i spent a very enjoyable math binge day learning about waves and what i learned is that waves are extremely fucked up
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This is like the tip of the iceberg of wavy fuckedness
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For some absolute cosmic bullshit, look into: Huygen’s principle, “optical lenses as Fourier transforms” and, maybe especially, like: “fourier transform wavefunction”
It’s been a while, but yeah the universe is wild and waves are cool
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I love Huyen's principle! I still use it to roughly intuit wave stuff sometimes!
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I love it but *why* is it!? Like “oh here’s a plane wave, let’s model that as circular waves emanating from every point along the wavefront; don’t worry, they’ll interfere *just right* for it to work out the same” 🤯
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Because every point in the space in a higher energy state ("on the wave") *has to* "contribute" an independent wave component, which (since it's a single point) of course propagates symmetrically (circle). Any point in a wave is in isolation its own wave
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Replying to @QiaochuYuan
Reminded of my Classical & Quantum Waves professor telling us shit like
"Every solution to the wave equation is a solution of the wave equation!"
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But isn’t that a *statement of* Huygens principle? Rather than an explanation of it?
Still crazy IMO that the math works out at all
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Well
this is physics
the statement/explanation dichotomy *does* kind of break down a bit
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It's interesting how you might ask
"Why can you decompose a plane wave into overlapping circular waves from a plane of points??"
or
"Why do the overlapping circular waves from this plane of points propogate as a plane??"
Either frame COULD be your intuitive starting point
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Replying to
it’s fucked up how vector spaces have different bases. i still can’t quite visualize how to convert between pairs of traveling waves and pairs of standing waves on a vibrating string. even though mathematically it’s just the sum-to-product and product-to-sum formulas!