Someone needs to do a better visual explanation of these particle interactions. If you can describe it mathematically then surely you can create a computer simulation.
To the point, I've founded a startup precisely for that: https://quantumflytrap.com/
What the parent meant was real particle simulation, for example simulating the collision between two electrons or computing the dipole moment of a muon, from fundamental standard model constants. It requires numerically solving 12 dimensional PDE's. That's much more complicated than entanglement simulations.
Put your links when your mouth is. :) There is a handful of interactive simulations for qubits. I don't know any other interactive simulation for quantum many-particle systems.
> It's basically just linear matrix algebra with complex numbers.
It always has been. For Quantum Field Theory it gets much more complicated, and classical simulations are way to slow to simulate most systems. Quantum computers (or even quantum simulators) are likely to change the game. Anyway, being able to simulate does not result in being able to visualize in a meaningful way.
List of available QC simulators grouped by programming language: https://quantiki.org/wiki/list-qc-simulators
I count more than 40 QC simulator projects. All open source. There is an abundance of quantum computer (QC) simulators, as opposed to a paucity of quantum field theory (QFT) simulators (most of them written in Fortran, yuck).
As "easier" I mean that 2^10 is still managable, as you can use dense vectors and operators. For, say, this quantum optics simulation you get roughly 1000 dimensions per particle. For 3 particles it is 10^9. Don't even think about dense vectors, let alot - dense operators. Sparse operators are not enough, as even identity is big; so for any real-time-ish simulation there are considerably more tricks and methods.
Simulting QFT you need to deal with much more complexity (including continuous dimensions). Instead of numerically pretty much you need to solve some intergrals. (Side note: I wanted at some point to write an interactive editor of Feynman diagrams, turning it into formulae and integrating.)
Think of it like knowing the rules, but the rules not being efficient to compute with.
Squiggles. Little arrows. Hand-drawn scribbles.
I've looked into why there's a total vacuum of numerical simulation, and the reason is simply snobbery. There's a philosophy that numerical methods are what mere engineers do, and not as intellectually pure as symbolic solutions.
You regularly hear comments like: "Such and such cannot be solved", what is often meant is: "It can only be solved numerically, but not with closed form algebraic expression."
People that say things like the former statement have excluded numerical solutions as valid in their mind. Such solutions may as well not exist, as far as they're concerned.
I see this attitude everywhere in theoretical physics.
The other issue is that because of the seventeen layers of assumptions and abstractions, most physicists are now at the point where they're not really making theories about physics, but instead they're debating the properties of the abstractions themselves. It's like kids trading basketball cards and saying one player is better than the other because his card is printed better.
This can all be boiled down to an acid test: Can you render your equations? As in, full 3D numerical simulation with an image as an output? Not a graph, not a scalar value, but a picture?
For simple (non-diffracting) optics? Yes! That's literally every 3D computer renderer!
For classical electromagnetics the answer is: yes.
For plasma physics the answer is: yes.
Even for special and general relativity, the answer is: yes.
For QED? Err... maybe? I've seen some toy examples in 2D, and I think I've seen a 3D example once. In principle, it's doable.
For anything else? Nothing. Or at any rate, I've seen nothing despite years of searching.
E.g.: Can you show me any "rendering" that extends a QED simulation with the weak interaction?
Can you find any animated examples of any particle interaction? E.g.: a free electron being captured by a proton, or an electron changing orbitals?
Again: Images or animations please. Not graphs or scalars. Everyone I ever challenge gets confused and links me to a paper with a histogram in it. That's not what I mean!
Are you asking for a picture of 2 spheres and then another sphere? What are asking for?
Pick any one.
I find even questions like this revealing: Why are you asking me such incredibly basic questions instead of having a dozen renderings ready to hyperlink?
If you ask a NASA guy to link some airflow simulations, he won't retort with "what criteria would satisfy you?". He'll just straight up link a bunch of gorgeous renderings of physically accurate airflow simulations.
Not cartoons.
I guess my confusion (which may be from ignorance of physics) is about how to handle depicting superpositions of whether or not the electron has been absorbed by the proton.
I don’t mean that that isn’t a problem with a good (known?) solution, just I don’t know one.
This is the "measurement problem", and nobody can give you a straight answer.
This is why I give this acid test: it reveals this gap in the theory that is otherwise easy to gloss over.
It's the difference between pseudocode on a whiteboard, and something that compiles, runs, and gives the correct answer.
You can hand-wave one of those and claim correctness. The other will give you a compiler error.
This is why I asked you to specify what you were asking for.
There's no visualisation of what goes on at the interaction point. Just an idealisation of what goes on far from it.
Where in that diagram can I see diffraction? Interference? Entanglement? The particles interacting?
Or can I not see any of that because it's a cartoon representation that shows the classical measurements only?
This is basically false as far as I can see. Numerical methods are basically the only way to solve either general relativity or quantum equations, but even then it's extremely difficult to get accurate calculations with a practical amount of compute power. There's intense competition over who can get the best results here (in fact the leading group in lattice QCD keeps their code a secret, which is not great science).
I think the core reason you don't see much visualisations is the visualisations are not very useful. The little visualisations I've seen of extremely simplified versions quickly dissolve into complete mush as everything overlaps. It would not suprise me if the more complex interactions (like two real particles in 3d) were basically unintelligable and extremely difficult to make intelligable without becoming 'cartoons'.
So it's only doable for tiny N.