I get what you mean, but one thing about which we are certain is that you cannot apply Einstein"s model of gravity at these scales, because his theory is only an approximation that determines the metric of space from an averaged density of the energy and momentum of matter, not from the energy-momentum 4-vectors of the particles that compose matter.
So Einstein's theory depends in an essential way on matter being continuous. This is fine at human and astronomic scales, but it is not applicable at molecular or elementary particle scales, where you cannot approximate well the particles by an averaged density of their energy and momentum.
Any attempt to compute a gravitational escape velocity at scales many orders of magnitude smaller than the radius of a nucleus are for now invalid and purposeless.
The contradiction between the continuity of matter supposed by Einstein's gravity model and the discreteness of matter used in quantum physics is great enough that during more than a century of attempts they have not been reconciled in an acceptable way.
The offset of the spin is likely to be caused by the fact that for particles of non-null spin their movement is not a simple spinning, but one affected by some kind of precession, and the "spin" is actually the ratio between the frequencies of the 2 rotation movements, which is why it is quantized.
The "action" is likely to be the phase of the intrinsic rotation that affects even the particles with null spin (and whose frequency is proportional with their energy), while those with non-null spin have also some kind of precession superposed on the other rotation.
> The offset of the spin is likely to be caused by the fact that for particles of non-null spin their movement is not a simple spinning, but one affected by some kind of precession, and the "spin" is actually the ratio between the frequencies of the 2 rotation movements, which is why it is quantized.
I don’t expect this to work. For one thing, we already know the conditions under which the spin precesses. That’s how they measure g-2 .
Also, orbital angular momentum is already quantized. So, I don’t know why you say that the “precession” is responsible for the quantized values for the spin.
the representations of SU(2) for composite particles, combine in understood ways, where for a combination of an even number of fermions, the possible total spin values match up with the possible values for orbital angular momentum.
Could you give an explanation for how you think precession could cause this difference? Because without a mathematical explanation showing otherwise, or at least suggesting otherwise, my expectation is going to be that that doesn’t work.
The orbital angular momentum is quantized for the same reason as the spin, both are ratios between the phases of 2 separate rotation movements, the orbital rotation or the spin rotation and the intrinsic rotation corresponding to the de Broglie wave (whose phase is proportional to Hamilton's integral, i.e. the integral of the Lagrangian over time).
I have used "precession" for lack of a better term for suggesting its appearance, because while there is little doubt about the existence of 2 separate kinds of rotations in the particles with non-null spin, there exists no complete model of how they are combined.