Could quantum mechanics have been invented earlier? Counterfactual questions like this aren't meant to be taken literally, but I think it's interesting anyway.
Once upon a time it was noticed that light rays follow the shortest path - for some definition of shortest [1]. This generated interest in rewriting Newtonian mechanics in a similar way and so Maupertuis came up with his principle [2].
AFAICT the idea of recasting physics as shortest length problems was adopted almost like a religion. Maupertius's principle, like Fermat's, only described the path, not the dynamics over time. For that Hamilton found his principle [3].
But I think this was all driven by an apparent analogy with Fermat's principle. And with the understanding that light is a wave, researchers wanted to find a wave formulation of mechanics too. This idea predates quantum mechanics by centuries but is motivated by the idea that Newtonian particles are similar to light, and yet light is described by a wave. According to wikipedia this dates back to Bernoulli and somehow I'd never heard this before. I'm amazed.
The wave formulation found was the Hamilton-Jacobi formulation (HJE) [4]. It's basically the Schrodinger equation in the limit as ℏ goes to zero. A nice piece of the machinery of QM is there in disguised form. If you take one more tiny step to shoehorn HJE so it looks more like the wave equation for light - replace the action A with exp(iA) and use (+,×) instead of (min,+) for some of the arithmetic - then QM pops out. I think researchers came remarkably close without any evidence like the photoelectric effect.
[1] https://en.wikipedia.org/wiki/Fermat%27s_principle
[2] https://en.wikipedia.org/wiki/Maupertuis%27s_principle
[3] https://en.wikipedia.org/wiki/Hamilton%27s_principle
[4] https://en.wikipedia.org/wiki/Hamilton%E2%80%93Jacobi_equation
Dan Piponi /
npub1xs…fgrae
2025-05-05 19:07:33
Author Public Key
npub1xs30e0pj7velktf5sxewnqf93tu2pdt3s6wtl6fug2tzgy8zxthsgfgraePublished at
2025-05-05 19:07:33Event JSON
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"content": "Could quantum mechanics have been invented earlier? Counterfactual questions like this aren't meant to be taken literally, but I think it's interesting anyway.\n\nOnce upon a time it was noticed that light rays follow the shortest path - for some definition of shortest [1]. This generated interest in rewriting Newtonian mechanics in a similar way and so Maupertuis came up with his principle [2].\n\nAFAICT the idea of recasting physics as shortest length problems was adopted almost like a religion. Maupertius's principle, like Fermat's, only described the path, not the dynamics over time. For that Hamilton found his principle [3].\n\nBut I think this was all driven by an apparent analogy with Fermat's principle. And with the understanding that light is a wave, researchers wanted to find a wave formulation of mechanics too. This idea predates quantum mechanics by centuries but is motivated by the idea that Newtonian particles are similar to light, and yet light is described by a wave. According to wikipedia this dates back to Bernoulli and somehow I'd never heard this before. I'm amazed.\n\nThe wave formulation found was the Hamilton-Jacobi formulation (HJE) [4]. It's basically the Schrodinger equation in the limit as ℏ goes to zero. A nice piece of the machinery of QM is there in disguised form. If you take one more tiny step to shoehorn HJE so it looks more like the wave equation for light - replace the action A with exp(iA) and use (+,×) instead of (min,+) for some of the arithmetic - then QM pops out. I think researchers came remarkably close without any evidence like the photoelectric effect.\n\n[1] https://en.wikipedia.org/wiki/Fermat%27s_principle\n[2] https://en.wikipedia.org/wiki/Maupertuis%27s_principle\n[3] https://en.wikipedia.org/wiki/Hamilton%27s_principle\n[4] https://en.wikipedia.org/wiki/Hamilton%E2%80%93Jacobi_equation",
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