by Jim Baggott
Einstein argued that this ‘assumes an entirely peculiar mechanism of action at a distance, which prevents the wave continually distributed in space from producing an action in two places on the screen’.5 This would later become widely known as ‘spooky action at a distance’. The particle, which according to the wavefunction is somehow distributed over a large region of space, becomes localized instantaneously, the act of measurement appearing to change the physical state of the system far from the point where the measurement is actually recorded. Einstein felt that this kind of action at a distance violates one of the key postulates of his special theory of relativity: no physical action, or information resulting in physical action, can be communicated at a speed faster than light. Any physical process that happens instantaneously over substantial distances violates this postulate.
We should note right away that all this talk about physical action betrays the fact that these concerns are based on a realistic interpretation of the wavefunction, in the spirit of Proposition #3. This is not to say that Einstein wanted to ascribe reality to the wavefunction in the same way that Schrödinger did (we will see shortly that their views were quite different). But it’s important to realize that, from the outset, the Bohr–Einstein debate involved a clash of philosophical positions. At great risk of oversimplifying, it was a confrontation between realism and anti-realism, between acceptance and rejection of Proposition #3.
What I find quite fascinating is that Einstein was attacking a position that Bohr wasn’t actually defending. But by teasing out the physical consequences of his realist assumptions, Einstein sought to expose inconsistencies with what was fast becoming the standard or default interpretation.
As far as Bohr himself was concerned, the Copenhagen interpretation obliges us to resist the temptation to ask: But how does nature actually do that? Like emergency services personnel at the scene of a tragic accident, Bohr advises us to move along, as there’s nothing to see here. And there lies the rub: for what is the purpose of a scientific theory if not to aid our understanding of the physical world? We want to rubberneck at reality. The only way to do this in quantum mechanics is to take the wavefunction more literally and realistically.
The discussion continued in the dining room of the Hôtel Britannique, where the conference participants were staying. Otto Stern described what happened next:6
Einstein came down to breakfast and expressed his misgivings about the new quantum theory, every time [he] had invented some beautiful experiment from which one saw that [the theory] did not work…. Pauli and Heisenberg, who were there, did not pay much attention, ‘ach was, das stimmt schon, das stimmt schon’ [ah well, it will be all right, it will be all right]. Bohr, on the other hand, reflected on it with care and in the evening, at dinner, we were all together and he cleared up the matter in detail.
Einstein developed a series of hypothetical tests, or gedankenexperiments (thought experiments), based on the presumption of Proposition #3. These were about matters of principle; they were not meant to be taken too literally as practical experiments that could be carried out in the laboratory.
He began by attempting to show up inconsistencies in the interpretation of the uncertainty principle, but each challenge was deftly rebutted by Bohr. However, under pressure from Einstein’s insistent probing, the basis of Bohr’s counterarguments underwent a subtle shift. Bohr was obliged to fall back on the notion that measurements using classical apparatus are just too ‘clumsy’, implying limits on what can be measured, rather than limits on what we can know. This was precisely the position for which he had criticized Heisenberg earlier in the year.
In the eyes of the majority of physicists gathered in Brussels, Bohr won the day. But Einstein remained stubbornly unconvinced, and the seeds of a much more substantial challenge were sown.
‘At the next meeting with Einstein at the Solvay Conference in 1930,’ wrote Bohr some years later, ‘our discussions took quite a dramatic turn.’7
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. 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 short time interval sufficient to allow a single photon to escape. The shutter closes. We reweigh the box and, from the mass difference and E = mc2, we determine the precise energy of the photon that escaped. By this means, we have measured both the energy and the time interval within which a photon has been released from the box, with a precision that contradicts the energy–time uncertainty relation. This is Einstein’s ‘photon box’ experiment.
Bohr was quite shocked, and he didn’t see the solution right away. He had a sleepless night, searching for the flaw in Einstein’s argument that he was convinced must exist. By breakfast the following morning he had an answer.
On the blackboard Bohr drew a rough, pseudo-realistic sketch of the apparatus that would be required to make the measurements in the way Einstein had described them (Figure 9). 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.
Figure 9 Einstein’s ‘photon box’ gedankenexperiment.
After the release of one photon, the small weight is replaced by another, slightly heavier weight. This compensates for the weight lost through release of the photon so that the pointer returns to the zero of the scale. We suppose that the weight required to do this can be determined independently with unlimited precision. The difference in the two weights required to balance the box gives the mass, and hence the energy, of the photon that was released, as Einstein had argued.
So far, so good.
Bohr now drew attention to the first weighing, before the photon escapes. Obviously, the clock is set to trigger the shutter at some predetermined time and the box is sealed. We can’t look at the clock because this would involve an exchange of photons—and hence energy—between the box and the outside world.
