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I was hoping finally for some insight into how mass/energy/acceleration might emerge from Fourier analysis or quantum mechanics, but this didn't happen.

But the good news is that this post is a good counter to the misunderstanding that Heisenberg's Uncertainty Principle is something physical, not just the basic mathematical nature of measurement and the relationship between a function and its derivative or integral.

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Unfortunately, I don't yet have a clear signal theoretic interpretation of the Hamiltonian yet. Is that what you’re asking? In any case, thank you for the feedback (it means a lot to me). Also, please consider subscribing, because I'd appreciate your feedback on future posts as well!

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