Exploring Dimensions in Physics: Can We Apply Laws in Different Dimensions?

[Arman777]

I have couple questions related to dimension and general physics law

1- Can we apply physics law in lower/higher dimensions. In another words does physics law makes sense in 2D or in 7D.
2- Is it possible that a 2D particle contains charge ?
3- Is it possible a 2D "object" exist in 3D ?

 

[Orodruin]

What do you mean by "general physics law"? Whether a physics model is applicable or generalisable to a higher or lower number of dimensions - or if it even makes sense to think about a different number of dimensions - depends a lot on how what is being considered is modeled. Did you have anything specific in mind?

 

[Arman777]

Thanks for your reply.

Whether a physics model is applicable or generalisable to a higher or lower number of dimensions

I mean this one, actually. I am wondering the physics law would be change or how would be change If we consider 2D universe. Since in 2D universe we would have only 2D objects so in that case I wonder how the physics would work like gravity or electromagnetism.

or if it even makes sense to think about a different number of dimensions

Well It may not be since we can't test or etc. but we can approach theoretically I think.

depends a lot on how what is being considered is modeled. Did you have anything specific in mind?

Okay let's take the case of 2D universe. Is it possible to think electromagnetic force in 2D ? Which that question also brings my second question on sight.
"Is it possible that a 2D particle contains charge"

 

[anorlunda]

Are you asking these questions for science fiction purposes? If so, are you aware of the famous book on that topic called Flatland?

https://www.amazon.com/dp/1420954229/?tag=pfamazon01-20

 

[Arman777]

Are you asking these questions for science fiction purposes?

No I am not asking in a science fiction way. I am just thinking about it.

 

[Arman777]

3- Is it possible a 2D "object" exist in 3D ?

I think the answer is no because its just physically impossible a 2D object in a 3D world (I am talking about the real world, not in mathematical structure).

I think question 1 either requires higher math or the question itself doesn't make sense. I ll stick with the "question doesn't make sense" part, since I don't think even we can't define a mass in this sense. Because we can't define a particle in 2D. In this sense, it seeems to me awkward that we can model Newtonian gravity in 1D ( we can simply draw a point ##p## a vector in the ##-y## axis and magnitude of ##g## and here we have a gravitational force acting on that point ##p##). Is this really how things work in dimensions. In mathematically its perfectly makes sense. We can act a mass like its a "point mass" then its just done. And this "model" describes the reality in 3D. But in real 1D I don't think the things would work like this.

 

[Arman777]

In this sense we are 4D creatures living in 4D. And all physics laws are working under 4D ?

 

[robphy]

Possibly interesting reading:

http://www.dwc.knaw.nl/DL/publications/PU00012213.pdf
P. Ehrenfest, In that way does it become manifest in the fundamental laws of physics that space has three dimensions?
KNAW, Proceedings, 20 I, 1918, Amsterdam, 1918, pp. 200-209

http://rsta.royalsocietypublishing.org/content/310/1512/337.short
J. D. Barrow, Dimensionality
Phil. Trans. R. Soc. Lond. A 1983 310 337-346; DOI: 10.1098/rsta.1983.0095.

http://aapt.scitation.org/doi/abs/10.1119/1.11057
Peter Collas, General relativity in two‐ and three‐dimensional space–times
American Journal of Physics 45, 833 (1977); https://doi.org/10.1119/1.11057

http://www.physics.princeton.edu/~mcdonald/examples/2dem.pdf

and a very old thread
https://www.physicsforums.com/threads/why-is-space-time-3-1-dimensional.109090/

 

[Arman777]

Possibly interesting reading:

http://www.dwc.knaw.nl/DL/publications/PU00012213.pdf
P. Ehrenfest, In that way does it become manifest in the fundamental laws of physics that space has three dimensions?
KNAW, Proceedings, 20 I, 1918, Amsterdam, 1918, pp. 200-209

http://rsta.royalsocietypublishing.org/content/310/1512/337.short
J. D. Barrow, Dimensionality
Phil. Trans. R. Soc. Lond. A 1983 310 337-346; DOI: 10.1098/rsta.1983.0095.

http://www.physics.princeton.edu/~mcdonald/examples/2dem.pdf

and a very old thread
https://www.physicsforums.com/threads/why-is-space-time-3-1-dimensional.109090/

These articles are amazing. Thank's a lot.
1- In Barrow's article I noticed something (page 341, paragraph 2) . He is explaining that in even numbered dimensions signal reverberation will be happen (for light). And then he is explaining that this result may lead us to think that we live in a odd dimension world so that high fidelity information transmission at a neurological level can happen or etc. Then how we are living in a 4D world ?

If 3D refers to just a space dimension then why time dimension would be different then the space dimension in the content of relativity ?

2- Again in Barrows article, where Fundamental units are defined, what's the meaning of the Eqn. 20. I didnt understand that part. What he is introducing to the reader.

3- In your last article that you shared, I realized that even in 1+1 dimension we can have an electric charge and electric field related to it, quoting

"In 1 + 1 electrodynamics, with one spatial dimension, x, the field tensors (44) have components,

There is no magnetic field associated with moving electric charge, and no electric field due to moving magnetic charge. That is, the electric field is only due to electric charge, and the magnetic field is only due to magnetic charge."

Thats really amazing to define a charge in 1+1. Or in Barrows article the dimension of charge, changes relative to the length that's also interesting and I didnt quite understand it (like dimension is about length yes but is it changes about the properities of the charge ?)