Category 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.

Black Hole Information Paradox

A Cafe I visit routinely on my morning commute exploded yesterday. We also took pictures of a black hole for the first time. My son used his potty for the first time.

Feeling slightly overwhelmed by the crazy confluence of scales which intersected in my life yesterday. On our weekly date, Shelley asked me about the long term structure and fate of the universe. Hard not to think, absurd as it is, about my own child careening into the future. Is some distant descendant going to look out the window at an earth which can barely support life on account of the increase in solar radiation or suffer some other painful sense of final detachment from the universe?

The owner of the cafe died in the explosion. I talked to him on Monday when I stopped to get a tea on the way to work. Now that impression of a friendly old man framed by the accoutrements of a bustling cafe has taken on a hyper-reality, like the morning light streaming in from the windows as the sun came up over the buildings across the street really was the excitation of a mysterious quantum field. One characterized by nothing more or less than handful of symmetry relations which ascended picoseconds after the universe began and whose reign will still be absolute when the universe is nothing but black holes and the distant, cooling, cosmic horizon.

Notes on `Quantum Computing Since Democritus, Chapter 1`

For a long time, I’ve been interested in the sorts of questions exemplified by the following example:

Suppose we are Isaac Newton or  Gottfried Leibniz. We have at our disposal two sources of inspiration: data, collected by intrepid philatelists like Tycho Brahe and something like theory, in the form of artifacts like Kepler’s Laws, Galileo’s pre-Newtonian laws of motion (for it was he who first suggested that objects in motion retain that motion unless acted upon), and a smattering of Aristotelian and post-Aristotelian intuitions about motion (for instance, John Philoponus’ notion that, in addition to the rules of motion described by Aristotle, one object could impart on another a transient impetus). You also have tables and towers and balls you can roll on them or drop from them. You can perform your own experiments.

The question, then, is how do you synthesize something like Newton’s Laws. Jokes about Newton’s extra-scientific interests aside, this is alchemy indeed, and an alchemy to which most training physicists receive (or at least I received) does not address itself.

Newton’s Laws are generally dropped on the first year physics student (perhaps after working with statics for awhile) fully formed:

First law: When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force.[2][3]
Second law: The vector sum of the external forces F on an object is equal to the mass m of that object multiplied by the acceleration vector aof the object: F = ma.
Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

(this formulation borrowed from Wikipedia)

The laws are stated here in terms of a lot of subsidiary ideas: inertial reference frames, forces, mass. Neglecting the reference to mathematical structures (vector sums), this is a lot to digest: and it is hard to imagine Newton just pulling these laws from thin air.  It took the species about 2000 years to figure it out (if you measure from Zeno to Newton, since Newton’s work is in some sense a practical rejoinder to the paradoxes of that pre-Socratic philosopher), so it cannot be, as some of my colleagues have suggested, so easy to figure out.

A doctorate in physics takes (including the typical four year undergraduate degree in math, physics or engineering) about ten years. Most of what is learned in such a program is pragmatic theory: how to take a problem statement or something even more vague, identify the correct theoretical approach from a dictionary of possibilities, and then to “turn the crank.” It is unusual (or it was unusual for me) for a teacher to spend time posing more philosophical questions. Why, for instance, does a specific expression called the “Action,” when minimized over all possible paths of a particle, find a physical path? I’ve had a lot of physicist friends dismiss my curiosity about this subject, but I’m not the only one interested (eg, the introductory chapter of Lanczos’ “The Variation Principles of Mechanics”).

What I am getting to here, believe it or not, is that I think physicists are over-prepared to work problems and under-prepared to do the synthetic work of building new theoretical approaches to existing unsolved problems. I enjoy the freedom of having fallen from the Ivory Tower, and I aim to enjoy that freedom in 2016 by revisiting my education from a perspective which allows me to stop and ask “why” more frequently and with more intensity.

Enter Scott Aaronson’s “Quantum Computing Since Democritus,” a book whose title immediately piqued my interest, combining, as it does, the name of a pre-Socratic philosopher (the questions of which form the basis, in my opinion, for so much modern physics) with the most modern and pragmatic of contemporary subjects in physics. Aaronson’s project seems to accomplish exactly what I want as an armchair physicist: stopping to think about what our theories really mean.

To keep myself honest, I’ll be periodically writing about the chapters of this book – I’m a bit rusty mathematically and so writing about the work will encourage me to get concrete where needed.

Atoms and the Void

Atoms and the Void is a short chapter which basically asks us to think a bit about what quantum mechanics means. Aaronson describes Quantum Mechanics in the following way:

Here’s the thing: for any isolated region of the universe that you want to consider, quantum mechanics describes the evolution in time of the state of that region, which we represent as a linear combination – a superposition – of all the possible configurations of elementary particles in that region. So, this is a bizarre picture of reality, where a given particle is not here, not there, but in a sort of weighted sum over all the places it could be. But it works. As we all know, it does pretty well at describing the “atoms and the void” that Democritus talked about.

The needs of an introductory chapter, I guess, prevent him from describing how peculiar this description is: for one thing, there is never an isolated region of the universe (or at least, not one we are interested in, I hope obviously). But he goes on to meditate on this anyway by asking us to think about how we interpret measurement where quantum mechanics is concerned. He dichotimizes interpretations of quantum mechanics by where they fall on the question of putting oneself in coherent superposition.

Happily, he doesn’t try to claim that any particular set of experiments can definitely disambiguate different interpretations of quantum mechanics. Instead he suggests that by thinking specifically of Quantum Computing, which he implies gets most directly at some of the issues raised by debates over interpretation, we might learn something interesting.

This tantalizes us to move to chapter 2.