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Does the Einstein-Podolsky-Rosen Argument show that Quantum Theory is Incomplete?

How does science work? One way to get hold of this is to look at how new ideas enter into science and are tested - after all, 'those who refuse to learn from history are doomed to repeat it'. The last century could be called 'the century of quantum mechanics' - at least as far as physics is concerned.

This essay has been reformatted for on-line presentation.

 

Essay Outline

 


'Spooky Action at a Distance'
(Einstein, 1935)

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Introduction

The question addressed here is, 'Does the Einstein-Podolsky-Rosen argument show that quantum theory is incomplete?' I will forestall the necessity to read the whole paper to find my answer by giving it now; No. The Einstein-Podolsky-Rosen argument (hereafter 'EPR') does not show that quantum theory is incomplete. In this essay I will attempt to justify my answering in the negative. We will see that the answer to this simple question actually is very revealing. Although ostensibly a question about physics, and the ideas that physicists hold, the basis of the question is actually metaphysical; the argument revolves around different ideas and versions of what reality is. My approach to this will be first to explain the issues in minimal detail, so that we can clearly understand what's at stake. I will give the barest outline of some features of quantum theory – which are also the essential elements of what is known as the Copenhagen Interpretation of quantum theory – and of the implications of these elements. I will follow up with a description of the EPR question, explain what the terms 'complete', 'locality' and 'action at a distance' indicate and imply, and the exact significance of the EPR question in these terms. I will then present my answer, supported in part by experimental work –specifically that of Alain Aspect (1982)– together with some criticisms of this work. In the discussion section, I will argue that although EPR fails, quantum theory nonetheless is incomplete, indeed, that physics is necessarily incomplete. In my view, 'completeness' would be indicative of  'it's science, but not as we know it, Jim'

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Exposition

Background to quantum theory

At the end of the 19th century, many physicists felt that physics was almost complete. There were just three major anomalies; the pattern of energy radiated from a black-body, the photo-electric effect and the bright-line radiation spectrum of atoms. The investigation into and resolution of the anomalies was what gave rise to quantum mechanics; it fully and completely describes the experimental results in each case. These three problems were resolved by Max Planck, Albert Einstein and Niels Bohr, respectively. The solution lay in the proposal of Einstein (in response to the photoelectric effect) that energy interactions with the atom were quantised, that is emitted and absorbed in discrete packets of size E=hvh being Planck's constant – and in integer units of 1, 2, 3 and so on. He provisionally extended this to the assertion that all electromagnetic radiation was quantised, hence quantum theory. I could not describe it fully here, of course, even if I understood it well enough to do so, which I do not. I will just give the barest outline of the assertions that have caused most contention:

  1. The probability wave function

    this was Born's interpretation of Schr÷dinger's wave equation for the wave ψ. Born showed that the square of this value ψ2 gave the probability that a particular quantum state existed, and that there was no exact prior answer available for this state; all possible states of the particle exist simultaneously, that is, the states are superposed.

  2. The collapse of the probability wave function

    Born stated that the probable state of the particle was resolved through the collapse of the probability wave function to a particular state through the act of measurement or observation. Born said '…our knowledge of the system suddenly changes'.

  3. The uncertainty principle

    Heisenberg showed that it was not possible even in principle to simultaneously know the exact position and momentum of a sub-atomic particle.

I am unable to prove or disprove the mathematics behind these assertions so I will simply accept them; they have been extensively examined, probed and criticised for sixty years without any errors yet having been identified, so I feel on reasonably safe ground in doing so.

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The Copenhagen Interpretation

'I must say in everyday context, quantum theory is unshakeable, unchallengeable, undefeatable – it's battle tested”
Wheeler (1995), quoted in McEvoy & Zarate: p. 173

The Copenhagen Interpretation has been the dominant interpretation of quantum mechanics since Bohr proposed it in 1927. I emphasise that it is an interpretation. The various differing interpretations of quantum mechanics do not disagree on the phenomena they are trying to explain. The disagreement arises when attempts are made to say what quantum mechanics actually means, that is to say, what the phenomena are interpreted as indicating about physical reality. Bohr's Copenhagen Interpretation specifically refuses to make any inference from quantum theory in terms of physical reality.

