Say we have all the empirical evidence from 19th-century science prior to the observation of the wavelike diffraction of matter particles, plus 21st-century math and theory to construct an alternative explanation.
Sure. It could be an abstraction based on physics in a higher universe to which there are impossible barriers to accessing further understanding.
Just look at any video game universe.
It would be pretty hard. There’s a reason quantum mechanics is the current explanation, and it doesn’t start with the Bell entanglement experiments.
Black body radiation would have some bizarre behavior without quantum mechanics.
The radiation spectrums of stars are also very dependent on quantum mechanics.
Some related phenomena such as transistors and phosphorescence are hard to explain without quantum mechanics.
A big one is chemistry is highly dependent on quantum mechanics. You could have a limited understanding of ionic compounds with just the Columbic force, but covalent bonds require quantum mechanics to explain.
Most of physics history is studying the edge cases and gaps in the current understanding, and filling those in. Quantum mechanics didn’t just appear suddenly; it was derived as an explanation for many previously unexplained phenomena in pieces my many different people over time.
If you did come up with an alternative explanation, you would have to reinvent just about everything. Ever seen what it would take for the flat earth idea to hold water? Yeah, that level of reinvention plus some more of that vibe.
But let’s say that in this alternate universe those wild models are actually true, valid and they end up producing a universe that looks like ours. Since it’s based on completely different physics, there will also be some strange differences. Even if those galaxies look like ours, it doesn’t mean that biochemistry or life would be possible.
Sure, if you’re making up all the rules you can make up all the rules. Matter could be composed of the body of a dead god, for example.
Whatever rules you make up must be consistent with macroscopic observation, though. So if you postulate that matter is formed from the flesh of a dead god, you still need to prove that it doesn’t need to quiver.
Why would it need to quiver?
To contain the arrows of time and entropy, obviously.
To explain any macroscopic effects that necessarily depend on matter waves. If there are any. Which is my question.
This is a pretty difficult question to answer since all phenomena are quantum. A star is powered by nuclear (quantum) fusion. Permanent magnets depend on the quantized angular momentum of electrons. Could these phenomena be allowed by something other than quantum mechanics? Maybe. But a constant goal of science is to find the simplest explanation for all we observe, meaning that whatever alternative explanations you come up with, should they be correct, then taking them all together will constitute a theory that at least looks an awful lot like matter waves (mathematically, at least).
Superconductors and Bose-Einstein condensates are both macroscopic phenomena that result from coherent matter waves.
Maybe there aren’t any in our conceptual universe.
