Tag Archives: quantum mechanics

A Quick Look at 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.

Why Physicists Need Their Space

A few weeks ago I attended the Rutgers/Columbia Symposium on the Metaphysics of Quantum Field Theory. This morning in the shower a few things I’ve been thinking about snapped into place relating to that conference and my own hobby-level interest in related questions.

Some background: Ontology, meaning “what stuff is fundamental and what stuff is derived?” is important in the question of the foundations of physics. You can see this going all the way back to Thales (624 – c. 546 BC) who, in the traditional account, is the first “scientist” exactly because he proposed an ontology: water is real, all other phenomena are derived from water. (Note that the idea of supervenience enters into the discussion here: in Thales’ account, for instance, because a rock is fundamentally a sort of water, we can say that the higher level properties of rock supervene upon the fundamental properties of water in some way.) Contrast this with the atomists, who posit that atoms are fundamental objects and other things supervene upon them. Or contrast it with idealists, like Plato, who claim that in some sense forms are ontologically fundamental and that real things supervene upon them.

Now, one of the many ways to see what is hard about QM is that it challenges the ontological status of space itself. This is, in fact, one of the most important ways it’s challenging from a philosophical point of view. That is, for lots of reasons (of which more later), we tend to believe that space is fundamental.

But why do we care so much about space? There are ways of deriving the Schrodinger Equation (which governs the behavior of quantum mechanical systems) from ontologies which don’t include space at all (consequently, space isn’t part of the ontology of these theories at all). See Lee Smolin 2014 – Nonlocal Beables. (NB the vogue is to call observables “beables”). It seems like, if we can find a nice way of getting QM from a more fundamental theory without any of the other weirdnesses (like considering that the wave function is real, for instance) that explains why it seems like wave function collapse constitutes action at a “distance”, then we ought to take it. After all, if we can show that space isn’t ontologically real then we shouldn’t be afraid of some non-spacelike aspects to our theory. Space “emerges” from some low-level dynamics of a non-spatial system. It isn’t fundamentally challenging that some of those dynamics won’t be space like and so we don’t need to grind our teeth and rend our garments about Bell’s Inequality or other Entanglement related phenomena: they are just the fundamentally non-spacey nature of reality peaking around the corners of a low energy/classical limit.

Considering that entanglement presents us with some otherwise very unusual epistemological challenges, this seems to me like a great escape hatch. Or at least it did until I spent some time thinking about how important geometry is to physics.

Believe it or not, action at a distance isn’t a new controversy in physics. It goes back way before entanglement was a twinkle in Schrödinger’s eye. The ancient Greeks were obsessed with it and Descartes and Newton worried a lot about it too. One way of telling the story is to think about planetary motion. The critical insight to planetary motion (this account more or less derives directly from Crowe’s Mechanics from Aristotle to Einstein, 2007) was that objects have momentum (which even Newton conceived of as a kind of force). Without the idea of momentum its hard to imagine what keeps planets in their orbits. The most common explanation at the time of Newton was some sort of substance filling space which had vorticial motion, and thus which carried the planets along in their circular orbits. What was particularly appealing about this to someone like Descartes (for reasons about which I could write a whole other essay) is that it was a theory without action at a distance. The sun might have been the source of a vortex which carried earth around it, but it was the local motion of the fluid which pushed the earth along, and that motion was transmitted from the sun to the location of the earth by local interactions in the fluid itself. That is, there was not some mysterious tendency transmitted over empty space which caused the motion. Everything was local. At the heart of this is both the idea that there is no action at a distance, that inanimate objects don’t move on their own and a deep underlying notion that interactions are always local (which is part and parcel with the sense that space is part of our ontology).

The irony is that Newton, the great hero of the scientific perspective, is the less materialist of the two. In The Principia (1687) he makes such enormous progress by dispensing with the notion that he needs to worry about precisely how the interaction between massive bodies is mediated and instead focuses purely on its mathematical description. In a way, Newton is thus in the “shut up and calculate” camp. Newton doesn’t throw space out of the ontology but he does profoundly weaken its role by at least suggesting that we don’t need to think of every interaction in the universe as mediated in a purely local sense (though he never outright claims gravitation force is nonlocal). If your goal is to calculate the motion of the planets, then this is a great tactic and is, in a way, the essence of good model building: whatever the underlying structure of space-time, its certainly true to a high degree of accuracy that gravity appears to act instantaneously across empty space to produce a force on distant objects. (By the way, Max Jammer’s 1957 Concepts of Force has enlightening things to say on this subject since it helps ground the philosophical notion of force exactly in the physiological experience of pushing or pulling, though we are about to see a compelling reason to believe that the gravitational force is nothing like that at all).

In a way, we can see Newton’s Principia as leapfrogging science’s ability to calculate far ahead of philosophy’s ability to account for what is exactly happening. In that sense, there is an analogy between General Relativity and Newtonian Mechanics and between some heretofore undiscovered ur-theory and Quantum Mechanics: General Relativity provided a kind of philosophical closure between the Cartesian and Newtonian split over the locality of interactions by re-inventing an ontological role for space(time).

General Relativity tells us that no force at all pulls or pushes on the planets. Instead, it says the planets move the way they when the true geometry of space-time is taken into account, they are simply following what locally looks like the plain old Newtonian notion that objects in motion continue to move in a straight line unless acted upon.

Supersymmetry is an attempt to resolve the problems of quantum field theory by imagining that every fermion (boson) in the standard model has a bosonic (fermionic) super-symmetric partner. At this point the theory is out of favor: we’ve never seen these super-symmetric particles in accelerators which means they’d have to be very massive indeed. But one interesting aspect of the theory which was developed in a talk by David Baker at the Rutgers/Columbia Conference is that the addition of such supersymmetric particles introduces aspects of the theory which you could consider elevating to space-time coordinates (however Grassman valued). Why would you want to do that? Well, because its very natural to say that space-time symmetries generate or cause physics. This is the essence of General Relativity and of Yang-Mills style theories, so it underlies both GR and one of the best tools we have to develop useful Quantum Field Theories. Even my passing familiarity with both disciplines is enough to sniff out that these theories are extremely local and geometric. That is practically what differential geometry means.

That is the point of this essay. Modern physics is so used to treating geometry (of spacetime) as ontologically prior that the idea that geometry itself might supervene upon some more fundamental physics is truly challenging. From this point of view, you might prefer to do something like just say the wavefunction is real, even though doing so drastically expands the universe (by introducing a vast number of new observers into it, for instance).