[ { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/n1fzr-6ag25", "eprint_id": 122297, "eprint_status": "archive", "datestamp": "2023-08-22 21:28:49", "lastmod": "2023-10-20 20:25:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles T." }, "orcid": "0000-0001-7671-2141" } ] }, "title": "Eliminating Electron Self-repulsion", "ispublished": "pub", "full_text_status": "public", "keywords": "General Physics and Astronomy; History and Philosophy of Science; Philosophy", "note": "\u00a9 2023 Springer Nature.\n\nThank you to Jacob Barandes, Maaneli Derakhshani, Michael Miller, Logan McCarty, Simon Streib, and anonymous reviewers for helpful feedback and discussion.", "abstract": "Problems of self-interaction arise in both classical and quantum field theories. To understand how such problems are to be addressed in a quantum theory of the Dirac and electromagnetic fields (quantum electrodynamics), we can start by analyzing a classical theory of these fields. In such a classical field theory, the electron has a spread-out distribution of charge that avoids some of the problems of self-interaction facing point charge models. However, there remains the problem that the electron will experience self-repulsion. This self-repulsion cannot be eliminated within classical field theory without also losing Coulomb interactions between distinct particles. But, electron self-repulsion can be eliminated from quantum electrodynamics in the Coulomb gauge by fully normal-ordering the Coulomb term in the Hamiltonian. After normal-ordering, the Coulomb term contains pieces describing attraction and repulsion between distinct particles and also pieces describing particle creation and annihilation, but no pieces describing self-repulsion.", "date": "2023-08", "date_type": "published", "publication": "Foundations of Physics", "volume": "53", "number": "4", "publisher": "Springer", "pagerange": "Art. No. 65", "id_number": "CaltechAUTHORS:20230717-55375900.3", "issn": "0015-9018", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230717-55375900.3", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1007/s10701-023-00702-0", "resource_type": "article", "pub_year": "2023", "author_list": "Sebens, Charles T." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/btfgb-drp15", "eprint_id": 118861, "eprint_status": "archive", "datestamp": "2023-08-20 08:00:39", "lastmod": "2023-10-24 23:31:29", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles T." }, "orcid": "0000-0001-7671-2141" } ] }, "title": "Eliminating Electron Self-Repulsion", "ispublished": "unpub", "full_text_status": "public", "note": "Thank you to Jacob Barandes, Maaneli Derakhshani, Michael Miller, and Logan McCarty for helpful feedback and discussion.\n\n
Accepted Version - 2206.09472.pdf
", "abstract": "Problems of self-interaction arise in both classical and quantum field theories. To understand how such problems are to be addressed in a quantum theory of the Dirac and electromagnetic fields (quantum electrodynamics), we can start by analyzing a classical theory of these fields. In such a classical field theory, the electron has a spread-out distribution of charge that avoids some of the problems of self-interaction facing point charge models. However, there remains the problem that the electron will experience self-repulsion. This self-repulsion cannot be eliminated within classical field theory without also losing Coulomb interactions between distinct particles. But, electron self-repulsion can be eliminated from quantum electrodynamics in the Coulomb gauge by fully normal-ordering the Coulomb term in the Hamiltonian. After normal-ordering, the Coulomb term contains pieces describing attraction and repulsion between distinct particles and also pieces describing particle creation and annihilation, but no pieces describing self-repulsion.", "date": "2023-01-20", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20230119-194747912", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230119-194747912", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.48550/arXiv.2206.09472", "primary_object": { "basename": "2206.09472.pdf", "url": "https://authors.library.caltech.edu/records/btfgb-drp15/files/2206.09472.pdf" }, "resource_type": "monograph", "pub_year": "2023", "author_list": "Sebens, Charles T." