Terry Rudolph is a seemingly young professor at Imperial College already world-renowned as the third author of the so-called PBR theorem (I’m so envious he’s got a theorem named after himself…). His result allegedly shakes the foundations of Quantum Mechanics by stating that either quantum states are “real” (whatever that means) or else the theory is “wrong” (whatever that means!). I look forward to reading more about all this stuff, with the mindset of a person convinced that physics is ultimately about measurement and information, and that Quantum Mechanics is the “symbolism of atomic measurements” – a much beloved sentence due to Schwinger.
But for the moment, I’ll focus on his book “Q is for Quantum”, which is a piece of art, though not perfect (fortunately, or I’d already be hanging from a beam). Rudolph also runs a webpage with updates, and I’m not the first to review this book.
The first great merit of this book is that it is self-produced with very good taste for layout. As such its contents are free and direct (e.g. it does not include a biography of the author, and the self-comments on the back cover are quite witty*). I already bought two copies and you should as well. Its second greatest virtue is… brevity. The book is extremely concise, it goes straight to the point. Its purpose is to show how some of the most intriguing aspects of Quantum Mechanics can be understood (or, better, explored and manipulated) with very little machinery, and in particular without linear algebra (up to a mysterious minus sign to create interference, whose mystery is never really resolved… but you can buy that – and interestingly, it turns out that Quantum Computation done that way is universal, so there’s nothing to loose in principle). It does so presenting the material in a logically rigorous fashion, without getting lost in the usual blend of metaphors and anecdotes that “embellish”, so to say, the usual pop science literature, and without losing time to give credits to this or that scientist or explaining useless technical jargon (as is the case with the very deep, but quite pedantic Un’occhiata alle carte di Dio [A glimpse at God’s cards] by Gian Carlo Ghirardi). A dictionary to make connections to modern literature is served to the specialist at the very end. The style of writing is quite entertaining, the kind of nerdy fun for XKCD lovers. The exposition does not spare the reader some combinatoric games and a lot of thinking, both of which might make the book much more challenging for readers who do not have a proper training than the author seems to believe (let’s see, I’m running this experiment with a friend of mine…). In principle all of the calculations can be tackled with pencil, paper and patience provided readers stick by the rules of the game – as far as the rules of the game are well explained before the game starts (I’m always disappointed when friends invite me to play a new table game they are expert on, and only at the end a new rule comes out I didn’t know about, one that makes them win by loads – incidentally this is also what happens in most of Nolan’s movies, but now I’m going way astray…).
The book includes three chapters: the first showing how and why quantum computation is more powerful than classical computation, the second explaining entanglement, and the third the problems of interpretation of Quantum Mechanics and of the measurement process, including hidden variables and such amenities. It’s really amusing to see how the latest achievement – quantum computation – can actually be used to introduce quantum mechanics in a less contrived way, assuming that classical computation already makes some sort of sense to the reader (while the author does spend some time explaining classical gates, he gives for granted that people are ready to accept the very idea that logical operations can be processed mechanically and with binary symbols). The formalism also allows to introduce a version of Bell inequalities, and to present with incredible clarity the “no faster than light communication” argument. Also, the author manages to scoop in some of his own insights on the matter, in particular some elements of the PBS theorem mentioned above and of the Author’s own take on the interpretation of Quantum Mechanics. Which means that a smart teenager reading and understanding this book will peer at the frontline of research today – an incredible achievement, although this will not spare him years and years of university etc.
– – – Good cop exits the scene. Bad cop enters the scene – – –
The one chapter that falls a bit short with respect to its pretentious claims is the third, on “reality”. The subject matter is, of course, monstrous. In fact, we are begged to drop all philosophical subtleties at the start. Never so!
The logical development of this chapter is still clear, but the narrative is not quite to-the-point as the previous two. Several phrases are redundant, and because I had the feeling of walking on eggshells and always expected a new load of concepts at very sentence, repetition of previous concepts did not actually help: I tended to assume the next sentence would always add something I had not thought about before, and therefore I put an intensity that maybe was not even necessary. Or, maybe, it was necessary! Which means I didn’t get the point… In any case, while a second reading might help, and I did get a faint idea of the Pooh-Bear argument, for that I might prefer to go to the original article, which has already been piled up with tons of other papers-soon-to-be-read (ahem…).
Also, unfortunately, Rudolph falls in Nolan’s usual mistake: he defines a new rule towards the end of the story. What is “real” is only defined on p. 122, and not in a very satisfactory way: “By hypothesis, what we mean by the real state is anything and everything that can affect the outcome of an experiment”. What does that mean?
This leads us to the more conceptual core of the problem, and here I’d like to weight in my own misconceptions about physics. So from now own I’m going to ramble, please stop reading.
The point is, well before the Pooh argument, I’m already a bit in disagreement. If I understood well, we are asked to assume that it makes sense to define “reality” as a set of variables whose detailed knowledge would underlie any probabilistic concept, and this independently of whether the inferential machinery governing the states of knowledge of the observer are going to be classical or quantum. The Pooh-bear argument is then laid down to show that the wave function can be thought of as such a “real” state, dispensing with an argument by Einstein why it couldn’t.
I’m one of those freaks who don’t believe that, even in classical statistical mechanics, probability as a state of knowledge is actually supported by a “truth of matter” of what the real states of a system are according to their volume in phase space (as I argued at length in this paper). The volume measured by whom? e.g., what is the “real” entropy of a body? I don’t think this question even makes sense. What only makes sense is that the underlying degrees of freedom will also be subjected to a process of measurement, their probability analyzed, then perfectioned by Bayesian update, and so on and so forth. For example, the fact that today we take, for ideal gases, the position and momenta of the particles of the gas to be “equiprobable a priori” (up to lots and lots of corrections) is not due to any “reality” or fundamental nature of position and momenta of the gas molecules, it’s just that we have been running a lot of science before getting to that conclusion, updating previous hypothesis until we found the one that works reasonably well. If, instead, say gravitational interaction had been much stronger, and one couldn’t neglect the effect of General Relativity in the determination of the equation of state of a perfect gas, we would have given to the “microcanonical ensemble” a quite different meaning, with a complete distortion of the “real” state space. Exactly the history of QM (and in particular Quantum Field Theory) reveals that obsession with the “real” values of physical properties ends up in nothing. In fact, the more “fine-grained” states that Rudolph draws on his planes of reality would have exactly the same quantum nature as the more “coarse grained” states the macroscopic observer measures, and there would have to be a microscopic observer, but an observer nonetheless, that makes quantum measurements, and eventually there will be a proper way to compare the observations of the one and of the other observer. To me, what is really relevant is that measurements turn out to be consistent. This is actually (at present) my general philosophy of science: a reasonably self-consistent body of knowledge whose credibility does not come from the fact that it compares to “reality”, but from the fact that the scientific community has established practices which allowed it to acquire authoritativeness in certain fields of knowledge. The demarcation of these fields where the scientific method works was determined in a somewhat evolutionary manner, therefore when people say “science works”, for me this is more of a definition then of a property…
OK, as usual I became all-too-serious. To go back to the book, personally I would not have created a separation between misty states and rocky states, I would have always put things in the mist, even after being measured (then, measurement becomes just another logical gate). This gives great unity, and operationally it does not make any difference, as far as one sees QM as an inferential machine that manipulates symbols.
* The last authors I’ve seen writing their own notes were Luther Blisset, funnily also the authors of “Q”. But a completely different book.