Einstein's Other Theory of Everything

not possible after 5 minutes

> without relying on gravity to serve as a model of gravity (which always bothered me a bit)

Why though? Would it help if the sheet were in a centrifuge?

The "balls on a rubber sheet" is a pain because nothing is in free-fall: there are dissipative contact forces between the balls and the rubber sheet. Consequently realistic initial [position, velocity] values for the test ball cannot give you a stable circular orbit around the central mass ball. Venus isn't about to fall into the sun. Now try setting up Earth-Moon or the Jovian-Gallilean systems on the rubber sheet.

It's fun to try to peel away defects in the "ball on a rubber sheet" in an effort to arrive at Newtonian limit equations of motion for balls in placed around it. (First advanced question: how do we adapt Einstein-Hilbert to reflect trapping onto the sheet? Does dimensional reduction work?) What sort of membrane in constant acceleration could generate scaled 2+1 timelike geodesics for model solar system objects placed on it? Can one scale this to a model of the solar system with all orbits flattened onto the membrane? For instance, what do the IVs look like for a ~ 1050:1 mass ratio between a model sun and a model Jupiter that is shrunk down to classroom size and retains a good match to Jupiter's real orbital parameters (or if you prefer, lengths and angles) across many orbits? Without destroying this scale model orbit, can we add the inner solar system? Can we get sensible orbits of scale model Galilean moons?

(And of course all of the above has completely neglected the rotations of these bodies about their axes, which is clearly always very wrong with a typical in-classroom rubber sheet + balls demonstration. We can blame friction for that.)

I'm not sure what you're representing on silly putty: are the drawn lines solutions to geodesic equations? What would the twists-pulls of the putty in a scale model ~kg:g Sun and Jupiter system look like? Or are you thinking about a relativistic regime somewhere in the right half of this diagram : https://en.wikipedia.org/wiki/Post-Newtonian_expansion#/medi...> ?

An electron falling (electrostatically) toward a proton will reach the speed of light at some point. This is of course the same distance where inside it would need an escape velocity greater than c. So that's an event horizon due to a different force.

Some claim matter falling into a black hole never really does from the point of view of an outside observer. I've seen weird sounding descriptions like it "spreads out over the surface". What if electron orbitals are some kind of equivalent to that?

When I ask these (admittedly naive) questions, physicists will usually say something like "oh you have to treat that with quantum mechanics". But why? Isn't trying to resolve it using more conventional means (including concepts from relativity) a good idea? I feel like it's not right to reject one approach simply because nobody has figured out how to make it work while another does. That's different from showing that it can't work. Or have such approaches somehow been categorically proven inviable?

Another layman observation, based on your last paragraph: In terms of electron orbitals, the definition of what quantum mechanics means varies. For example: Are you using quantum mechanics when describing an electron in hydrogen's orbital?

I have heard both answers. It's spread out over space and is not like the classical pre-Bohr models, but it's described by a classical wave equation, and can be viewed at as a differential equation solution; a function over 3D space (For a time snapshot; or 4D spacetime with rotating phase). In this definition, you are not doing quantum mechanics until dealing with things like anti-symmetry, spin statistics, exchange interactions etc.