Do we really have to choose between wave and particle? What does the "particle" model bring to the table that a localized (wavelength-sized) wave/vibration could not?
What they differ about is the interpretation of that model. The equations are the same, but differ in what the variables refer to in the real world. It's really a matter of solving the equation for X vs Y, saying which one is independent and which is dependent.
The purpose is to take the fact that none of the variables correspond directly to anything we have any experience with. The best we can hope for is to isolate part of it and say "this much is like this thing we understand, but there's an additional thing that we'll treat as a correction".
We can try to take the whole thing seriously, and just call it "a quantum thingy" which is not like anything else. This is sometimes called "shut up and calculate", but even that makes assumptions about what things are feasible to calculate and which are hard. That skews your understanding even if you're trying to let it speak for itself.
There is one set of observations, and many many models to describe them: Schrödinger equation formulation, matrix mechanics (Heisenberg, Born, and Jordan), path integral formulation (Feynman), phase space formulation, density matrix formulation, QFT or second quantization, variational formulation, pilot wave theory aka de Broglie-Bohm theory, Hamilton-Jacobi formulation, PT-symmetric quantum mechanics, Dirac equation formulation (well, not really independent, just for spin 1/2 particles).
They all give the same results, and are therefore mathematically equivalent, but different models tend to be associated with different interpretations:
Schrödinger Equation : Copenhagen, Bohmian Mechanics, Many-Worlds
Matrix Mechanics : Copenhagen
Path Integral : Many-Worlds, Stochastic
Density Matrix: Ensemble, Decoherence-based
Second Quantization : Many-Worlds
Pilot Wave Theory : Bohmian Mechanics
Consistent Histories : Decoherence-based
Relational QM : Relational Interpretation
Stochastic Models : Stochastic Interpretations, GRW (Ghirardi–Rimini–Weber) CollapseLuckly, sometimes the exact solution can be very accuately aproximated with a wave ecuation.
Luckly, sometimes the exact solution can be very accuately aproximated with a particle ecuation.
(Sometimes, the exact solution can be aproximated saying that the lowest energy state is an eigenvector of the Schoedinger equation. Is that a wave? It's not localized, but not very wavy.)
But neither are the exact solution, just aproximations that solve tpgether 99% of the experiment.
It's difficult to explain, because to explaing the detials you need like two years of algebra and calculus and then like another 2 years of physics, and now you get a degree in physics.
It's possible to solve the difficult ecuation only in very simple cases like electron-electron colissions, if you allow some cheating and a tiny error. For more complicated systems like electron-muon there are some problems. And for more complicated systems, you get more technical problems and more aproximations.
My understanding is that theoretically energy transfer is a function of wavelength.
However, this is not true for EM interactions. If you shine infrared light on a solar panel, you'll see 0 current from it, even with an extremely powerful source of light (at some point the material might heat up enough it starts showing some thermo-electric effect, but that's a different thing). However, if you take even a very low intensity ultraviolet source, you'll see a measurable current right away. This is the unexpected behavior that quantized interactions have, which can't be reproduced with non-qunatized waves like sound waves.
OTOH, the energy of a photon is such an abstract concept (not like the kinetic energy of a ball) that I'm not sure it really helps explain it.
However, photo-detections with sub-poissonian statistics cannot be explained under this semi-classical model, but it can be explained with properly quantized EM field (i.e. with photons).
For reference, see Mandel and Wolf's Quantum Optics textbook.
But in order to track state changes from free agents, when you get close to that geometry the engine converts it to discrete units.
This duality of continuous foundation becoming discrete units around the point of observation/interaction is not the result of dueling models, but a unified system.
I sometimes wonder if we'd struggle with interpreting QM the same way if there wasn't a paradigm blindness with the interpretations all predating the advances in models in information systems.
Classic labelling issue.
A lot of the article is about this. Start with the section "The Wave Function of Two Particles and a Single Door". The wave packet view can't explain why you don't for example see a "particle" (that is, a dot on a detector) show up simultaneously having gone through two different doors. You have to think about it in terms of a wave in the space of possible joint particle positions.
The problem in these discussions is how to build an intuition about the underlying physical model.
I fail to have an intuition of how can a quantized unit of wave propagate through both slits.
I know that the equations say that the probability of finding the particle at a given location is given by the amplitude squared of the wave function (Born rule).
The image that a "quantized unit of wave propagates through two slits simultaneously" doesn't help me build any further intuition.
Do the two parts going through the two different paths carry half the unit? Clearly that's not the case otherwise they wouldn't be quanta anymore. So does it mean that the entire wavefront is "one unit" no matter how spread out? But in that case, "one unit" of what?
If you have two slits, with a detector to determine which slit the photon went thru, then it'll behave as if it only went thru one of the two slits, at random, and what'll build up on the screen will be the two (slit A + slit B) overlayed diffraction patterns.
Finally, if you have two slits with NO detector, then what will build up on the screen is the interference pattern as if the photon had gone thru both slits simultaneously and the two resulting banded diffraction patterns interfered with each other. So, what SEEMS to be happening in this case is that the quantum state of the system post-slit is that of the photon simultaneously having gone thru both slits, each slit having diverted it per diffraction, and then these diffraction patterns (probabilities) interferering. Wave collapse can only be happening after this interference (if it was before then there would only be one diffraction pattern and no interference), presumably when quantum state interacts with the screen.
So, yeah, it seems that the "photon" does "go" through both slits, but this is a quantum representation, not a classical one.