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The Relation Between Mathematics and Physics by Paul Dirac (1939)

172 points · 84 comments · rramadass

  1. Xmd5a · · focus · HN ↗
    > The dominating idea in this application of mathematics to physics is that the equations representing the laws of motion should be of a simple form. The whole success of the scheme is due to the fact that equations of simple form do seem to work. The physicist is thus provided with a principle of simplicity, which he can use as an instrument of research.

    <a href="https:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;math-ph&#x2F;0009007" rel="nofollow">https:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;math-ph&#x2F;0009007

    &gt; Occam&#x27;s Razor as a Formal Basis for a Physical Theory

    &gt; We introduce the principle of Occam&#x27;s Razor in a form which can be used as a basis for economical formulations of physics. This allows us to explain the general structure of the Lagrangian for a composite physical system, as well as some other artificial postulates behind the variational formulations of physical laws. As an example, we derive Hamilton&#x27;s principle of stationary action together with the Lagrangians for the cases of Newtonian mechanics, relativistic mechanics and a relativistic particle in an external gravitational field.

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