John Polkinghorne’s Quantum Theory – a Very Short Introduction is a decent enough introduction to quantum theory, but might have been even better if 30% shorter.
The first two chapters are a pretty good introduction to the historical motivation and some basic features of the theory. But the third chapter is more problematic – perhaps in part because it is discussing philosophy rather than physics, and in philosophical discussions it is easier to misinterpret and/or misrepresent the opinions of others.
On pp42-43 Polkinghorne alludes to an “error” that some claim to have discovered in the work of John von Neumann, but many others read vN as not having ever actually made the claim that is found to be wrong.
On page 45 he makes the incorrect assertion that “the electron’s magnet can only point in two opposing directions”, when in fact the magnetic moment of the electron can be measured (and found to be nonzero) along any axis we like. What is true is that for whatever direction we choose to measure, there can only be two possible observed values, which will be seen with probabilities depending on how the electron was prepared (eg on what previous measurement it has been subjected to); and this more correct statement is actually sufficient to motivate the subsequent discussion of “collapse”, so perhaps that error can be overlooked.
I don’t think Polkinghorne says anything particularly wrong or unfair about most of the approaches to the measurement/collapse issue, but as an advocate of the ‘Irrelevance/RelativeState’ school/sub-school I find it odd that he considers “seems very odd” to be a serious objection to an interpretation of Quantum Theory. Surely we all agree that, compared to our natural intuition, quantum theory is indeed “very odd”. Also I think he misses the point that the predictions of any human theory of physics are about what a human observer will see, so we should not be surprised that it’s also true of quantum theory; and the relative state approach does not actually depend on consciousness per se, as it can be applied more generally for states of one part of the universe relative to another regardless of whether or not the “observing” part corresponds to a conscious entity. And to call what is perhaps the most widespread approach among physicists “abhorrent to the mind of the scientist” is a bit presumptuous – as is the misuse of “treason of the clerks” to refer to an attitude of philosophical restraint when the term was originally used with regard more to the opposite.
When he gets back to proper physics in Chapter 4, I think the content is a pretty good summary of what is going on, but I start to have issues again in Chapter 5.
In particular the claim on p.79 that “the majority view leads to the conclusion that measurement on 1 produces an instantaneous change at 2” is, I think, false. Although the Bertelmann’s socks analogy does not in fact resolve the more sophisticated conundrums related to Bell’s inequality, it does show how the existence of a correlation does not necessarily imply any transmission of effect. And the spurious “produces an instantaneous change” language is especially odd since Polkinghorne does end the chapter pretty well clarifying that no FTL information transfer is enabled by quantum correlations.
Finally, while I don’t really find anything to object to in the more philosophical Chapter 6, neither do I see it as adding anything useful to our understanding of the physics.