Single beam of electrons diffracts like single beam of light, but otherwise electrons behave very differently than light: two electron beams interfere with each other, while two light beams do not.
If everything is a field, then light is simply a three dimensional wave in that field. This makes the double slit experiment seem much easier to grasp:
A single photon (which is a wave with a discreet amount of energy) travels through both slits at the same time. This causes the wave to interfere with itself and when it hits the wall it registers as a single point, as the photon must always be a discreet quantum of energy.
To me, this makes intuitive sense and removes a lot of the mystery and confusion that gets invoked whenever pop-sci writers explain the experiment. They tend to say something along the lines of: photons are like billiard balls, so they can only go through one slit or the other, but if you don't detect which slit it goes through it seems to go through both.
Am I close to what's actually going on, or am I way off?
There are experiments that show that light is not a particle (in the classical sense) and other experiments that show that light is not a wave (in the classical sense). Quantum mechanics is the result of trying to find a theory consistent with both sets of experiments.
Originally, the double slit experiment was seen as proof that the wave theory is correct. So if you want to challenge your wave theory, look to different experiments. Wave theory of light was predominant from the mid-19th century to the emergence of quantum mechanics in the early 20th century, so I would focus on science from the early 20th century, such as the ultraviolet catastrophe and the photoelectric effect.
Consider the photoelectric effect. If light were a wave that carried energy, this wouldn’t explain why an equal amount of energy has a different effect depending on its wavelength. The quantum explanation is that one packet of light contains a different amount of energy, which depends on wavelength. “Light is a wave” kind of falls apart as a theory, because it is unable to explain this.
Not by itself but the accompanying theory - classical EM theory - does explain why different frequencies interact differently. Absorption/dispersion spectra are well described by wave theory. What the classical wave theory can't explain easily are coincidence counts in extremely weak light (antibunching), or things such as the Compton scattering.
Im fairly certain you could make an experiment where one photon went through some apparatus and two specks of light appeared at the photo detector (with new wavelengths of course). What mechanism in your wave-only theory describes this split? Why do these waves sometime split or fuse and other times stay as single particles? The 'it stays as one particle cause it started as one particle' explanation would lead to a very monochromatic universe!
If you literally try one photon only once, well, you can't really talk about probabilities; whatever happened happened (possibly you witnessed an unlikely event). But if you repeat the experiment N times, even if you do it spaced by many miles and many days, and collect the data you'll notice that the measurements cluster in ways that are compatible with interference bands.
If an actual physicist can tell me whether that I wrote above is fundamentally wrong, I'd be happy and have more questions
Moreover, if we assume conservation of energy, changing a photon w/ wavelength A into B leaves over some energy C, that again, assuming some mechanism of changing energy into light, a new photon could be emitted.
So which assumption is wrong? (1) Light comes in many different wavelengths (2) Conservation of energy (3) Non-light energy can be changed into light energy (4) Light color follows the photon model for the relation between energy and wavelength.
(or just do a simple google search: https://arxiv.org/abs/2009.03039 where it's sounds like it's been observed directly)
Unfortunately, I would say it doesn't help (and could actually block you) when you want to build intuition around QFT and high-energy processes.
In your mind, you would still then think of a photon as a wave running around interacting with electronwaves that then oscillate and produce new photon waves.. and you'd think for example that "hey, I can just solve the wave equation and I solve the experiment".
While it's really so much more messy, as you'd note when you start considering the number of degrees of freedom involved required in your simulation to approximate reality. It's not classically interacting waves timestepped forward in time, it just looks like that in the most trivial situations.
Photons do interact! There is no two-photon vertex, that’s true, since there is no fundamental interaction between two photons. But put four photon/charged particle vertices together and you’ll get the 4-photon box diagram [1], whose contribution is nonzero.
[1]: Since I’m not good at painting diagrams in ASCII on HN, here’s a link to the Wikipedia article with the box rendered nicely: https://en.wikipedia.org/wiki/Two-photon_physics
Maybe you meant there’s no 2–>1 vertex.