How did the Copenhagen Interpretation become the dominant interpretation? It would be reasonable to describe it as Einstein's fault. Bohr struggled for months with the problem of wave-particle duality. This is thrown up by the classical approach to physics, under which an electron, say, had to be either a wave or a particle. However, Bohr realised that both explanations were necessary to describe the experimental evidence, but that they contradicted each other in some conditions. He therefore proposed his Principle of Complementarity, which defined the problem out of existence by a simple stratagem; he observed that since wave-like and particle-like behaviours were only obtained using different experimental conditions, then neither of them should be regarded as a complete description: rather, they were to be seen as complementary and partial descriptions. This proposal, taken with the probability wave function for the state of a particle, the collapse of the probability wave by the act of measurement and the uncertainty principle, makes up the Copenhagen Interpretation of quantum mechanics, known for brevity as the CHI.

Einstein made his view clear at the Solvay conference in the same year (1927); he did not like Bohr's principle of complementarity, he did not like the probabilistic collapse of the wave function, he most certainly did not like the collapse due to measurement and he did not believe the theory was of more than 'temporary' utility. Thereafter he proposed a series of thought experiments, each of which was intended to show a flaw in Bohr's reasoning, and each of which was demolished by Bohr.

The penultimate of these was presented at the 1930 Solvay conference. There is not space to detail the experiment here, but like all the thought experiments it attempted to produce an idealised arrangement that could indeed show simultaneously the position and momentum of a particle, in contradiction of the uncertainty principle. This penultimate attempt backfired badly on Einstein; his reasoning in the thought experiment was shown to be faulty as he had forgotten to apply his own General Theory Of Relativity to the results; when it was applied, exactly Bohr's predicted level of uncertainty was demonstrated. Thereafter, the CHI became the 'standard model'. Bohr denied that quantum theory should be treated as describing anything real; '…an independent reality in the ordinary physical sense can neither be ascribed to the phenomena nor to the agencies of observations'. That is, before the observation, there were no properties to observe.

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The EPR argument

The EPR argument was the last of these many attempts by Einstein to present a reductio ad absurdem in the form of a thought experiment that would disestablish the prevalent acceptance of the CHI. All Einstein's previous efforts along these lines had been triumphantly repudiated by Bohr. EPR argues that the CHI involves non-locality – in Einstein's phrase, “creepy action at a distance”. The thought experiment put forward by Einstein, Podolsky and Rosen in 1935 consists of this:

  1. Let us take one particle that will decay into two others, an electron and an anti-electron or positron, say.

  2. There are many features we could measure; but here, let us concern ourselves with the spin of the system.

  3. The original particle, let us say, had zero spin; it was not spinning.

  4. The two products of decay, which do spin in opposing orientations, by conservation of angular momentum must have spins that add up to the original spin – zero, so the spins of the two particles are equal and opposite.

Now, let the two particles move off away from each other – since this is a thought experiment, we can let them travel a few light years away from each other.

  1. Then we measure the spin of one particle.

  2. We can choose what sort of spin we measure; for example, 'spin up' or 'spin right'.

  3. By the mathematics of the wave function and by conservation of angular momentum, whatever the result for the particle we measure, the other particle must instantaneously be fixed in the complementary spin - without our measuring it.

  4. By CHI, there is no state attributable to either particle until such time as the measurement is made, so neither had a value for spin before the measurement.

  5. But the particles are a few light years apart; it would therefore take a few years for the signal about the state of one particle to reach the other at light speed, which is the limiting velocity of space-time.

So, for the non-measured particle's state instantly to collapse, we require non-locality ('creepy action at a distance') and we require faster-than-light communication – both of which had been outlawed (more or less) by Einstein's General theory of relativity. Hence this is presented as a sort of paradox, and it is known as the 'EPR paradox'.

Einstein hoped to show that because the predicted instantaneous collapse of the wave function for the non-measured particle involved one of these anomalies, this would undermine the CHI. Furthermore, if we now substitute the words 'observer, observation' for the words 'measure, measurement' in the description I have given above, we can see how the attack on CHI is also an attack on the critical importance of the observer in CHI. Einstein detested this 'essential, irreducible' central r¶le of the observer. Famously, he said 'God does not play dice'. Barrow & Tipler point out, '…to a realist like Einstein, who held that a physical reality existed independently of Man the Observer, Bohr's view was anathema.' Einstein had no idea that it would be possible to test this thought experiment in practice – but that is exactly what came about in 1982, as we shall see.

