Theoretical 2D World Vs our 3D world?

[TheCuriousMind]

Today I have been reading Flatland: A Romance of Many Dimensions by Edwin Abbott

Things get quite weird, but in an intriguing way.

And I have only touched the surface of this book.

While digging around the internet, I read online in an article that Gravity would not work in a Theoretical 2D World.

This got me questioning! 

What other Physical properties would also be different.

Modern Knowledge explains that things in our universe are made of ATOMS, a particle that consists of a nucleus of protons and neutrons surrounded by a cloud of electrons.

I assumed, before researching anything, that atoms themselves would be 3 Dimensional themselves, but I didn't want to leave it as an assumption, so I dug a tiny bit deeper. 

And my source I found is here Molecules in 3D (wisc.edu)

Turns out. "Atoms arrange themselves in three-dimensional aggregates with specific molecular shapes. Factors which influence the shape of a molecule are: the number of bonds, non-bonding electrons, atomic radii, bond length among others "

So now that I had found more information, it led me to my next question, and I was unable to find any other topics really related to what I wanted to ask.

Question: What would a theoretical 2-Dimensional object be made of? 

[Genady]

There would not be photons either, because electro-magnetic wave needs 3D. Without photons, charged particles would not interact. Thus, there will be nothing to hold atoms intact.

There would not be objects, just a chaos.

[TheCuriousMind]

Quote

There would not be photons either, because electro-magnetic wave needs 3D. Without photons, charged particles would not interact. Thus, there will be nothing to hold atoms intact.

There would not be objects, just a chaos.

Its mind blowing to me, all of this! I don't know why, but all of this intrigues me a lot! Thank you for your reply

 

 

[studiot]

2 hours ago, TheCuriousMind said:

While digging around the internet, I read online in an article that Gravity would not work in a Theoretical 2D World.

Well they would be wrong about this, but it would certainly be different from the gravity we experience.

 

Several comments about dimensiosn.

 

Firstly obviously a space on n dimensions cannot support an object of higher ( >n) dimensions.

But there is a huge amount of established theory for objects of lesser dimension than n embedded in n (or more) dimensions.

So for example in one dimension there are only lines and in two dimensions there are only surfaces.

But there are also lines in two dimensions

And there are lines and surfaces in three dimensions

and so on.

 

Another thing about dimensions are the properties and actions that are possible depend upon the number of dimensions.

Rotations are impossible in one dimension.

They are incomplete but possible in two dimensions. By incomplete I mean that you need a third dimension to fully describe them.

Rotations are complete in three dimensions. By this I mean that you do not need another dimension to describe them every rotational axis is available in three dimensions.

You do not need a fourth dimension for rotations. In fact rotations in the fourth dimension come in pairs.

 

Similarly comments apply to curves since they are related to rotations.

No curves are possible in one dimension,

One curvature is available in two dimensions

Two curvatures are available in three dimensions.

 

I do not know of any truly one dimensional objects (except abstract ones)  in two or more simensions but a shadow can be a truly two dimensional object in 3 dimensions, although the 2D surface may be a very complicated shape.

They a

Edited February 16, 2023 by studiot

[Markus Hanke]

14 hours ago, studiot said:

a shadow can be a truly two dimensional object in 3 dimensions

Good point, this never occurred to me +1

14 hours ago, studiot said:

Well they would be wrong about this, but it would certainly be different from the gravity we experience.

Very different indeed. In fact, based on GR in 2D, the only gravity that could exist in such a world would be found in the interior of mass-energy distributions - there could be no gravity at all in vacuum.