'Penguin Diagram' (2018) BWR, oil on canvas
About
Hi there. I'm a practitioner of Arts & Sciences and Professor of Philosophy, Logic & Scientific Method at LSE, where I have worked since 2013. From 2019-2020 I was a Fellow at Trinity College, Cambridge, and from 2019-2022 taught in the Part III programme in the Department of Applied Mathematics and Theoretical Physics (DAMTP) at Cambridge. I was Director of the LSE Centre for Philosophy of Natural and Social Sciences (CPNSS) from 2020-2024. Since 2024 I have been co-chair of an LGBTQIA+ 🏳️🌈 staff network called Spectrum.
I am British-American, born in Los Angeles, and banter in English 🇬🇧, Spanish 🇪🇸, French 🇫🇷, and Croatian 🇭🇷, having fallen in love in many places.
In matters of little importance I find that it is style that matters most, whereas in matters of great importance, it is again style that matters most.
Contact me at b.w.roberts@lse.ac.uk / @soulphysics / ORCiD / LAK 4.01, or see my Curriculum Vitae.
Research
My research is a mix of aesthetics, philosophy, mathematics, and physics: quantum, thermo-statistical, relativistic, and their combination. My style is mathematical, but I find ineffable questions irresistible and am a softy for pretty pictures. When I was a PhD student I maintained a blog called Soulphysics that discussed lovely ideas like time observables and the Kadison-Singer theorem.
I won the Leverhulme Prize in 2019, currently co-coordinate Philosophy of Physics Bootcamp, and manage an ERC Consolidator grant.Edge of the Universe
The Philosophical Foundations of the Edge of the Universe project is a team studying boundary conditions as they apply to the universe as a whole, funded by a European Research Council (ERC) consolidator grant. Come work with us!
The Arrow of Time
Reversing the Arrow of Time (2022) is a theory of symmetry, time, and time's arrow. Reviewers have called it "highly formal" but "essential reading". You can buy it or read it for free. This project was so difficult it completely changed how I look at my bookshelf: you poor, poor authors!
Philosophy of Science
Philosophico-Scientific Adventures (2015) is a free ebook giving an illustrated and animated overview of modern philosophy of science, from a Pittsburgh perspective.
Space, Time, & Einstein
Space, Time and Einstein is my YouTube channel introducing relativity theory and the philosophy of modern spacetime physics. No background in physics is required. Like, comment, subscribe!
Articles
2022 (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.
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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.
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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.
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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.'
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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 |
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.
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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.
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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.
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2012 Time, symmetry and structure: A study in the Foundations of Quantum Theory. PhD dissertation supervised by John Earman and John D. Norton, History and Philosophy of Science, University of Pittsburgh. Defended 20 May 2012. Pittsburgh ETD.
Recent talks
Misdirected Arrows of Time
A technical philosophy of physics talk about my view on time reversal and the arrow of time, given at a conference in Buenos Aires.
Cautionary news about killing people
An ethics-meets-philosophy of science lecture on how time asymmetry figures into utilitarian thinking about irreversible acts.
Why do we become older but not younger?
An easier public lecture at the LSE on the philosophy and physics of the arrow of time.
I have appeared on podcasts like the LSE IQ Podcast "How to win an argument, BBC Crowd Science "If a tree falls in the forest...", and the Radio 4 Moral Maze. I've also written for the Atlantic.
London School of Economics
I work at the London School of Economics & Political Science, but am not an economist. My Department was founded by Karl Popper, who came here after writing The Open Society, and the Department has been a centre for scientific philosophy ever since.
BSc & MSc Courses
I created a few philosophy of science courses that are accessible to everyone, although MSc students get a chance to work on more advanced material if they wish.
Ph230/Ph430 Einstein for Everyone: An accessible introduction to the philosophy of relativistic spacetime. Past version. |
Ph232/Ph431 Physics and Uncertainty: On the quantum, the statistical, and the application of these ideas to financial markets. Past version. |
Ph201/Ph400 Philosophy of Science: An opinionated introduction to the Philosophy of Science, in the Pittsburgh style. Past version. |
Part III: Philosophical Foundations of Quantum Field Theory. My course with Jeremy Butterfield in the Department of Applied Mathematics and Theoretical Physics, University of Cambridge. 2021, 2020, 2019 version. |
PhD Supervision
My PhD students in Philosophy have worked in all areas of the philosophy of physics: quantum, relativistic, thermo-statistical, and their combination. The Edge of the Universe project will help fund one such PhD student in the coming years.
Read more here about the LSE MPhil/PhD in Philosophy and how to apply. My current and past PhD students:
- DOMINIC RYDER (Exp. 2026), "Philosophical foundations of Hawking radiation". His paper "The black hole idealisation paradox" is forthcoming in BJPS.
- ALEXANDER NIEDERKLAPFER (Exp. 2026), "Particles in the foundations of quantum field theory".
- ANDREAS VON ACHEN (PhD 2023), "Conventionality, Underdetermination, and the Inter-Theory Transport of Concepts". He now teaches in the Institut for Naturfagenes Didaktik in Copenhagen.
- JAMES WILLS (PhD 2022), "Identity and indistinguishability in thermal physics". He went on to become a data scientist, and is author of two great philosophy publications on indistinguishability in mechanics (BJPS) and thermodynamics (Philosophy of Science).