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Locality, non-locality and action at a distance

Locality is a description of the radius of action of a particle. If a particle can be regarded as a single point then the causal effects of that particle are restricted to the other particles with which it can directly interact, by coming into contact with them. For example, let us say that we measure the existence a photon by allowing it to strike a piece of photographic film – that is, we take a photograph. Each photon that impinges on the film appears as a particular dot of photographic film with a changed state; however much it may behave as a wave before it reaches the film, the final effect of each photon is local and as if it were a point or particle. Each separate photon that strikes the film is indeed local; I don't have to worry about photons on the other side of the galaxy when I take my holiday snaps.

However, in CHI we have a pair of particles that cannot be treated as separate – their states are entangled in such a way that the act of measurement or observation on one fixes a state of the other, without us having to specify in advance what state this will be. If they are not in the same place (and they are not, by virtue of being two particles) then the effect of an action on one particle is non-local – it immediately affects (according to CHI) the other particle at whatever distance it might be from the first. This is instantaneous action-at-a-distance. According to this view, my taking a photo does indeed instantaneously affect the states of all the other photons entangled with those whose state I collapse – wherever they are. Perhaps holiday snaps may be more important than is immediately apparent...

Action at a distance was one of the problems Newton faced with his Principia. The instantaneous action of gravity, which had no obvious physical mediating force, was described by detractors as 'action-at-a-distance'. Einstein in his General theory of relativity had reconceived the problem to dispose of action at a distance. In his version, space-time is not flat but curved; planets in their orbits follow the geodesic, the least-energy path through the curved space-time, with no need to invoke any mysterious action at a distance. It is no surprise then that he described its return – by the back door, as it were – as 'creepy'.

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Complete versus Incomplete

The original Einstein-Podolsky-Rosen paper was entitled 'Can Quantum-mechanical Description of Physical Reality be Considered Complete?' and I see it as a special pleading for one sort of realism. What is 'complete'? By 'complete' they mean nothing missing, that there were no entities absent from the quantum-mechanical description. The EPR argument of course was intended to show that QM was 'incomplete' by demonstrating an 'impossible' implication, and therefore that there were other factors – 'hidden variables' of reality – that were mediating the visible transactions between the separated particles. By understanding the hidden variables, it would be possible to predict the actual state of each particle in the EPR when it was measured, rather than take the probabilistic result of the collapse of the wave function.

Einstein spent years working on a theory of hidden variables, based on de Broglie's pilot wave theory. After his death the project was taken up by David Bohm; however, to this day CHI continues to be the dominant approach.

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Development

I hold that the EPR thought experiment does not show that QT is incomplete. Why? There are two answers, and these are of two sorts of reasons:

  1. A Naturalistic epistemological reason

    that is, since Newton, questions in physics are regarded as being answered by experiment, and experiment has shown EPR to be wrong.

  2. An inherent logical reason

    that is, the argument put forward by EPR is flawed in its logic and could not prove CHI to be wrong.

Let us start with the experiments; then we will examine the logic.

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Bell's Inequality theorem

In a sabbatical year taken in 1964, J.S. Bell of the University of Belfast calculated the differential cumulative probabilities for correlated photons, taking as a given the truth of Einstein's condition of locality. This work derived from an investigation of Bohm's hidden variables theory, which still had to predict the same results found and predicted by quantum mechanics [NOTE 1] . As a result Bell derived an inequality : that is, if reality was local, then one set of probabilities would arise from the statistics of quantum mechanics; if non-local, then another, different set of probabilities would arise. He proved that non-locality is a necessary condition to arrive at the statistical predictions of quantum mechanics. Moreover he concluded that 'hidden variables' theories could not completely agree with the predictions of quantum theory. Therefore, if experiment showed that the inequality was violated, then this should be taken as showing that non-locality was a true feature of reality and that hidden variables theories were false.

