[ktrask]

Yes, exactly. That is why we think the extra dimensions might be small, und the inverse square law is only violated at and below the size of the extra dimensions. This is also why we are using the Yukawa Potential to constrain that possibility, because it has a length scale and a strength of a potential deviation from the inverse square law. See also: https://en.wikipedia.org/wiki/Fifth_force

[baxtr]

How can a dimension be smaller compared to other dimensions?

[codethief]

It could be a compact[0] dimension, i. e. of finite length. In the simplest case you might imagine it as a circle attached to every point in our 3-dimensional Euclidean space. The aforementioned length scale would be the circumference of that circle.

[0]: https://en.m.wikipedia.org/wiki/Compact_space

[taneq]

Trying to wrap my head around this explanation and I’m picturing a looping gif. You have your normal x and y dimensions and then time through the gif. If the loop length is very short then distance between any two pixels will mostly only depend on x and y. Is that right?

[jiggawatts]

The classic example is a garden hose seen from afar looks like a line, but up close it is a cylinder that can be walked “around” by an ant.

[trhway]

Interesting case if we are the “ants” and it is our 3 dims happen to be compact looping somewhere beyond our event horizon. Multitude of Universes in that garden hose in which gravity can be falling as cube or more while at small scale if our compact Universe we’ll see square, and only very precise measurements may notice a bit larger than square.

Another possibility is if our brane has a lot of folds coming close/touching - that would make gravity there stronger like say that dark matter idea inducing rotation speed curve of the disk stars.

[codethief]

> Interesting case if we are the “ants” and it is our 3 dims happen to be compact looping somewhere beyond our event horizon. Multitude of Universes […]

I think you're mixing up two different cases here: 1) Our established 3 dimensions are actually compact, i.e. loop around or hit a boundary somewhere. No multiverse here. 2) There are extra dimensions, meaning that for every point in that extra dimension there's another 3-dimensional universe as we know it.

[MPSimmons]

Would also be nice for possibly bridging gaps

[codethief]

In the simplest case, yes. Though, once curvature (gravity) enters the picture, it could (in theory) become more complicated, as the additional dimension could get stretched or compressed.

[rcxdude]

Another visual that may be useful is imagine being stuck between two portals squeezed close together.

[317070]

Yes, that sounds right.

[moralestapia]

And yet that circle has as many "points" as any other 1-dim independent axis, so ...

[codethief]

The "number" of points is irrelevant, topologically these are very different spaces (one is compact, one isn't).

[DennisP]

Imagine if Flatland were a very long string in a big circle. In one direction you go around the big circle and it's a long distance. At a right angle to that, you go around a tiny little circle.

[mnky9800n]

Why does the extra dimension need to be small?

[addaon]

Because gravity will be observed to decay with distance cubed for distances on the scale of the extra dimension, and distance squared beyond that; and we have not found a scale where we see gravity decay faster than distance squared (but it gets harder and harder to measure at small scale, so the error bars grow).

[ben_w]

If it was big, you could see it.

IIRC experimental gravity data rules out any compactified dimension bigger than 50μm, but a question I keep coming back to is "surely the pictures of atomic bonds taken by electron microscopes rules compactified dimensions larger than 1Å?"

[cmrx64]

interesting question. my (somewhat naive) thought about it is that bonds are maintained by the EM force, which is so strong that it swamps out any contribution from gravity.

[moralestapia]

Not necessarily, 2D cannot easily see 3D, etc...

[ben_w]

If a compactified spatial dimension exists in our universe, and was big enough to fit an atom, why couldn't we see two atoms that seem like they're in the same 3-dimensional coordinates?

Sometimes compactified dimensions are analogised to a straw: seen from a distance it seems one dimensional, up close (an ant's perspective) it's got one long dimension and one short dimension.

I don't know how far to take the analogy. It sounds like surely photons with wavelengths smaller than the compactified dimension would be likely to take a spiral path, looping around compact dimension n times for every m units of 3-space travelled, which would seem like they were mysteriously slow if you weren't expecting the compact dimension to exist.

I vaguely remember the idea of wavelength-dependent speed of light is a thing that's been ruled out by tests with supernova data, but not to what wavelength or sigma.

[MichaelZuo]

The same reason why flatlanders don’t see two circles in the same 2D coordinates, even if a 3D tube was penetrating through their world.

Because they can’t see above or below to the rest of the tube. They can only see a single infinitely thin slice of the tube.

[ben_w]

I think you're describing a completely different geometry than I'm describing.

An ℝ²-brane such as flatland existing in a ℝ³ bulk is different to an ℝ²⨯S¹.

If the S¹ part* is present in our universe to the degree that it can explain anything about gravity, it should also have an impact on everything else in the universe larger than the radius of the S¹ dimension's circumference.

* well, S^n ⨯ T^m, the version of string theory I hear most about has n+m = 6, but there are others, and this thread is a toy model where n=1, m=0

Edit: Apparently the U+1D54A character is stripped, so put a plain ASCII "S" back in.

[ionwake]

Yes but you would sure as heck bump into it if it was big.

Like literally in the middle of your sitting room. Isn’t it a known meme horror thing - monster slices from another dimension splicing across into ours as they move through their planes .

Basically it doesn’t happen but the dimensions do exist so they must be small.

Hence why we don’t bump into them.