After more thought on black hole singularities being coordinate singularities (or if I'm using the term wrong, rather: singularities that disappear depending on where you view them from), I figure that the solution that makes the most sense is that, uh...
Say you're outside a black hole and that most of its mass is in the singularity, but not all of it is. As you pass the event horizon and approach the singularity, suppose that rather than the singularity disappearing, that more and more of its mass appears as "normal matter" outside the singularity, which itself becomes less massive. You could approach it "forever" as it expands spatially the closer you are to it, and more of its mass would expand out of it until you realize that you're surrounded by a universe that came from the "shrinking" singularity that you're still chasing.
In order for that to be possible, the mass distribution of a black hole cannot be uniform or homogeneous or whatever. There would not be a hard boundary between outside and inside it (other than the event horizon, which is a precise boundary but there is no physical wall of matter or energy there). It would be distributed along something that looks like f(r) = 1/r or 1/r2, with the density at 0 undefined (representing the singularity), and the density approaching infinity as r approaches 0.
Extrapolating this idea from black holes to all matter, we get the following conjecture:
- All mass is non-homogeneous in terms of energy or mass distribution.
- All mass has a singularity at its center.
Basically this would mean that the concentration of any distinct quantity of mass is greatest at its center, and tapers off to blend seamlessly into the surrounding nothingness, rather than there being a distinct boundary between mass and surrounding space. Depending on how you look at the mass, it could be that it has no size and 100% of its mass is contained in a singularity, or half of its mass is, or just a tiny fraction of its mass is contained in the singularity, yet that still represents infinite density for that small mass.
We can extrapolate further and imagine that any mass can be described as a distinct unit in the same way. On the smallest scale, all particles could be viewed as individual masses with individual singularities. On a larger scale: If you were far enough away or warped space in the right way, all of Earth could be viewed as a combined mass with most of its matter contained in one singularity at its center. If you were outside the universe, most of it would be in one singularity, with some of its mass outside the singularity (and each particle of that outside mass containing its own singularity).
Then since we're speculating without restraint anyway, why not conjecture that all fundamental forces are due to non-homogeneity of geometry, IE. curvature of spacetime. Just as large-scale curvature effects gravity, small-scale curvature may effect electromagnetism and/or nuclear force.
Thrown in there is the idea that any mass might be described as a particle, depending on how and from where you viewed it. Thus, particles might be defined as an observer-defined quantization of matter into individual indivisible components. Then, just as a universe might be fully contained in a singularity, or might "spill out" into something with size (eg. a black hole) and divisible mass, so too might an elementary particle be a singularity or a divisible mass, depending on how it is viewed.
A simplification of this idea might be:
- All mass results in space-time curvature (already accepted with general relativity?)
- The point of maximum curvature of any curve in spacetime is always a singularity. (There are no "gentle bumps" in spacetime.)
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