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Alain Aspect

In 1982 Alain Aspect and his group carried out a definitive practical test of EPR, using instead of the electron/positron pair mentioned in the earlier example a pair of correlated photons as proposed in Bell's Inequality theorem. The test involved the polarisation of the photons, and the decision as to which aspect of the polarisation to measure was taken after the photons were on their way by changing the state of an optical switch. Bell's inequality was found to be violated. Bohr and the CHI were fully supported; it seems that Einstein was wrong. There would indeed appear to be faster-than-light communications between correlated photons.

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Criticisms of Aspect

There are various criticisms that have been made of Aspect. Before looking at these, I should point out that Aspect's work has been replicated many times, and earlier tests also generally gave the same results. What, then, are the main criticisms?

  1. The first (and strongest) criticism is that the switches used to implement the 'decision' as to which aspect of polarisation to measure are controlled in a systematic, semi-random but periodic way. Although the switching happens so quickly that there is not time for information about the state of one switch to be propagated at the speed of light to the other switch, 'clever' hidden variables might be able to infer the state of the other switch. This could be fixed, of course, by using a pure random choice.

  2. Most photon pairs are not detected because of the inefficiency of the detectors. Perhaps the non-detected pairs were those that did not show non-locality.

  3. The switches exist within the same space-time region if the Minkowski space-time cones of the switches are extended backwards, that is into the past. In this way perhaps they influence each other.

Shimony comments: “Most students of the subject, however, do not regard the exploitation of these loopholes to be promising”. Gribbin points out that quibbles over Aspect are not really to the point; Bell proved that “… any interpretation of quantum theory must involve non-locality.” The Bell inequality is in fact violated on experiment, and not by the Aspect experiment alone; therefore, local reality must be abandoned, even if quantum theory is totally in error.

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What is proof?

Let us imagine that Aspect had found that the predictions of quantum theory were wrong. Would this prove that quantum theory was incomplete? No, it could not. The EPR argument reduced to (what I conceive as being) its bare elements is this:

  1. Special relativity makes a set of predictions. These are based on well-established assumptions, such as the limiting velocity of the speed of light and the absence of action at a distance. Special relativity is supported by experiment.

  2. Quantum theory makes a set of predictions. These imply that information is transferred from one entangled particle to another instantaneously; that is, action at a distance and communication at faster than the speed of light.

  3. If the predictions of quantum theory are correct, then the predictions of Special relativity are violated.

  4. Special relativity is correct.

  5. Therefore quantum theory is incomplete.

Put in this way, the essential flaw is clear; it arises at step IV. This puts the theoretical status of special relativity above that of the theoretical status of quantum theory; yet the sorts of evidence available for each of these are identical. Both theories were adopted, against resistance, because they solved observational problems. In other words, both theories are supported by the sort of evidence that we call inductive; they are inferential. It is worth noting that EPR was put forward long before Popper (and indeed, Kuhn and Feyerabend) promoted their various ideas. Popper, in an attempt to rid science of the problems of induction, [NOTE 2]  abandoned the idea of attempting 'proofs'. He introduced instead the idea that scientific statements and theories were subject to falsification. This is often described as the Hypothetico-deductive model. Scientists must have been impressed with falsification; they elected Popper to Fellowship of the Royal Society, not a common honour for a philosopher. 

In Popperian terms, the success of the EPR argument would not in any case prove anything. It would show that there was an error somewhere in physics, but such an error could be in CHI or elsewhere. Alternatively, can we see EPR as an attempt at falsification of CHI? Certainly that was the intention of Einstein et al. The difficulty then would be that only one prediction of quantum theory would have been contradicted; yet the notable feature of quantum theory is its endless list of successes. What would one failure count in an inductive framework, when set against these many successes?

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Is quantum theory complete?

Quantum theory is not complete. It is incomplete because, for example, there is a separation between quantum theory and relativity. It is incomplete because, for example, attempts to understand gravity in terms of quantum mechanics have failed. Thus, the theory is incomplete. In the next section, I will argue that physics and science necessarily are incomplete.

