Can quantum mechanical description of physical reality be considered complete?

That was the title of a ground-breaking article published in 1935 in the Physical Review by Einstein, Podolsky and Rosen (EPR). In this article they brought to the attention of physicists the strange correlations predicted by quantum mechanics for observations involving what are now called entangled systems. They used those predictions to argue that quantum mechanics, which had already been very successful in explaining many phenomena at the atomic level, gives an incomplete description of reality.

I’ve been asked a few times to write a blog entry about EPR to the layman reader, and so here it is. The details may take some attention to follow, but it is a nice story, which culminates with what has been called “the most profound discovery of Science” [H. Stapp]. Of Science, not just Physics. And he didn’t specify just the 20th century. So bear with me.

Before the EPR paper, Bohr, Heinsenberg and others had already set up the standard interpretation of the then-young quantum theory; the development of the basic postulates was completed around 1927, after a couple of decades of work by those physicists and others such as Schrödinger, Planck and Einstein himself. This interpretation, commonly referred to as the “Copenhagen interpretation”—in reference to the city where Bohr’s institute was located—painted a very unsettling picture of reality for the physical intuition of Einstein and his co-authors.

In the picture of Bohr and Heinsenberg, quantum systems cannot be said to have physical properties independently of a process of measurement that can determine them empirically. Since there are multiple ways in which one can observe a quantum system, and since some of those are incompatible observations (for example, one can measure the position or the momentum of a particle, but not both at the same time, with arbitrary accuracy), then it follows that not all physical properties can be said to have simultaneous existence, in the Copenhagen view.

[The term “physical properties” has in fact fallen in disuse when talking about quantum mechanics, being replaced by the less metaphysically committed observables; similarly, the term object has been replaced by system.]

According to the Copenhagen interpretation, if one decides to measure the position of a system, then “position” will have an empirical meaning, and it will be meaningless to ask what the “momentum” of the particle would have been if it had been measured instead. This was reflected mathematically by Heinsenberg’s Uncertainty Principle, which states that one cannot reproducibly measure incompatible observables of a physical system with arbitrary precision.

Not being able to determine something with arbitrary precision does not necessarily imply that it doesn’t exist, of course. Einstein, Podolsky and Rosen noticed that the correlations that quantum mechanics predicted between what was later termed (by Schrödinger) entangled systems could be used to challenge the Copenhagen interpretation. With an entangled pair of particles, sent to two distant observers—usually called Alice and Bob these days—it would be possible for one observer (Alice, say) to determine with arbitrary precision either of two incompatible properties such as the position or the momentum of Bob’s system, at a distance, without touching Bob’s system or allowing time for any communication to occur (with a signal not exceeding the speed of light) between the two sub-systems.

It would be absurd, in the light of Einstein’s theory of relativity, which postulated a limit to the velocities of physical systems—the speed of light—to imagine that any kind of instantaneous “action at a distance” could connect the two subsystems, and EPR concluded that because Alice could determine either of them at a distance at her will, the properties associated with both position and momentum must have existed before they were measured.

Although it challenged the orthodoxy, this was nothing more than a careful defence of the common sense idea behind most of modern science, that correlations can always be explained by a sequence of local events. If there is an outburst of a disease at around the same time in different locations, say, one would look for a common cause for that coincidence—presumably some previous interaction between the patients allowed the transmission of a pathogen; they must have either come in close contact or some microorganism must have been transmitted through the air or other medium between the two patients. All that EPR were defending was that some analogue of the “microorganisms” (later termed in that context “hidden variables”) should be responsible for generating the correlations.

For some strange reason, perhaps because of the eloquence of Bohr’s metaphysical positions, or perhaps because it was more practically useful to think of the theory in Bohr’s way, EPR’s argument was largely thought to be wrong for at least three decades. This was aided by some mistaken “no-go” theorems, such as that due to Von Neumann, which (erroneously, it was much later realised) purported to show that no theory of hidden variables could reproduce the quantum mechanical predictions.

