The right magnitude for things to get weird must be very small, but nobody can say whether that scale is a million times greater than the Planck length or a million times smaller than the Planck length.
Therefore using the Planck length for any purpose is meaningless.
For now, nobody can say anything about the value of a Schwartzschild radius in this range, because until now nobody succeeded to create a theory of gravity that is valid at these scales.
We are not even certain whether Einstein's theory of gravity is correct at galaxy scales (due to the discrepancies non-explained by "dark" things), much less about whether it applies at elementary particle scales.
The Heisenberg uncertainty relations must always be applied with extreme caution, because they are valid in only in limited circumstances. As we do not know any physical system that could have dimensions comparable with the Planck length, we cannot say whether it might have any stationary states that could be characterized by the momentum-position Heisenberg uncertainty, or by any kind of momentum. (My personal opinion is that the so-called elementary particles, i.e. the leptons and the quarks, are not point-like, but they have a spatial extension that explains their spin and the generations of particles with different masses, and their size is likely to be greater than the Planck length.)
So attempting to say anything about what happens at the Planck length or at much greater or much smaller scales, but still much below of what can be tested experimentally, is not productive, because it cannot reach any conclusion.
In any case, using "Planck length" is definitely wrong, because it gives the impression that there are things that can be said about a specific length value, while everything that has ever been said about the Planck length could be said about any length smaller than we can reach by experiments.
By “things get weird” I meant “our current theories/models predict things to get weird”.
So, like, I’m saying that if Einstein’s model of gravity is applicable at very tiny scales, and if the [p,x] relation continues to hold at those scales, then stuff gets weird (either by “measurement of any position to within that amount of precision results in black-hole-ish stuff”, OR “the models we have don’t correctly predict what would happen”)
Now, it might be that our current models stop being approximately accurate at scales much larger than the Planck scale (so, much before reaching it), but either they stop being accurate at or before (perhaps much before) that scale, or things get weird at around that scale.
Edit: the spins of fermions don’t make sense to attribute to something with extent spinning. The values of angular momentum that you get for an actual spinning thing, and what you get for the spin angular momentum for fermions, are offset by like, hbar/2.
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.