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energy is proportional to the frequency, but what about classical physics?
a certain duration ( i.e. one wavelength)
I have integrated the energy of a pulse wave that has a certain duration
I think you could notice from chemical reactions that Ultraviolet light is able to trigger some chemical reactions that visible light or infra-red light cannot. This would apply even if you reduce the power level of the UV to far less than the power of the IR.If you look at the photoelectric effect, you would notice that UV light ejects photons with more energy (in eV) than visible or IR light. This applies regardless of the intensity of the illumination. This tells you something along the lines that higher frequency/shorter wavelength light has more energy, which is not proportional to power level. It was Einstein's brilliance that deduced quantum effects and earned him a Nobel prize.
One wavelength is not a fixed duration, when you are varying the wavelength.
If you take two waves of different frequencies, but a fixed power (eg 1 Watt) and duration (eg 1 second), then you will produce a pulse of fixed energy (1 Joule).
If you now doppler-shift this pulse by traveling at relativistic speeds, you can shift the energy from visible into UV.The duration of the pulse is now shorter, and the power of the wave is now higher, but the energy of the pulse is unchanged (I think?).
But this doesn't give the idea that the energy is quantized.
It was the measurement of the energy of emitted electrons in the photoelectric effect that let Einstein to extrapolate to a minimum unit of energy in a photon, which led to the concept of quantum theory.https://en.wikipedia.org/wiki/Photoelectric_effect
Doppler shift doesn't require relativistic speeds.
Classical physics when analyzing massive bodies though can easily show that a body has more energy seen by an observer moving towards that body.
Einstein showed that photons have energy and mass.But if you were dealing with Maxwell's equations and assuming that light was a wave, would you assume that light had mass?
Water has mass, but you would assume that waves don't have mass (not any more than still water).Similarly, you might assume that an aether had mass, but light had no mass.Kinetic Energy E=½mv2 is not very great when m=0.
Just as EM waves don't travel but simply the volumes ahead amplitudes rise, I think massive particles don't travel either, but their fields propagate similarly. The 1/2 spin is also an indication of a different wave geometry enabling them to have rest energy mass. But I digress.
I don't think using static fields equations will ever work as I think these are only apparently static
Just as in my example with the trapped photons, the electrons as charge carriers might have a structure enabling them to appear slower than c or even at rest but in their inner strucure the fields dynamic work by propagating the amplitudes at the same c.
The problem with my idea is now the field transformations that don't seem to work for waves.