| >they're space-time shapes with a singularity at the middle Upon googling "black hole singularity", the first "People also ask" is "Does black hole contain singularity" and the answer is, "No, black holes in our universe, that is to say the real universe, do not contain singularities." While this doesn't in itself invalidate your point, it does seem to raise questions. >The black hole at the center of our galaxy extends across 16 million miles, or a little over eighteen times the size of our sun. I think what you are doing here is conflating the physical effects of the thing (the gravitational field of force) with the mathematical description of the thing itself (a precisely defined geometric structure). If you are talking about extremely strong gravity fields, such as those that bind entire galaxies (or galaxy clusters or even larger organizational patterns), then that is one class of things (empirical), but the purely theoretical notion of physical singularities is an entirely different class of things altogether (a class, which, IMO is perfectly self-contradictory). >That's because solutions to the Laplace equation smooth themselves out as quickly as possible as you move away from the boundary condition. This seems incorrect. I find that solutions to the Laplace equation typically "smooth themselves out" in a quasi-linear way (ie, the way sines and cosines do). The most vexing question in Quantum Mechanics is in fact why quantum states (i.e. the eigenfunctions that are solutions to PDE's such as Laplace's equation) appear to us as localized packets rather than how their "wave functional" mathematical descriptions would dictate (diffuse). The way this conundrum is resolved in QM is by way of a perfectly ad-hoc procedure called "collapsing the wave function". |