04282012, 08:36 PM



2,854 posts, read 1,873,775 times
Reputation: 348


the bohr model has only one variable., the "n" quantum number which represents the distance between the nucleus and the orbiting electron.
However in 4 spatial dimensions 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 also the "l" quantum number.
Aufbau principle  Wikipedia, the free encyclopedia
orbitals with a lower n + l value are filled before those with higher n + l values

08032012, 01:52 PM



2,854 posts, read 1,873,775 times
Reputation: 348


if the atom is 4 dimensional, and I am not saying that it is but IF it is,
and if this explains the order of filling of orbitals, and I am not saying that it does but IF it does,
then the following would have to be true

08032012, 05:29 PM



15,921 posts, read 19,290,841 times
Reputation: 7675


Quote:
Originally Posted by 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 4 spatial dimensions 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 also the "l" quantum number.
Aufbau principle  Wikipedia, the free encyclopedia
orbitals with a lower n + l value are filled before those with higher n + l values

And the point of the OP is?

08042012, 03:19 AM



2,854 posts, read 1,873,775 times
Reputation: 348


in 4D the electric field follows an inverse cube law
which is exactly what the force due to centrifugal force follows
(if angular momentum is constant)
so the net effect of the electric field is simply to reduce but not eliminate the centrifugal force.
if so then 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

08042012, 05:27 AM



Location: Westwood, MA
4,657 posts, read 6,105,372 times
Reputation: 5589


Quote:
Originally Posted by 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 4 spatial dimensions 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 also the "l" quantum number.
Aufbau principle  Wikipedia, the free encyclopedia
orbitals with a lower n + l value are filled before those with higher n + l values

You're trying to solve a problem that was solved nearly a century ago. The Bohr model gave way to wave mechanics, which did a much better job of explaining experimental results. The "n" and "l" quantum numbers are the eigenvalues of the radial and angular parts of the Schrodinger equation.
QED does an even better job. QED is a 4 (3 space + time) dimensional theory formulated with inherent Lorentz invariance. Is that what you mean by a 4 dimensional theory? You certainly don't need 4 dimensions to explain the atom, as 3 dimensional wave mechanics explains the bulk of atomic physics. You definitely don't need 4 spatial dimensions.

08052012, 09:32 AM



2,854 posts, read 1,873,775 times
Reputation: 348


you will notice that the spherical orbitals (11, 22, 33, 44, 55)
are not where conventional theory says they would be
(which is in the first column)

08082012, 06:07 AM



2,854 posts, read 1,873,775 times
Reputation: 348


in 4 spatial dimensions the magnetic field is no longer a vector field.
it becomes a bivector field.
instead of there being a vector with a certain orientation and magnitude at each point
there is a plane with a certain orientation and magntitude at each point
Geometric Calculus R & D Home Page
Last edited by granpa; 08082012 at 06:24 AM..

10062012, 03:35 AM



2,854 posts, read 1,873,775 times
Reputation: 348


Quote:
Originally Posted by granpa
in 4D the electric field follows an inverse cube law
which is exactly what the force due to centrifugal force follows
(if angular momentum is constant)
so the net effect of the electric field is simply to reduce but not eliminate the centrifugal force.
if so then 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

Please ignore the comment about centrifugal force.
Angular momentum isnt constant.
Its quantized but it isnt constant.

10062012, 04:52 AM



Location: Westwood, MA
4,657 posts, read 6,105,372 times
Reputation: 5589


Quote:
Originally Posted by granpa
Please ignore the comment about centrifugal force.
Angular momentum isnt constant.
Its quantized but it isnt constant.

In an isolated system angular momentum is both quantized and conserved. You should ignore the comment about centrifugal force because the electron is delocalized and in the ground state the angular momentum is zero. It does not orbit the nucleus like a planet.

10062012, 04:56 AM



2,854 posts, read 1,873,775 times
Reputation: 348


in the ground state orbital angular momentum is zero but spin is not
http://en.wikipedia.org/wiki/Total_a...quantum_number

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