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Well, this subject deserves some effort and a help form philosophy of science. But if you are looking for a mathematical and physical approach I would suggest you to read the paper by Carlo Rovelli. Here's the link. Summarizing, the paper argues that within the conditions Aristotle lived his physics can be taken as an empirically grounded theory.

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I spent a long time researching this question for Carver Mead (mentioned by Art Brown) in 2008, because we were both curious what Feynman meant. Carver thought Feynman's "better way of presenting electrodynamics" would be something along the lines of his own "Collective Electrodynamics," but that turned out to be only partly true, as I discovered in four ...

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It's not completely clear what you're asking, but I can make one thing clear: quantum mechanics was not developed with the specific aim of correctly describing the precise amounts to which CHSH inequalities can be violated. Quantum mechanics was developed in the 1920s and early 30s. Bell published his first paper on Bell inequalities in 1964. The first ...

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Michael Faraday by L. Pearce Williams. Lots of biographical information but also detailed explications of his work referencing his published papers and diary. No math though, since Faraday wasn't a mathematician, but he was a great experimentalist!

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Complex numbers are used for practical reasons only: QM includes helices and similar functions. The Euler formula $${e^{i\alpha}} = sin \alpha + i cos \alpha$$ is describing three-dimensional helices in a very simple way, but if you want to use it you must replace one real axis by an imaginary axis. This is why QM generally works with an imaginary axis. ...

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He did a pendulum experiment. The experiment: http://galileoandeinstein.physics.virginia.edu/lectures/Newtons2ndLaw1.htm Read 'Principia Mathematica' Online - the one that Sir Isaac Newton published: http://ia802706.us.archive.org/0/items/newtonspmathema00newtrich/newtonspmathema00newtrich.pdf N.B: NO COPYRIGHT INTENDED

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Is Nash's equation interesting? That is a matter of taste, but objectively I can say that his equations have (independently) interested physicists in the recent past. The equation of motion in your question originates from an action with higher-derivatives and without the usual Einstein-Hilbert action:  S = \int d^4 x \sqrt{-g}\left[2 ...

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Newton formulated his Law of Gravitation from observation and experimentation. He termed this method as 'induction'.

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To answer the question in your title, he used his newly found fluxions (calculus) to prove that Kepler's laws of planetary motion imply a radial, inverse square law. Feynman's Lost Lecture is a mixture both of Feynman's attempts to give the simplest possible explanation of how one goes about this derivation and his insights into the history of how Newton ...

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Of course, now we've adopted Schrödinger equation as a postulate: it is true. However, Schrödinger derived the equation from previous knowledge. Schrödinger thought his equation from Hamilton-Jacobi formalism. If you take the classical limit in that equation you'll find the Hamilton-Jacobi equation. You can also read the original Schrödinger papers in ...

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If you assume that one mass does not inhibit the force from any other mass, then the result follows from the multiplicity of all pairwise interactions. Without loss of generality* you can imagine partitioning each object into an integer number of small pieces, all of the same mass. Then the force of each piece in one object on each piece in the other ...

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You can't figure it out just from Kepler's law. An electron orbiting a proton will follow the same path, even though force has nothing to do with the masses of the proton and the electron. However, there are a few basic assumptions that will make it clear. If the force wasn't proportional to the falling mass, then different bodies would accelerate at ...

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