Stability of atoms and stable orbits in higher dimensions

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

Stability of atoms and stable orbits in higher dimensions

Postby anderscolingustafson » Sun Oct 18, 2015 6:34 am

I decided to look up atoms in 4d and I found an interesting article that talks about why gravity and electromagnetism would have a 1/r potential in higher dimensions.

https://www.zarm.uni-bremen.de/fileadmi ... Macias.pdf

It talks about how when we assume that gravity and the force between two charges have a drop off of 1/r^(d-1) then stable orbits are in fact impossible but the only reason that we tend to assume a force of 1/r^(d-1) is because we assume that Maxwell's equations for electromagnetism, Newton's Field Equations, and Einstein's Field Equations would be the same in higher dimensions and try to extrapolate what effects they have on higher dimensions. It says though that Rutherford's Scattering Experiments seem to indicate that the 1/r potential is actually more fundamental than Maxwell's Equations for Electromagnetism so that in higher dimensions it would be Maxwell's Equations that are modified to fit the 1/r potential instead of the other way around. This means that in any number of dimensions the force between two charges is 1/r^2 instead of 1/r^(d-1). It also says that for Gravity we can assume a 1/r potential and modify Newton's field equations, and Einstein's Field Equations in order to get the 1/r potential for gravity which would also produce an inverse square law. This also means that there would be stable orbits in higher dimensions because the gravitational force between two masses is 1/r^2 in any number of dimensions instead of 1/r^(d-1). This seems to be saying that it is not only possible to adjust Maxwell's Equations as well as Newton's, and Einstein's Equations to produce stable orbits and stable atoms but that if there is the same kind of gravity, electromagnetism in higher dimensions then modifying Maxwell's Equations as well as Newton's, and Einstein's Equation is required.
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Re: Stability of atoms and stable orbits in higher dimension

Postby Teragon » Sat Oct 24, 2015 9:15 am

Having no Gaussian law would be very couterintuitive. The concept of field lines would break down. I see Gauss' law as fundamentally related to geometry. It expresses the simple fact that the surface of an n-sphere grows like r^(n-1).

I just started with the article and it's not clear to me how the authors come to the assumption that Rutherford scattering was independent of the dimension, as we can only test it in three dimensions. And it's not explained why in theory. I would still assume a 1/r²-potenial in 4D and a logarithmic potential in 2D. Really confining particles to only two dimensions in an experiment would be placing them between two planes of a material that has the property to repel all electric field lines, so that the may not penetrate, and the distance of the planes has to be smaller than the distances for which the potential is evaluated. Otherwise the experiment makes no sense as the field lines still propagate into three dimensions. It's easier to confine an electric field to two dimensions by extending the dimension of the field source. If you do that the electric field goes like 1/r in 2D and Gauss' law is still valid. If you confine it to one dimension, it's independent of r and Gauss law is still valid.
What is deep in our world is superficial in higher dimensions.
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