In problem number 6 of his famous list of 23 mathematical problems, David Hilbert asked for the axiomatisation of physics. My question is what does he really mean by that? Is not the problem solved by the fact that we use mathematics (which is built from accepted axioms - as found in any real analysis course) to perform physics calculations and settle its 'disputes' (as in quantum mechanics etc.)? I also read that special theory of relativity, Thermodynamics and Electromagnetism were axiomatised in the beginning of the 20th century.
2026-04-06 04:26:27.1775449587
Axiomatising Physics
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If I have understood your question correctly, I hope the answer is as follows. I hope you are already familiar with the postulates in quantum physics. The whole quantum physics framework is based on those postulates. When Einstein proposed his special theory of relativity he took that the speed of light in vacuum should be invariant (which is 'c') in all inertial frames (the frames where Newtons second law hold) and the effects of length contraction, time dilation etc. just the consequence of taking that the speed of light in vacuum is invariant in all inertial frames. In case of thermodynamics- it is based on the zeroth, first, second and third law of thermodynamics. So in this sense you can say that physics is also axiomatised. I hope you would find my explanation helpful. .