The first to show (indirectly) the error in Von Neumann’s “theorem” was Bohm, who in 1952 developed precisely what Von Neumann claimed to have demonstrated to be impossible: a hidden-variable theory of quantum phenomena which agreed with all empirical predictions of the “bare theory” formulated in the Copenhagen fashion. It was however, an explicitly nonlocal theory. Particles had definite positions at all times, but they could affect each other instantaneously, at a distance, in precisely the way that EPR rejected out of hand as absurd. Later, in 1964, John S. Bell showed, after pointing out the error in Von Neumann’s alleged proof, that nonlocality was indeed not an accident of Bohm’s formulation, but a necessary feature of any theory which attempts to explain quantum phenomena (and ultimately, the world) in terms of underlying physical properties existing independently of the processes that reveal them.

Bell showed—through what is now called Bell’s theorem—that the correlations between entangled quantum systems were much stronger than EPR realised. The correlations considered by EPR were, as humourously illustrated by Bell himself, no more mysterious than the correlations between the socks of his physicist friend Bertlmann:

…The philosopher in the street, who has not suffered a course in quantum mechanics, is quite unimpressed by Einstein–Podolsky–Rosen correlations. He can point to many examples of similar correlations in everyday life. The case of Bertlmann’s socks is often cited. Dr. Bertlmann likes to wear two socks of different colours. Which colour he will have on a given foot on a given day is quite unpredictable. But when you see that the first sock is pink you can be already sure that the second sock will not be pink. Observation of the first, and experience of Bertlmann, gives immediate information about the second. There is no accounting for tastes, but apart from that there is no mystery here. And is not the EPR business just the same?…

[J. S. Bell, in “Bertlmann’s socks and the nature of reality”,
Speakable and Unspeakable in Quantum Mechanics,
Cambridge University Press]

The EPR business, Bell showed, was not the same. Bell was able to show that the correlations between the multiple incompatible observations which are available to be performed by Alice and Bob cannot be given any local explanation whatsoever, even if you allow the most general imaginable model (called a Local Hidden Variable (LHV) model) by which the outcomes of those observations could be correlated. With the type of state EPR were considering, the correlations between the same measurements (position at Alice/position at Bob, momentum at Alice/momentum at Bob) was amenable to a LHV explanation, as pointed by EPR; but when some other equally possible observations are considered, a LHV model is no longer possible. This would be demonstrated by the violation, by a carefully set-up experiment, of what are now called Bell inequalities—mathematical inequalities that follow logically from the assumption of a LHV model.

Up to some open technical problems (due to logical loopholes exploiting experimental imperfections) those correlations have been observed, and Bell inequalities violated, in multiple labs around the world, since the work of Alain Aspect and others in the 1980’s. There really are correlations in the world that cannot be given any possible local explanation. In this (negative) sense, the world really is nonlocal, independently of whether or not hidden variables exist underlying quantum phenomena

[unless you are willing to allow backwards-in-time causality, or something that Bell called superdeterminism, a class of conspiratorial theories whereby the choice of which of the possible incompatible measurements will performed in the future of a quantum system is already determined by the same hidden variables that determine the present properties of the system itself. But I won’t go into that here.]

[People often confuse the commonly used term “local realism” to be a conjunction of two independent terms — “locality” and “realism” — and choose to maintain “locality”, thus claiming that Bell’s theorem suggests the failure of “realism”. It is not always clear what is meant by “realism” in these contexts, and it is my considered opinion that locality (or more precisely, what Bell termed “local causality”) is proven to be false by Bell’s theorem (though see note above). Which is a distinct assertion from saying that something like the “active” nonlocality of Bohmian mechanics is true. The failure of local causality is merely the assertion that a local, separable, description of the phenomena is impossible. Even if there are no hidden variables, at the very least one must treat the entangled system as one indivisible system, not composed of separable parts amenable to independent (but correlated) descriptions.]

