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This! 99% of modern physics was developed for pen & paper mathematics, not numeric simulations. Even when computers became readily available it was seen as som
by jiggawatts 4y ago
This!
99% of modern physics was developed for pen & paper mathematics, not numeric simulations. Even when computers became readily available it was seen as somehow "less than" symbolic solutions. More practically, special-case solutions that were tractable symbolically require far too much computer power if approached from a fully general "local" simulation perspective.
QED is essentially a Monte Carlo simulation, just like ray tracing in computer graphics. The difference is that QED will correctly model diffraction (and other more complex physical effects) that the simplified graphics-only model doesn't bother with.
Both QED and raytraced computer graphics rely on a mathematical dualism where a wavefront can be tracked either as a surface OR as a vector perpendicular to the wavefront. The whole "summing up but mostly cancelling" is just accounting for the wavefronts. The use of complex numbers is mostly also just a method for tracking the cyclic nature of wavefronts.
If you skip the "waves" part, it becomes traditional computer graphics. Less accurate, but essentially the same.
Computer graphics could also simulate light transport by using a 3D volume, which is roughly speaking how some diffuse light simulations work in real-time games like the Unreal engine. The problem is that to get decent accuracy, you need a lot of memory to store that 3D volume. For low-resolution scene lighting this is fine.
Monte Carlo enables a solution to be built up incrementally with much less memory required, needing only a 2D accumulator in the image plane instead of a 3D simulation in object space. This allows a vastly more complex and detailed simulation to be calculated, which is important for the tiny wavelength of physical light instead of some non-diffracting idealisation of it.
For a physics problem the memory requirements of any non-trivial system would be gigantic, that's why everyone just ignores this approach even though it makes a lot more intuitive sense.
- consilient 4y ago> that's why everyone just ignores this approach even though it makes a lot more intuitive sense. - No one ignores the correspondence between QFTs and stochastic processes (which is what I assume you're talking about, since the claim that QED is just Monte Carlo is extremely false if taken literally), any halfway decent intro QFT class will cover it. - It only "makes more intuitive sense" because you've papered over all the gory details. There's very little intuitive or natural about analytic continuation in C^{\infty}, for instance.
- trashtester 4y agoStochastic processes is one thing. But most calculations in QFT is done using various perturbation theories (kind of like Taylor series expansion), instead of by using exact calculation. That could be interpreted kind of like ray tracing with finite resolution and a finite number of reflections. EDIT: Feynman diagrams serve as an attractive way to rationalize the various perturbations, but it may be that a "true" theory needs to be able to solve the (for us) unsolvable integrals directly. Especially since the perturbation theory integrals (that we can solve) diverge, and require renormalization to avoid infinities.
- BrandoElFollito 4y ago> it was seen as somehow "less than" symbolic solutions This reminds me of an old prof during my PhD studies (physics) who was always telling how immature and simple minded computer users were. I told him once that using a computer requires intelligence and aptitudes that some people who criticize indeed lack. It did not go well.
- Karellen 4y ago> It did not go well. Insulting people rarely does. Even if the insult is unintended, or is plausibly deniable, if the person ends up being insulted anyway, then it is unlikely to go well. In totally unrelated news, it might be worth noting that "being right" is not a relevant defence against the charge of "being an asshole". It's entirely possible to be one without being the other.
- BrandoElFollito 4y agoSee, there is a tendency for students to feel like they have to take on them any insults (or similar) coming from a higher-up. I understand that you are fine being called an idiot and that the proper response is a smile and nod of understanding. Some do not. I do not. Have you worked in academia, especially in the ones where you have a medieval approach to hierarchy? EDIT: something liake http://amandabauer.blogspot.com/2011/08/how-academics-see-each-other.html http://amandabauer.blogspot.com/2011/08/how-academics-see-ea... (the humorous way of looking at it)
- deleted 4y ago[deleted]
- Karellen 4y ago> I understand that you are fine being called an idiot and that the proper response is a smile and nod of understanding. Some do not. I do not. Because the only possible responses are "smile and nod of understanding" and "call the professor an idiot in return", and no middle ground exists where you can draw attention to someone's mistaken beliefs without escalating the situation, or even without putting them on the defensive? I don't believe you believe that.
- orbifold 4y agoWhile in principle you can evaluate certain path integrals by using MCMC, in practice you run into all kinds of issues like the sign problem, which even with things like complex Langevin dynamics can't be resolved to this day completely.
- credit_guy 4y agoThis sounds like a very intuitive way of understanding quanum mechanics. Do you have any links for this analogy?