to a principle?’24 Offering no further thoughts of his own, Lorentz invited Bohr to address the meeting. As he spoke about the ‘epistemological problems confronting us in quantum physics’, it was clear to all present that Bohr was attempting to convince Einstein about the correctness of the Copenhagen solutions.25
When the conference proceedings were published in French in December 1928, many mistook Bohr’s contribution, then and later, as one of the official reports. When asked for an edited version of his comments for inclusion, Bohr requested that a much-expanded version of his Como lecture, which had been published the previous April, be reprinted in lieu of his remarks. Bohr being Bohr, his request was granted.26
Einstein listened as Bohr outlined his belief that wave-particle duality was an intrinsic feature of nature that was explicable only within the framework of complementarity, that complementarity underpinned the uncertainty principle which exposed the limits of applicability of classical concepts. However, the ability to communicate unambiguously the results of experiments probing the quantum world, Bohr explained, required the experimental set-up as well as the observations themselves to be expressed in a language ‘suitably refined by the vocabulary of classical physics’.27
In February 1927, as Bohr was edging towards complementarity, Einstein had given a lecture in Berlin on the nature of light. He argued that instead of either a quantum or a wave theory of light, what was needed was ‘a synthesis of both conceptions’.28 It was a view he had first expressed almost twenty years earlier. Where he had long hoped to see some sort of ‘synthesis’, Einstein now heard Bohr imposing segregation through complementarity. It was either waves or particles depending on the choice of experiment.
Scientists had always conducted their experiments on the unspoken assumption that they were passive observers of nature, able to look without disturbing what they were looking at. There was a razor-sharp distinction between object and subject, between the observer and observed. According to the Copenhagen interpretation, this was not true in the atomic realm, as Bohr identified what he called the ‘essence’ of the new physics – the ‘quantum postulate’.29 It was a term he introduced to capture the existence of discontinuity in nature due to indivisibility of the quantum. The quantum postulate, said Bohr, led to no clear separation of the observer and the observed. When investigating atomic phenomena, the interaction between what is measured and the measuring equipment meant, according to Bohr, that ‘an independent reality in the ordinary physical sense can neither be ascribed to the phenomenon nor to the agencies of observation’.30
The reality Bohr envisaged did not exist in the absence of observation. According to the Copenhagen interpretation, a microphysical object has no intrinsic properties. An electron simply does not exist at any place until an observation or measurement is performed to locate it. It does not have a velocity or any other physical attribute until it is measured. In between measurements it is meaningless to ask what is the position or velocity of an electron. Since quantum mechanics says nothing about a physical reality that exists independently of the measuring equipment, only in the act of measurement does the electron become ‘real’. An unobserved electron does not exist.
‘It is wrong to think that the task of physics is to find out how nature is’, Bohr would argue later.31 ‘Physics concerns what we can say about nature.’ Nothing more. He believed that science had but two goals, ‘to extend the range of our experience and to reduce it to order’.32 ‘What we call science,’ Einstein once said, ‘has the sole purpose of determining what is.’33 Physics for him was an attempt to grasp reality, as it is, independent of observation. It is in this sense, he said, that ‘one speaks of “physical reality”’.34 Bohr, armed with the Copenhagen interpretation, was not interested in what ‘is’, but in what we can say to each other about the world. As Heisenberg later stated, unlike objects in the everyday world, ‘atoms or the elementary particles themselves are not as real; they form a world of potentialities or possibilities rather than one of things or facts’.35
For Bohr and Heisenberg, the transition from the ‘possible’ to the ‘actual’ took place during the act of observation. There was no underlying quantum reality that exists independently of the observer. For Einstein, a belief in the existence of an observer-independent reality was fundamental to the pursuit of science. At stake in the debate that was about to begin between Einstein and Bohr was the soul of physics and the nature of reality.
After Bohr’s contribution, three others had already spoken when Einstein indicated to Lorentz that he wanted to break his self-imposed silence. ‘Despite being conscious of the fact that I have not entered deeply enough into the essence of quantum mechanics,’ he said, ‘nevertheless I want to present here some general remarks.’36 quantum mechanics, Bohr had argued, ‘exhausted the possibilities of accounting for observable phenomena’.37 Einstein disagreed. A line had been drawn in the microphysical sands of the quantum realm. Einstein knew that the onus was on him to show that the Copenhagen interpretation was inconsistent and thereby wreck the claims of Bohr and his supporters that quantum mechanics was a closed and complete theory. He resorted to his favourite tactic – the hypothetical thought experiment conducted in the laboratory of the mind.
Figure 13: Einstein’s single-slit thought experiment
Einstein went over to the blackboard and drew a line representing an opaque screen with a small slit in it. Just behind the screen he drew a semicircular curve representing a photographic plate. Using the sketch, Einstein outlined his experiment. When a beam of electrons or photons strikes the screen, some will pass through the slit and hit the photographic plate. Because of the narrowness of the slit, the electrons passing through it will diffract like waves in every possible direction. In keeping with the demands of quantum theory, Einstein explained, the electrons travelling outwards from the slit towards the photographic plate do so as spherical waves. Nonetheless, the electrons actually strike the plate as individual particles. There were, said Einstein, two distinct points of view concerning this thought experiment.
Figure 14: A later rendition by Bohr of Einstein’s single-slit thought experiment
According to the Copenhagen interpretation, before any observation is made, and striking the photographic plate counts as such, there is a non-zero probability of detecting an individual electron at every point on the plate. Even though the wave-like electron is spread over a large region of space, the very moment a particular electron is detected at point A, the probability of finding it at point B or anywhere else on the plate instantly becomes zero. Since the Copenhagen interpretation maintains that quantum mechanics gives a comple
te description of individual electron events in the experiment, the behaviour of each electron is described by a wave function.
Here’s the rub, said Einstein. If prior to the observation the probability of finding the electron was ‘smeared’ over the entire photographic plate, then the probability at B and everywhere else had to be instantaneously affected at the very moment the electron hit the plate at point A. Such an instantaneous ‘collapse of the wave function’ implied the propagation of some sort of faster-than-light cause and effect outlawed by his special theory of relativity. If an event at A is the cause of another at B, then there must be a time lapse between them to allow a signal to travel at light speed from A to B. Einstein believed the violation of this requirement, later called locality, indicated that the Copenhagen interpretation was inconsistent and quantum mechanics was not a complete theory of individual processes. Einstein proposed an alternative explanation.
Each electron that passes through the slit follows one of many possible trajectories until it hits the photographic plate. However, the spherical waves do not correspond to individual electrons, argued Einstein, but to ‘a cloud of electrons’.38 quantum mechanics does not give any information about individual processes, but only about what he called an ‘ensemble’ of processes.39 Though each individual electron of the ensemble follows its own distinct trajectory from slit to plate, the wave function does not represent an individual electron but the electron cloud. Therefore, the square of the wave function, , represents not the probability of finding a particular electron at A, but that of finding any member of the ensemble at that point.40 It was, Einstein said, a ‘purely statistical’ interpretation, by which he meant that the statistical distribution of the large number of electrons striking the plate produced the characteristic diffraction pattern.41