by Jay

# 2

Epistemic status: Wildly speculative.  I am not a physicist.  It may quickly become apparent that I have no idea what I'm talking about.  Nevertheless, I found the thought experiment interesting.

The set of models known as superstring theory posits the existence of multiple compactified dimensions in addition to the usual three spatial and one temporal dimension, which I'll call 3+1 space.  Here I will suggest that an observer approaching a black hole might perceive 3+1 space collapsing into a 2+1 space.  By extension, our 3+1 space may have resulted from gravitational collapse in a higher dimensional space (possibly more than once).

Consider an observer approaching a black hole.  If the observer is well clear of the event horizon, the observer has three degrees of spatial freedom.  We can describe its position in space using the common spherical coordinates of r, phi, and theta.  R is the distance between the observer and the center of the black hole.  Phi and theta are two angles equivalent to latitude and longitude on Earth.

As the observer approaches the black hole, the gravitational force Fg increases.  The forces acting on the observer in the radial dimension can be summarized as Fg+X, where X is all other forces acting on the observer in the radial dimension. As the observer approaches the singularity, Fg grows without bound and X becomes increasingly irrelevant.

At this point, the observer's position in the radial dimension r is, for all practical purposes, a function of time.  The observer has lost all capability to affect its motion in the r dimension.  Any length the observer may have had along the r dimension will be stripped away in the process of spaghettification.  The observer would no longer be able to perceive r and time as separate dimensions.  The point r=0 would be, to the observer, both the center of the universe and the infinite future.

Two spatial dimensions would remain, phi and theta, and the observer would be able to freely move across the surface of the sphere (subject to the constraint that the accessible sphere is changing with time).  The observer would live in a 2+1 universe (if whatever remained of the observer was capable of surviving).

Note that particles of very low mass are not completely localized in space.  Even under the influence of the black hole, such particles would not be completely localized in the radial dimension.  The behavior of such particles might seem rather odd.

# 2

New Comment

as usual with weird hypotheses, pbs spacetime covers them nicely and discusses the caveats:

this does not seem to consider the possibility that compactified dimensions are because of a black hole, and I suspect that that would be a misunderstanding of string theory, though I'm not a physicist either. see also their other stuff about black holes, https://www.youtube.com/@pbsspacetime/search?query=black%20hole, and https://www.youtube.com/@ScienceClicEN which has one of, my favorite, visualizations of, relativity (though maybe still not the most true one possible?)

and see also high quality though less, relevant, others, if, you, want, deeper, physics, lectures

kagi summary of the video:

- Some physicists have theorized that the universe could be inside a black hole based on mathematical similarities between black hole singularities and the Big Bang.
- Both black holes and the Big Bang involve infinite densities where Einstein's theory of general relativity breaks down.
- Black holes and the early universe both have event horizons beyond which light and matter cannot escape.
- The interior of a white hole, which is the time reverse of a black hole, resembles the expanding universe with a past singularity.
- An FLRW metric, which describes our homogeneous and isotropic universe, can be embedded inside both black holes and white holes.
- If a white hole was large enough, its interior could be indistinguishable from our observable universe.
- Hawking radiation suggests black holes and white holes may be equivalent objects.
- Cosmological natural selection proposes universes are born from white holes formed by black hole collapse.
- If our universe is inside a black hole, the exterior could contain other universes with observers making the same conjecture.
- While intriguing, there is currently no conclusive evidence that our universe is within a black hole.

At this point, the observer's position in the radial dimension r is, for all practical purposes, a function of time.  The observer has lost all capability to affect its motion in the r dimension.  Any length the observer may have had along the r dimension will be stripped away in the process of spaghettification.

The idea of spaghettification is, if your feet are 3 feet away from the center of the black hole, and your head is 9 feet away, then by the inverse square law your feet are getting pulled by gravity 9x harder than your head is.  It's not that your body gets compressed flat along the radial dimension; rather, you get pulled apart into pieces.

It's true that, as this process happens, every contiguous piece of you will be a piece where radial distance is mostly the same.  But, like... at time A, your pelvis will be one intact piece, and at time B, it'll split and you'll have a top half of your pelvis and a bottom half of your pelvis; at time X, all remaining structures are 20 atoms high, and at time Y, they break and now you have twice as many structures that are 10 atoms high.  (Making some drastically oversimplifying assumptions here, but that's the idea.)  If you still have an intact piece you can call an "observer" when all surviving pieces are 10 atoms high, just wait until they get yanked apart into "5 atoms high" pieces, and so on.  Even when you get down to 1 atom high, where atoms are connected in a row... if some atoms are a nanometer higher than the others, they'll get ripped away from the others soon.  So I don't think this will work the way you have in mind.

(Also, of course, in this example, if your feet are 3 feet away from the center of the black hole, and you're getting pulled strongly enough to get pulled apart, then you'll reach the singularity in a fraction of a second, so you wouldn't be living for very long.  Meanwhile, if you're entering the event horizon of an enormous black hole, zillions of miles in diameter, then the tidal forces at that point are tiny [your feet are pulled only microscopically harder than your head], and there would be no perceptible spaghettificiation.)

I think the idea expressed in the post is for our entire observable universe to be a remnant of such spaghettificiation in higher dimensions, with basically no thickness along the direction leading to the singularity remaining. So whatever higher dimensional bound structure the local quantum fields may or may not usually be arranged in is (mostly) gone, and the merely 3+1 dimensional structures of atoms and pelvises we are used to are the result.

I wouldn't know off the top of my head if you can make this story mathematically self-consistent or not.

[-]Jay4mo10

Yeah, that's the idea I was going for.

Black holes are indeed cool, but they are also complicated and misunderstood. Sean Carroll just published a book that describes diving into a black hole (at the end of a lot of discussion of physics), or if you prefer short story format I think there's a pretty accurate Greg Egan story about the process, though I don't remember if that goes into the whole "time gets rotated to become a spacelike dimension" thing.