Which takes us back to the original question: “Can quantum mechanical description of physical reality be considered complete?” The answer is still debatable, if what the question is asking is whether or not hidden variables underlying quantum phenomena really exist. But in search of an answer, EPR, Bohm and Bell have unearthed the astounding fact that our classically intuitive descriptions of a reality in which things exist independently of each other, interacting only locally to create the multiplicity of phenomena we experience, is demonstrably untenable. Anybody with a scientifically or philosophically inclined mind who is not bothered by this discovery—as pointed out by an anonymous Princeton physicist to the physicist David Mermin—“must have rocks in [their] head”.

Advertisements

6 thoughts on “Can quantum mechanical description of physical reality be considered complete?

  1. Yes, Serafino, you’re right. I had actually read that before also in the page of my friend Michael Seevinck, but I obviously forgot. I guess I was thinking about how Bohm was the first to show the error in Von Neumann by construction, producing a hidden-variable model that fully reproduces quantum mechanics. (Bohm’s work relates to the earlier work by de Broglie, presented already in the 1927 Solvay conference, but de Broglie’s model couldn’t fully repoduce quantum mechanics.)

    Thanks for the correction!

  2. Hi e1saman. The article you mention is somewhat misleading, and frankly, the idea is not really new. (Btw, it can also be found for free, although in an older version apparently, here: [http://arxiv.org/abs/0909.0950]).

    It is misleading (in the Nature Physics version) when they say in the abstract that “if the particle is prepared entangled with a quantum memory, a device that might be available in the not-too-distant future, it is possible to predict the outcomes for both measurement choices precisely.”

    First of all, a “quantum memory” in this case is nothing but a system with which your system of interest is entangled with, and well, that’s actually been done to exhaustion; it’s in the not-too-distant past as opposed to future. Sure, it is a technical challenge to do that for many particles and maintaining the coherence for long times, but all you need for the purpose of that paper is a bipartite entangled state.

    Now what is terribly misleading in that abstract is that you can only predict the outcomes of *either* measurement, not both! This is precisely the same situation as with the original EPR paradox.

    And furthermore, they didn’t cite other works that have interpreted the EPR paradox in terms of the violation of a conditional Heinsenberg uncertainty principle. This was already done in 1989 by Margaret Reid [1] for the original EPR case of position-momentum. This idea has been extended for the general case by me and Reid in 2007 [2] and we have even recently published a review article about all of that [3]! This apparent violation of HUP also relates to the phenomenon of steering for which I and coauthors have derived criteria [4]. Even the proposed applications (for entanglement witnessing and cryptography) were already part of those earlier efforts as you can see in the review paper.

    The novelty of that Nature Physics paper as far as I can see is really only that they write a bound on how much quantum theory allows you to have this apparent violation of the HUP depending on the degree of entanglement, which is a nice result, but hardly worth all the hype.

    As far as the unpredictability of the quantum world is concerned, it is still alive and well. In fact entanglement *strengthens* that conclusion instead of weakening it [5].

    [1] Physical Review A 40, 913 (1989)
    http://link.aps.org/doi/10.1103/PhysRevA.40.913
    [2] Journal of Modern Optics 54, 2373 (2007)
    http://www.informaworld.com/smpp/content~db=all~content=a787786271
    http://arxiv.org/abs/0711.2315
    [3] Reviews of Modern Physics 81, 1727–1751 (2009)
    http://rmp.aps.org/abstract/RMP/v81/i4/p1727_1
    http://arxiv.org/abs/0806.0270
    [4] Phys. Rev. A 80, 032112 (2009)
    http://link.aps.org/doi/10.1103/PhysRevA.40.913
    http://arxiv.org/abs/0907.1109
    [5] http://arxiv.org/abs/0911.2504

  3. Dear Eric,

    You might be interested in an unusual mathematical perspective on a possible resolution of the non-locality dilemma—as raised by EPR— that I presented to the workshop on Logical Quantum Structures at Unilog’2013 in Rio. I just updated and uploaded it to my blog:

    http://foundationalperspectives.wordpress.com/

    Bhup

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s