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/21a7w-1wp50", "eprint_id": 117711, "eprint_status": "archive", "datestamp": "2023-08-22 18:18:24", "lastmod": "2023-10-24 22:38:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles T." }, "orcid": "0000-0001-7671-2141" } ] }, "title": "The Disappearance and Reappearance of Potential Energy in Classical and Quantum Electrodynamics", "ispublished": "pub", "full_text_status": "public", "keywords": "General Physics and Astronomy", "abstract": "In electrostatics, we can use either potential energy or field energy to ensure conservation of energy. In electrodynamics, the former option is unavailable. To ensure conservation of energy, we must attribute energy to the electromagnetic field and, in particular, to electromagnetic radiation. If we adopt the standard energy density for the electromagnetic field, then potential energy seems to disappear. However, a closer look at electrodynamics shows that this conclusion actually depends on the kind of matter being considered. Although we cannot get by without attributing energy to the electromagnetic field, matter may still have electromagnetic potential energy. Indeed, if we take the matter to be represented by the Dirac field (in a classical precursor to quantum electrodynamics), then it will possess potential energy (as can be seen by examining the symmetric energy-momentum tensor of the Dirac field). Thus, potential energy reappears. Upon field quantization, the potential energy of the Dirac field becomes an interaction term in the Hamiltonian operator of quantum electrodynamics.", "date": "2022-12", "date_type": "published", "publication": "Foundations of Physics", "volume": "52", "number": "5", "publisher": "Springer", "pagerange": "Art. No. 113", "id_number": "CaltechAUTHORS:20221104-609510400.2", "issn": "0015-9018", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20221104-609510400.2", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1007/s10701-022-00630-5", "resource_type": "article", "pub_year": "2022", "author_list": "Sebens, Charles T." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kn8v3-apv86", "eprint_id": 117023, "eprint_status": "archive", "datestamp": "2023-08-22 17:49:33", "lastmod": "2023-10-23 20:19:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles T." }, "orcid": "0000-0001-7671-2141" } ] }, "title": "The fundamentality of fields", "ispublished": "pub", "full_text_status": "public", "keywords": "General Social Sciences; Philosophy", "note": "Thank you to David Baker, Jacob Barandes, Jeffrey Barrett, Sean Carroll, Eddy Keming Chen, Maaneli Derakhshani, Benjamin Feintzeig, Mario Hubert, Dustin Lazarovici, Logan McCarty, Tushar Menon, David Mwakima, Ward Struyve, Roderich Tumulka, Jim Weatherall, and anonymous reviewers for helpful feedback and discussion. \n\nI have no conflicts of interest to disclose.", "abstract": "There is debate as to whether quantum field theory is, at bottom, a quantum theory of fields or particles. One can take a field approach to the theory, using wave functionals over field configurations, or a particle approach, using wave functions over particle configurations. This article argues for a field approach, presenting three advantages over a particle approach: (1) particle wave functions are not available for photons, (2) a classical field model of the electron gives a superior account of both spin and self-interaction as compared to a classical particle model, and (3) the space of field wave functionals appears to be larger than the space of particle wave functions. The article also describes two important tasks facing proponents of a field approach: (1) legitimize or excise the use of Grassmann numbers for fermionic field values and in wave functional amplitudes, and (2) describe how quantum fields give rise to particle-like behavior.", "date": "2022-10", "date_type": "published", "publication": "Synthese", "volume": "200", "number": "5", "publisher": "Springer Science and Business Media LLC", "pagerange": "Art. No. 380", "id_number": "CaltechAUTHORS:20220916-665813000", "issn": "1573-0964", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220916-665813000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1007/s11229-022-03844-2", "resource_type": "article", "pub_year": "2022", "author_list": "Sebens, Charles T." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/msw1n-tkx40", "eprint_id": 115378, "eprint_status": "archive", "datestamp": "2023-08-20 07:02:54", "lastmod": "2023-10-24 16:29:13", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles T." }, "orcid": "0000-0001-7671-2141" } ] }, "title": "The Fundamentality of Fields", "ispublished": "unpub", "full_text_status": "restricted", "note": "Thank you to David Baker, Jacob Barandes, Jeffrey Barrett, Sean Carroll, Eddy Keming Chen, Maaneli Derakhshani, Benjamin Feintzeig, Mario Hubert, Dustin Lazarovici, Logan McCarty, Tushar Menon, David Mwakima, Ward Struyve, Roderich Tumulka, Jim Weatherall, and anonymous reviewers for helpful feedback and discussion.", "abstract": "There is debate as to whether quantum field theory is, at bottom, a quantum theory of fields or particles. One can take a field approach to the theory, using wave functionals over field configurations, or a particle approach, using wave functions over particle configurations. This article argues for a field approach, presenting three advantages over a particle approach: (1) particle wave functions are not available for photons, (2) a classical field model of the electron gives a superior account of both spin and self-interaction as compared to a classical particle model, and (3) the space of field wave functionals appears to be larger than the space of particle wave functions. The article also describes two important tasks facing proponents of a field approach: (1) legitimize or excise the use of Grassmann numbers for fermionic field values and in wave functional amplitudes, and (2) describe how quantum fields give rise to particle-like behavior.", "date": "2022-07-07", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20220707-170614632", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220707-170614632", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.48550/arXiv.2202.09425", "resource_type": "monograph", "pub_year": "2022", "author_list": "Sebens, Charles T." