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March 20, 2018

CATEGORY: Blog [back]
TOPIC: Review of "Foundations of Quantum Mechanics: An Exploration of the Physical Meaning of Quantum Theory," by Travis Norsen [refresh]
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Blogger Ian Durham wrote on Jan. 10, 2018 @ 20:45 GMT
I remember being out to dinner once with some folks from the American Physical Society's Division of Quantum Information (at the time it was only a Topical Group) at which we were discussing some of the sessions that we sponsor at the annual March Meeting. In particular, I remember discussing the various foundations-related sessions which are often controversial and frequently include a wide range of viewpoints. At some point, in a rather exasperated response to something someone had said, Matt Leifer remarked "foundations is hard." I don’t remember the exact context or the person to which he was responding, but that statement – foundations is hard – has always stuck with me. It might be better to amend that statement to "foundations is hard to do well" because anyone can do foundations but not everyone can do it well, but hopefully you get the idea.

Part of the problem is that foundational questions are so deeply subtle that merely understanding them (let alone answering them) has eluded the grasp of some of the most famous physicists in history. Now consider attempting to explain these questions to an undergraduate student. It’s a task that Travis Norsen has taken up in his book Foundations of Quantum Mechanics: An Exploration of the Physical Meaning of Quantum Theory (Springer, 2017, $44.99). Norsen is a lecturer in physics at Smith College in Northampton, Massachusetts in the US and is a member of FQXi. He has published numerous papers on the de Broglie-Bohm pilot wave, Bell's theorem, and more. He is one of those physicists who can do foundations research well.

One of the traps of foundations work is an illusion of simplicity. While I am a firm believer in Occam's razor, it is nevertheless too easy to fall into the trap of oversimplifying when it comes to foundations. In that regard, I think Norsen has succeeded in that he has eschewed overly simple explanations in favor of more rigorous but complex ones. That's not to say that I always agree with his assessment or even his pedagogy, but simply that he has chosen to take the approach that foundations is hard to do well and students should, at the very least, understand that point.

That being said, I think Norsen may have slightly overestimated the average undergraduate physics major. While it is true that this book grew out of notes from an advanced undergraduate course that he teaches at Smith, it's hard to deny that Smith is known for having exceptional students with very strong backgrounds. In his description of Bell's formulation of locality, which is referred to repeatedly throughout the book and which is thus of crucial importance to the book's overarching aims, is perhaps a tad overly abstract. One of the subtle things I have only recently started to understand about how the human mind works, is that on average it can only abstract so far. Even some pure mathematicians, for example, find category theory too abstract. But the point at which we lose a lot of people is, oddly enough, in the symbols and their definitions. This was actually noticed nearly eighty years ago by Arthur Eddington who wrote,

"If in a public lecture I use the common abbreviation No. for a number, nobody protests; but if I abbreviate it as N, it will be reported that "at this point the lecturer deviated into higher mathematics"." (A.S. Eddington, The Philosophy of Physical Science, Cambridge University Press, Cambridge, 1939, p. 137.)

The point is not that we should ditch the symbols (obviously). The point is that subtle differences in notation and definition can have an oddly outsized effect on understanding. Here is where I think Norsen's expectations may have been a bit on the high side. While his notation describing the probabilities associated with spacelike-separated events isn't, by itself, necessarily confusing, the explanation of the symbols seemed a bit obtuse and convoluted, as did some of his diagrams. Far too often, I find that physicists trying to explain a complex idea to non-specialists end up sounding like Yoda (from Star Wars). As heretical as this may sound, I think Bell was one of the worst offenders in this regard even though his works are masterpieces.

At any rate, I think Norsen's brief review summary of quantum physics in the next chapter is excellent (though it might pay to define a few terms such as "ansantz" and "gauge" just in case students have not encountered them before). Likewise I found his conceptual description of the measurement problem to be quite good, but things start to get a bit muddy in the formal treatment. Several times he falls into the infamous trap that gets nearly every textbook author at some point when he says things like "it is very easy to see…" I can already see students cursing him under their breaths. While it may not be worth working out the details, as a rule statements of this ilk are best avoided.

