21–30 of 63 posts
I've never gotten a satisfactory explanation of what sort of mathematical object a physical unit (meter, kilo, second etc) is. There are plenty of bones of contention between maths and physics, but this one bothers me the most. Anyone interested in coming at physics from a mathematics perspective should read Arnold's mechanics book.
For those looking for alternatives, Leonard Suskid's "Theoretical Minimum" books in 2 Volumes are way more accessible and easier to read.
Okay...I think this might be interesting. I've seen and read a lot of "math for dumb physicists" works, which as a physicist...yeah, I see their point. This could help me understand the math wizards a little better.
I was more math oriented during my studies, and I hated physics (couldn't openly admit that). I still don't get a lot of the physics I was taught, but I did juggle my way out of it using math, learning some formulas and getting a passing grade. Deep inside I admire physicist more, because for them the things that never clicked for me are natural.
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Skimmed some of the articles, particularly those nearer to my field. Seems like a generally good set of informal notes. Random comments: >when the states evolve in time and the observables don’t we are using Liouville’s picture; when the observables evolve in time and the states don’t we are using Hamilton’s picture. I have never heard this terminology, I have only heard Schrodinger's picture vs. Heisenberg's picture…
I wrote the QM article a very long time ago at this point, and I actually can't reconstruct at the moment why I used those two names! I've also heard Schrodinger and Heisenberg much more frequently. Might be worth an edit.
Earlier quoted context omitted.
I was more math oriented during my studies, and I hated physics (couldn't openly admit that). I still don't get a lot of the physics I was taught, but I did juggle my way out of it using math, learning some formulas and getting a passing grade. Deep inside I admire physicist more, because for them the things that never clicked for me are natural.
imho, high-level physics is harder than pure math. With math you can specialize and focus on some formulas or areas of interest, but this is not really possible with physics. With physics you have to know all the areas of math very well--group theory, differential equations, differential geometry, etc. You have to have know all the math well and all the physics from Maxwell and beyond. It's just much more material in…
Spivak (of differential geometry fame) wrote a book with this precise title: https://archive.org/details/physics-for-mathematicians-mecha... It's a very interesting take on classical mechanics.
I've never gotten a satisfactory explanation of what sort of mathematical object a physical unit (meter, kilo, second etc) is. There are plenty of bones of contention between maths and physics, but this one bothers me the most. Anyone interested in coming at physics from a mathematics perspective should read Arnold's mechanics book.
One concern is that measures, out of the box, have issues in 3+ dimensions. Concretely due to paradoxes such as Banach-Tarski, that arise from the Zermelo Fraenkel (ZF) + Axiom of Choice (AC) = ZFC axiomatic formulation for set theory. Since things need to conserve in pyhsics, one has to account for this issue and doing so is harder than it may seem as AC is part of the "fabric" of most mathematics which, at large, c…
Speaking as a physicist, we don't care at all about stuff like Banach-Tarski, and there is essentially zeo expectation that stuff like ZF vs ZFC will have any impact on physics.
Earlier quoted context omitted.
One concern is that measures, out of the box, have issues in 3+ dimensions. Concretely due to paradoxes such as Banach-Tarski, that arise from the Zermelo Fraenkel (ZF) + Axiom of Choice (AC) = ZFC axiomatic formulation for set theory. Since things need to conserve in pyhsics, one has to account for this issue and doing so is harder than it may seem as AC is part of the "fabric" of most mathematics which, at large, c…
IMHO that is the result of Gibbs style vectors and the cross product only being validated in R^3 Lie groups and geometric algebra remove a lot of problems. It also applies to differential calculus and ML methods like back propagation and gradient decent. Gibbs style vectors and the cross are convenient as they tend to match our visual intuitions. But lots of the 'physics isn't real math' claims just don't understand…
As an aside, I'd like to emphasise that geometric algebra gives exactly the same physics outcomes as doing the maths with vectors or tensors or whatever else you like. The difference is essentially just notation. Some things look prettier.