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Sick of ridiculous KVL infighting
Nominal Animal:
--- Quote from: RoGeorge on January 17, 2022, 11:58:15 pm ---Now, I would expect to get some failed prediction in terms of QED, too, when \$\hbar \to 0\$ (as it is in Maxwell), similar with the failed predictions from the spectrum of the black body radiation when the quantization aspect was not considered, but I don't know any examples where Maxwell fails to predict correctly.
What would be such an example?
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The Wikipedia article lists a few.
The photoelectric effect is probably the easiest case to verify and understand, where Maxwell's equations fail to predict the phenomena. Maxwell's laws suggest that a low-frequency (long-wavelength) light beam at high intensity would accumulate enough kinetic energy in the outermost electrons of the atoms, exciting them until they're kicked out from the atoms, and thus releasing photoelectrons, but that does not happen. The photons need to exceed a threshold energy (frequency, wavelength) for it to happen.
A typical silicon photovoltaic cell has a minimum bandgap of about 1.12 eV. Photons having this energy have wavelength of about 1100 nm, which is near infrared, just outside human visible spectrum. Maxwell's equations don't predict any kind of threshold effect, and photons with longer wavelengths (and thus lower energies) should work just fine, just provide less energy. However, in reality, photons with lower energy (higher wavelengths) won't produce a photoelectric effect.
This is easier to see with semiconductors with bandgaps in the visible spectrum, for example gallium phosphide (as used in e.g. old-style green LEDs), which has a bandgap of 2.26 eV, corresponding to photon wavelength of about 550 nm. Use a red laser (over 600 nm) to exite gallium phosphide, and nothing happens. Use a blue laser (under 500 nm), and it exhibits the photoelectric effect.
(A laser, such as a cheap laser pointer, is just an easy source of monochromatic light, which is the point here: the photons all have the same wavelength. In a laser, they also have the same phase, but that is not important here. This experiment works with non-coherent monochromatic light of suitable wavelengths.)
--- Quote from: bsfeechannel on January 18, 2022, 03:34:50 am ---[Lewin] left the explanation of his demo as a homework to his students.
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Funnily enough, I see this as the biggest difference between mathematicians or theoretical physicists, and experimental physicists or others who apply mathematics as a tool.
Mathematicians show the formulae and their derivation, and leave the interpretation and application to the student.
Experimental physicists and those who teach applied mathematics describe a family of problems, their description in mathematical terms, and the applied tools that can be used to find the solutions –– exactly the part that is left to the students by mathematicians.
To some people, the latter is the natural, better approach. To some people, the former is the natural, better approach. A lot of people can work things out either way. Very, very few people can teach both ways effectively. And this creates a big part of the dichotomy, since very few people can bridge the two effectively. It also explains why some believe string theory is physics, while others consider it only mathematics thus far.
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