The summer vacation in US without enrolling in any class has come to an end. I got the visa 17 days before traveling to UK. The class registration will begin a week or so after I already move into the dorm there. Let’s hope that mechanics, math methods 1&2, and quantum information don’t clash.

At first I intended to write the previous post “My Blogging Statement and Quantum Foundations” in English, but what I had in my mind at that time is already the thing of the past. So this’s more like an updated and shorter version of that blog.

Firstly, I try to make this blog useful, unlike a newspaper that usually has a lifespan of one day. There may be a correction in some old post from time to time if it doesn’t warrant a whole separated post. Also I think it’s a better idea to browse the posts by category since only the excerpts will be shown, and it looks cleaner that way. On a side note, I don’t want my varying blogging frequency to bother you. Now I’ve plenty of time so I blog often, but I was afraid that it’d wear out and drive away the reader. On the contrary, once the school begins, this place may be deserted for a while.

**Quantum Foundations**

Even though I deleted the series of posts “What is a Thing?,” after arriving at the conclusion that I shouldn’t try to be philosophical and imprecise at the same time, I knew from the beginning that trying to gather information about QF to write will teach me something. Indeed, a little venture into quantum foundations taught me to distinguish between foundations and interpretations. I found a blog that’s like an introduction to QF, which I never thought existed. Matthew Leifer has, in his blog, insightful posts and comments drew from personal experience, yet I think his coverage is diverse enough to be informative, actually very informative. (Too bad the blog’s been on hiatus since the beginning of 2008.)

To let us get some ideas about QF, I want to point out to this post “What is the point of Quantum Foundations?” especially point 2 and 3 that he made.

2. The goal of QF is not to contradict QM within its domain of applicability, but it should suggest possible alterntive approaches in cases where we are currently uncertain how to go about applying quantum theory. The archetypal example of this is quantum gravity, although to be fair it is more common to hear foundations people give this response than to find them actually working on it. Notable exceptions are the work of Gell-Man, Hartle, Isham and collaborators, which draws on the Consistent Histories formalism, and the recent work of Lucien Hardy.

3. The goal of QF is not to contradict QM at all, but it should suggest a variety of different ways to conceptualize the subject, suggesting new possible experiments and theory that would have been difficult to imagine without considerable insight from QF. The main example we have of this is the field of quantum information. David Deutsch arrived at quantum computing by thinking about the many-worlds interpretation and Schumacher compression bears some similarity to the frequentist justifications of the quantum probability rule that began in Everett’s thesis. More recently, the Bayesian viewpoint of Caves, Fuchs, Schack, et. al. leads to new ways of doing quantum tomography and new variants of the quantum de-Finetti theorem, which have applications in quantum cryptography.

This’s pretty much the truncated list of what I want to see. For 2, I want to know more how de Broglie-Bohm formulation^{1} tackles things such as the prediction of tunneling time and nonequilibrium phenomena (from this set of lectures which I haven’t gone through). Works like that of John Bell (Bell’s inequality) or more recently Leggett’s inequality are works in foundations, not just interpretations. GHZ paradox in one of my post is one of them too. I hope I can try to clarify in this blog more its relation to the mind-boggling local realism argument, which, for someone, is the first instance of *experimental* philosophy.

I wish to see a book that treats QF without muddling it too much with interpretations. At least Robert Spekkens^{2}is writing one. I’ve read a bit of Einstein, Bohr and the Quantum Dilemma, which’s up-to-date and comprehensive account of QF (or QF in disguised, quantum information (QI)). The big plus for some readers here is that it’s for lay audiences, which’s also a downside for some others since it refuses to use mathematical formula and thus makes it harder to really understand. Nevertheless, it clarifies some of my doubt from QM class such as when exactly to interpret a quantum state as classical ignorance. (It turns out that this has been problematic even until now.)