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Discussion

“I think it obvious that if quantum mechanics has brought the observer back into physics (and it has) then to do good physics we must include the total effect of the observer. So far no one has been able to do that.'
McCusker (1996)

Why did Einstein make so much fuss over the non-local nature of quantum theory? It doesn't bother me at all. There are two possible reasons for why I'm not bothered; first, I have grown up with quantum theory buzzing around the back rooms of my worldview, whereas Einstein grew up with the classical view of physics, which he did so much to overthrow. For myself, then, I am perfectly happy to accept the findings of experiment. That's how it – reality – is. If a theory fails to describe the findings of an experiment, well, so much the worse for the theory.

The second possible reason is the metaphysical one. Einstein was a realist:

…the concepts of physics refer to a real external world, i.e. ideas are posited of things that claim a 'real existence' independent of the perceiving subject (bodies, fields, etc.) and these ideas are, on the other hand, brought into as secure a relationship as possible with sense impressions… Further, it appears to be essential for this arrangement of the things introduced in physics that, at a specific time, these things claim an existence independent of one another, insofar as these things 'lie in different parts of space'

I am not a realist, for reasons that are not relevant here [NOTE 3] . It would seem to me that Bohr also was not a realist in the sense that Einstein was. What do I mean by 'realist'? Here I refer to the variety of realism that maintains there is a real external world independent of the observer. It is generally agreed that a fundamental tenet of physics is some version of realism that includes an implicit acceptance of simple causality; that is, this action causes that effect. With quantum theory, the boundaries of cause, effect and realism are at the least stretched, if not steamrollered flat.

Searle gives a nice simple definition for realism:

“Properly understood, realism is not a thesis about how the world is in fact. We could be completely wrong about how the world is in every detail and realism could still be true. Realism is the view that there is a way things are that is logically independent of all human representations. Realism does not say how things are but only that there is a way that things are.

Realism (at least for Searle) is thus clearly revealed as a metaphysical position, in case there had been any doubt of it. Is it possible to do physics without being a realist? Well, why not? The version of reality taken as 'real' has changed often enough over the years. Even if we agree that modern physics was born with Newton then the version of what is real has changed many times since then.

Shimony argues that Bohr's thought is related to the Kantian position in which the thing in itself – the ding an sich – is inherently unknowable. For example, in answer to EPR Bohr argues:

Of course there is in a case like that just considered no question of a mechanical disturbance of the system under investigation during the last critical stage of the measuring procedure. But even at this stage there is essentially the question of an influence on the very conditions which define the possible types of predictions regarding the future behaviour of the system. Since these conditions constitute an inherent element of the description of any phenomenon to which the term 'physical reality' can be properly attached, we see that the argumentation of the mentioned authors does not justify their conclusion that quantum-mechanical description is essentially incomplete.

Yet Bohr also argues like this:

Without entering into metaphysical speculations, I may perhaps add that an analysis of the very concept of explanation would, naturally, begin and end with a renunciation as to explaining our own conscious activity.

- a comment which I would, myself, have to take as a metaphysical speculation. Schr÷dinger took a different position:

…The 'real world' around us and 'we ourselves', i.e. our minds, are made up of the same building material, the two consist of the same bricks, as it were, only arranged in a different order – sense perception, memory images, imaginations, thought.

That is (in my reading of the comment), he rejected dualism. However, he also argued that there is only one Mind in the world, the appearance of a multitude of different subjects actually being an illusion. This brings to err… 'mind' one of the other interpretations of quantum theory, Everett's many-worlds theory. I have always found this interesting as it is, in my view, one of the few approaches that stands some chance of dealing with the essential solipsism of human experience; that is, that I only experience my self. I can't deal with that here, though; there is no time or space for (possible) red herrings, but I will look at it closely later.

I suspect that Einstein's strongest reservations were concerned with the crucial fact that the observer – you or I – takes a part in creating reality. This clearly is not a popular notion with anyone who holds to realism. Against this view, it is argued that this collapse of the wave-function by observation is restricted to the quantum level: at the macro level of lumps of matter the size of human beings, the act of observation does not collapse a wave function. I'm not convinced that the mere act of observation cannot have effects on macroscopic reality. Let me give an absurd example: a single observation of my best friend in bed with my teenaged daughter will definitely have a major effect on our various realities. Wigner, in referring to Schr÷dinger's Cat, said:

“The consciousness of the observer makes the difference. When we become conscious of something we bring about the crucial collapse of the wave function, so that the perplexing mix of life and death disappears.”

