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