Tangled Up in Quantum Mechanics

Obligatory photo of Albert Einstein and Niels Bohr, who argued a lot over the interpretation of quantum mechanics.

If I had to pick one area of quantum mechanics that has the greatest tendency both to bend the mind and to cause mass confusion, that area would be quantum entanglement. Possibly more nonsense has been written and spoken about entanglement than any other concept; even physicists who understand it struggle to explain it to others. That’s not even getting into the challenge of comprehension: it can seem profoundly disturbing, and I would say that if it doesn’t bother you on some level, you haven’t thought about it carefully.

In general terms, entanglement involves the following steps:

  1. A single quantum system is prepared carefully, then split into two. An example of this is two spin-1/2 particles that are combined into a single spin-0 system (as I described in an earlier post). Separating the spin-1/2 particles creates two new systems, on which measurements can be performed.
  2. Because the two new systems were originally one, their properties are not independent: if one particle is “spin-up”, then the other must be “spin-down”. However, there is no way to know which one has which spin without measuring: it’s indeterminate, and as usual in quantum physics, the best we can do is assign probabilities to each possible outcome of a measurement.
  3. If you perform a measurement on one of those systems, then you know what the outcome of the same measurement on the second system must be, no matter how far the systems have become separated.

So here’s the problem: the first measurement does not cause anything to happen with the second system: they cannot be in communication in any way, because the distance between them is arbitrary. In other words, they could be separated by several parsecs without changing the outcome, so if they were actually passing information, that would be in violation of relativity. You can’t send signals faster than light using entanglement as a result: the only way you could kinda-sorta communicate is if you had two groups of researchers who agreed in advance on what the settings of their instruments would be before they parted company; no new information would be available, since the real communication takes place at light-speed or slower, before the measurements are even performed.

Something else must be going on, then: either things truly are indeterminate and non-local (meaning the quantum system doesn’t depend on where the measurements are performed), or there is a “hidden variable” (which may involve a random fluctuation) connecting the two far-flung systems that determines what the outcome of each measurement must be, or yet another idea that I may not know about. The first general explanation is from the standard “Copenhagen” interpretation of quantum theory: it says not to worry about things being non-local, as long as no information is being transferred. The Copenhagen interpretation declares: there is no independent reality beyond our measurements, so all we need is the probability of a particular outcome. Other explanations are plagued by difficulties: they involve interpretation only, and so are not subject to experimental tests, or they are difficult to distinguish from the Copenhagen interpretation, or they predict things that just ain’t so.

Historical Digression

The first paper to try to grapple with quantum entanglement came from Albert Einstein, Boris Podolsky, and Nathan Rosen, so it is known as the EPR paper. (Although the “Schrödinger’s cat” thought experiment is better known, it deals primarily with a separate problem with the interpretation of quantum mechanics—the interaction between a microscopic system dictated by quantum processes and a macroscopic cat—so I think it’s not very useful for understanding entanglement itself.) The EPR paper, published in 1935, is titled “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?”; whenever a headline asks a “yes or no” question, the authors are expecting the answer is “no”, and this paper is no different. Einstein and his coauthors conclude that the standard interpretation of quantum mechanics must be wrong.

Though I just spent the last 20 minutes rereading it, I’m not going to explain the original EPR paper in detail, since the experiment they propose is eminently impractical, not to mention kind of messy to discuss. I don’t think anyone has ever proposed carrying it out, so pretty much every discussion of entanglement following EPR is based on later papers by David Bohm and Yakir Aharonov (the same dudes as the Aharanov-Bohm effect) and especially John S. Bell. My explanation above is an oversimplified version of this thought experiment. While no one has carried out the literal experiment described in the Bohm-Aharonov or Bell papers either, the basic concept is adaptable to a variety of experiments involving photons that have been performed.

An Actual Entanglement Experiment

Inverse Thunderdome: one photon goes in, two come out. The two top pictures are a schematic of a laser shining on a crystal, which then emits two. The bottom two pictures are a schematic of the internal quantum transition of an electron within the crystal. The two new photons have correlated polarizations: they are entangled.

The experiment I’m describing here is a simplified version of the eight-photon entanglement experiment I covered for Ars Technica. A laser is trained on a special crystal, which reacts in a particular way: the absorption of a photon leads to the emission of two new photons. One property of light is its polarization—the way a photon’s electric field is oriented—which is also the carrier of its spin, which is a fundamental quantity that must be conserved in interactions. In other word, the total spin going in must be the same as the spin going out, so the two new photons must have correlated polarization orientations. However, the specific polarization of either one of those photons is indeterminate (whether you think that’s from fundamental reasons, as in the Copenhagen interpretation, or from one of the alternate explanations).

Schematic of the entanglement experiment.

The new photons are sent along different paths, which can be very long, just so they aren’t tampered with en route. At the end of each path, the photons meet up with some kind of filter that measures their polarization with respect to the filter orientation. Polarization can be any angle as long as it’s perpendicular to the path the photon follows, so experimenters have a lot of freedom in the filter choice. John Bell proposed changing the filter orientations while the photons are actually in transit, to rule out dynamic changes in photon properties (as well as preclude any goofy ideas about photon communication or telepathy).