Well, that 'perplexing mix of life and death' that we each experience will certainly collapse one day, for each of us, to the condition of unmixed death.

Let me finally come to the question of whether completeness is compatible with science. Let us imagine for a moment that a new unified theory is presented that is complete in every way and passes every conceivable test. What happens to physics? Bird gives an interesting view of the question, 'What is science?' He takes as his starting point the criteria used by an American judge in deciding whether creationism is or is not scientific. I find this of interest in two ways: first, we have here a legal as against a scientific or philosophical view of what science is, a view in accord with society at large, perhaps – or perhaps not. Second, the criteria are of interest in themselves. What are they? By this ruling, a scientific theory must be:

  1. Guided by natural law

  2. Explanatory by reference to natural law

  3. Testable against the empirical world

  4. Tentative; that is, its conclusions are not necessarily final

  5. Falsifiable

The influence of Popper is very clear here; however, is there anything here that scientists or philosophers would find problematic? Take item 4. Clearly this distinguishes between a religious theory - which is inescapably absolute and thus final - and a scientific theory, which is neither. Now, a complete theory of physics would necessarily be final. But by this criterion, any complete theory is not tentative. It would cease to be a theory and become absolute, and thus enters the realm of religion, in the same moment leaving the realm of science. I therefore argue that necessarily science and its theories must remain incomplete in order that they remain science.

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Conclusion

Let's make this brief. In my view the EPR paradox does not show that the Copenhagen Interpretation of quantum theory is incomplete. Quantum theory is nonetheless incomplete, and indeed all theories in science must necessarily be incomplete. If this was not the case, we would not have two entities - science and religion - but one, science-religion.

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Bibliography

Barrow, J & Tipler, F. (1986) The Anthropic Cosmological Principle. OUP: Oxford.
Bird, A (1998) Philosophy of Science. UCL: London.
Bohm, D. (1980) Wholeness and the Implicate order. Ark: London.
Bohr, N. (1934). Atomic theory and the description of nature. CUP: Cambridge.
Feymna, R. (1985 ) QED : Penguin: London
Gjertsen, D. (1989) Science and Philosophy. Penguin: London
Gribbin, J. (1984 ) In search of Schr÷dinger's Cat: quantum physics and reality. Black Swan: London
Gribbin, J. (1995 ) Schr÷dinger's Kittens and the search for reality. Phoenix: London
McCusker, B. (University of Sydney). Private Communication, 1996.
McEvoy, J. & Zarate, O. Quantum Theory for Beginners. Icon: Cambridge.
O'Hear, A. (1989) An Introduction to the Philosophy of Science. Clarendon Press: Oxford.
Penrose, R. (1990) The Emperor's New Mind. Vintage: London.
Penrose, R. (1995) Shadows of the Mind. Vintage: London
Penrose, R. (1997) The Large, the small and the human mind. CUP: Cambridge
Redhead, M. (1995) From Physics to Metaphysics. CUP: Cambridge.
Searle, J. (1995) The Construction of Social Reality. Penguin: London
Shimony, A. (1993a) Search for a Naturalistic world view. Vol. 1. CUP: Cambridge
Shimony, A. (1993b) Search for a Naturalistic world view. Vol. 2. CUP: Cambridge
Trigg, R. (1993) Rationality and Science. Blackwell: London


Footnotes

 [Note 1] Bell was actually hoping, of course, to show that EPR were correct. He was disappointed in this hope!

 [Note 2] They are still there, though. If not, why would David Deutsch devote much effort to defining them out of existence?

 [Note 3] The fact that I am not a 'realist' does not (I hope!) mean that I am 'unrealistic', or that I deny that anything is 'real'. Rather, it means that I take 'realism' (in Searle's sense, qv) to be an unprovable metaphysical position. If you doubt my position, fine; demonstrate to me that reality is real - from first principles, without invoking features of 'reality'. Oh - and forget Dr. Johnson: I went to the school he refounded, so I've had plenty of time to consider and reject his demonstration

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