Abstract
The purpose of this book is to demonstrate the existence of a mathematical structure that is common to all physical theories of the macrocosm and to explain the origin of this common structure. The starting point of this investigation is the analysis of physical variables under a new profile: we take into consideration all those geometric features that are usually overlooked in physics books.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 2.
The coincidence of the number of symmetry classes in crystal classification and of the distinct space-time elements is purely a matter of chance.
- 3.
The reason for this astonishing correspondence is not clear, but we take it as an assumption supported by the evidence.
- 4.
See also Fig. 8.9 on p. 236.
- 5.
Duhem [60, p. 95].
- 6.
- 7.
Whittaker [254, Vol. I, p. 241].
- 8.
Feynman et al. [69, Vol. II; pp. 12–12].
- 9.
Post [184, p. 630].
- 10.
See pp. 290 and 291.
- 11.
The Web site: http://discretephysics.dicar.units.it/ has collected a large number of papers dealing with this method.
References
Bohm, D., Hiley, B.J., Stuart, A.: On a New Mode of Description in Physics. Int. J. Theor. Phys. 3(3), 171–183 (1970)
Duhem, P.: The Aim and Structure of Physical Theory. Atheneum, New York (1977)
Feynman, R.P., Leighton, R.B., Sands, M.: Lectures on Physics, vol. I-II-III. Addison-Wesley, Reading, MA (1963)
Maxwell, J.C.: Remarks on the mathematical classification of physical quantities. Proc. London Math. Soc. 3(34), 258–266 (1871) [Reprinted by Niven, W.D.: The Scientific Papers of J.C. Maxwell. Dover, New York (1965)]
Post, E.J.: Kottler-Cartan-Van Dantzig (KCD) and noninertial systems. Found. Phys. 9, 619–640 (1978)
Rosen, J.: Fundamental manifestations of symmetry in physics. Found. Phys. 20(3), 283–307 (1990)
Schönberg, M.: Quantum Theory and Geometry. In: Max Planck Festchrift, pp. 321–338. Deutscher, Berlin (1958)
Whittaker, E.: A History of the Theories of Aether and Electricity, vol. 2. Humanities Press, New York (1973)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Tonti, E. (2013). Introduction. In: The Mathematical Structure of Classical and Relativistic Physics. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-7422-7_1
Download citation
DOI: https://doi.org/10.1007/978-1-4614-7422-7_1
Published:
Publisher Name: Birkhäuser, New York, NY
Print ISBN: 978-1-4614-7421-0
Online ISBN: 978-1-4614-7422-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)