Norsen is at his best when dissecting the historical record and summarizing the existing state of some of the challengers to the Copenhagen orthodoxy. In particular, he does an excellent job of setting the record straight about Einstein's actual concerns vis-à-vis the EPR problem. In the broadest of senses, he also does a good job getting across the differences between the various theories he discusses and how each of them deals with the measurement problem, locality problem, and ontology problem (though I would have liked to have seen a discussion of the PBR theorem and I thought his discussion of Schrödinger's Cat missed the crucial difference between superposition states and mixed states). But he struggles a bit to make the more technical discussions approachable.

For any reader who is an avid proponent of spontaneous collapse or many-worlds theories, a word of caution is warranted: Norsen is an unabashed proponent of the de Broglie-Bohm pilot wave theory and sometimes his conclusions seem tailor-made for it. In other words, while he certainly tries to be even-handed in his analysis, one gets the impression that his conclusions are designed to agree with a pilot wave theory. For example, in his chapter on Bell's theorem, he concludes that faster-than-light causal influences really do exist in Nature. While that is certainly one way to interpret the results of experimental tests of Bell's inequalities, it is certainly not the only way. In addition, he fails to mention that such influences (if that's what they really are) nevertheless cannot be used for superluminal signaling in the practical sense of the term.

Despite these concerns, I do think this is a book worth buying for anyone interested in the foundations of quantum mechanics. I also think it would make an excellent supplemental text for a course on the subject. My hesitancy in recommending it as the sole text for such a course is largely due to its clear bias toward the pilot wave theory. But it contains a lot of deep, meaty ideas ripe for classroom discussion. In addition, the chapters include "Projects" (more like lengthy homework problems) to stimulate further discussion.

In summary, while I do think it has its issues (what book doesn't?), I think Foundations of Quantum Mechanics is an excellent addition to the library of physicists and philosophers working on these problems, and makes a very good supplemental text for related advanced undergraduate courses.

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Robert H McEachern wrote on Jan. 15, 2018 @ 19:44 GMT
"Part of the problem is that foundational questions are so deeply subtle that merely understanding them (let alone answering them) has eluded the grasp of some of the most famous physicists in history."

That problem has little to do with subtlety. It has to do with the fact that physicists are highly disinclined to look outside their own field, and thus have failed to realize that many of their foundational questions have fairly well-known answers in other fields.

Rob McEachern

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Jonathan J. Dickau replied on Jan. 19, 2018 @ 16:25 GMT
I agree Rob,

I've seen the same thing. Scientific knowledge is arranged in information silos with walls so high and opaque that you can be very close to the answer you seek, but need to go down to ground level, walk to the next building, take an elevator upstairs, then go down a long corridor - to get to a place but a few meters from where you began - before you can see it.

I recently read that studies in quantum thermodynamics have showed up the appearance of extra degrees of freedom or independent variables, which the author labeled as completely new territory. One would guess that those researchers never heard of Onsager reciprocity, or dealt with nonlinear entropy in the mesoscale regime, so didn't know they were re-inventing the wheel.

All the Best,


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Peter Warwick Morgan wrote on Jan. 26, 2018 @ 19:21 GMT
It's at a graduate student level, or good for a mathematically inclined undergraduate, but perhaps you could also do a review of Klaas Landsman's "Foundations of Quantum Theory: From Classical Concepts to Operator Algebras", Springer, 2017, which is Open Access at that link.

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Steve Dufourny wrote on Feb. 16, 2018 @ 19:18 GMT
Hi all ,

I am happy that for the contest , many thinkers speak about the sphères, the spherical comportments ,I am honored, people focus now about this universal truth, it is cool, I am happy ,good luck to all in this contest


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