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/a4ead-0e652", "eprint_id": 115412, "eprint_status": "archive", "datestamp": "2023-08-20 07:46:06", "lastmod": "2023-10-24 16:30:17", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hubert-Mario-G", "name": { "family": "Hubert", "given": "Mario" }, "orcid": "0000-0002-1170-6020" }, { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles T." }, "orcid": "0000-0001-7671-2141" } ] }, "title": "Absorbing the Arrow of Electromagnetic Radiation", "ispublished": "unpub", "full_text_status": "public", "note": "We wish to thank Craig Callender, Eddy Keming Chen, Erik Curiel, Olivier Darrigol, Sheldon Goldstein, Tim Maudlin, John Norton, Jill North, Sterl Phinney, Jos Uffink, David Wallace, and the anonymous reviewers for helpful comments and discussions.\n\nSubmitted - 2205.14233.pdf
", "abstract": "We argue that the asymmetry between diverging and converging electromagnetic waves is just one of many asymmetries in observed phenomena that can be explained by a past hypothesis and statistical postulate (together assigning probabilities to different states of matter and field in the early universe). The arrow of electromagnetic radiation is thus absorbed into a broader account of temporal asymmetries in nature. We give an accessible introduction to the problem of explaining the arrow of radiation and compare our preferred strategy for explaining the arrow to three alternatives: (i) modifying the laws of electromagnetism by adding a radiation condition requiring that electromagnetic fields always be attributable to past sources, (ii) removing electromagnetic fields and having particles interact directly with one another through retarded action-at-a-distance, (iii) adopting the Wheeler-Feynman approach and having particles interact directly through half-retarded half-advanced action-at-a-distance. In addition to the asymmetry between diverging and converging waves, we also consider the related asymmetry of radiation reaction.", "date": "2022-05-27", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20220707-204126218", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220707-204126218", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.48550/arXiv.arXiv.2205.14233", "primary_object": { "basename": "2205.14233.pdf", "url": "https://authors.library.caltech.edu/records/a4ead-0e652/files/2205.14233.pdf" }, "resource_type": "monograph", "pub_year": "2022", "author_list": "Hubert, Mario and Sebens, Charles T." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/q3bhn-7bn74", "eprint_id": 94586, "eprint_status": "archive", "datestamp": "2023-08-20 07:06:12", "lastmod": "2023-10-20 18:05:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles T." }, "orcid": "0000-0001-7671-2141" } ] }, "title": "The Mass of the Gravitational Field", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Authors. Published by The University of Chicago Press for The British Society for the Philosophy of Science. \n\nPublished: 18 January 2019. \n\nThank you to Craig Callender, Erik Curiel, Neil Dewar, John Dougherty, Dennis Lehmkuhl, Jim Weatherall, and anonymous referees for helpful feedback and discussion. This project was supported in part by funding from the President's Research Fellowships in the Humanities, University of California (for research conducted while at the University of California, San Diego). I would also like to thank LMU Munich for their hospitality during a visit in the winter of 2018.\n\nSubmitted - 1811.10602.pdf
", "abstract": "By mass\u2013energy 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.", "date": "2022-03", "date_type": "published", "publication": "British Journal for the Philosophy of Science", "volume": "73", "number": "1", "publisher": "Oxford University Press", "pagerange": "211-248", "id_number": "CaltechAUTHORS:20190409-111728426", "issn": "0007-0882", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190409-111728426", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "University of California, San Diego" } ] }, "doi": "10.1093/bjps/axz002", "primary_object": { "basename": "1811.10602.pdf", "url": "https://authors.library.caltech.edu/records/q3bhn-7bn74/files/1811.10602.pdf" }, "resource_type": "article", "pub_year": "2022", "author_list": "Sebens, Charles T." