Comment by azalemeth
3 days ago
I think perhaps the 'maths' at the bottom is a bit of a retelling of the Yukawa potential which you can get in a "relatively understandable" way from the Klein-Gordon equation. However, the KG equation is very very wrong!
Perhaps an approach trying to actually explain the Feynman propagators would be more helpful? Either way, I agree that if someone wanted to understand this all properly it requires a university education + years of postgrad exposure to the delights of QED / electroweak theory. If anyone here wants a relatively understandable deep dive, my favourite books are Quantum Field Theory for the Gifted Amateur [aka graduate student] by Stephen Blundell [who taught me] and Tom Lancester [his former graduate student], and also Quarks and Leptons by Halzel and Martin. It is not a short road.
The Yukawa potential is also just a more "classical" limit of an inherently quantum mechanical process. Sure you can explain things with it and even do some practical calculations, but if you plan on going to the bottom of it it'll always fail. If you want to explain Feynman propagators correctly you basically have to explain so many other things first, you might as well write a whole book. And even then you're trapped in the confines of perturbation theory, which is only a tiny window into a much bigger world. I really don't think it is possible to convey these things in a way that is both accurate (in the sense that it won't lead to misunderstandings) and simple enough so that people without some hefty prerequisites can truly understand it. I wish it were different. Because this is causing a growing rift between scientists and the normal population.
IIRC, Feynman said something like "I can't explain magnetism to a layperson in terms they can understand."
> ...causing a growing rift between scientists and the normal population.
True.
The full quote is better.
Ie: “I can’t explain it in terms of something else you’re more familiar with because I don’t understand it terms of anything else you’re more familiar with.”
Yet Einstein said something like "If you can't explain it simply, you don't understand it well enough". So maybe Feynman didn't understand it "well enough"
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I haven't read the other two, but I'll second 'Quarks and Leptons'. I do believe it's Halzen though, rather than Halzel...
> the KG equation is very very wrong!
How so? It's the standard equation for a scalar (spin zero) field.
The biggest glaring issue with it (eg in the form (square^2+m^2)\psi=0) is that it is a manifestly Lorentz invariant equation in which particle number is conserved (which is highly unlikely for any relativistic interaction). I know that you can extend it into a scalar field theory proper, quantize it, and sidestep around those issues (and use it as a model in cmp!), but the bigger problem I think is that you really need spin -- and ideally all other interactions...