Bryan W. Roberts

Philosophy, Logic & Scientific Method
London School of Economics & Political Science
Houghton Street, London, WC2A 2AE / +44 (0)20 7107 5484

Bryan Roberts

I am a philosopher of physics and assistant professor in Philosophy, Logic and Scientific Method at the London School of Economics and Political Science. My research is about the foundations of physics, among other exciting things.

Boring Official Bio / CV / twitter

Bryan W. Roberts is a philosopher of physics at the London School of Economics and Political Science. His fields of expertise include philosophy, mathematical physics, and especially their intersection. His current projects have to do with what's "observable" in physics. His research has also included exploring the fundamental physics behind the arrow of time, as well as the general role of symmetry in physics. He has published in philosophy, history as well as physics journals. In 2012 he received his Ph.D. in the History and Philosophy of Science from the University of Pittsburgh. He then held the Provost's Postdoctoral Fellowship at the University of Southern California in 2012-2013, before becoming an Assistant Professor in the Department of Philosophy, Logic and Scientific Method at the LSE in 2013. He lives in London with his wife Alma C. Roberts, a campaign manager at the World Wildlife Fund, UK.


Much of my work has been about asymmetry, especially the arrow of time, and the observable, especially in quantum mechanics. The latter includes studies on how we measure time in physics, and the impact of a general mathematical limitation known as Pauli's theorem. I'm also a history of science buff, and have written a few articles about Galileo.

See my Articles on PhilSci-Archive / CV

Latest Manuscripts

"Observables, Disassembled" Preprint / Abstract

We explore the ways that non-self-adjoint operators can be observables. There are in fact only four ways for this to occur: non-self-adjoint observables can either be normal operators, or be symmetric, or have a real spectrum, or have none of these three properties. I explore each of these four classes of observables, arguing that the class of normal operators provides an equivalent formulation of quantum theory, whereas the other classes considerably extend it.

"Kähler Representation Theory" (with Nicholas J. Teh) Preprint / Abstract

We show that Jordan-Lie-Banach algebras, which provide an abstract characterization of quantum theory equivalent to C* algebras, can always be canonically represented in terms of smooth functions on a Kähler manifold.

"Disregarding the 'Hole Argument'" Preprint / Abstract

Jim Weatherall has suggested that the hole argument of Earman and Norton (1987) is based on a misleading mathematical argument. I argue on the contrary that the hole argument is in no new danger at all.

"Does quantum time have a preferred direction?" Preprint / Abstract

This paper states and proves a precise sense in which, if all the measurable properties of an ordinary quantum mechanical system are ultimately derivable from position, then time in quantum mechanics can have no preferred direction. In particular, I show that when the position observable forms a complete set of commuting observables, Galilei invariant quantum mechanics is guaranteed to be time reversal invariant.


Forthcoming. "Unreal observables." To appear in Philosophy of Science. Preprint / Abstract

This note argues that quantum observables can include not just self-adjoint operators, but any member of the class of normal operators, including those with non-real eigenvalues. Concrete experiments, statistics, and symmetries are all expressed in this more general context. However, this more general class of observables also introduces a new restriction on which sets of operators can be interpreted as observables at once. These sets are referred to here as 'sharp sets.'

Forthcoming. "Three myths about time reversal in quantum theory." To appear in Philosophy of Science. Preprint / Abstract

This paper seeks to dispel three myths about the concept of time reversal in quantum theory, by providing a novel derivation of the meaning of time reversal in non-relativistic and relativistic contexts, without appeal to classical mechanics.

2016. "Curie's Hazard: From electromagnetism to symmetry violation." Erkenntnis 81(5):1011-1029. Article / Preprint / Abstract

We explore the facts and fiction regarding Curie's own example of Curie's principle. Curie's claim is vindicated in his suggested example of the electrostatics of central fields, but fails in many others. Nevertheless, the failure of Curie's claim is still of special empirical interest, in that it can be seen to underpin the experimental discovery of parity violation and of CP violation in the 20th century.

2016 (with John Byron Manchak). "Supertasks," in The Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.), Article / Abstract

A supertask is a task that consists in infinitely many component steps, but which in some sense is completed in a finite amount of time. Supertasks were studied by the pre-Socratics and continue to be objects of interest to modern philosophers, logicians and physicists. The term “super-task” itself was coined by J.F. Thomson (1954). This encyclopedia article begins with an overview of the analysis of supertasks and their mechanics. We then discuss the possibility of supertasks from the perspective of general relativity.

2015. "Three merry roads to T-violation." Studies in History and Philosophy of Modern Physics. Article / Preprint / Abstract

This paper is a tour of how the laws of nature can distinguish between the past and the future, or be T-violating. I argue that, in terms of the basic argumentative structure, there are really just three approaches currently being explored. I show how each is characterized by a symmetry principle, which provides a template for detecting T-violating laws even without knowing the laws of physics themselves. Each approach is illustrated with an example, and the prospects of each are considered in extensions of particle physics beyond the standard model.

