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In Number Theory and other areas of Pure Mathematics, whatever theorems we have are there forever because they are derived logically from a set of axioms. I would like to know which theories in Physics are constructed logically from indisputable axioms and experimentally verified? I think Special Relativity qualifies for this. What about GR, QM and QFT? String Theory is not yet experimentally verifiable.

Qmechanic
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Rajaram Venkataramani
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  • Does this answer your question? Is physics rigorous in the mathematical sense? – Stéphane Rollandin Feb 03 '23 at 17:21
  • Special relativity or relativity as whole is least qualified because there is no proof of relative invariance while evidences are contradictory i.e. doppler shift. Quantum is another theory based on assumption that energy is qiantized while thermal radiation solely depends upon temperature. – Neil Libertine Feb 03 '23 at 17:23
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    No physics theory is constructed from indisputable axioms, since no mathematics is constructed from indisputable axioms. See the Gödel theorem, axiom of choice and the history of the foundation of mathematics in general. But, keeping these issues in the foundations of mathematics under the rug, even statements such as space and time being $\mathbb{R}^4$ are extremely non-trivial statements that are simply empirical, not "indisputable". – Void Feb 03 '23 at 17:26
  • The closest thing to Mathematical Axioms in Physics are postulates. These postulates (example: "The speed of light is invariant" is a postulate) are based on empirical evidence. Math is a tool to understand the consequences of these postulates. Empirical evidence is always disputable - perhaps our measuring devices aren't sensitive enough. Perhaps we are not interpreting our observations correctly, etc. So "indisputable" is too high a requirement for any physical postulate. In Math, disputability isn't relevant at all - the axioms are arbitrary and don't necessarily reflect any "reality" – Amit Feb 03 '23 at 17:39
  • Energy levels can be continuous or discrete in quantum mechanical systems. Also, claims that the Doppler shift calls relativity into question require citations. – Connor Behan Feb 03 '23 at 18:05
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    Claims that the Doppler shift calls relativity into question are nonsense fringe views unrelated to mainstream physics. The relativistic Doppler effect is well-understood and verified. – Ghoster Feb 03 '23 at 18:19

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