The Einstein-Podolsky-Rosen Paper
Guess what. Einstein didn’t like it.
In an earlier essay, I described how in 1927 Albert Einstein and Danish physicist Niels Bohr engaged in a debate that was notionally about the interpretation of quantum theory, but was in fact concerned with the very purpose of science itself. Is it the purpose of science merely to provide an accurate description of phenomena, whether we can understand the description or not? Or is it the ultimate (and meaningful) truth of things? Bohr and his colleagues were in a hurry, insistent on closing the new theory of quantum mechanics; 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. Einstein peppered Bohr with thought experiments devised to reveal confusions or contradictions that he believed were inherent in quantum theory. Their exchanges went on like a game of chess.
In 1930, Einstein’s challenge involved a box filled with photons. By carefully timing the release of a single photon from the box, and by weighing the box before and after this release, Einstein argued that it would be possible to ‘beat’ the uncertainty principle that had been discovered in 1927 by Werner Heisenberg, and which formed a central plank in the structure of quantum theory.
According to this principle, precision in the measurement of one of two so-called ‘conjugate’ properties is traded for imprecision (uncertainty) in the other. Examples of such conjugate properties include position and momentum (speed and direction) and energy and time. In the ‘photon box’ experiment, there would appear to be no point of principle – no inescapable law of physics – that denies us access to unlimited precision in our measurements of the time of release of the photon and, from weighing the box before and after release (and E = mc2), the energy of the photon. The uncertainty principle denies that this is possible.
Bohr sought to dismantle the challenge by using Einstein’s own general theory of relativity against him. But Bohr’s rebuttal contained much sleight-of-hand and some circular reasoning, and he was never comfortable with it. A rough sketch of the photon box apparatus was drawn on his blackboard the day he died in 1962.
In truth, Einstein’s challenge was not directed at the uncertainty principle, which he had not doubted for some time. His main argument was better revealed in a simple extension of the photon box thought experiment, in which the released photon travels half a light-year to a mirror, which reflects it back to the laboratory. If we choose to measure the exact time of release (in a way which works around the effects of general relativity), then the uncertainty principle demands that the energy of the photon must be uncertain. If this energy places the photon in the visible region of the spectrum, this means we can’t precisely determine its colour. But if we choose instead to weigh the box before and after release, we can determine the precise energy of the photon. Suppose 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. Bohr conceded that this extension of the photon-box experiment ‘might seem to enhance the paradoxes beyond the possibilities of logical solution’.
A Bolt from the Blue
In 1933, Einstein fled Nazi Germany to the new Institute for Advanced Study in Princeton. From there, two years later, he issued a new challenge derived in part from the extension of his photon-box experiment. This time Einstein was not alone. The challenge came from him and two Russian-Jewish associates of the Princeton Institute, Boris Podolsky and Nathan Rosen.
The Einstein-Podolsky-Rosen (EPR) paper was a tidal wave in the field of quantum interpretation. It shook Bohr’s citadel in Copenhagen. His associate Léon Rosenfeld declared: ‘This onslaught came down upon us as a bolt from the blue. Its effect on Bohr was remarkable’. It looked superficially like several earlier challenges by Einstein, but it had a clever twist to it that gave him pause.
Suppose two quantum particles, 1 and 2, interact through a physical mechanism that correlates their properties. (Later in 1935, Erwin Schrödinger would coin the term ‘entangled’ to describe such correlation.) They then separate. We study particle 1 in the laboratory, and set particle 2 free to travel an enormous distance, out of our reach. Nothing prevents us from measuring either the position or momentum of particle 1 with as exquisite a precision as our apparatus will allow. But we know, because EPR and simple algebra confirm it, that the difference in the positions of the two particles and the sum of their momenta are quantities that are not constrained by the uncertainty principle.
So, if we measure the position of particle 1 precisely, we can deduce the precise position of particle 2. Alternatively, if instead we measure the precise momentum of particle 1, we can deduce the precise momentum of particle 2. But the position-momentum uncertainty principle denies that particle 2 can simultaneously possess precise position and momentum. Apparently, without observing particle 2, we can infer more about it than the uncertainty principle appears to allow.