2015. "Comment on Ashtekar: Generalization of Wigner's Principle." In Studies in History and Philosophy of Modern Physics. Article / Preprint / Abstract

Ashtekar (2013) has illustrated that two of the available roads to testing for time asymmetry can be generalized beyond the structure of quantum theory, to much more general formulations of mechanics. The purpose of this note is to show that a third road to T-violation, which I have called "Wigner's Principle," can be generalized in this way as well.

2014. "A general perspective on time observables." Studies in History and Philosophy of Modern Physics. Article / Preprint / Abstract

I propose a general geometric framework in which to discuss the existence of time observables. This frameworks allows one to describe a local sense in which time observables always exist, and a global sense in which they can sometimes exist subject to a restriction on the vector fields that they generate. Pauli's prohibition on quantum time observables is derived as a corollary to this result. I will then discuss how time observables can be regained in modest extensions of quantum theory beyond its standard formulation.

2013. "When we do (and do not) have a classical arrow of time." Philosophy of Science. Article / Preprint / Abstract

I clarify the sense in which classical mechanics is time reversal invariant. I first point out that some common folk wisdom about time reversal invariance is strictly incorrect, by showing some explicit examples in which classical time reversal invariance fails. I then propose two ways capture the sense in which classical mechanics is time reversal invariant.

2013. "The simple failure of Curie's principle." Philosophy of Science. Article / Preprint / Abstract

There is a simple sense in which the standard formulation of Curie's Principle is false, when the symmetry transformation it describes is time reversal.

2012. "Kramers degeneracy without eigenvectors." Physical Review A. Article / Preprint / Abstract

Wigner gave a well-known proof of Kramers degeneracy, for time reversal invariant systems containing an odd number of half-integer spin particles. But Wigner's proof relies on the assumption that the Hamiltonian has an eigenvector, and so does not apply to all potentially relevant quantum systems. Adopting an algebraic definition of degeneracy, this note shows that Kramers degeneracy can be derived more generally, for Hamiltonians with or without eigenvectors.

2012 (with John D. Norton). "The Scaling of Speeds and Distances in Galileo's Two New Sciences: A reply to Palmerino and Laird." Centaurus. Article / Preprint / Abstract

In this reply, we respond to the comments of Palmerino and Laird on our article, "Galileo's Refutation of the Speed Distance Law of Fall Rehabilitated," published in the same issue of Centaurus.

2012 (with John D. Norton). "Galileo's refutation of the speed-distance law of fall rehabilitated." Centaurus. Article / Preprint / Abstract

Galileo's refutation of the speed-distance law of fall in his Two New Sciences is routinely dismissed as a moment of confused argumentation. We urge that Galileo's argument correctly identified why the speed-distance law is untenable, failing only in its very last step. Using an ingenious combination of scaling and self-similarity arguments, Galileo found correctly that bodies, falling from rest according to this law, fall all distances in equal times. What he failed to recognize in the last step is that this time is infinite, the result of an exponential dependence of distance on time. Instead, Galileo conflated it with the other motion that satisfies this ‘equal time’ property, instantaneous motion.

2011. "How Galileo Dropped the Ball and Fermat Picked It Up." Synthese. Article / Preprint / Abstract

This paper introduces a little-known episode in the history of physics, in which a mathematical proof by Pierre Fermat vindicated Galileo's characterization of freefall. The first part of the paper reviews the historical context leading up to Fermat's proof. The second part illustrates how a physical and a mathematical insight enabled Fermat's result, and that a simple modification would satisfy any of Fermat's critics. The result is an illustration of how a purely theoretical argument can settle an apparently empirical debate.

2011. "Group Structural Realism." The British Journal for the Philosophy of Science. Article / Preprint / Abstract

We present a precise form of structural realism, called group structural realism, which identifies 'structure' in quantum theory with symmetry groups. However, working out the details of this view actually illuminates a major problem for structural realism; namely, a structure can itself have structure. This article argues that, once a precise characterization of structure is given, the 'metaphysical hierarchy' on which group structural realism rests is overly extravagant and ultimately unmotivated.


2012. Time, symmetry and structure: A study in the Foundations of Quantum Theory. Department of History and Philosophy of Science, University of Pittsburgh; John Earman and John D. Norton, supervisors. Defended May 20, 2012. Pittsburgh ETD.

This dissertation is about the sense in which the laws of quantum theory distinguish between the past and the future. I begin with an account of what it means for quantum theory to make such a distinction, by providing a novel derivation of the meaning of "time reversal." I then show that if Galilei invariant quantum theory does distinguish a preferred direction in time, then this has consequences for the ontology of the theory. In particular, it requires matter to admit "internal" degrees of freedom, in that the position observable generates a maximal abelian algebra. I proceed to show that this is not a purely quantum phenomenon, but can be expressed in classical mechanics as well. I then illustrate three routes for generating quantum systems that distinguish a preferred temporal direction in this way.