A variety of experiments, starting with Alain Aspect and his team in the early 1980s, have demonstrated that the photons’ polarizations are correlated even though they cannot be directly interacting at the time of measurement. Later experiments have entangled more than two photons, but the principle is still the same: that the photons were originally part of a single system means that the results of measurements on one are not independent of measurements on the others. Interpretation is always tricky, and I don’t really want to get into that now—not because it isn’t interesting, but because I’d rather keep things short(ish).

What Entanglement Is Not

Note that in everything above, whether it was the impractical EPR proposal or the real experiments, the key was preparing a system before any experiment is done. The amount of interaction is highly restricted, to prevent interference from other parts of the apparatus (or random particles coming in and introducing different interactions). Keep that in mind as you read this passage from physicist/rockstar Brian Cox:

I recently gave a lecture, screened on the BBC, about quantum theory, in which I pointed out that “everything is connected to everything else”. This is literally true if quantum theory as currently understood is not augmented by new physics. This means that the subatomic constituents of your body are constantly shifting, albeit absolutely imperceptibly, in response to events happening an arbitrarily large distance away; for the sake of argument, let’s say on the other side of the Universe.

In other words, Cox seems to argue that every particle is entangled with every other, across the entire cosmos. Besides the problems with relativity and its ban on faster-than-light interactions (which are very well established!), his idea of what a system comprises is too broad. (Tom Swanson has more on this.) Just as entanglement doesn’t allow instantaneous communication, it doesn’t follow that entanglement from every electron in the universe is responsible for the results of energy levels within an atom. Quantum interactions don’t work that way, and we have strong evidence in support of that.

(As an aside, Scott Adams in a Dilbert cartoon many years ago said you could use entanglement to communicate faster than light. If I recall correctly, he evoked a conspiracy theory to explain why nobody has actually done that. I nearly wrote him a letter about that, since he screwed up the physics so royally, but I never did. Scott Adams, if you’re reading this: you messed up, dude. Just letting you know. Brian Cox, if you’re reading this: please don’t be a Dilbert.)

I agree that entanglement is a difficult subject, and one that stretches our brains like no other in quantum physics. Any alternative interpretation of quantum theory has to grapple with it, and many comforting resolutions to the paradox turn out simply not to be viable. As I write this, I am sincerely hoping I explained the subject well, and if I haven’t, I hope I am mature enough to accept correction and requests for clarification.


6 responses to “Tangled Up in Quantum Mechanics”

  1. You summarized EPR nicely. I have thought and written quite a bit about this and firmly believe that a local hidden variable theory must exist to resolve this conundrum about the foundations of QM. My view is that entanglement is a property of quantum mechanics but not of Nature. Also I believe that qm, as you say, is a theory of measurement, but I believe that their are states that cannot be measured, and these, when average over their local hidden variables, will give the measured results (Aspects or Weihs’ data).

    I also do not believe the interpretation of Bell’s theorem (you did not say much about that). I believe that Bell’s spin assumption is incorrect and the locality assumption is ok.

    Here is a link to my blogs if you are interested.


  2. […] so researchers figured out how to make one set of phonons control another set, which may lead to entangling phonons with each […]

  3. […] start with an idea I still wrestle with, and which has no 100% satisfactory explanation for me: quantum entanglement. In brief, entanglement involves a single system (usually two photons with opposite, but unknown, […]

  4. …”If you perform a measurement on one of those systems, then you know what the outcome of the same measurement on the second system must be, no matter how far the systems have become separated.”

    So how is this any different than a classical system? If I have a volume of water, split it, by definition, in half, send the two halves away in different directions and then intercept them only to discover that when you measure one to be 500 mils, that the other will be 500 mils.

    1. It’s not quite an analogous situation, though, because you’re performing the same type of measurement on the two volumes of water. Entanglement shows up when you’re taking measurements of complementary quantities: two different polarization orientations, for example. The original EPR paper used measuring momentum and position; nobody’s figured out how to do that in practice, but the concept is the same.

      A better classical example might be a collision between two billiard balls. The total momentum and spin of the system are conserved (in the ideal case, of course), so in principle you could know what the momentum and spin of the second ball are by measuring those quantities for the first ball. However, there’s nothing preventing you (again in principle) from measuring all the relevant physical properties of one ball, whereas in quantum physics you’re restricted in the kinds of simultaneous measurements you can make on a single isolated system. That’s why the example in the post above isn’t quite the same thing as the billiard ball case, even though polarization is similar to the ball’s spin.

      Does that make sense?

      1. Granted my analogy was wide of the mark, so let’s use your analogy: “So how is this any different than a classical system?”

        My point being that I’ve never read a description of entanglement that was not “explained” by a hidden variable. I’m pretty sure I’m missing something. I’ve just not been able to understand what I’m missing.

        Love you columns, -john-

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