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Comment by the__alchemist | Hacker News Reader

> Gravity, the thinking goes, can escape our brane and extend into the bulk. That explains why it’s so weak. All the other forces must play in only three spatial dimensions, while gravity can extend itself out to four, spreading itself much too thin in the process.

Wouldn't this cause gravitational force to fall off with distance using something other than an inverse-square law? I think this explanation would be a better fit for the weak force than gravity for this reason. Thoughts?

More broadly: inverse-square behavior (Gravity, EM etc) strikes me as an intrinsic property of 3D geometry; more so of a tell of dimensionality than the magnitude of the force. (I believe the article is inferring higher dimensionality from relative magnitude, vice distance falloff)

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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

How can a dimension be smaller compared to other dimensions?

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

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?

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.

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.

> 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.

> Our established 3 dimensions are actually compact, i.e. loop around

Do they not loop? What other option is there? I assume you can't sail off the edge of the disk, so to speak.

Option 1: They loop.

Option 2: They go on forever without looping.

Option 3: They end - there is some kind of boundary to spacetime.

The expansion of the space is the feature which prevents any physical process inside to distinguish between those options. Kind of a hack - make compact Universe, add expansion and it would inside look and feel indistinguishable from non-compact.

How does option 2 fit with the big bang? The obvious issue (at minimum) being accounting for the CMB.

the 1. makes 2. "easier", i.e. having a multitude of compact Universes is "cheaper" than having a multitude of non-compact ones

Would also be nice for possibly bridging gaps

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.

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

Yes, that sounds right.

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

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

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.

Why does the extra dimension need to be small?

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).

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?"

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.

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

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.

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.

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.

I’m describing why the flatlanders wouldn’t see multiple circles even though a 3D tube is composed of infinitely many 2D circles.

I noticed you were doing so, yes.

The "tube" (compactified dimension) isn't a higher dimensional object going through our space, in string theory it is an actual part of our space.

To put it another way: for compactified dimensions, we're not in flatland.

(For brane theory, we are in flatland, but they're two different ideas about how stuff might work).

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.

Fun fact: Newton attributed the inverse square law to Pythagoras. It’s esoteric, but it relates to harmony of the spheres and the fact that the weight/tension of a string has an inverse square relation to tone. More here, in this Royal Society article: https://www.researchgate.net/publication/250902005_Newton_an...

I wonder if a higher dimension could also be the explanation for extra mass in the universe instead of dark matter. It's outside our perceptible space, but it still exists as mass, poking through into black holes or gently resting on the skin of our 3d volume.

The weird thing about it though is that whatever the dark matter is it has to be spread out. It couldn’t be little planets or brown dwarfs or burned out stars (in a hidden dimension or not) because we’d see more gravitational lensing events than we do

https://en.wikipedia.org/wiki/MACHO_Project

After digging a bit into astromy, computationally myself... There are some heavy assumptions used in the functions that maps pixels to mass densities. Outsider's 2c, but I assess a misalignment between CDM confidence in papers, and this mapping.

Interesting. It would be extraordinary if many of the discrepancies dark matter is required to explain are actually caused by some flaw in the data analysis. It seems unlikely, but not impossible.

I'm not familiar with the topic. Did you have any particularly suspect assumptions in mind?

I am overall suspicious of the degree of confidence used in papers in conjunction with the sheer number of assumptions regarding luminosity, the model of gas and stars in galaxies etc, vs what is discernible in the images (It's a low-resolution set of pixels). Of particular note is inferring mass (or lack thereof) that doesn't correspond to leading-edge luminosity. I.e. gas and stars that are away from the camera, and dim gas.

> The weird thing about it though is that whatever the dark matter is it has to be spread out.

In fact, they'd have to be so spread out that rotation curves remain flat past a million light years [1]. There seems to be no plausible particle dark matter distribution that can satisfy all of the necessary constraints at this point.

[1] https://tritonstation.com/2024/06/18/rotation-curves-still-f...

I thought dark matter was only observed through movements of matter within galaxies. Outer layers of spiral galaxies are observed to move faster than they should, so there has to be additional gravity and therefore mass that binds them on their (fast) orbits around the center.

Perhaps there is a negative gravity outside of galaxies where space seems to bubble out of nowhere anyway and the universe is expanding.

This seems as an attempt to combine gravity with the standard model again, which in my very amateurish understanding comes with multiple extra dimensions anyway. Isn't the higgs field basically a recently discovered additional dimension already? Among the other forms of particles that can be seen as an excitation of fields that compose these dimensions.

But for extreme cases like neutron stars or black holes, we probably do need to combine these theories since gravity is a main reason these objects exist in the first place. And also isn't a curvature of space not already be an additional dimension as well? It would be mathematically as I understand it.

I guess it also implies the extra dimensions aren't massive. Unless that's the explanation for unexplained gravitation.

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