A Quick List of My Intellectual Future

I’m working on a giant post about the 2nd Annual Phenomenological Approaches to Physics Conference I attended a few months ago. My mid-life crisis has taken the form of a desire to get my head entirely around the issues related to the interpretation of quantum mechanics. I believe I am, after two years, getting the shape of the problem more or less together, in my head. Here is a rough map of the territory I want to focus on in the next few years.

  • General Relativity – the problem with quantum mechanics might just as easily be formulated as a problem with General relativity, since it is this theory which predisposes physicists to prize locality. The issue is typically developed in the context of special relativity, because wave function collapse seems incompatible with the fact that space-like separated events have no state of affairs with respect to temporal order (as I have come to see it). But General Relativity is also famously incompatible with Quantum Field Theory as we currently do it. This seems to be a minority position among philosophers, but its hard not to wonder whether the issues with the interpretations of quantum mechanics are entangled with the physical question of how to formulate a theory of quantum gravity.I’ve been doing Alex Flournoy’s Course from Colorado School of Mines using Carroll’s Spacetime and Geometry.
  • Probability – Regular probabilities enter in the interpretation of quantum mechanics in a surprisingly straightforward way, even if you can’t decide on what exactly is going on during a quantum measurement. The troubling issue with quantum mechanics is the way that measurements on ensembles of systems have surprising correlations, even when they are space-like separated. Thus, I want to have a very good account of the philosophy of probability itself. For instance, we take it for granted that, classically, correlations between distant events imply some timelike worldlines connecting them. Is this naive? I have a working knowledge of the basics of probability but I’m not yet sure where to get a good grounding in the underlying philosophical foundations of the field.
  • Mathematical Foundations of Physics – In the gedanken-experiment of Schrödinger’s Cat we’re asked to entertain the notion of a superposition of a classical object: a cat. But this superposition is quite different from those which we typically entertain in quantum mechanics because there isn’t any obvious symmetry group which allows us to view the superposition of “live” and “dead” as the eigenstate of some related measurement. It seems like this property in particular that tickle’s Einstein’s nose in the original EPR paper. My hunch is that there is such a group for the cat measurement operator but that its trivial – it contains only a single element or all of its elements have the property that their eigenvalues are indistinguishable from one another, classically. This is far beyond my current mathematical ability to appreciate. In general, an improvement in my mathematical literacy would help here.I’m planning on doing Frederic Schuller’s course on the mathematical foundation of physics.
  • Quantum Field Theory – Speaking of a lack of mathematical background, I’d like to get a firmer grasp on this subject. Most demonstrations of the problems with Quantum Mechanics depend on extremely basic single particle gedanken-experiments. I attended The Rutgers-Columbia Workshop on the Metaphysics of Science: Quantum Field Theories Conference in 2018 and it seemed from my very naive perspective that second quantization (or whatever) wasn’t particularly enlightening to the foundational questions. Its actually somewhat unclear whether effective QFTs can really serve as a foundational account of anything, given their probably lack of convergence and the issues associated with normalization,  even in the case of standard model physics (to say nothing of GR). Still, a working knowledge of the field might be enlightening.

    I’ve got A. Zee’s “Quantum Field Theory in a Nut Shell” but in many respects its over my head.

  • Statistical Mechanics  – The realist point of view is, of course, that quantum mechanics is just statistical mechanics of some unknown quantum mechanical system. Even in the case of ordinary interpretation of the theory, without any desire to reduce it to a classical system, it would be handy for me to have a better grasp of stat mech. I did well in this course in undergrad but I don’t have the material at my fingertips anymore. Open to suggestions on this too.

This is enough material to occupy a full time employed dad for like 15 years, which is something I try not to think about.

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