Research                                                           {Return to Home Page}

Particles, Fields, and the Measurement of Electron Spin

This article compares treatments of the Stern-Gerlach experiment across different physical theories, building up to a novel analysis of electron spin measurement in the context of classical Dirac field theory. Modeling the electron as a classical rigid body or point particle, we can explain why the entire electron is always found at just one location on the detector (uniqueness) but we cannot explain why there are only two locations where the electron is ever found (discreteness). Using non-relativistic or relativistic quantum mechanics, we can explain both uniqueness and discreteness. Moving to more fundamental physics, both features can be explained within a quantum theory of the Dirac field. In a classical theory of the Dirac field, the rotating charge of the electron can split into two pieces that each hit the detector at a different location. In this classical context, we can explain a feature of electron spin that is often described as distinctively quantum (discreteness) but we cannot explain another feature that could be explained within any of the other theories (uniqueness).

The Mass of the Gravitational Field
in The British Journal for the Philosophy of Science (forthcoming)

By mass-energy equivalence, the gravitational field has a relativistic mass density proportional to its energy density. I seek to better understand this mass of the gravitational field by asking whether it plays three traditional roles of mass: the role in conservation of mass, the inertial role, and the role as source for gravitation. The difficult case of general relativity is compared to the more straightforward cases of Newtonian gravity and electromagnetism by way of gravitoelectromagnetism, an intermediate theory of gravity that resembles electromagnetism.

Putting Positrons into Classical Dirac Field Theory
in Studies in History and Philosophy of Modern Physics (2020)

One way of arriving at a quantum field theory of electrons and positrons is to take a classical theory of the Dirac field and then quantize.  Starting with the standard classical field theory and quantizing in the most straightforward way yields an inadequate quantum field theory.  It is possible to fix this theory by making some modifications (such as redefining the operators for energy and charge).  Here I argue that we ought to make these modifications earlier, revising the classical Dirac field theory that serves as the starting point for quantization (putting positrons into that theory and removing negative energies).  Then, quantization becomes straightforward.  Also, the physics of the Dirac field is made more similar to the physics of the electromagnetic field and we are able to better understand electron spin.

How Electrons Spin
in Studies in History and Philosophy of Modern Physics (2019)

There are a number of reasons to think that the electron cannot truly be spinning. Given how small the electron is generally taken to be, it would have to rotate superluminally to have the right angular momentum and magnetic moment. Also, the electron's gyromagnetic ratio is twice the value one would expect for an ordinary classical rotating charged body. These obstacles can be overcome by examining the flow of mass and charge in the Dirac field (interpreted as giving the classical state of the electron). Superluminal velocities are avoided because the electron's mass and charge are spread over sufficiently large distances that neither the velocity of mass flow nor the velocity of charge flow need to exceed the speed of light. The electron's gyromagnetic ratio is twice the expected value because its charge rotates twice as fast as its mass.

Electromagnetism as Quantum Physics
in Foundations of Physics (2019)

One can interpret the Dirac equation either as giving the dynamics for a classical field or a quantum wave function.  Here I examine whether Maxwell's equations, which are standardly interpreted as giving the dynamics for the classical electromagnetic field, can alternatively be interpreted as giving the dynamics for the photon's quantum wave function.  I explain why this quantum interpretation would only be viable if the electromagnetic field were sufficiently weak, then motivate a particular approach to introducing a wave function for the photon (following Good, 1957).  This wave function ultimately turns out to be unsatisfactory because the probabilities derived from it do not always transform properly under Lorentz transformations.  The fact that such a quantum interpretation of Maxwell's equations is unsatisfactory suggests that the electromagnetic field is more fundamental than the photon.

Forces on Fields
in Studies in History and Philosophy of Modern Physics (2018)

In electromagnetism, as in Newton's mechanics, action is always equal to reaction. The force from the electromagnetic field on matter is balanced by an equal and opposite force from matter on the field. We generally speak only of forces exerted by the field, not forces exerted upon the field. But, we should not be hesitant to speak of forces acting on the field. The electromagnetic field closely resembles a relativistic fluid and responds to forces in the same way. Analyzing this analogy sheds light on the inertial role played by the field's mass, the status of Maxwell's stress tensor, and the nature of the electromagnetic field.

Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics
with Sean Carroll
in The British Journal for the Philosophy of Science (2018)

A longstanding issue in attempts to understand the Everett (Many-Worlds) approach to quantum mechanics is the origin of the Born rule: why is the probability given by the square of the amplitude? Following Vaidman, we note that observers are in a position of self-locating uncertainty during the period between the branches of the wave function splitting via decoherence and the observer registering the outcome of the measurement. In this period it is tempting to regard each branch as equiprobable, but we argue that the temptation should be resisted.  Applying lessons from this analysis, we demonstrate (using methods similar to those of Zurek's envariance-based derivation) that the Born rule is the uniquely rational way of apportioning credence in Everettian quantum mechanics.  In doing so, we rely on a single key principle: changes purely to the environment do not affect the probabilities one ought to assign to measurement outcomes in a local subsystem.  We arrive at a method for assigning probabilities in cases that involve both classical and quantum self-locating uncertainty. This method provides unique answers to quantum Sleeping Beauty problems, as well as a well-defined procedure for calculating probabilities in quantum cosmological multiverses with multiple similar observers.

Constructing and Constraining Wave Functions for Identical Quantum Particles
in Studies in History and Philosophy of Modern Physics (2016)

I address the problem of explaining why wave functions for identical particles must be either symmetric or antisymmetric (the symmetry dichotomy) within two interpretations of quantum mechanics which include particles following definite trajectories in addition to, or in lieu of, the wave function: Bohmian mechanics and Newtonian quantum mechanics (a.k.a. many interacting worlds).  In both cases I argue that, if the interpretation is formulated properly, the symmetry dichotomy can be derived and need not be postulated.

Killer Collapse: Empirically Probing the Philosophically Unsatisfactory Region of GRW
in Synthese (2015)
[published version] [PhilSci archive version]

GRW theory offers precise laws for the collapse of the wave function. These collapses are characterized by two new constants, λ and σ. Recent work has put experimental upper bounds on the collapse rate, λ. Lower bounds on λ have been more controversial since GRW begins to take on a many-worlds character for small values of λ. Here I examine GRW in this odd region of parameter space where collapse events act as natural disasters that destroy branches of the wave function along with their occupants. Our continued survival provides evidence that we don't live in a universe like that.  I offer a quantitative analysis of how such evidence can be used to assess versions of GRW with small collapse rates in an effort to move towards more principled and experimentally-informed lower bounds for λ.

Quantum Mechanics as Classical Physics
in Philosophy of Science (2015)

Here I explore a novel no-collapse interpretation of quantum mechanics which combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical predictions of quantum mechanics, the theory looks surprisingly classical. All there is at the fundamental level are particles interacting via Newtonian forces. There is no wave function. However, there are many worlds.

Many Worlds, the Born Rule, and Self-Locating Uncertainty
with Sean Carroll
, in Quantum Theory: A Two-Time Success Story, Yakir Aharonov Festschrift (2014)
[published version (original)] [arXiv version (updated)]

We provide a derivation of the Born Rule in the context of the Everett (Many-Worlds) approach to quantum mechanics. Our argument is based on the idea of self-locating uncertainty: in the period between the wave function branching via decoherence and an observer registering the outcome of the measurement, that observer can know the state of the universe precisely without knowing which branch they are on. We show that there is a uniquely rational way to apportion credence in such cases, which leads directly to the Born Rule.

A Laws-First Introduction to Quantum Field Theory
[chapter 4 of my thesis]

Here I present an atypical introduction to the foundations of quantum field theory (QFT).  I seek to be especially clear about the space of physical states and the laws of the theory, as well as the connection between quantum field theory and the theories it unifies: quantum mechanics, special relativity, and classical field theory.  Part 1 of the paper introduces QFT as an extension of non-relativistic quantum mechanics with two important modifications (introduced one at a time): the number of particles is allowed to be indeterminate and the energy of a state is given by a relativistic expression.  In part 2, I present QFT as a quantum version of the classical theory of fields where the wave functions over particle configuration space of NRQM are replaced by wave functionals over the space of classical field configurations.  The limiting case of classical field theory is then derived using path integrals.  Throughout, I use the Schrodinger picture.  I seek to prepare readers for derivations of Feynman rules and experimental predictions, but I do not cover such machinery here.  I further limit my treatment by not discussing (much) spin, fermions, or renormalization.  I will instead focus on theories of interacting bosonic particles (or real scalar fields, depending on how you look at it).