- PHILIPPE VAN BASSHUYSEN (PhD 2019), "Philosophical and ethical aspects of economic design". He is now a Professor of Public Health Ethics at Leibniz University Hannover. Read about him here.
LGBTQIA+ Life at the LSE 🌈
The UK Gay Liberation Front (GLF) was founded in a basement at the LSE against the wishes of School managers, and the LSE Troubles once involved sit-ins and protests against social injustice like apartheid South Africa. Today comparable struggles are alive and well on campus. The LSE is also home to the largest queer archive in the UK, the Hall-Carpenter archive. There are lots of ways to be a part of the community here, if you're looking for that:
- Spectrum is the LGBTQIA+ Staff Network at the LSE for queer events, advocacy, and policy development on campus. All LGBTQIA+ staff (academics, PSS, and GTAs) and allies are welcome.
- LGBTQ+ Society and the LGBTQ Sabbatical Officer are great ways for LSE students to get connected, and regularly collaborate with Spectrum.
- Minorities And Philosophy (MAP) Chapter at LSE is an opportunity for all traditionally underrepresented groups in Philosophy to meet and network.
LSE is in central London and filled with wonderful queers and allies. So, despite the School's regrettable withdrawal from Stonewall we are making progress.
Guides for Students
A few resources for students and practitioners of philosophy and physics.
7 Steps to a Better Philosophy Paper. An intentionally brief (4 pages) guide to the essentials of writing a philosophy paper. |
On Writing an MSc Dissertation and my MSc Dissertation Timeline. The deadlines are tuned for LSE Philosophy but the main ideas generalise broadly. MSc students working with me should use it to guide our meetings. |
How to give an academic talk. My thoughts on a remarkably under-discussed subject in philosophy. Philosophers of physics, see also these lovely guides to giving mathematical talks. Some examples of my talks are here and here. I make talks using reveal.js., which is easy if you know html/latex and also free. If you don't know html/latex there is a more user-friendly version slides.com, but not free. But I find it's more about the design than the background system. |
Journal-Access Bookmarklet. I made a handy javascript bookmarklet for LSE folks to access journals off-campus. Easily modified for other schools and sci-hub. To make your research a little smoother and faster. |
Open Access
Among researchers, power resides in access to data, from scientific data sets to journal articles. It has been largely captured by a few wealthy institutions and for-profit publishers, who concentrate that data among elites behind paywalls. The Open Access movement is an attempt to redistribute that power in a more equitable way by giving everyone access to data.
I have been involved in several projects in that spirit.
BSPS Open. Together with David Teira I co-founded BSPS Open, an open access book series for philosophers of science. The principle is that funds are raised from Societies, book sales, and charitable donations, so that authors and readers do not have to pay a penny. It began as a partnership with the British Society for Philosophy of Science with the University of Calgary Press. |
Philosophy of Physics. When a notorious for-profit publisher closed down my discipline's main journal, a breakaway band of philosophers of physics responded by calling one of our field's largest meetings ever in an international Zoom call. Together we founded a new professional society, the Philosophy of Physics Society, who launched a new Open Access journal Philosophy of Physics thanks to a partnership I helped negotiate with our wonderful in-house publishers at the LSE Press. Our open access model is to some extent repeatable and scalable: read about it here. |
PhilSci-Archive. I have helped manage PhilSci-Archive since I was a graduate student at Pitt. It is a preprint server for philosophers of science that is nearly as old as arxiv.org. Preprint servers are an essential resources for providing access to academic work to everyone in a speedy and equitable way without paywalls. It's also a nice way to share your work and stay connected to the philosophy of science community. |
Aesthetics
I spent a lifetime developing a theory of aesthetics. I am still in the research phase.
Visual
As a mathematics undergrad I read Betty Edwards and became convinced that creating visual art is associated with a radical shift in human perception, from a focus on meaning and language to one focused on direct visual experience. Neural imaging now shows some evidence for this shift in the move from ventral stream neural activity to dorsal stream. The meta-cognitive awareness of that shift is for me what the creation of visual art is about: I try to refine both together. Some recent examples below.
Portrait of Foad (2023)
Tiger Lily (2022)
Swiftly (2020)
Make Everything OK (2019)
Musical
In the English language, the same verb 'to play' is used to refer both to what a musician does with an instrument and what a child does with a toy. I find it delightful to do both at once. Here are a few instances. Let's play together sometime.
Graphic and Web Design
One of the most effective delivery devices for culture is graphic design. I have long been involved with web-design, and have even created a few well-known designs in my field, including the Philosophy of Physics Society website and design (inspired by Soviet constructivism), the Philosophy of Physics journal logo and cover, and the logo and website of the British Society for the Philosophy of Science.
Philosophy of Physics (PoP) logo, 2022
Philosophy of Physics Society homepage, 2022
BSPS logo and homepage, 2015
I designed the webpage you are now reading in December 2024, as a simple academic homepage built on a single page of html. It uses Bootstrap for mobile responsiveness and a bit of javascript for animations. You are welcome to use it: if you go to "View Page Source" in your browser you'll find the annotated html.
Site Design © CC BY 4.0 By Bryan W Roberts