I would like to start bringing to the attention of my (almost inexistant) readership some articles/preprints which I have particularly liked. The objective is to put forward works that may have been overlooked or that are original in some way. As I have never done such a thing in the past, I have a huge backlog of articles to consider and thus no lack of inspiration. To keep this post decently short, I chose to start with only 3 papers but in wildly different fields: stochastic thermodynamics, philosophy of physics and quantum optics.
This articles introduces Hidden Markov Models (HMM), a framework that is well known to probabilists but usually ignored by physicists and that, to my mind, is extremely useful to understand stochastic thermodynamics and especially information powered engines (Maxwell demons). A HMM is simply a model in which there is a fundamental yet unknown Markov process randomly jumping from one site to another of a discrete finite graph. It is “hidden” in the sense that we only have a partial information on the process. One is typically given a series of imperfect observations and the whole game is to reconstruct the “best” estimate of the process position at some time (a priori or a posteriori) given these partial bits of information. The important thing in this framework is that there can be two sources of randomness: the fact that the fundamental process is intrinsically random and the fact that its state is not even perfectly well known (some heat related randomness and some “informational randomness). John Bechhoefer explains very clearly why this is the correct framework for stochastic thermodynamics and how to compute the basic quantities one is naturally interested in in this context. It is a good pedagogical article (requiring basically only undergraduate notions) that gives a clear conceptual underpinning to methods that are routinely used in stochastic thermodynamics. In my opinion, extending this formalism is the key to construct a meaningful theory of quantum stochastic thermodynamics.
Are fields really necessary as fundamental objects in physics or are they just useful computational tools? In this very nicely written article, my friend Dustin explains in a crystal clear way why it is entirely possible (and in his mind preferable) to abandon fields and keep only particles. The core idea, if I may caricature it this way, is that fields appear when one tries to rewrite globally defined dynamics as Cauchy problems, i.e. as problems with a solution that can be propagated forward in time. What Dustin shows is that fields can be seen as no more than book-keeping tools. As a result, they are sometimes helpful but can also yield problems, such as divergences, the latter being pure artifacts of their introduction. To illustrate his point, he considers the (unfortunately) not so well known Wheeler-Feynman formulation of classical electrodynamics which provides a global formulation of electrodynamics without electromagnetic field (incidentally, the article gives an excellent ressource to learn the basics of the W-F approach).
All in all, I think Dustin makes the best case there is for a minimalist ontology of particles (at least for classical physics). Of course, as I have recently been working on approaches based primarily on fields, either for QFT or semi-classical gravity, I think a case can be made for fields as well (especially when fields obey non-linear equations, as is the case for gravity, it is harder to remove them from the picture with Green functions). But in the end I think the strongest point to know is that in many cases one can in principle understand everything without fields. Whether one ought to do so is perhaps slightly more open and provisionally a matter of taste.
As an aside, I think Dustin could have submitted a shorter version of this article to the latest FQXi essay contest, which deals with the tension between dynamical laws and teleological pictures (that is, pictures of physics in terms of final purposes). Although it is a bit of a stretch, one could defend the case (if only for the thought experiment) that the laws of Nature are ultimately always teleological (in a weak sense, that is written as global optimization problems on all space-time, I am not being religious), and that it is only the practical need to propagate some past knowledge about the state of things forward that forces upon us the use of dynamical representations and fields (and this is where one could use Dustin’s point). This is of course the kind of speculation I would find annoying in a regular scientific article, but it would seem suited for an essay (too bad the deadline was a month ago).
3 — Quantum trajectories for propagating Fock states
by Ben Q. Baragiola and Joshua Combes (2017) arXiv:1704:00101
This preprint has been posted very recently and thus my understanding of it is only a bit superficial but I think it could have important practical applications in quantum optics. Instead of the usual Markovian bosonic bath almost always considered in open quantum system theory, the authors consider a setup in which a quantum system of interest interacts with a propagating Fock state.
The entangled Fock state is then measured (with photodetection or homo/hetero-dyne detection). This gives a quantum trajectory for the quantum system of interest that can be computed explicitly. Although the machinery used is essentially that of “standard” continuous measurement theory, the result is a genuinely non-Markovian (and physically relevant) evolution that was not known before. The article is also nice in that everything is done explicitly with a solid introduction of the required formalism.
A tiny warning perhaps, the examples shown are a bit too simple to understand what can happen in the most general setting with the full-fledged theory (or at least this is my understanding so far, I would gladly be corrected). The fact that the total number of clics of the detector is equal to the number of photons in the incident Fock state comes from the interaction considered in the example (which is admittedly physically relevant). In the general case, the system can typically release an arbitrarily high number of photons into the field and solving the stochastic master equation requires, in principle, some truncation of the total Hilbert space.