Abstract
We describe here what we mean by a “physical theory.” Actually we develop the main standard formalisms for it. There are actually three such formalisms
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Notes
- 1.
Based on da Costa and Doria (2011).
- 2.
Actually an assertion out of Newton’s First and Second Laws.
- 3.
We follow the convention in general relativity, that distinguishes contravariant vectors—with components denoted by upstair indices, and covariant vectors, with components given by downstair indices. Contravariant vectors are actual vectors, while covariant vectors are linear forms.
- 4.
We will see the practical reason for “upstairs” and “downstairs” indices when we discuss tensor formalism in general relativity.
- 5.
This step horrifies mathematicians…
- 6.
Yes, downstair indices! But this is just a cavalier-like computation.
- 7.
We admit that’s a kind of savage derivation of some important objects and equations in the analytico-canonical formalism. However it provides a roiugh draft of the main ideas we’ll require for our formal background in physics.
References
da Costa, N. C. A., & Doria, F. A. (2011). Physics: A primer for philosophers of science. Preprint. www.Lulu.com.
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da Costa, N.C.A., Antonio Doria, F. (2022). Classical Mechanics. In: On Hilbert's Sixth Problem. Synthese Library, vol 441. Springer, Cham. https://doi.org/10.1007/978-3-030-83837-9_2
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DOI: https://doi.org/10.1007/978-3-030-83837-9_2
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