Bryan W. Roberts

Philosophy, Logic & Scientific Method
London School of Economics & Political Science
Houghton Street, London, WC2A 2AE / @soulphysics
Dashing recent portrait photo of the author

I am a philosopher of physics, lost artist, and Associate Professor at the LSE, where I direct the Centre for Philosophy of Natural and Social Sciences (CPNSS). From 2019-2022 I also taught in the Department of Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge.

I work on foundational issues in quantum theory, spacetime and gravitation, thermodynamics, gauge physics, and other things that fill one with wonder about the world. I am also an advocate of improving LGBTQ+ rights at the LSE, about which one can learn a lot here.

Boring Official Bio / CV / @soulphysics

Bryan W Roberts is a philosopher of physics, Associate Professor of Philosophy, Logic and Scientific Method, and Director of the Centre for Philosophy of Natural and Social Sciences (CPNSS) at the London School of Economics. His fields of expertise lie in the intersection of philosophy and mathematical physics, with projects ranging from the arrow of time in particle physics, to the interpretation of general relativity, to the nature of the "observable", in addition to hosting a YouTube channel called Space, Time and Einstein. He publishes philosophy, physics, and history journals, and his book Reversing the Arrow of Time was published by Cambridge University Press in 2022 and made available Open Access. He receiving the Leverhulme Prize in 2017, an NSF grant in 2018, and a visiting Fellowship at Trinity College, Cambridge in 2019. He also taught in the Department of Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge from 2019 to 2022. Dr Roberts received his Ph.D. in 2012 from the University of Pittsburgh under John Earman and John D. Norton, and then held the Provost's Postdoctoral Fellowship at the University of Southern California from 2012-2013, before finally settling in London at the LSE in 2013.


See my Articles on PhilSci-Archive / CV

Book: Reversing the Arrow of Time

Reversing the Arrow of Time book cover

I wrote a book about the arrow of time! It was published on 24 November 2022 by Cambridge University Press, and is Open Access, so you can read it for free.

This project completely changed how I look at academic book-writers, not to mention my bookshelf. You poor things: what a remarkable journey you all embarked on.

Some Video Talks

Representing the arrow of time, given at the 2023 Buenos Aires workshop on the arrow of time, February 2023.
Why do we become older but not younger? Public lecture at the LSE, 29 Nov 2022.
Spacetime symmetries and the origin of antimatter, lecture at the University of Bristol, 6 June 2021
The good news about killing people, given for the LSE Choice Group, 18 March 2020
Time reversal, given for the Geneva Symmetry Group at the University of Geneva, 13 March 2019.
Some curious examples of mathematical representation, given at the Hole Shebang workshop at the LSE, 15 July 2016.
Weak Interactions and the Curious Little Arrow of Time, given at the ETH in Zurich in 2015, for the D-Phys Workshop on Time in Physics.
Noodling on a Wurlitzer, somewhere in East London.


2021 (with Henrique Gomes and Jeremy Butterfield) "The Gauge Argument: A Noether Reason". Preprint / Abstract

Why is gauge symmetry so important in modern physics, given that one must eliminate it when interpreting what the theory represents? In this paper we discuss the sense in which gauge symmetry can be fruitfully applied to constrain the space of possible dynamical models in such a way that forces and charges are appropriately coupled. We review the most well-known application of this kind, known as the 'gauge argument' or 'gauge principle', discuss its difficulties, and then reconstruct the gauge argument as a valid theorem in quantum theory. We then present what we take to be a better and more general gauge argument, based on Noether's second theorem in classical Lagrangian field theory, and argue that this provides a more appropriate framework for understanding how gauge symmetry helps to constrain the dynamics of physical theories.

2021 "Time reversal". Chapter 43 of Knox and Wilson (Eds.), The Routledge Companion to the Philosophy of Physics, Routledge, pp.605-619. Preprint / Abstract

Time reversal is a wonderfully strange concept. It sounds like science fiction at first blush, and yet plays a substantial role in the foundations of physics. This chapter introduces one little corner of the rich literature on time reversal, which deals with the question of what time reversal means. I begin with a presentation of the standard account of time reversal, with plenty of examples, followed by a popular non-standard account. I will then argue that, in spite of recent commentary to the contrary, the standard approach to the meaning of time reversal is the only one that is philosophically and physically viable. I conclude with a few open research problems about time reversal.

2020 (with Jeremy Butterfield) "Time-energy uncertainty does not create particles." Journal of Physics 1638:012005. Article (Open Access) / Preprint / Abstract

We criticise the claims of many expositions that the time-energy uncertainty principle allows both a violation of energy conservation and particle creation, provided that this happens for a sufficiently short time. But we agree that there are grains of truth in these claims: which we make precise and justify using perturbation theory.

2020 "Regarding 'Leibniz Equivalence'." Foundations of Physics 50(4):250-269. Article (Open Access) / Preprint / Abstract

Leibniz Equivalence is a principle of applied mathematics that is widely assumed in both general relativity textbooks and in the philosophical literature on Einstein's hole argument. In this article, I clarify an ambiguity in the statement of this Leibniz Equivalence, and argue that the relevant expression of it for the hole argument is strictly false. I then show that the hole argument still succeeds as a refutation of manifold substantivalism; however, recent proposals that the hole argument is undermined by principles of representational equivalence do not fare so well.

2020 (with Jim Weatherall) "New Perspectives on the Hole Argument" Foundations of Physics 50(4):217-227. Article / Preprint / Abstract

This special issue of Foundations of Physics collects together articles representing some recent new perspectives on the hole argument in the history and philosophy of physics. Our task here is to introduce those new perspectives.

2018 "Observables, Disassembled." Studies in History and Philosophy of Modern Physics 63:150-162. Article / 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.

2017 "Unreal observables." Philosophy of Science 84(5). Article / 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.'

2017 "Three myths about time reversal in quantum theory." Philosophy of Science 84(2):315-334. Article / 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. Supervised by John Earman and John D. Norton, History and Philosophy of Science, University of Pittsburgh. Defended 20 May 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.


2017 Leverhulme Prize (2018-2020)
National Science Foundation (NSF) Grant #1734155 "Extending the Observable", with collaborator Nicholas Teh, University of Notre Dame.

Public Media

Podcast LSE IQ Podcast, "How to win an argument".
Audio BBC Crowd Science, "If a tree falls in a forest... does it make a sound?".
Audio BBC Radio 4 Moral Maze, "Is Science Morally Neutral?" 12 March 2016.

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.


YouTube Channel

Image of outer space

I animated and recorded a series of YouTube videos introducing Einstein's theories of space, time and gravity.

Courses at the 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: The Big Questions Course Page

Courses Elsewhere

Cambridge: Philosophy of Quantum Field Theory (Website / Summary)

Part III (Masters level) course on quantum field theory and its philosophical foundations for the Department of Applied Mathematics and Theoretical Physics (DAMTP), co-taught in 2019-2020 and 2020-2021 with Jeremy Butterfield.

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. How to do the mammoth task of writing an MSc dissertation in the Department, which applies more broadly of course.


PhilSci-Archive I am co-editor in chief of the BSPS Open book series, a free open access book series for philosophy of science.

PhilSci-Archive I'm also a co-director of PhilSci-Archive, the field's main preprint server. If you're a philosopher of science that doesn't use PhilSci-Archive, stop what you're doing and go sign up! 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

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 grew up in the Pacific Northwest between the shadows of this volcano and this one, 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.