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/b4k65-6tp08", "eprint_id": 105473, "eprint_status": "archive", "datestamp": "2023-08-22 12:23:53", "lastmod": "2023-10-20 22:02:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles T." } } ] }, "title": "Particles, fields, and the measurement of electron spin", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Electron spin; Dirac equation; Dirac field; Stern\u2013Gerlach experiment", "note": "\u00a9 2020 Springer Nature Switzerland AG. \n\nReceived 12 March 2020; Accepted 20 August 2020; Published 03 September 2020. \n\nThank you to Valia Allori, Jacob Barandes, Jeffrey Barrett, Mario Hubert, and the anonymous reviewers for helpful feedback and discussion.", "abstract": "This article compares treatments of the Stern\u2013Gerlach 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).", "date": "2021-12", "date_type": "published", "publication": "Synthese", "volume": "198", "number": "12", "publisher": "Springer", "pagerange": "11943-11975", "id_number": "CaltechAUTHORS:20200922-132154675", "issn": "0039-7857", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200922-132154675", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1007/s11229-020-02843-5", "resource_type": "article", "pub_year": "2021", "author_list": "Sebens, Charles T." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vktac-ka932", "eprint_id": 110029, "eprint_status": "archive", "datestamp": "2023-08-22 10:42:00", "lastmod": "2023-10-23 18:15:42", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles T." } } ] }, "title": "Electron Charge Density: A Clue from Quantum Chemistry for Quantum Foundations", "ispublished": "pub", "full_text_status": "public", "keywords": "Electron charge density; Quantum chemistry; Hartree-Fock; Density functional theory; GRW; Many-worlds; Bohmian mechanics", "note": "\u00a9 The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021. \n\nReceived 17 February 2021; Accepted 07 June 2021; Published 30 June 2021. \n\nThank you to Craig Callender, Eddy Keming Chen, Scott Cushing, Maaneli Derakhshani, Mario Hubert, Joshua Hunt, Gerald Knizia, Logan McCarty, and Eric Winsberg for helpful feedback and discussion.\n\nAccepted Version - 2105.11988.pdf
", "abstract": "Within quantum chemistry, the electron clouds that surround nuclei in atoms and molecules are sometimes treated as clouds of probability and sometimes as clouds of charge. These two roles, tracing back to Schr\u00f6dinger and Born, are in tension with one another but are not incompatible. Schr\u00f6dinger's idea that the nucleus of an atom is surrounded by a spread-out electron charge density is supported by a variety of evidence from quantum chemistry, including two methods that are used to determine atomic and molecular structure: the Hartree-Fock method and density functional theory. Taking this evidence as a clue to the foundations of quantum physics, Schr\u00f6dinger's electron charge density can be incorporated into many different interpretations of quantum mechanics (and extensions of such interpretations to quantum field theory).", "date": "2021-08", "date_type": "published", "publication": "Foundations of Physics", "volume": "51", "number": "4", "publisher": "Springer", "pagerange": "Art. No. 75", "id_number": "CaltechAUTHORS:20210727-173040478", "issn": "0015-9018", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210727-173040478", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1007/s10701-021-00480-7", "primary_object": { "basename": "2105.11988.pdf", "url": "https://authors.library.caltech.edu/records/vktac-ka932/files/2105.11988.pdf" }, "resource_type": "article", "pub_year": "2021", "author_list": "Sebens, Charles T." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wegsx-8sn96", "eprint_id": 106861, "eprint_status": "archive", "datestamp": "2023-08-20 00:08:55", "lastmod": "2023-10-23 15:07:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles T." } } ] }, "title": "Possibility of small electron states", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 American Physical Society. \n\nReceived 11 August 2020; revised 29 October 2020; accepted 2 November 2020; published 30 November 2020. \n\nI thank Logan McCarty for bringing the papers by Bracken, Flohr, and Melloy to my attention. I also thank Jacob Barandes, Noel Swanson, and the anonymous reviewers for helpful feedback and discussion.\n\nPublished - PhysRevA.102.052225.pdf
Submitted - 2010.16255.pdf
