Hamiltonian Privilege
Annalen der Philosophie - Trang 1-24 - 2023
Tóm tắt
We argue that Hamiltonian mechanics is more fundamental than Lagrangian mechanics. Our argument provides a non-metaphysical strategy for privileging one formulation of a theory over another: ceteris paribus, a more general formulation is more fundamental. We illustrate this criterion through a novel interpretation of classical mechanics, based on three physical conditions. Two of these conditions suffice for recovering Hamiltonian mechanics. A third condition is necessary for Lagrangian mechanics. Hence, Lagrangian systems are a proper subset of Hamiltonian systems. Finally, we provide a geometric interpretation of the principle of stationary action and rebut arguments for privileging Lagrangian mechanics.
Tài liệu tham khảo
Abraham, R., & Marsden, J. E. (1978). Foundations of mechanics (2nd ed.). Benjamin-Cummings Publishing Company.
Arnold, V. I. (1989). Mathematical methods of classical mechanics (2nd ed.). Translated by K. Vogtmann and A. Weinstein: Springer.
Baez, J. C. (unpublished). Struggles with the Continuum. arXiv:1609.01421.
Barrett, T. W. (2018). Equivalent and inequivalent formulations of classical mechanics. The British Journal for the Philosophy of Science.
Belot, G. (2013). Symmetry and equivalence. In R. Batterman (Ed.), The Oxford handbook of philosophy of physics (pp. 318–339). Oxford: Oxford University Press.
Butterfield, J. N. (2004). Between laws and models: Some philosophical morals of Lagrangian mechanics. https://arxiv.org/abs/physics/0409030.
Butterfield, J. N. (2006). Against pointillisme about mechanics. The British Journal for the Philosophy of Science, 57, 709–753.
Carcassi, G., & Aidala, C. A. (2020). Hamiltonian mechanics is conservation of information entropy. Studies in History and Philosophy of Modern Physics, 71, 60–71.
Carcassi, G., & Aidala, C. A. (2021). Assumptions of physics. Michigan Publishing.
Carcassi, G., Aidala, C. A., Baker, D. J., & Bieri, L. (2018). From physical assumptions to classical and quantum Hamiltonian and Lagrangian particle mechanics. Journal of Physics Communications, 2, 045026.
Cline, D. (2021). Variational principles in classical mechanics. LibreTexts.
Curiel, E. (2014). Classical mechanics is Lagrangian; it is not Hamiltonian. The British Journal for the Philosophy of Science, 65, 269–321.
Dorr, C., & Hawthorne, J. (2014). Naturalness. In K. Bennett & D. W. Zimmerman (Eds.), Oxford studies in metaphysics (Vol. 8, pp. 3–77). Oxford: Oxford University Press.
Earman, J. (1986). A primer on determinism. Dordrecht: Reidel.
Gelfand, I. M., & Fomin, S. V. (1963). Calculus of variations. Translated by Richard A. Silverman. Englewood Cliffs, NJ: Prentice-Hall.
Gilton, M. J. R. (2021). Could charge and mass be universals? Philosophy and Phenomenological Research, 102, 624–644.
Healey, R. (2007). Gauging what’s real: The conceptual foundations of contemporary gauge theories. Oxford: Oxford University Press.
Hunt, J. (2021). Understanding and equivalent reformulations. Philosophy of Science, 88, 810–823.
Hunt, J. (2022). Symmetry and reformulation: On intellectual progress in science and mathematics. Ph.D. Thesis, University of Michigan.
Lewis, D. (1983). New work for a theory of universals. Australasian Journal of Philosophy, 61, 343–377.
North, J. (2009). The structure of physics: A case study. The Journal of Philosophy, 106, 57–88.
Norton, J. (2008). The dome: An unexpectedly simple failure of determinism. Philosophy of Science, 75, 786–798.
Smith, S. R. (2008). Symmetries and the explanation of conservation laws in the light of the inverse problem in Lagrangian mechanics. Studies in History and Philosophy of Modern Physics, 39, 325–345.
Swanson, N., & Halvorson, H. (2012). On north’s the structure of physics. http://philsci-archive.pitt.edu/9314/.
Teh, N., & Tsementzis, D. (2017). Theoretical equivalence in classical mechanics and its relationship to duality. Studies in History and Philosophy of Modern Physics, 59, 44–54.
Wilson, M. (2013). What is classical mechanics anyways? In R. Batterman (Ed.), The Oxford handbook of philosophy of physics (pp. 43–106). Oxford: Oxford University Press.
Yablo, S. (2014). Aboutness. Princeton: Princeton University Press.