It's probably a good bet that we are going to discover that to rectify the complexities of QM, there is some assertion most people have fundamentally accepted and is quite uncomfortable to let go but is necessary to simplify the equations. I can't really guess what it's going to be though.
Have you ever actually looked at the Schrödinger equation? [1] It's pretty simple. If you've had freshman physics, you can learn enough to derive it in a matter of days or at most weeks. There's not a lot of room in there for the kind of thing you are suggesting.
It's much more plausible that the uncomfortable human-centric thing we need to let go is the idea that our perceptions about macroscopic reality should be indicative of how things actually are.
The system of epicycles was made of pretty simple, easy things: circles. It's when they were combined things went complicated.
Same with Schrödinger equation: it's very simple for one particle in an empty Universe, but things go more complicated when more particles are considered.
There is no guarantee that a different approach can replace QM and describe things in a simpler way. But I suspect that attempts to look for such approaches are not useless.
What do you mean by "derive" the Schrödinger equation? As best as I know, there is no "derivation" beyond some analogy with the classical wave equation. It's an equation penned down by Schrödinger, motivated by the classical wave equation and insights from de broglie's theory.
Indeed, early progress with QM in the first place required letting go of some expectations that were based on macroscopic phenomena. There was a certain effort to clarify those expectations so they could be gotten rid of. This is, at least, what I remember being taught about it.
That would, indeed, be an uncomfortable thing to let go of, since they are our direct perceptions.
Relativity tells us things get weird at high velocities, but our daily perception is basically correct. Quantum theory seems to suggest that solid, tangible reality isn't at all like our day-to-day experience. That's a pretty decent leap to ask of people.
Plato and a few others told about the world of ideas and the world of matter: both exist and are connected somehow. I wonder if QM is this bridge between the two worlds and the wrong assumption we make is that QM describes the world of matter. In other words, the probability waves may actually exist, but they exist in the world of math, and the real question is how exactly the two worlds are connected.
That's not good enough. I want a specific claim about how one or more of the postulates of QM are likely to be incorrect (or even stranger, how they have to do with "putting Earth at the center", whatever that means, or some anthropomorphism baked into the postulate).
Saying "we don't know what we don't know" is both a tautology and completely useless. It's like my saying: "I believe that you committed a crime last week." You ask for more details about why I think that and what the crime was, and I reply "we just don't know." I hope you see how ludicrous that is.
It's been awhile since I thought deeply about epicycles, but if my memory can be trusted... They weren't incorrect. They did a decent job of predicting the motions of the planets given the assumption that Earth was pegged at the center of the coordinate frame (which then required a whole bunch of "hidden behavior" in terms of non-apparent phenomena dictating the rotation of all other bodies).
Re-framing the whole system to be heliocentric allowed for the massive simplification of Kepler's Laws (and, not too much later, the further simplification of describing Kepler's laws via Newton's law of gravitational attraction).
We currently have an understanding of QM that doesn't reconcile well with macroscopic observation and requires a lot of intuitions to be broken (including, possibly, the singular nature of existence, time-forward causality, or lightspeed-constrained information locality). I can't help but wonder if there's some equivalent to "Assuming Earth is the center of the coordinate frame" that we currently do that forces these unintuitive (though working) solutions.
The solar system moved in epicycles because "it just did," until several leaps of intuition allowed us to see how it didn't. I wonder if there are similar leaps of intuition waiting on the horizon to allow us to explain quantum entanglement without nonlocal information sharing (hidden variables, we have shown, is not it).
> We currently have an understanding of QM that doesn't reconcile well with macroscopic observation and requires a lot of intuitions to be broken
Why should physics care about human "intuition" at the macroscopic level? That's an incredibly anthropic point of view to take on a cosmos that couldn't care less if we didn't exist.
When Newton developed the theory of gravity it wasn't intuitive that all matter in the universe attracts all other matter. But also wasn't incompatible with our intuitions---it was learnable.
What I see in QM right now "smells" like we're having to compromise too many intuitions to reconcile what the experiments are showing us with the way we expect the universe ought to be working. I agree that the universe is under no obligation to work the way we expect it to---problem, what we have right now in QM is a lack of agreement on how to even rework our intuitions to match our observations and the reality the theory describes. That suggests to me that---much like epicycles, or like gravity being separated from acceleration before relativity---the stories we are telling ourselves about what we see are still too complicated, and a simpler explanation that requires us to sacrifice fewer pieces of intuition has not yet been reached.
This is, to be clear, extrapolation. I have no way to know whether such simplification exists or whether we have hit the boundary where nature actually refuses to conform in such a way to our senses and minds that we can change our intuitions to follow her. It's not impossible that this is the case. But if it is, it's a break from the pattern of physics discovery up to this point in human history.
Round Earth and heliocentrism were counterintuitive too and people struggled a lot to understand them, it's not unprecedented. Ironically Aristotle refuted heliocentrism with the same argument, that heliocentrism doesn't correspond to observation.
We have intuition to understand QM, people struggle with myths, not lack of intuition. Absence of conservation of energy is one of those myths, only those myths need to be sacrificed.
The “putting the earth in the center” is wave function collapse. If you get rid of wave function collapse then all the paradoxes go away except that our experience is a tiny branch of a massive tree
That might be the case. But something still smells in the many worlds theory---it's hard to reconcile conservation of energy or mass with the notion of an infinitely branching multiverse, and if there is no way to interact with those other branches, are they real or just a story we're telling ourselves to try and justify the math?
if they are just a story, it feels like a complicated story to get to the goal.
At the same time, I completely agree that the story of wave function collapse also smells. It creates a distinction between observer and observed reality, and that creates its own set of paradoxes (we can put Schrodinger's cats in nested boxes all day long, and some of the boxes even include experimenters who think they are observing the cat, but experimenters outside the lab don't agree with them that they are the observers!).
> That might be the case. But something still smells in the many worlds theory---it's hard to reconcile conservation of energy or mass with the notion of an infinitely branching multiverse, and if there is no way to interact with those other branches, are they real or just a story we're telling ourselves to try and justify the math?
Looking at the multiverse as branching is where the confusion comes in. There's one Universal wave-function. Why we don't experience the wave-function directly is the mystery.
It's probably a good bet that we are going to discover that to rectify the complexities of QM, there is some assertion most people have fundamentally accepted and is quite uncomfortable to let go but is necessary to simplify the equations. I can't really guess what it's going to be though.