", "abstract": "Some authors have claimed that there exists a minimum size (on the order of the Compton radius) for electron states composed entirely of positive-frequency solutions to the free Dirac equation. Other authors have put forward counterexamples to such claims. This article asks how the counterexamples of A. J. Bracken and G. F. Melloy [J. Phys. A. 32, 6127 (1999)] bypass two arguments against their possibility. The first is an old argument that, because of the prohibition on faster-than-light motion, the electron must be larger than a certain minimum size if it is to have the correct angular momentum and magnetic moment. This challenge can be addressed by analyzing the flow of energy and charge for the counterexample states. The second argument is an explicit proof (presented in C.-P. Chuu et al. [Solid State Commun. 150, 533 (2010)]) that there is a minimum size for purely positive-frequency electron states. This proof hinges on the assumption of a small spread in momentum space, which is violated by the counterexamples that have been put forward.", "date": "2020-11", "date_type": "published", "publication": "Physical Review A", "volume": "102", "number": "5", "publisher": "American Physical Society", "pagerange": "Art. No. 052225", "id_number": "CaltechAUTHORS:20201201-104227498", "issn": "2469-9926", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201201-104227498", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1103/PhysRevA.102.052225", "primary_object": { "basename": "2010.16255.pdf", "url": "https://authors.library.caltech.edu/records/wegsx-8sn96/files/2010.16255.pdf" }, "related_objects": [ { "basename": "PhysRevA.102.052225.pdf", "url": "https://authors.library.caltech.edu/records/wegsx-8sn96/files/PhysRevA.102.052225.pdf" } ], "resource_type": "article", "pub_year": "2020", "author_list": "Sebens, Charles T." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wy587-5xt76", "eprint_id": 100423, "eprint_status": "archive", "datestamp": "2023-08-19 21:08:50", "lastmod": "2023-10-18 19:56:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles T." } } ] }, "title": "Putting Positrons into Classical Dirac Field Theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 Elsevier Ltd. \n\nReceived 22 April 2019, Revised 12 September 2019, Accepted 9 October 2019, Available online 1 February 2020.\n\nSubmitted - 1905.01773.pdf
", "abstract": "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.", "date": "2020-05", "date_type": "published", "publication": "Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics", "volume": "70", "publisher": "Elsevier", "pagerange": "8-18", "id_number": "CaltechAUTHORS:20191223-154016646", "issn": "1355-2198", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191223-154016646", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1016/j.shpsb.2019.10.003", "primary_object": { "basename": "1905.01773.pdf", "url": "https://authors.library.caltech.edu/records/wy587-5xt76/files/1905.01773.pdf" }, "resource_type": "article", "pub_year": "2020", "author_list": "Sebens, Charles T." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xjs66-atp16", "eprint_id": 86983, "eprint_status": "archive", "datestamp": "2023-08-19 18:24:32", "lastmod": "2023-10-18 20:45:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles T." } } ] }, "title": "How Electrons Spin", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 Elsevier Ltd. \n\nReceived 22 May 2018, Revised 12 March 2019, Accepted 22 April 2019, Available online 28 June 2019. \n\nThank you to Adam Becker, Dirk-Andr\u00e9 Deckert, John McGreevy, Lukas Nickel, Hans Ohanian, Laura Ruetsche, Roderich Tumulka, David Wallace, and anonymous referees for helpful feedback and discussion. This project was supported in part by funding from the President's Research Fellowships in the Humanities, University of California.\n\nSubmitted - 1806.01121.pdf
", "abstract": "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.", "date": "2019-11", "date_type": "published", "publication": "Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics", "volume": "68", "publisher": "Elsevier", "pagerange": "40-50", "id_number": "CaltechAUTHORS:20180612-074244101", "issn": "1355-2198", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180612-074244101", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "University of California" } ] }, "doi": "10.1016/j.shpsb.2019.04.007", "primary_object": { "basename": "1806.01121.pdf", "url": "https://authors.library.caltech.edu/records/xjs66-atp16/files/1806.01121.pdf" }, "resource_type": "article", "pub_year": "2019", "author_list": "Sebens, Charles T." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2ve7w-w6833", "eprint_id": 95516, "eprint_status": "archive", "datestamp": "2023-08-22 01:16:25", "lastmod": "2023-10-20 20:18:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles T." } } ] }, "title": "Electromagnetism as Quantum Physics", "ispublished": "pub", "full_text_status": "public", "keywords": "Photon wave function; Electromagnetism; Weber vector; Bohmian mechanics; Field Particle; Quantum field theory", "note": "\u00a9 2019 Springer Science+Business Media, LLC, part of Springer Nature. \n\nReceived 03 October 2018; Accepted 05 March 2019; First Online\n19 March 2019. \n\nThank you to Steve Carlip, Sheldon Goldstein, Chris Hitchcock, Michael Kiessling, Matthias Lienert, Ward Struyve, A. Shadi Tahvildar-Zadeh, Roderich Tumulka, David Wallace, and an anonymous referee for helpful feedback and discussion. This project was supported in part by funding from the President's Research Fellowships in the Humanities, University of California (for research conducted while at the University of California, San Diego).\n\nSubmitted - 1902.01930.pdf