BBC Audio BBC Radio 4 Moral Maze, "Is Science Morally Neutral?" 12 March 2016. I appear as an expert witness.

Article (with Zach Musgrave). "Humans, Not Robots, Are the Real Reason Artificial Intelligence Is Scary" In The Atlantic, 14 August 2015. Abstract

Unfortunately, much of the recent outcry against artificial-intelligence weapons has been confused, conjuring robot takeovers of mankind. This scenario is implausible in the near term, but AI weapons actually do present a danger not posed by conventional, human-controlled weapons, and there is good reason to ban them. Intelligent weapons are too easily converted by software engineers into indiscriminate killing machines.

Video "Time, time travel and the philosophy of physics." 2015 video introduction to the philosophy of physics.

Audio "The unreasonable effectiveness of mathematics in the sciences." 1 May 2014 Forum for European Philosophy podcast on the surprising role of mathematics in science, and in particular physics. I am the chair and the second speaker (beginning around 10:13).


Courses at LSE

PH230/PH430: Einstein for Everyone Course Overview

PH232/PH431: Physics and the City Course Overview

PH201/PH400: Philosophy of Science Free Textbook

PH227/PH427: Genes, Brains and Society Course Notes

PH103: Reason, Knowledge and Values.

Courses at Other Schools

USC: Methodologies of the Sciences (Website / Syllabus / Summary)

This is an introduction to the philosophy of science that I taught at the University of Southern California, covering the major areas of general philosophy of science, as well as selected recent topics in the special sciences.

USC: Einstein's Spacetime Revolution (Website / Syllabus / Summary).

This course is an introduction to Einstein's science and philosophy of science, based on John Norton's wonderful Einstein for Everyone course at Pittsburgh.

Pitt: Morality & Medicine (Website / Syllabus / Summary)

An introductory course on the foundations of bioethics, with an emphasis on statistical applications, that I taught at Pittsburgh.

Pitt: Principles of Scientific Reasoning (Website / Syllabus / Summary)

A critical thinking course that I taught using Merrilee Salmon's book. I do not recommend this book, due to the Wadsworth's practice of regularly producing new editions of the book with few substantial changes other than rearranged chapters and a sparkling new price tag.

My Textbooks and Guides

Philosophico-Scientific AdventuresPhilosophico-Scientific Adventures. I wrote an ebook introducing some topics in the philosophy of science. I'm continually developing it, adding chapters when I can, so please excuse any errors!

7 Steps to a Better Philosophy Paper. A short writing guide for beginners in philosophy: 7 steps, 10 tips, and only 4 pages!

Writing an MSc Dissertation. A guide for MSc students on writing an MSc dissertation, developed out of the 7 steps.


PhilSci-Archive I am a board member and Conference and Volumes coordinator for PhilSci-Archive. If you're a philosopher of science that doesn't use PhilSci-Archive, stop what you're doing and go sign up. PhilSci-Archive is the official online preprint server of the Philosophy of Science Association. Visit us at

USC Logic Web I was a javascript programmer and remain part of the design committee for USC Logic Web, a free online resource that introduces students to the basics of symbolic logic. USC Logic Web is available to the public in preliminary form at

Soul Physics Blog. I have a little soap box for when I want to carry on about the philosophy of physics.

I sometimes embarrass myself with a paint brush and with musical instruments of various kinds, and I'm a sport skydiver with a USPA A-license. I've recently become interested in animal behavior, through animal-lover Alma Roberts (who is also my wife). We have two cats.

I grew up on the west coast of the United States, where I developed an unreasonable attraction to dramatic deserts, temperate rain forests and snow-capped peaks.



Website. The site is written in simple html/css/javascript, using bootstrap for mobile responsiveness. Feel free to borrow or steal. Inspired by Schupbach via Beall via Sider. If you come up with a variation or improvement, I'd love to see.
Emacs Zen: I write everything in emacs. You can see my setup on github.
Be more efficient. The The Pomodoro Technique is hands-down the most important trick I used to complete my dissertation on time in grad school, and I still use it regularly. There are lots of free timer apps online.
Dirt Simple ToDo List: My work flow, explained as a screencast by me in 2010. I still do basically the same thing.
Handling academic citations. If you use something a lot, you may as well make it easier on yourself: screencast from 2009. Know a better way? Tell me!
Teach with online problem sets. For all the controversy about the Khan Academy, the online problem set framework they developed is uncontroversially fantastic. Incredibly, it's also open source. This is a huge untapped resource for universities. You can download the essential components at Github, where there is also a decent documentation wiki. Familiarity with javascript is required.
Journal Access Bookmarklet. I made a handy javascript bookmarklet for LSE folks to access journals off-campus. Easily modified for other schools.
Give better talks. Give better talks. Giving an academic talk? Read Paul Edwards' How to Give an Academic Talk, but also watch this video on how to give great talks in any context. Giving a talk on a technical subject? Check out this excellent advice from Bob Geroch and from David Tong.