'Strange metals' point to a whole new way to understand electricity

But the specific word they were looking for is "quintic". (And the corresponding word for 4th-degree, in case anyone is curious, is "quartic"; one sometimes sees "biquadratic", which unfortunately is also sometimes used to describe a particular subset of quartics.)

Not just like photons. For one thing, they can travel slower than light. But many experiments on photons can also be done on electrons, such as diffraction. You can perform a double-slit experiment with electrons. Also, they're fermions, but photons are bosons.

> > > Mathematically a photon is defined as a state of the EM field (which has been quantised into a set of harmonic oscillators called "normal modes") in which there is exactly one quantum of excitation of a specific normal mode (with given wavevector and frequency). Depending on which kind of modes you consider, a photon could be a gaussian beam, or even a plane wave, so not something localised like you would say of a particle.

> Think of it like this: From the perspective of the photon, it lives and dies in the same instant. Even if it traveled across the entire universe.

Would an appropriate analogy be a "glider" from Conway's Game of Life? "Lives and dies in the same instant" isn't exactly the same, but I'm thinking of how no parts of the glider move while the glider as a whole "moves" across the board.

TL;DR: the analogy is helpful at a high level, but has limitations when you look closely.

> Ok, it's different in that liquid flows through pipes and electrons flow through crystal lattices or whatever, so electrons go between and around the material while liquid is bounded by it.

This is not perfect, but it works at a high level.

The main difference with e.g. water flows is that what restricts electron flux is traps. Electrons are not limited by walls that prevents them from going outside channels, instead they are held in place by atoms’ nuclei.

In a conductor, the “force” holding them is effectively zero, so when an electron comes in on one side, another one comes out of the other.

In a semiconductor. An electron needs some energy to get out of its trap before it can move. Then, “freed” electrons hop from trap to trap and the current is the overall effect of this. Electrons do not have to move far to create a current, there just needs to be enough of them. There is no real macroscopic analogy for this.

In an insulator, electrons just don’t get out of their traps because the energy required is too large.

This ignores a lot of details and quantum effects, but it is still a useful way to think about this.

> It makes me speculate that electron flow through a metal is sort of like liquid flowing through a compressible boundary tube, whereas flow through a non-metal has rigid walls.

Not really. Electrons moving in a metal are slowed down by a lot of different phenomena but this cannot really be considered as a compressible fluid. The effect is more similar to viscosity than compressibility.

In non-metals, electrons just don’t move unless they are made available, for example by doping or with a source of energy.

> Non-metals reject the electrons, metals allow them to play Spiderman and hitch a temporary ride

The general model is that metals let electrons flow and non-metals hold on to them.

> If resistivity is determined by the equivalent of turbulence, though, I've no idea what the graph against temperature should be. Do electrons travel faster when there's less resistance?

The analogy kind of breaks down here. There are competing effects and conductivity as a function of time is often highly non-trivial. In general, the number of electrons available increases with temperature, but scattering by other electrons, vibrations and defects also increases. Overall, resistivity tends to increase with temperature in metals and decrease in semiconductors, but there are exceptions.

AFAIK nothing stops an electron from existing in the same space as a proton or neutron - they don't have to go around. Indeed that's required for certain kinds of radioactive decay to occur. Not all electron orbitals overlap the nucleus, but some do.