", "abstract": "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 in Phys Rev 105(6):1914\u20131919, 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.", "date": "2019-04", "date_type": "published", "publication": "Foundations of Physics", "volume": "49", "number": "4", "publisher": "Springer", "pagerange": "365-389", "id_number": "CaltechAUTHORS:20190515-135120517", "issn": "0015-9018", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190515-135120517", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "University of California, San Diego" } ] }, "doi": "10.1007/s10701-019-00253-3", "primary_object": { "basename": "1902.01930.pdf", "url": "https://authors.library.caltech.edu/records/2ve7w-w6833/files/1902.01930.pdf" }, "resource_type": "article", "pub_year": "2019", "author_list": "Sebens, Charles T." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4762y-et079", "eprint_id": 119500, "eprint_status": "archive", "datestamp": "2023-08-19 13:31:09", "lastmod": "2023-10-25 14:42:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles" }, "orcid": "0000-0001-7671-2141" } ] }, "title": "What's everything made of?", "ispublished": "pub", "full_text_status": "public", "abstract": "To answer whether the fundamental building blocks of reality are particles, fields or both means thinking beyond physics.", "date": "2019", "date_type": "published", "publication": "Aeon", "publisher": "Aeon Media Group", "id_number": "CaltechAUTHORS:20230224-181800409", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230224-181800409", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "resource_type": "article", "pub_year": "2019", "author_list": "Sebens, Charles" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7xfz7-9y693", "eprint_id": 87013, "eprint_status": "archive", "datestamp": "2023-08-19 10:41:02", "lastmod": "2023-10-18 20:47:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles T." } } ] }, "title": "Forces on fields", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 Elsevier Ltd. \n\nReceived 21 March 2017, Revised 18 August 2017, Accepted 15 September 2017, Available online 8 October 2017. \n\nThank you to Craig Callender, Dirk-Andr\u00e9 Deckert, Mario Hubert, and Mark Lange for valuable discussions and helpful feedback on drafts of the paper. Special thanks to Erik Curiel, Dennis Lehmkuhl, and James Weatherall. Thanks also to the anonymous referees who provided useful comments on the paper.\n\nSubmitted - 1707.04198.pdf
", "abstract": "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.", "date": "2018-08", "date_type": "published", "publication": "Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics", "volume": "63", "publisher": "Elsevier", "pagerange": "1-11", "id_number": "CaltechAUTHORS:20180612-133231822", "issn": "1355-2198", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180612-133231822", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1016/j.shpsb.2017.09.005", "primary_object": { "basename": "1707.04198.pdf", "url": "https://authors.library.caltech.edu/records/7xfz7-9y693/files/1707.04198.pdf" }, "resource_type": "article", "pub_year": "2018", "author_list": "Sebens, Charles T." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6ap8g-4e106", "eprint_id": 87046, "eprint_status": "archive", "datestamp": "2023-08-20 13:32:24", "lastmod": "2023-10-18 20:49:16", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles T." } } ] }, "title": "Constructing and Constraining Wave Functions for Identical Quantum Particles", "ispublished": "unpub", "full_text_status": "public", "note": "I would like to sincerely thank David Baker, Eddy Keming Chen, Laura Ruetsche, and anonymous reviewers for helpful feedback on drafts of this paper, Adam Caulton and Sheldon\nGoldstein for useful discussion, and the audience at the So Cal Philosophy of Physics Reading Group--in particular Jeffrey Barrett and Benjamin Feintzeig.\n\nSubmitted - 1608.08590.pdf
", "abstract": "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.", "date": "2018-06-13", "date_type": "published", "id_number": "CaltechAUTHORS:20180613-082631497", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180613-082631497", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.48550/arXiv.1608.08590", "primary_object": { "basename": "1608.08590.pdf", "url": "https://authors.library.caltech.edu/records/6ap8g-4e106/files/1608.08590.pdf" }, "resource_type": "monograph", "pub_year": "2018", "author_list": "Sebens, Charles T." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/a0vv6-h2t23", "eprint_id": 52922, "eprint_status": "archive", "datestamp": "2023-08-19 08:11:28", "lastmod": "2023-10-18 21:46:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles T." } }, { "id": "Carroll-S-M", "name": { "family": "Carroll", "given": "Sean M." }, "orcid": "0000-0002-4226-5758" } ] }, "title": "Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 The Author. Published by Oxford University Press on behalf of British Society for the Philosophy of Science. \n\nRevision Received: 28 May 2015; Accepted: 05 June 2015;\nReceived: 30 January 2016; Published: 02 July 2016. \n\nCharles Sebens would like to thank John-Mark Allen, David Baker, Gordon Belot, Adrian Kent (see Kent [2014]), David Manley, Daniel Peterson, Barry Loewer, and Laura Ruetsche for very useful comments on drafts of this article. He would also like to thank Simon Saunders and David Wallace for a wonderful introduction to the Everett interpretation.