If quantum theory applies to individual particles and events, as Bohr and his colleagues claimed, how is particle 2 supposed to ‘know’ what we chose to measure in the laboratory? By signalling across the vast distance between the particles at a speed faster than light? Or by an action at a distance abhorred by all true physicists?
Alternatively, we could presume that the future position and momentum of particle 2 are pre-ordained by the nature of their interaction and already fixed before measurement. Our measurements on particle 1 then simply reveal their values. How might that have happened? Einstein and his collaborators, content to observe that the silence of quantum theory on this question proved its incompleteness, volunteered no alternative.
But, of course, inferring is not the same as measuring. EPR tried to overcome this objection with the following criterion:
If, without in any way disturbing a system, we can predict with certainty (i.e. with a probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.
EPR thus declared that a quantity whose value can be predicted with absolute certainty must exist whether measured or not. Like Galileo thinking about falling weights on a moving ship, we can know the answer without looking.
Rearguard Action
The challenge from EPR energized Bohr’s defenders. Wolfgang Pauli alerted Heisenberg to Einstein’s new attack, mounted with Podolsky and Rosen, ‘in other respects not very good company’. What about their argument? ‘I must grant that if an undergraduate had made such objections, I would have regarded him as very intelligent and promising’. However, Pauli went on, the argument rests on an elementary error, a misunderstanding of the way two systems combine in quantum theory. Einstein believes that quantum theory is correct but incomplete, a juvenile belief, an oxymoron: any new ‘hidden variables’ supposed necessary for completion would either change the theory and bring it into conflict with proven results, or not change it and so serve no practical purpose.
But (Pauli continued) Einstein is certainly right in suspecting something messy about the notion of measurement, about the composition and separation of the elements of an experiment. This is just the problem of where the observer decides to place the dividing line between the object under study from the instrument of observation: between the quantum and classical domains. Heisenberg was prompted further to elaborate his ideas concerning what became known as Heisenberg’s cut.
Heisenberg withheld his draft paper from publication because Bohr had already prepared an answer to EPR. Bohr concluded that inferring is not measuring. He argued the difference in the particle positions and the sum of their momenta cannot be measured simultaneously using the same apparatus. Bohr’s arguments carried the day, though revisiting his published response today will likely leave the reader with a sense of dissatisfaction ranging from niggling to profound.
Perhaps the most instructive responses came from Carl Wilhelm Oseen, professor of physics in Uppsala, who had followed Bohr’s work closely from its beginnings, and Philipp Franck. At last, I understand, Oseen wrote, what you have been saying all along. Before a measurement an atom’s state with respect to the quantity measured is not defined. That was only half of it. Frank understood Bohr to mean that ‘physical reality’ should not be ascribed to the quantities we associate with quantum entities. Quantum theory as interpreted by Bohr and his colleague characterized measuring procedures and results, not the things measured. Bohr acknowledged that that was what he had in mind.
Buried Alive
Between the publications of the EPR paper in mid-May 1935 and Bohr’s response in mid-October, its foremost critic was Einstein himself. He complained to Schrödinger that ‘because of language considerations’ Podolsky had written most of the paper after thorough discussion among the authors, but the main point had been ‘buried alive, so to speak, by erudition’. No earlier drafts of the paper survive in the Einstein collection and no correspondence suggests that he had seen it before Podolsky submitted it for publication just before leaving Princeton to take up a position, procured with Einstein’s help, at the University of Cincinnati. Podolsky’s incivility can be ascribed to the same impulse to self-promotion that had prompted him to leak the content of the paper to the New York Times before its formal publication in a scientific journal.
The editors of the newspaper were eager to have the scoop. A readership existed responsive to such headlines as ‘Einstein Attacks Quantum Theory ... Find it is Not “Complete” Even Though “Correct”’. Einstein was incensed: he had not been consulted and he deplored the unprofessional practice of announcing new scientific results in newspapers. The Times subsequently printed a statement by him to that effect. According to Israeli physicist Asher Peres, Einstein was so upset by Podolsky’s indiscretion and impropriety that he never spoke with him again.
