4 dimensional bohr atom and magnetism in 4D

[granpa]

the bohr model has only one variable.
The n quantum number which represents the distance between the nucleus and the orbiting electron.

however in 4D a rotating object can rotate in 2 different ways simultaneously.
a rotating electron cloud would therefore have 2 variables.
this could explain not just the n quantum number but alos the l quantum number.


if the atom is 4 dimensional and if this explains the order of filling of orbitals
then something like the following would have to be true



in 4D the electric field follows an inverse cube law
and as a result there are no stable orbits.
therefore there must be another force to keep the electron cloud in orbit.

if this force follows a first power law (like the strong force)
then the math becomes extremely simple.
(even for complex 4D orbitals with different radii in different dimensions

the electric field is a vector field and the magnetic field is always at a right angle to the electric field.
in 3 dimensions the magnetic field is a vector field but in 4 dimenstions it becomes a bivector field.
in stead of defining a line segment at each point it defines a plane at each point.
to learn more about this google clifford algebra or geometric algebra

[wendy]

The stability of the orbits in Bohr's atom is not due to elliptical orbits, but the quantisation of angular momentum (h-bar).

I am not sure how to bring magnetism into 4d, or even if it has a place. Magnetism is a result of a finite speed of waves, as applied to electricity. There is a corresponding magnetism for gravity (zb oliver heaviside's co-gravitation). One must then suppose that magnetism is an outcome of three dimensions, i suppose. Also, the curl function is heavily involved, and this is a feature of 3d space.

[dodecahedron]

I don't understand why it must follow the inverse cube law.Also ,we have clouds,where they are most likely to be.

[quickfur]

I don't understand why it must follow the inverse cube law.Also ,we have clouds,where they are most likely to be.

The inverse cube law comes from the assumption that the strength of a force is proportional to the number (or rather, density) of force carriers emanating from the source of the force.

In 3D, say you have a force that's originating from some given point P in space. Then you may imagine that there are some number of force carriers radiating from P. Assuming that P emanates the force equally in all directions, the density of the force carriers at some given radius R from P would be proportional to the surface area of a sphere with radius R. You can visualize this by drawing, say, a square some distance away from P, representing the object that the force acts on. The further away from P you are, the less number of lines will intersect P, so it feels a weaker force. How much weaker? Well, the number of "force lines" roughly fall in inverse proportion to R^2, since the number of force carriers emanating from P is constant, but the surface area of the sphere of radius R is proportional to R^2, so there will be less force lines per unit area of the sphere, exactly proportional to 1/R^2. So one would expect that in 3D, force strength fall in inverse proportion to R^2.

And indeed, we find in 3D that forces like gravity and electromagnetism diminish according to an inverse square law.

Generalizing this idea to 4D, then, if we have a point P where some given force is originating, then if you draw, say, n "force lines" from P, and consider some object at radius R from P, then how much force will that object experience? It would have to be proportional to the surface area of the 4D hypersphere of radius R, centered on P. Now, the surface area of a 4D hypersphere increases in proportion to R^3, so given a constant number of force lines, one would expect that the density of force lines at radius R would be inversely proportional to R^3. That is, forces in 4D should obey an inverse cube law.

[gonegahgah]

Hi Quickfur. I'm busy doing music and other stuff this year so has kept me away. Next year I hope to actually do some programming again albeit sadly not for 4D.
I do wish I had a whole lot more time... as this stuff is fun!

Anyhoo, I understand that gravity does diminish with an inverse plane law (3-planes being square and 4-planes being cube-seeming-like).
But, my understanding is that this differs for magnetism and electromagnetism. Otherwise we could just use magnetism to leave the Earth's gravity well.
It has to do with how those fields spread.
The Magnetic field acts and spreads through the poles and then outpours into the same space whereas gravity spreads in all directions directly into that space.
This causes the magnetic field to be strong at the pole but weaken at a faster rate.
So although the magnetic effect is greater than the gravitational effect at the interface; the effect dies off at a quicker rate for magnetism allowing gravity to take over.