4 ms·
What's astonishing: many laws of physics emerge from statistical approximations of quantum mechanics. One day, if I really get into quantum mechanics, I will t
by sylware 4y ago
What's astonishing: many laws of physics emerge from statistical approximations of quantum mechanics.
One day, if I really get into quantum mechanics, I will try to understand how they rebuilt maxwell equations from QED.
- programmer_dude 4y agoI think you mean "ab initio".
- killjoywashere 4y agoQED = Quantum electrodynamics, for which Feynman won the Nobel Prize.
- sylware 4y agoYeah, I meant the latest QED based on the lastest QFT.
- programmer_dude 4y agoMy bad.
- mfn 4y agoRegarding how to derive Maxwell’s equations from QED, I’d recommend this lecture: https://theoreticalminimum.com/courses/special-relativity-and-classical-field-theory/2012/spring/lecture-9 https://theoreticalminimum.com/courses/special-relativity-an... This derivation is in the context of classical field theory, but QED is only a short hop away through path integrals. It’s quite remarkable how the complexity of Maxwell’s equations can be reduced to a single term in the Lagrangian - (F_uv)(F^uv), assuming no charges. That’s really it!
- mhh__ 4y agoRead Quantum field theory for the gifted amateur
- ThomPete 4y agoNot if you submit to the Everett interpretation.
- marginalia_nu 4y agoClassical behavior emerges from quantum mechanics as you enter the classical domain. This can be explained through phase decoherence. As temperature rises, random phase shifts are introduced, which effectively removes the quantum effect. You can show mathematically how this works. Consider the young experiment: https://imgur.com/FqogDJj https://imgur.com/FqogDJj For a plane wave ψ ~ e^(ipx/ħ-iωt), the wave function at X is the sum of two components <X|ψ> = <X|P> + <X|Q> Where for some path-independent normalization function ψ(X,t), and using the small angle assumption (QX-PX = 2Xa/L), the components are: 1 ipXa/ħL <X|P>= ψ(X,t)- e 2 1 -ipXa/ħL <X|Q>= ψ(X,t) - e 2 And the probability of finding the particle at X is 2 2 2 pXa |<X|ψ>| = |ψ(X,t)| cos ----- ħL That is what you'd expect from the Young experiment. If we introduce a constant phase shift ϕ between P and Q, you get this average instead: 2 2 2 pXa |<X|ψ>| = |ψ(X,t)| cos (--- + ϕ) ħL If this phase shift is instead random, the formula becomes 2 1 ^ pXa 2 |<X|ψ>| - (1 + | dϕ P(ϕ)cos(2 --- + 2ϕ)) |ψ(X,t)| 2 v ħL Where P(ϕ) is a probability function for the phase shift. If the probability function is flat, the integral is zero since you're integrating the cosine across its domain. What you get is the classical result! 2 2 |<X|ψ>| = |ψ(X,t)| You can even re-phrase random phase shifts into a diffusion equation, and find that given α as the diffusion coefficient 2 2 1 -αt 2 pXa |<X|ψ>| = |ψ(X,t)| - (1 + e cos (--- + ϕ) ) 2 ħL i.e. the transition behavior from quantum to classical dependent on a direct measure of the decoherence! α small => quantum result, α = large, classical result.
- _yb2s 4y agoHow did you typeset all of that math into hn?
- marginalia_nu 4y agoPainstakingly.