Podolsky was certainly capable of indiscreet self-promotion. He had returned from Caltech to Russia in 1930 with a doctorate in theoretical physics to work at the Ukrainian Institute of Physics and Technology, where he collaborated with important theorists, including the visiting Dirac. He came back to the US in 1933 to take up a fellowship at the Institute for Advanced Study. Einstein had then rated him highly. Podolsky remained attached to the Soviet cause, however if, as SVR (the post-Soviet incarnation of the KGB) documents suggest, he was the atomic spy codenamed QUANTUM, who supplied information on uranium isotope separation during 1943 in the hope of obtaining a position in the Soviet Union.
The substantive part of Podolsky’s sin, the main point that had been buried in the EPR paper, concerned the ‘separability’ of the two particles. Quantum theory requires that the state arising from their interaction be described by a single, two-particle ‘wavefunction’. EPR’s analysis assumes that, when well separated, each particle can be described by its own wavefunction. ‘My way of thinking is this,’ he wrote Schrödinger, ‘you cannot get the better of the Talmudist without an additional principle: [a] “Separation principle” [Trennungsprinzip]’. This is an assumption later labelled ‘Einstein separability’. Particles so separated can be considered as ‘locally real’.
The main point was that quantum theory appeared to strip interacting particles of their separate identities so that, even after parting company, they remained mysteriously connected, just like the photon and its box. This had nothing to do with ad hoc criteria of physical reality and everything to do with the conflict between separability and completeness. Either the two particles are separable and locally real, and quantum theory is incomplete, or quantum theory is complete and the particles are mysteriously bound together, even over vast distances and times. Both cannot be true.
Einstein: Philosopher-Scientist
In 1949, a volume celebrating Einstein’s 70th birthday appeared in The library of living philosophers edited by Paul Arthur Schilpp, a philosopher at Northwestern University in Illinois. Each volume of Schilpp’s library featured essays teasing out what the life’s work of a towering philosopher ‘really meant’ while the subject was alive enough to answer.
Einstein’s volume began with ‘Autobiographical Notes’ (‘Here I sit in order to write, at the age of 67, something like my own obituary’) in which he returned to the main point of EPR as elaborated in correspondence with Schrödinger, without the unnecessary and philosophically vulnerable criterion of physical reality. ‘If one asks: does a [wave]-function of the quantum theory represent a real factual situation in the same sense in which this is the case of a material system of points or of an electromagnetic field, one hesitates to reply with a simple “yes” or “no”: why?’ Physicist A might argue that the wavefunction offers an incomplete description of the real situation of the system since it expresses only what we know based on former measurements, to which physicist B might reply that the individual system has no definite value prior to measurement. The value arises only in co-operation with the unique probability which is given to it by the act of measurement itself: the wavefunction is an exhaustive description of the real situation of the system. How to decide?
In the case of two spatially separated but correlated (or, as we now say, entangled) systems, S1 and S2, in which ‘the real factual situation of the system S2 is independent of what is done with the system S1’ (the systems are ‘Einstein separable’), then there is a real and very substantial contradiction. Quantum theory predicts that the ‘character of [the result for S2] then depends on what kind of measurement I undertake on S1’. This is the main point. ‘One can escape from this conclusion only by either assuming that the measurement of S1 (telepathically) changes the real situation of S2 or by denying independent real situations as such to things which are spatially separated from each other. Both alternatives appear to me entirely unacceptable’.
That was to state the situation with unexceptionable clarity. EPR does not require a definition or preconceived notion of physical reality. Nor, for those few paying attention, did EPR have to do merely with inferring the properties of a distant particle from measurements on its nearer partner. Its argument rested on the practical confrontation of the ‘non-locality’ implied by entanglement with the local realism demanded by the assumption of Einstein separability. If S1 and S2 are assumed to be separable and locally real then they must communicate telepathically via some ‘peculiar mechanism of action at a distance’. Let the experiment be done, measure the properties of both entangled particles and see what you get. If S1 and S2 cannot be considered as separable and locally real – if entanglement over vast distances and times is a real phenomenon – a gaping explanatory hole opens.
