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Preliminary

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On Hilbert's Sixth Problem

Part of the book series: Synthese Library ((SYLI,volume 441))

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Abstract

However things aren’t just as simple, for the specter of undecidability and incompleteness, which was unknown and, we may say, unsuspected in 1900, raises its head.

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Notes

  1. 1.

    In the AMS 1976 translation.

  2. 2.

    Also, we may uncover unusual interpretations, who knows?

  3. 3.

    Of course Einstein himself contributed to the early formulations of quantum mechanics.

  4. 4.

    A partial answer, but one that encompasses all kinds of time-dependent physics.

  5. 5.

    Of course we can consider unsound or even inconsistent theories. This is just a starting point.

  6. 6.

    This is the actual way most courses in theoretical physics are taught.

  7. 7.

    “The Principles of Mechanics Presented in a New Form.”

  8. 8.

    Said to have been Richard Palais.

  9. 9.

    We will proceed in an informal way, and leave to the archetypical interested reader the toil and trouble of translating everything that we have done into a fully formal, rigorous, treatment of our presentation.

References

  • Abraham, R., & Marsden, J. (1978). Foundations of mechanics (2nd. ed.) Addison–Wesley.

    Google Scholar 

  • Cho, Y. M. (1975). Higher-dimensional unifications of gravitation and gauge theories. Journal of Mathematical Physics, 16, 2029.

    Article  Google Scholar 

  • Corson, E. M. (1953). Introduction to tensors, spinors and relativistic wave-equations. Blackie & Sons.

    Google Scholar 

  • Dirac, P. A. M. (1967) The principles of quantum mechanics. Oxford U. P.

    Google Scholar 

  • Einstein, A. (1967). The meaning of relativity. Methuen.

    Google Scholar 

  • Einstein, A., and others, The principle of relativity, Dover.

    Google Scholar 

  • Emch, G. (1972). Algebraic methods in statistical mechanics and quantum field theory. Wiley.

    Google Scholar 

  • Hertz, H. (1956). The principles of mechanics, Transl. by D. E. Jones & J. T. Walley. Dover.

    Google Scholar 

  • Jackson, J. D. (1962). Classical electrodynamics, John Wiley.

    Google Scholar 

  • Jeans, J. H. (1925). Mathematical theory of electricity and magnetism. Cambridge U. P.

    Google Scholar 

  • Lanczos, C. (1970). The variational principles of mechanics. University of Toronto Press.

    Google Scholar 

  • MacLane, S. (1968). Geometrical mechanics. Monograph. Department of Mathematics, University of Chicago.

    Google Scholar 

  • Maxwell, J. C. (1954). A treatise on electricity and magnetism, I and II. Dover.

    Google Scholar 

  • O’Rahilly, A. (1965). Electromagnetic theory, I and II. Dover.

    Google Scholar 

  • Sternberg, S. (1964). Lectures on differential geometry. Benjamin.

    Google Scholar 

  • Stratton, J. A. (1941). Electromagnetic theory. McGraw–Hill.

    Google Scholar 

  • Tonnelat, M. A. (1965). Les Théories Unitaires de l’Électromagnétisme et de la Gravitation. Gauthier–Villars.

    Google Scholar 

  • Utiyama, R. (1956). Invariant theoretical interpretation of interaction. Physical Review, 101, 1597.

    Article  Google Scholar 

  • van der Waerden, B. L. (Ed.) (1968). Sources of quantum mechanics, Dover.

    Google Scholar 

  • Weyl, H. (1952). Space time matter, Dover.

    Google Scholar 

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da Costa, N.C.A., Antonio Doria, F. (2022). Preliminary. In: On Hilbert's Sixth Problem. Synthese Library, vol 441. Springer, Cham. https://doi.org/10.1007/978-3-030-83837-9_1

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