\nSean Carroll would like to thank Scott Aaronson, David Albert, Andreas Albrecht, Hirosi Ooguri, Simon Saunders, and David Wallace for helpful conversations. \n\nFunding: National Science Foundation (DGE 0718128 to Charles Sebens); Department of Energy (DE-FG02-92ER40701 to S.C.); Gordon and Betty Moore Foundation through Caltech Moore Center for Theoretical Cosmology and Physics (776 to Sean Carroll and Charles Sebens).\n\nSubmitted - 1405.6903v1.pdf
", "abstract": "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 to the environment alone 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.", "date": "2018-03-01", "date_type": "published", "publication": "British Journal for the Philosophy of Science", "volume": "69", "number": "1", "publisher": "Oxford University Press", "pagerange": "25-74", "id_number": "CaltechAUTHORS:20141216-201958532", "issn": "0007-0882", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141216-201958532", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF Graduate Research Fellowship", "grant_number": "DGE-0718128" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92ER40701" }, { "agency": "Gordon and Betty Moore Foundation", "grant_number": "776" } ] }, "other_numbering_system": { "items": [ { "id": "68-2927", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Moore-Center-for-Theoretical-Cosmology-and-Physics" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1093/bjps/axw004", "primary_object": { "basename": "1405.6903v1.pdf", "url": "https://authors.library.caltech.edu/records/a0vv6-h2t23/files/1405.6903v1.pdf" }, "resource_type": "article", "pub_year": "2018", "author_list": "Sebens, Charles T. and Carroll, Sean M." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wcaaa-hv825", "eprint_id": 87250, "eprint_status": "archive", "datestamp": "2023-08-20 14:09:12", "lastmod": "2023-10-18 20:59:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles T." } } ] }, "title": "Quantum Ontology: A Guide to the Metaphysics of Quantum Mechanics [Book Review]", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 Notre Dame Philosophical Reviews. \n\nBook review of: Quantum Ontology: A Guide to the Metaphysics of Quantum Mechanics, by Peter J. Lewis, Quantum Ontology: A Guide to the Metaphysics of Quantum Mechanics, Oxford University Press, 2016, 207pp., ISBN 9780190469818.", "abstract": "The revolution in physics that brought us to a quantum picture of the world was so radical that it does not merely force a rethinking of physics, but metaphysics as well. Quantum physics may imply that the world is fundamentally indeterministic, that it is fundamentally indeterminate, that causes are not always local to their effects, that there are many more than three spatial dimensions, that wholes are not simply sums of their parts, that our world is just one among many, etc. According to Peter J. Lewis, \"we can say quite confidently that quantum mechanics is metaphysically revisionary even if it is not clear what form the revisions should take.\" (p. xvii) The reason it is so hard to say what the implications of quantum mechanics are for metaphysics is that physicists and philosophers have developed a variety of alternative theories that all attempt to explain why quantum experiments turn out the way they do. These theories disagree on what exists and what rules that stuff obeys. That is, they disagree about the ontology of quantum mechanics and the physical laws that govern that ontology. Understanding the various alternatives and their metaphysical implications is not easy, but Lewis makes it remarkably accessible. Quantum Ontology is an outstanding guide to contemporary philosophy of quantum mechanics.\n\nThe book's intended audience is philosophers who are knowledgeable about metaphysics and curious about the relevance of quantum mechanics to metaphysical debates. For this audience, the book is ideal. Lewis relentlessly avoids overly technical presentations of the physics, using simple examples and helpful visualizations to get to the heart of the matter at hand. The questions that drive the text are questions of metaphysics and the metaphysical motivation for whatever is being discussed is always made clear.", "date": "2016-10-04", "date_type": "published", "publication": "Notre Dame Philosophical Reviews", "publisher": "University of Notre Dame", "id_number": "CaltechAUTHORS:20180620-082321863", "issn": "1538-1617", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180620-082321863", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "resource_type": "article", "pub_year": "2016", "author_list": "Sebens, Charles T." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/a3gk2-gz633", "eprint_id": 87103, "eprint_status": "archive", "datestamp": "2023-08-20 05:42:42", "lastmod": "2023-10-18 20:52:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles T." } } ] }, "title": "Quantum Mechanics as Classical Physics", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015 by the Philosophy of Science Association. \n\nReceived July 2013; revised August 2014. \n\nThanks to David Baker, Gordon Belot, Cian Dorr, Detlef D\u00fcrr, J. Dmitri Gallow, Sheldon Goldstein, Michael Hall, Daniel Peterson, Laura Ruetsche, Ward Struyve, Nicola Vona, and two anonymous referees for very useful feedback on drafts of this article. Thank you to Adam Becker, Sean Carroll, Dirk-Andr\u00e9 Deckert, Neil Dewar, Benjamin Feintzeig, Sophie Monahan, Cat Saint-Croix, Jonathan Shaheen, and Howard Wiseman for helpful discussions. This material is based on work supported by the National Science Foundation Graduate Research Fellowship under grant DGE 0718128.\n\nPublished - 680190.pdf
Accepted Version - 1403.0014
", "abstract": "Here I explore a novel no-collapse interpretation of quantum mechanics that 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.", "date": "2015-04", "date_type": "published", "publication": "Philosophy of Science", "volume": "82", "number": "2", "publisher": "University of Chicago Press", "pagerange": "266-291", "id_number": "CaltechAUTHORS:20180614-114551564", "issn": "0031-8248", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180614-114551564", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF Graduate Research Fellowship", "grant_number": "DGE-0718128" } ] }, "doi": "10.1086/680190", "primary_object": { "basename": "680190.pdf", "url": "https://authors.library.caltech.edu/records/a3gk2-gz633/files/680190.pdf" }, "related_objects": [ { "basename": "1403.0014", "url": "https://authors.library.caltech.edu/records/a3gk2-gz633/files/1403.0014" } ], "resource_type": "article", "pub_year": "2015", "author_list": "Sebens, Charles T." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9cdj7-axw89", "eprint_id": 52923, "eprint_status": "archive", "datestamp": "2023-08-22 11:12:26", "lastmod": "2023-10-18 21:46:35", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Carroll-S-M", "name": { "family": "Carroll", "given": "Sean M." }, "orcid": "0000-0002-4226-5758" }, { "id": "Sebens-C-T", "name": { "family": "Sebens", "given": "Charles T." } } ] }, "title": "Many Worlds, the Born Rule, and Self-Locating Uncertainty", "ispublished": "unpub", "full_text_status": "public", "keywords": "Wave Function; Hilbert Space; Quantum Mechanic; Unitary Transformation; Unitary Evolution", "note": "\u00a9 2014 Springer-Verlag Italia. \n\nA version of this paper appears as a chapter in Quantum Theory: A Two-Time Success Story, Yakir Aharonov Festschrift (2013), D.C. Struppa, J.M. Tollaksen, eds. (Springer-Verlag), p. 157. This work is a \nsummary of a more comprehensive paper [1]. Section 6 did not appear in the original published version. \n\nSean Carroll feels that it has been an honor and a pleasure to take part in the celebration of Yakir Aharonov's 80th birthday and would like to thank Jeff Tollaksen and the organizers of a very stimulating meeting. His work was supported in part by the U.S. Department of Energy, the National Science Foundation, and the Gordon and Betty Moore Foundation. Charles Sebens's work was supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE 0718128.\n\nSubmitted - 1405.7907v2.pdf
", "abstract": "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. [Editors note: for a video of the talk given by Prof. Carroll at the Aharonov-80 conference in 2012 at Chapman University, see quantum.chapman.edu/talk-14.]", "date": "2014", "date_type": "published", "publisher": "Springer", "place_of_pub": "Milan", "pagerange": "157-169", "id_number": "CaltechAUTHORS:20141216-203110170", "isbn": "978-88-470-5216-1", "book_title": "Quantum Theory: A Two-Time Success Story", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141216-203110170", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)" }, { "agency": "NSF" }, { "agency": "Gordon and Betty Moore Foundation" }, { "agency": "NSF Graduate Research Fellowship", "grant_number": "DGE-0718128" } ] }, "other_numbering_system": { "items": [ { "id": "68-2929", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Moore-Center-for-Theoretical-Cosmology-and-Physics" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "contributors": { "items": [ { "id": "Struppa-D-C", "name": { "family": "Struppa", "given": "Daniele C." } }, { "id": "Tollaksen-J-M", "name": { "family": "Tollaksen", "given": "Jeffrey M." } } ] }, "doi": "10.1007/978-88-470-5217-8_10", "primary_object": { "basename": "1405.7907v2.pdf", "url": "https://authors.library.caltech.edu/records/9cdj7-axw89/files/1405.7907v2.pdf" }, "resource_type": "book_section", "pub_year": "2014", "author_list": "Carroll, Sean M. and Sebens, Charles T." } ]