Monday, September 4, 2017

Speakable and Unspeakable in Quantum Mechanics by J.S. Bell

John S Bell is well known because of his development of what is known as Bell’s theorem – a proof showing that quantum entanglement means that local causality does not exist. This book, Speakable and Unspeakable in Quantum Mechanics, is a collection of 24 technical and semi-technical papers written by Bell on that topic. Bell’s outlook is partially physical and partially philosophical, making these papers quite interesting reading. At this point I would say it’s incredibly well-written and accessible, but I remember trying to read this as an undergraduate in the 90’s (when there were only 22 papers; I picked this one up because I lost the old one in a postdoc-postdoc transition) and having quite a lot of trouble with it.   Many of the papers seem to be addressed to philosophers, whereas others are standard physics papers. But most of them lay in the no man’s land between theoretical physics and the philosophy of science.

Many of Bell’s concerns run throughout the book, with slight variations from paper to paper. One of them is the incoherence of quantum mechanics:

So long as wave packet reduction is an essential component [of quantum mechanics], so long as we don’t know exactly how and when it takes over for the Schrödinger equation, we do not have an exact and unambiguous formulation of our most fundamental theory.
And that cannot stand. In order to have a reasonably scientific quantum theory, you should be able to express exactly when the wavefunction collapses. This is for several reasons, but what Bell really wants to know is this: if I measure the magnetic moment of an electron in a magnetic field, when does the electron decide which Sz state it is in (up or down)? Here are some options, which aren’t all of them:

  • Does it do so when I turn on the static magnetic field?
  • Does it do so when the microwave detection field reaches it?
  • Does it do so when the response is felt by the field?
  • Does it do so when the inductive current is generated in the pick-up coil?
  • Does it do so when the microwave current passes through the diode detector?
  • Does it do so when the detector is read by the multimeter?
  • Does it do so after the multimeter output is analyzed by the computer?
  • Does it do so when the analysis is displayed on the screen?
  • Does it do so when the graduate student save the data?
  • Does it do so when the Ph.D. looks at the charts?
  • Does it do so when the paper is submitted or accepted?
  • Does it do so when the paper is printed or earns an award? 
The Ph.D. gag was Bell’s favorite sarcastic line in these papers (judging by the number of re-uses), which were drawn from publications like Reviews of Modern Physics, Foundations of Physics, and so on, as well as invited lectures and symposia and book chapters. The important thing is that “measurement,” resulting in the collapse of the wavefunction, is an essential part of quantum theory, but it is not well defined theoretically. In Bell’s words:
The Landau-Lifshitz formulation…when applied with good taste and discretion is adequate for all practical purposes,” but it is “still ambiguous in principle about exactly when and exactly how the collapse occurs…”
 This is the same problem that led Schrödinger to torture analogical cats late at night in obscure journals.* Furthermore, Bell feels that “highly idealized ‘measurements’ should be replaced by an interaction of continuous, if variable, character.” This is essentially the thing that Aharonov explores in the book that started PhysicsFM off, Quantum Paradoxes.

Bell returns again and again to the Einstein-Poldosky-Rosen paradox (EPR, in case I use it again), its reformulation by Bohm into a more physical experiment, and finally, the Aspect Experiment which was the first practical test of the EPR paradox (the introduction to the new edition was written by Alain Aspect himself). The Aspect Experiment really turned Bell’s Theorem into an experiment, but Bell’s theorem was one that elucidated the true importance of what had been an almost forgotten result by Bohm – for the practical reason that no one could figure out how to do the experiment with 1950’s technology. The experiment took entangled photons (rather than electrons in Bohm’s experiment) and looked at their correlations. If you are looking at just up vs. down, clockwise vs. counterclockwise, and so on, then the correlations are fairly simple and come directly from conservation laws. However, when you tilt the detectors with respect to each other, the classical and quantum predictions diverge in such a way that an inspired and talented experimental physicist can tickle out the subtle differences. And when he did that experiment, Alain Aspect fount that quantum mechanics won and Bell’s theorem implied that local causality** was lost.

And at that point, “the concept of ‘reality’ [became] an embarrassing one for many physicists,” according to Bell.

Much of the book also discusses the interpretation of quantum mechanics. Bell looks at interpretations differently than most. In “Six Possible Worlds of Quantum Mechanics,” Bell categorizes theories into a 3 x 2 matrix. Bell’s three main categories are a no-nonsense measurement-based approach that doesn’t attempt to understand what is happening between measurements, that the wavefunction collapse is a real thing that happens to the quantum system and changes it, and that there are two or more subsystems in any quantum system that account for wave-particle duality (hidden variables). The “x2” breaks three interpretation into unromantic and romantic pairs. The romantic dual makes the interpretation interesting without adding any true meaning.

Thus, you have this practical approach being paired with the Bohrian Copenhagen interpretation where the universe holds complimentary views, macroscopic and microscopic, simultaneously. The collapse interpretation is paired with a Wignerian dualistic interpretation where it is the act of intelligent observation that collapses the wave function. The de Broglie-Bohm hidden variable interpretation is paired with Everett’s multiversal interpretation where each possible way in which something can happen does happen – just in another universe.

This is a very different view of Everett. Specifically, Bell’s interpretation of the many-worlds interpretation is to say that the many-worlds part is inessential. It is comforting, he says, to cosmologists (because it allows them to ignore the collapse of the universal wavefunction), but the additional “worlds” don’t add any new physics or understanding of what is happening. So, he says, if you strip the romantic multiverse from Everett, you have a (possibly different) nonlinear hidden variable theory than conjured by Bohm. I’ve never seen anyone else say that. To everyone else the many-worlds of the many-worlds interpretation are the point.

The most annoying gripe Bell makes is to continually harp on his theory of “Be-ables,” which would be a subset of quantum mechanical observables with certain properties that make things less weird. I don’t think it helps so much as he thinks, and it certainly wasn’t clear what the different was, other than terminology, the in the first half-dozen papers he mentioned them in.

In sum, I very much like this book. It is wonderfully written, physically insightful, and historically important. Many of the points, especially those from lectures, are very much Bell’s own thoughts and just his own thoughts that no one else thinks (beables), but even there he is trying to make points about the unsuitability of quantum theory without refinements that tell us what several of these mathematical objects that we use refer to in the physical world.

* Well, not really obscure. But still.
** “Local causality” might seem to be a strange combination of words, but it is what we normally think of as causality. First, if P causes Q, then P occurs before Q. Second, if P causes Q, it should be close enough to affect Q by special relativity. That is P is close enough to Q that light can travel from P to Q. It really is what you’d think about as causality in relativity theory.

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