Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-n4bck Total loading time: 0.252 Render date: 2022-08-08T14:32:30.721Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Algebraic Fields and the Dynamical Approach to Physical Geometry

Published online by Cambridge University Press:  01 January 2022

Abstract

Brown and Pooley’s ‘dynamical approach’ to physical theories asserts, in opposition to the orthodox position on physical geometry, that facts about physical geometry are grounded in, or explained by, facts about dynamical fields, not the other way round. John Norton has claimed that the proponent of the dynamical approach is illicitly committed to spatiotemporal presumptions in ‘constructing’ space-time from facts about dynamical symmetries. In this article, I present an abstract, algebraic formulation of field theories and demonstrate that the proponent of the dynamical approach is not committed, in special relativity, to the illicit presumptions to which Norton refers.

Type
Physical Sciences
Information
Philosophy of Science , Volume 86 , Issue 5 , December 2019 , pp. 1273 - 1283
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

I am very grateful to Adam Caulton, Harvey Brown, Nick Huggett, Oliver Pooley, James Read, and two anonymous referees for helpful spoken and written feedback.

References

Brown, Harvey R. 2005. Physical Relativity: Spacetime Structure from a Dynamical Perspective. Oxford: Oxford University Press.CrossRefGoogle Scholar
Brown, Harvey R., and Pooley, Oliver. 2001. “The Origins of the Spacetime Metric: Bell’s Lorentzian Pedagogy and Its Significance in General Relativity.” In Physics Meets Philosophy at the Plank Scale, ed. Callender, Craig and Huggett, Nick. Cambridge: Cambridge University Press.Google Scholar
Brown, Harvey R., and Pooley, Oliver. 2006. “Minkowski Space-Time: A Glorious Non-entity.” In The Ontology of Spacetime, ed. Dieks, Dennis. Amsterdam: Elsevier.Google Scholar
Field, Hartry. 1984. “Can We Dispense with Space-Time?” In PSA 1984: Proceedings of the 1984 Biennial Meeting of the Philosophy of Science Association, ed. Asquith, Peter D. and Kitcher, Philip, 3390. East Lansing, MI: Philosophy of Science Association.Google Scholar
Gelfand, I. M., and Naimark, M. A.. 1943. “On the Embedding of Normed Rings into the Ring of Operators in Hilbert Space.” Matematicheskii Sbornik 12:197213.Google Scholar
Geroch, Robert. 1972. “Einstein Algebras.” Communications in Mathematical Physics 26 (4): 271–75..CrossRefGoogle Scholar
Huggett, Nick. 2018. “A Philosopher Looks at Non-commutative Geometry.” Unpublished manuscript, PhilSci Archive. http://philsci-archive.pitt.edu/15432/.Google Scholar
Norton, John D. 2008. “Why Constructive Relativity Fails.” British Journal for the Philosophy of Science 59 (4): 821–34..CrossRefGoogle Scholar
Pooley, Oliver. 2013. “Substantivalist and Relationist Approaches to Spacetime.” In The Oxford Handbook of Philosophy of Physics, ed. Batterman, R.. Oxford: Oxford University Press.Google Scholar
Stevens, Syman. 2015. “The Dynamical Approach as Practical Geometry.” Philosophy of Science 82:1152–62.CrossRefGoogle Scholar
Wallace, David. 2017. “Who’s Afraid of Coordinate Systems? An Essay on the Representation of Spacetime Structure.” Studies in History and Philosophy of Science B.Google Scholar
5
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Algebraic Fields and the Dynamical Approach to Physical Geometry
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Algebraic Fields and the Dynamical Approach to Physical Geometry
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Algebraic Fields and the Dynamical Approach to Physical Geometry
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *