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Asked by Toni V on 7 Nov 2023.
Question: Like in mathematics are there Axioms of physics from which everything is built on and are undeniably true but yet cannot be proven,
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Joel Goldstein answered on 7 Nov 2023:
Although any given physics theory will be based on a number of unproven assumptions, these can (and will) be challenged if the theory’s predictions are not borne out by experiment.
A good example is that classical physics was built on the “axiom” that nature consists of particles with a definite position, but this cannot account for many of the features of the sub-atomic world. Classical physics has therefore been superseded by quantum mechanics with different starting assumptions.
So we try to keep an open mind about everything, and experiment is the ultimate test.
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Daniel Moise answered on 14 Nov 2023:
Short answer: no, you get to pick what’s fundamental and derive the rest
Long answer: historically physics has been driven by a loop of finding something unexplained –> coming up with theories to explain that –> testing the new predictions of these theories –> end up with a theory that withstands experimental scrutiny –> find something unexplained etc. Typically this new theory builds up on top of existing knowledge. For example, you can think of Maxwell’s theory of electromagnetism as an extension to electrostatics based on Coulomb’s law, or of quantum electrodynamics (QED) as an extension to Maxwell’s theory. Historically Coulomb’s law was discovered first, then Maxwell’s theory, then QED, so someone going into physics learns how to derive Maxwell from Coulomb and QED from Maxwell (+ a bunch of other things), and in this line of reasoning you can think of Coulomb’s as “fundamental”. But it is _not_ an axiom. An axion is immutable, whatever you do in flat geometry will get you back to Euclid’s postulates, that’s the kind of power an axiom has. In physics it just so happens that that’s the way we built our theory historically, there’s nothing stopping you from treating QED as “fundamental” and then deriving everything else.
So in physics there are some set of principles/theorems/equations/whatever that can explain a bunch of other things, but given the way physics works you have a liberty of selecting them that’s not available to a fundamental a concept as an axiom.
If you’d like to know more on the topic I highly recommend Richard Feynman’s take on this subject: https://www.youtube.com/watch?v=obCjODeoLVw the bit that’s particularly important to axions is right at the beginning and around the 5:20 mark.
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