Physicists had no way to describe how the initial brief encounter of the particles establishes their perpetual subsequent entanglement. The only reasonable conclusion, Einstein insisted, was EPR’s: ‘B will have to give up his position that the [wave]-function constitutes a complete description of a real factual situation’. Indeed, B should concede the game and look elsewhere. ‘I believe … that this [quantum] theory offers no useful point of departure for future development’. It will take time to find an alternative. Do not rush. Physicists in a hurry risk building on shaky foundations.
Einstein built on sound foundations but of a bygone era. In his interpretative essay in the Schilpp volume, Yale’s philosopher-physicist Henry Margenau wrote of Einstein’s concept of reality: ‘If we apply [quantum theory] correctly we must not ask what happens to a system during measurement; but content ourselves with the information given to us in that measurement’. Do not cling to cherished classical principles, do not listen to Einstein’s siren song, take the uncomfortable road to the future. ‘To travel it, one must leave much of classical physics behind; one must re-define the notion of physical state and accept the more rhapsodic form of reality which it entails’.
The masterpiece among the essays presented to Einstein in 1949 was Bohr’s account of their now famous debate. It took him two years to write, and then he revised it thoroughly. During this last stage he visited the Institute for Advanced Study at the invitation of J. Robert Oppenheimer, its new director, who helped with the rewriting. So also did a young member of the Institute, Abraham (Bram) Pais, a Dutch Jewish physicist who had studied with Hendrik Kramers and Rosenfeld before the war, survived it hidden in the apartments of friends, and begun his career after it by serving as Bohr’s assistant. (Later Pais would write influential biographies of both Einstein and Bohr.)
To the uncharitable eye, Bohr’s essay in the Schilpp volume reads as an extended summary, not of Einstein’s contributions to quantum physics but of Bohr’s achievements as its steward. ‘Realizing, however, the many obstacles for mutual understanding as regards a matter where approach and background must influence everyone’s attitude, I have welcomed this opportunity of a broader exposition of the development by which, to my mind, a veritable crisis in physical science has been overcome’. This crisis, presumably of Einstein’s making, was averted by recognition that ‘in quantum mechanics, we are not dealing with an arbitrary renunciation of a more detailed analysis of atomic phenomena, but with a recognition that such an analysis is in principle excluded’.
The Basic Positivistic Attitude
Einstein’s ‘Reply to Criticisms’, drafted in response to the contributions of his admirers and detractors, concedes nothing. His critics had lost their compass, they had abandoned the sound old concept of physics as ‘the complete description of any (individual) real situation (as it supposedly exists irrespective of any act of observation or substantiation)’. Sophisticates who ridiculed his naiveté were still stuck in the mire of Ernst Mach’s unyielding empiricism from which Einstein had escaped as he had mastered his craft:
Whenever the positivistically inclined modern physicist hears such a formulation his reaction is a pitying smile. He says to himself: ‘there we have the naked formulation of a metaphysical prejudice, empty of content, a prejudice, moreover, the conquest of which constitutes the major epistemological achievement of physicists within the last quarter-century.’ … What I dislike in this kind of argumentation is the basic positivistic attitude, which from my point of view is untenable, and which seems to me to come to the same thing as [the eighteenth-century philosopher George] Berkeley’s principle, esse est percipi [to be is to be perceived].
There are shades of sin, however, and Einstein placed his admirable friend Bohr’s among the venial. ‘Of the “orthodox” quantum theoreticians whose position I know, Niels Bohr’s seems to me to come nearest to doing justice to the problem’. Bohr had helped to expose the fact that the EPR paradox rests on the incompatibility of two assertions: the quantum theoretical description in terms of the wavefunction is complete, and the states of spatially separated entangled objects do not depend on one another. Bohr offered no solution or even a signpost toward a reconciliation of these positions.
In 2022, the Nobel prize in physics was awarded to the three physicists who, from the early 1970s onwards, had done the most to demonstrate experimentally that entanglement over substantial distances and times is a very real phenomenon. The states of spatially separated entangled objects do indeed depend on one another.
Nobody has yet been able to fill the resulting gaping explanatory hole.
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.
Fascinating.
Nice√. very informative ...