To weigh the box, a weight must be selected that sets the pointer to the zero of the scale. However, to make a precise position measurement, the pointer and scale will need to be illuminated—we need to be able to see it. But this apparatus is required to be extremely sensitive—the position of the box must change on the release of a single photon. So, as photons bounce off the scale, the box can be expected to jump about unpredictably. We can increase the precision of the measurement of the average position of the pointer by allowing ourselves a long time in which to perform the balancing procedure. This will give us the necessary precision in the weight of the box and, since we can anticipate the need for this, the clock can be set so that it opens the shutter only after this balancing procedure has been completed.
Now comes Bohr’s coup de grâce.
According to Einstein’s own general theory of relativity, a clock moving in a gravitational field is subject to time dilation effects. The very act of weighing a clock changes the way it keeps time. As the box bounces upwards, time slows down. As it bounces downwards, time speeds up. So, because the box is jumping about unpredictably in a gravitational field (owing to the act of balancing the weight of the box by measuring the position of the pointer), the rate of the clock is changed in a similarly unpredictable manner. This introduces an uncertainty in the exact timing of the opening of the shutter which depends on the length of time needed to complete the balancing procedure. The longer we make this procedure (the greater the ultimate precision in the measurement of the energy of the photon), the greater the uncertainty in its exact moment of release.
Bohr was able to show that the product of the uncertainties in energy and time for the photon box apparatus is entirely consistent with the uncertainty principle.
Although the photon box experiment would go on to spawn a number of r
esearch papers arguing both for and against the validity of Bohr’s counterargument, Einstein conceded that Bohr’s response appeared to be ‘free of contradictions’, but in his view it still contained ‘a certain unreasonableness’.8 At the time this was hailed as a triumph for Bohr and for the Copenhagen interpretation. Bohr had used Einstein’s own general theory of relativity against him.
But note that, once again, Bohr had been obliged to defend the integrity of the uncertainty principle using arguments based on an inevitable and sizeable disturbance of the observed quantum system. At first sight, there seems to be no way around this. Surely, measurement of any kind will always involve interactions that are at least as big as the quantum system being measured. How can a clumsy disturbance possibly be avoided?
Einstein chose to shift the focus of his challenge. Instead of arguing that quantum mechanics—and particularly the uncertainty principle—is inconsistent, he now sought to derive a logical paradox arising from what he saw to be the theory’s incompleteness. Although another five years would elapse, Bohr was quite unprepared for Einstein’s next move.
Despite its seeming impossibility, Einstein needed to find a way to render Bohr’s disturbance defence either irrelevant or inadmissible. This meant contriving a physical situation in which it is indeed possible in principle to acquire knowledge of the physical state of a quantum system without disturbing it in any way. Working with two young theorists, Boris Podolsky and Nathan Rosen, Einstein devised a new challenge that was extraordinarily cunning. They had found a way to do the seemingly impossible.
Imagine a situation in which two quantum particles interact and move apart. These particles may be photons, for example, emitted in rapid succession from an atom, or they could be electrons or atoms. For convenience, we’ll label these particles as A and B. For our purposes, we just need to suppose that, as a result of the operation of some law of conservation, the two particles are produced in a pair of physical states that are opposed. It really doesn’t matter what these states are, so let’s just call them ‘up’, which we denote as ↑, and ‘down’, denoted ↓. So, we imagine a physical process which produces a pair of quantum particles—A and B—in ↑ and ↓ states, such that if A is ↑, B must be ↓, and if A is ↓, B must be ↑.
Here’s the thing. According to quantum mechanics, the correct way to describe this kind of situation is by using a single wavefunction which encompasses both particles and both possible outcomes. Such a pair of particles are said to be entangled.
We follow the mathematical rules and write down an expression for this ‘total wavefunction’ which we express as a superposition of the contributions from the wavefunctions for both possible situations. In doing this we are obliged to include contributions in which A is ↑ and A is ↓, and B is ↑ and B is ↓. But our law of conservation explicitly excludes the possibility of observing pairs in which A and B are either both ↑ or both ↓. We’re therefore left with something like this:
Let’s now suppose that particles A and B separate and move a large distance apart. We make a measurement on either particle to discover its state. As this is a measurement on a two-particle total wavefunction, we are obliged to represent this in terms of the expectation value of the measurement operator acting on the total wavefunction:
And we see that the outcomes A↑B↓ and A↓B↑ are equally probable. But, of course, for each measurement we will only ever see one outcome, analogous to detecting a single spot as each electron passes, one at a time, through two slits. In a realistic interpretation we must therefore presume that the total wavefunction collapses to deliver only one outcome, either A↑B↓ or A↓B↑, such that in a series of repeated measurements on identically prepared systems we will get A↑B↓ 50% of the time, and A↓B↑ 50% of the time.
