Do electrons have a color? No, electrons don't have an intrinsic color since they are reflectors of em waves. They are more like perfect mirrors. If there is a fundamental em wave associated with an electron it would be at a wavelength far too short to be visible (ie. a color). Perfectly good question that deserves an answer.
Ok, I've answered your question. Now would you answer mine? What is the size and shape of a photon? If that's too hard, maybe you could start by saying whether a photon moves or not and at what speed it moves. I was under the impression that a photon from the Sun takes around 8 minutes to reach the Earth. Is that not true?
As an aside, if a unit step em wave hits a stationary point electron, at what distance from the point electron is the reflected wave's electric field equal to and opposite that in the input unit step? What is the significance of the distance? Of course, I'm asking for a classical analysis, if can lower yourself that far.
No, electrons don't have an intrinsic color since they are reflectors of em waves. They are more like perfect mirrors.
B.S.. I have somewhere around 10^28 electrons in my body. I'm not a mirror.
What is the size and shape of a photon?
That depends. Write a proper quantum mechanical operator for the property 'size', and calculate its expectation value. My QED is a little rusty, but I think you can do that without invoking creation and annihilation operators and mucking with the number of photons.
As an aside, if a unit step em wave hits a stationary point electron, at what distance from the point electron is the reflected wave's electric field equal to and opposite that in the input unit step
What makes you think a stationary electron (leaving aside the fact that a stationary electron cannot be localized at a single point) reflects em waves? Why would it do that?
A photon travels at the speed of light in a vacuum. Your request for "size and shape" really makes no sense. A photon is not really a particle, nor is it strictly a wave. It can behave like a wave in some respects, and like a particle in others. In order to talk about it's shape, you would have to localize it, compress it to a single point. That's not allowed by the Heisenberg Uncertainty principle.
How can you say that something with an FT of 1 (eg. a point) has a specific wavelength, which a photon is supposed to have? Nope, you're going to have to broaden that impulse out in time and decrease the amplitude before anything resembling a dominant wavelength emerges. So, how broad in time is a photon (I can handle multiplying by c all by myself)
If you were to try and localize a photon (treat it as a point) you would be compressing it to an incredibly short light pulse. Such pulses can (sort of) be generated. I used to work in a lab with a femtosecond pulse laser system. A pulse of about 25 femtoseconds (1fs = 10^-13 seconds) is spread out over a distance of less than a millimeter. You are correct that this could not have a single wavelength. It typically has a mix of around 40 nm around a central primary wavelength, as opposed to just a few nm for a standard, continuous laser. Photons are not point-like particles, though they can act like particles in specific circumstances (the photoelectric effect for example).
As an aside, if a unit step em wave hits a stationary point electron, at what distance from the point electron is the reflected wave's electric field equal to and opposite that in the input unit step? What is the significance of the distance? Of course, I'm asking for a classical analysis, if can lower yourself that far.
I think you're describing a photon scattering off an electron here, though I'm not quite certain. The problem is, you're asking for a classical response to a question that ONLY Quantum Mechanics will answer. For one thing, it is IMPOSSIBLE for a photon to scatter off an electron without having the elctron respond. If the photon has a wavelength anywhere near that of the size of an electron, it will also have enough energy to excite and move the electron. For this and other reasons, you NEED QM to solve this problem.