Inconsistency, Asymmetry, and Non-Locality: A Philosophical Investigation of Classical Electrodynamics

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Briefly mentions [Duhem](https://isidore.co/calibre/#panel=book_details&book_id=4506) and Ritz, but not Weber nor Ampère.heard about in this Philosophy StackExchange post: "[Inconsistency of Classical Electrodynamics](https://philosophy.stackexchange.com/q/65047/2014)" * * *pt. 1, ch. 2, §3 "The Inconsistency Proof" appears to amount to a criticism of the field concept (pp. 32-3): > The Maxwell–Lorentz equations allow us to treat two types of problems (see Jackson 1975, 1999). We can use the Maxwell equations to determine the fields associated with a given charge and current distribution, or we can use the Lorentz force law to calculate the motion of a charged particle in a given external electromagnetic field. In problems of the first type, the charges and currents are specified and, given particular initial and boundary conditions (which specify the source-free fields), the total electromagnetic field is calculated. In problems of the second type, the external electromagnetic fields are specified and the motions of charged particles or currents are calculated. Electric charges are treated *either* as being affected by fields *or* as sources of fields, but not both. That is, in both types of problems one ignores any effects that the field associated with a charge itself—the *self-field* —might have on the motion of that charge. (I'm surprised Frisch doesn't mention [Ampère's](https://www.ifi.unicamp.br/~assis/Amperes-Electrodynamics.pdf) or [Weber's](https://archive.org/stream/electricandmag02maxwrich#page/n457/mode/2up) instantaneous action-at-a-distance force laws.)See §3.1 "Multiple Definitions of the Field Concept" and §3.2 "These Different Field Definitions Contradict One Another" of * [Assis, André K. T.](https://www.ifi.unicamp.br/~assis/) [*Relational Mechanics and Implementation of Mach’s Principle with Weber’s Gravitational Force*](https://www.ifi.unicamp.br/~assis/Relational-Mechanics-Mach-Weber.pdf). Montréal: Apeiron, 2014, pp. 43-55. Assis, like Ampère would have,* considers the field concept useless "epicycles" or [scaffoldings](https://isidore.co/calibre/#panel=book_details&book_id=4506) of the physical theory. *cf. [Ampère, Assis, & Chaib 2015](https://www.ifi.unicamp.br/~assis/Amperes-Electrodynamics.pdf) §16.5 "'Ampère' Against the Field Concept", pp. 234-5I like how Frisch (p. 36) quotes Duhem's [*Aim & Structure of Physical Theory* p. 220](https://isidore.co/calibre/#panel=book_details&book_id=4506) regarding how a physical theory must "aim to preserve with jealous care a logical unity", but Frisch should've also cited [*ibid.* ch. 4 "Abstract Theories & Mechanical Models", §10 " *Should the Use of Mechanical Models* [e.g., fields] *Suppress the Search for an Abstract and Logically Ordered Theory?* "](https://isidore.co/calibre/#panel=book_details&book_id=4506).* * *Mathias Frisch provides the first sustained philosophical discussion of conceptual problems in classical particle-field theories. Part of the book focuses on the problem of a satisfactory equation of motion for charged particles interacting with electromagnetic fields. As Frisch shows, the standard equation of motion results in a mathematically inconsistent theory, yet there is no fully consistent and conceptually unproblematic alternative theory. Frisch describes in detail how the search for a fundamental equation of motion is partly driven by pragmatic considerations (like simplicity and mathematical tractability) that can override the aim for full consistency. The book also offers a comprehensive review and criticism of both the physical and philosophical literature on the temporal asymmetry exhibited by electromagnetic radiation fields, including Einstein's discussion of the asymmetry and Wheeler and Feynman's influential absorber theory of radiation. Frisch argues that attempts to derive the asymmetry from thermodynamic or cosmological considerations fail and proposes that we should understand the asymmetry as due to a fundamental causal constraint. The book's overarching philosophical thesis is that standard philosophical accounts that strictly identify scientific theories with a mathematical formalism and a mapping function specifying the theory's ontology are inadequate, since they permit neither inconsistent yet genuinely successful theories nor thick causal notions to be part of fundamental physics.