Now suppose we make a measurement on A and discover that it is ↑. This must mean that the total wavefunction has collapsed to leave B in a ↓ state. Likewise, if we discover that A is ↓, this must mean that the total wavefunction has collapsed to leave B in an ↑ state. There are no other possible outcomes.
The total wavefunction relates only the probability of getting one outcome or the other, so in principle we have no way of knowing in advance whether A will be measured to be ↑ or ↓. But this really doesn’t matter, for once we know the state of A, we also know the state of B with certainty, even though we may not have measured it. In other words, we can discover the state of particle B with certainty without disturbing it in any way. All we have to assume is that any measurement we make on particle A in no way affects or disturbs B, which could be an arbitrarily long distance away, say halfway across the Universe. We conclude that the state of particle B (and by inference, the state of particle A) must surely have been defined all along.
Devilish, isn’t it?
In their 1935 paper, which was titled ‘Can Quantum-Mechanical Description of Physical Reality be Considered Complete?’, Einstein, Podolsky, and Rosen (EPR) offered a philosophically loaded definition of physical reality:9
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.
It’s easy to see what they were trying to do. If the wavefunction is interpreted realistically, in accordance with Proposition #3, then it ought to account for the reality of the properties—the physical states of particles A and B—that it purports to describe. It clearly doesn’t. There is nothing in the formulation that describes what these states are before we make a measurement on A, so the theory cannot be complete.
The alternative is to accept that the reality of the state of particle B is determined by the nature of a measurement we choose to make on a completely different particle an arbitrarily long distance away. Whatever we think might be going on, this seems to imply ‘spooky action at a distance’ which is at odds with the special theory of relativity. EPR argued that: ‘No reasonable definition of reality could be expected to permit this.’10
Details of this latest challenge were reported in The New York Times before the EPR paper was published, in a news article titled ‘Einstein Attacks Quantum Theory’. This provided a non-technical summary of the main arguments, with extensive quotations from Podolsky who, it seems, had been the principal author of the paper.
There is much in the language and nature of the arguments employed in the EPR paper that Einstein appears later to have regretted, especially the reality criterion. All the more disappointing, perhaps, as the main challenge presented by EPR does not require this (or any) criterion, though it does rest on the presumption that, whatever we make of reality, it is assumed to be local, meaning that as particles A and B move apart, they are assumed to exist independently of each other. Einstein deplored The New York Times article and the publicity surrounding it.
Nevertheless, this new challenge from Einstein sent shockwaves through the small community of quantum physicists. It hit Bohr like a ‘bolt from the blue’.11 Pauli was furious. Paul Dirac exclaimed: ‘Now we have to start all over again, because Einstein proved that it does not work.’12
Bohr’s response, when it came a short time later, inevitably targeted the reality criterion as the principal weakness. He argued that the stipulation ‘without in any way disturbing a system’ is essentially ambiguous, since the quantum system is influenced by the very conditions which define its future behaviour. In other words, we have to deal with elements of an empirical reality defined not by the quantum system in abstract, but by the quantum system in the context of the measurements we make on it and the apparatus we use. These dictate what we can expect to observe. EPR’s error lies in their presumption that the wavefunction should be interpreted realistically, and the ‘spooky action at a distance’ is simply a consequence of this error. Just don’t ask how nature actually does this, as there really is nothing to see here.
Einstein was, at least, successful in pushing Bohr
to give up his clumsiness defence, and to adopt a more firmly anti-realist position. Those in the physics community who cared about these things seemed to accept that Bohr’s response had put the record straight.
Schrödinger wrote to congratulate Einstein shortly after the EPR paper appeared in print. In his letter he highlighted what is, in fact, the principal challenge. When interpreted realistically, the total two-particle wavefunction is necessarily ‘non-local’; it is distributed in just the same way that the electron wavefunction is distributed across the screen in the two-slit experiment. Our instinct is to imagine that, after moving a long distance apart, particles A and B are separated. They are distinct, independently existing, or ‘locally real’ particles. Quantum mechanics has absolutely no explanation for how we get from one situation to the other.
Einstein replied with enthusiasm, and as their correspondence continued through the summer of 1935 a further challenge to what had by now become the orthodox Copenhagen interpretation gradually emerged.
First, Einstein had to deal with Schrödinger’s insistence that the wavefunction be interpreted as a description of a real ‘matter wave’. Although he couldn’t be clear on the details, Einstein preferred to think of the wavefunction in terms of statistics. We describe the properties of an atomic gas in terms of physical quantities such as temperature and pressure. But if we consider the gas as a collection of atoms, we can use the classical theories developed by Ludwig Boltzmann and James Clerk Maxwell to deduce expressions for temperature and pressure as the result of statistical averaging over a range of atomic motions. In this case, we deal with statistics and probabilities only because we have no way of following the motions of each individual atom in the gas. Of course, we might not be able to account for such motions except in terms of statistics, but this doesn’t mean that atoms (or their motions) aren’t real.