**Choices**

Physicists are conservative, like the well known story of a drunk man looking for his key under the lamppost even though the key can be anywhere in the dark, because lamppost is the only place with light. (Why a drunk man anyway? I hope it’s just a little detail.) What is energy? We say that it’s something that’s globally conserved, unchanging. If we analyze every form of energy that we know and find that they’re not conserved in some situation, we don’t throw away the principle of conservation of energy; we set out to find unknown form of energy so that we add it in and “the energy” is conserved again.

To do something more with QM, we can take the unitary evolution (and QM) seriously. That view first gives us many-worlds interpretation, but now it yields a much more practical tool, decoherence. A very short and crude description of the consequence of decoherence is that coherent superposition is everywhere so it’s nowhere since we can only use local operators to observe the object of interest. Being practical, decoherence is also important in interpretations of QM. The interesting thing’s that how decoherence solves conceptual questions in QF depends crucially on the interpretation one adopts.

Or take that the wave function is not a “complete” description of an individual system i.e. taking probability seriously. Probability itself can be approached in various ways too. The easiest approach to teach probability is the frequentist one, which I think at least Peres’ and Ballentine’s books support (although Ballentine’s “ensemble” is not supposed to be Gibbsian ensemble in classical statistical theory where there’s a definite probability distribution of, say, positions and momenta. I’m not too sure about this though^{3}. And to emphasize, I don’t know exactly what Peres and Ballentine have in minds.) The other are mathematical probability theory approach e.g. by Lucien Hardy, and Bayesian inference approach by Christopher Fuchs. A nice introduction to this kind of non-frequentist approach is a paper by Appleby. Nevertheless, the prediction of QM ought to be the same whether there is one or more conscious observers weighing their belief or not.

Or we don’t have to take QM seriously at all as *the *mechanics. See, for example, Leggett’s idea.

Under Occam’s razor, I certainly want our interpretation to be minimal. However, advocates of each interpretation claim their interpretations to be minimal anyway. Even if you’re a purely empiricist, if you don’t want to be agnostic, you’ve to scrutinize your claim too. Nevertheless, I believe that studying the historical and personal aspect of the development of QM is always instructive. This belief, however, may not be true if I get stuck to some ideas. If you’re critical about it, it may well be even the razor itself.

** **

Books to kill time, if you have some to kill:

The Ghost in the Atom: A Discussion of the Mysteries of Quantum Physics

Quantum Physics: A First Encounter: Interference, Entanglement, and Reality

Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference** **

Lectures on Quantum Theory: Mathematical and Structural Foundations

Linear Operators for Quantum Mechanics

I’m too impatient to read any pop-sci book but I can read these, so that may tell you something. By the way, the last two are certainly not pop-sci books.

** **

1. I think it’s a formulation, not just interpretation. cf. Styer et al.’s“Nine Formulations of Quantum Mechanics”

2. His talk in the seminar “reconstructing quantum theory” is also interesting.

3. D. Home, M. A. B. Whitaker: Ensemble Interpretations of Quantum Mechanics. Phys. Rep.210(4), 223–317 (1992).

I remember that I found the paper on D. Home’s webpage but I can’t find his webpage now.

Thanks for your interest in my blog. It is always good to find other people interested in quantum foundations on the web. My only critical comment is that I wouldn’t call frequentism “safe” in any sense. Instead, I’d be inclined to call it just plain wrong. OK, so I’m a Bayesian, and a radically subjectivist one at that, but I think there is a fair consensus amongst people who work on the foundations of probability that frequentism just does not work on its own. The most popular option in the philosophy community seems to be the propensity viewpoint, which can be combined with either Bayesianism or frequentism.

Anyway, you may be interested in the list of resources on quantum foundations that I try to maintain on my site. If you come across anything that should be added to it then please let me know.

Thank you very much for your comment. I didn’t expect that at all. I’m just a learning undergrad and obviously have only little knowledge.

About frequentism, I’ll correct my post about it being not safe. It’s really a wrong word choice since what I had in mind while I was writing is that, it’s likely to be ‘the’ approach taught in an introductory QM class without much thinking. I don’t know exactly the reason that it can be wrong but I think it’s not mathematically meaningful, or even that useful in practice. (I haven’t read all the papers that I link to :))