Not always, actually. (At least, not in the sense you probably think of waves.)Yes, but people forget that it's the Schrödinger wave equation
That's not what happens in quantum physics. In QM the electron's momentum modes are all linear de Broglie waves, just like the photon's.and can’t seem to appreciate that pair production converts a wave moving linearly at c into two waves moving rotationally at c.
It is, at least as far as mainstream models are concerned, in the sense that it has point-like interactions. It's a quantum point particle (as opposed to, say, a quantum string). I've seen you go around "correcting" people telling them the electron is not like a classical billiard ball. That's pointless: nobody in physics thinks the electron is like a classical billiard ball. That's not what we mean when we say the electron is a point particle.I've had people insist to me that the electron is a point particle.
Have you ever wondered maybe why papers like those don't get much attention? Maybe their models don't actually accomplish what they say on the tin.It isn't my model. Various people have attempted to provide a model, but they tend not to get much attention. See for example Is the electron a photon with toroidal topology?, The nature of the electron, and Rotating Hopf-links: a realistic particle model by E Unz.
I understand QED just fine, thank you, and none of this contradicts what I told you: in quantum physics in general you can't model the electron as a photon bound state, and in QED this is not what happens. As AlphaNumeric explained to you (if you bothered to read his post) electrons are treated as fundamental particles in QED. In QED, the photons literally disappear and electrons appear in their place. The photon is an excitation of the quantum vector field usually noted $$A_{\mu}$$. The electron is an excitation of a quantum fermionic field usually noted $$\psi$$ (not to be confused with quantum wavefunctions, which are also often noted $$\psi$$ or $$\Psi$$).You’re misreading QED there. The experimental evidence of say Two-photon physics says that photons can interact to form fermions, see this report. In QED you’ll read that this is via “higher order processes” or you may read that a photon “can fluctuate into a fermion-antifermion pair”.
This isn't completely accurate. In QED the two photons don't interact directly - there's no such fundamental interaction. You see this on the Feynman diagram for the pair production process (from your own Wikipedia page):But again, take the hard scientific evidence at face value. You start with two photons, you end up with an electron and a positron, and nothing else was involved. Those two photons interacted all right, and they formed two spin ½ bound states.

What's depicted here is one photon splitting into an electron-positron pair, and the other photon being later absorbed by either the electron or the positron. The photons never interact directly.
None of this is true. For starters, not all wave equations are Lorentz invariant. For example, the non-relativistic Schrödinger equation, as its name would suggest, is not Lorentz invariant. Incidentally, the equation itself is:Because it doesn’t break it. See http://www.classicalmatter.org/ClassicalTheory/OtherRelativity.doc again. If you are made of waves, you always measure wave speed to be the same. Everything is made of waves, the apparent wave speed is unchanged, so Lorentz invariance holds.
$$
- \, \frac{\hbar^{2}}{2m} \, \frac{\partial^{2} \psi}{\partial x^{2}} \,=\, i \hbar \frac{\partial \psi}{\partial t} \,.
$$
If you're at all experienced with relativity, the easy way of seeing this is that the equation doesn't treat space and time the same way: it contains a second derivative with respect to x, but only a first derivative with respect to t. This is the same sort of argument I've used agains the idea of electromagnetism being curved space: the idea separates space and time and says the curvature is only happening in the space part. That immediately breaks Lorentz invariance.- \, \frac{\hbar^{2}}{2m} \, \frac{\partial^{2} \psi}{\partial x^{2}} \,=\, i \hbar \frac{\partial \psi}{\partial t} \,.
$$
(Also, though it's not really relevant here, Robert Close is wrong about another thing: the massless relativistic wave equation is not the only Lorentz invariant equation. He's way behind the times here. We've known how to easily contruct Lorentz invariant equations since Minkowski's geometrical formulation of special relativity around 1907 or so. Basically, any equation constructed out of four-vectors and tensors and using certain operations (addition, subraction, or comparison of equal rank tensors; tensor contraction) is automatically Lorentz invariant.)
What are you talking about? There is no evidence that electrons are actually made out of photons. There is only evidence that there are processes in which photons go in and electrons come out. That doesn't necessarily imply one particle is made out of the other. In fact this is specifically not the case, as I explained above and as AlphaNumeric has explained, in the best models we have for those interactions.No. It's not an issue of whether what I or anybody says is true. It's whether it fits with the scientific evidence, or it doesn't. For example photons don't form bound states and even if they could, they couldn't form a spin-1/2 bound state doesn't.
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