Predicting the spectra of Hydrogen

When you excite hydrogen gas by passing an electric current
through it, it produces a particular kind of light which is composed of only
certain frequencies. See:

http://hyperphysics.phy-astr.gsu.edu/hbase/tables/hydspec.html

One of the successes of quantum mechanics is its ability to
reproduce the formula for the hydrogen spectra.

The cubic atomic model can reproduce the Balmer formula
which predicts the spectra of hydrogen as well as the QM Schrodinger equations
can. A description of the Balmer formula can be found at:

http://www.colorado.edu/physics/2000/quantumzone/balmer.html

It can be expressed as: v = 1/l = R
(1/n1^2 - 1/n2^2)

In this formula l = wavelength, v =
frequency and R is the Rydberg constant. The values n1 and n2 represent any 2
integer values representing the electron energy levels. Using this formula, you
can precisely calculate the frequencies that are in the light produced by
hydrogen.

Conventional quantum mechanics
explain this as the result of an electron moving from one “electron shell” to
another. The problem with this picture is how do you explain why the electrons
maintain these “shells”? In atoms with dozens of electrons flying about, why
don’t they collide and scatter? What could possibly hold them in their proper
places? Quantum mechanics does not explain this and I think that it is
impossible for the electrons to maintain any “shells”.

The cubic atomic model does not
assume that the electrons are outside of the nucleus. It assumes that they are
an integral part of the nucleus. So how is the spectra of hydrogen generated if
there are no electron shells to generate the spectra?

The way I derive this is by assuming
that space is quantized, that is, space is made out of fixed sized grains, like
the grains of sand in a beach. Lets say we call L, the diameter of the grain of
space. This restricts the movements of electrons to only move in whole integer distances
n*L from the nucleus of the atom.

When you excite an atom, electrons
are knocked loose from the nucleus and they can only travel integer distances
away from the nucleus. So the main reason why electrons appear to have specific
energy levels is because they can only exist at specific distances away from
the nucleus. So there is no need to postulate that these electrons somehow
exist in a mysterious “energy shell” floating around the nucleus with no
apparent support. Instead when an atom is in the ground state, all the
electrons fall straight into the nucleus and stop.

To derive the Balmer formula using
the cubic atomic mode, we can trivially calculate the force between a hydrogen
nucleus and an electron using Coulomb's law:

F = KQ1Q2/R^2 where r = n*L and Q1, Q2 are the charges of a proton and an
electron.

Since we're dealing with hydrogen
with a single +1 charge and -1 charge, it simplifies to:

F = K/R^2

I claim that the energy of the
electronic transitions is exactly proportional to the difference in
electrostatic force as calculated by Coulomb's law for any 2 values of r where
R = n*L.

So for a transition from 2 to 3, we
calculate the difference. For simplification, we take L=1 (the diameter of an
aether particle) in arbitrary units. Since we are only talking about
proportionality, the constant K can be anything, so let us set it to K=1 so it
drops out as well:

Difference in force for a 2->3
transition = 1/2^2 -1/3^2

If we were to take a different
transition, say 3 to 5, we get:

Difference in force = 1/3^2 -1/5^2

In general, we have:

Difference in force = 1/n1^2 -1/n2^2
where n1 is the starting level and n2 is the finishing level.

Now note that this is EXACTLY, the
same format as the Balmer formula!

Since I claim proportionality, we
can add in any constant, so we can add the Rydberg constant R and equate it
directly to energy.

Energy = R(1/n1^2 -1/n2^2)

An since energy is inversely proportional
to wavelength for light, we can write the complete Balmer fomula as:

1/wavelength = R(1/n1^2 -1/n2^2)

This interpretation immediately
solves some questions about the Balmer formula. The use of 1/r^2 terms is not
just happenstance, it is a directly result of the forces calculated by
Coulomb's law. It also answers how an electron should actually be perceived
when it is radiating. It is simply an electron, moving fixed distances towards and
away from the central proton as it being ionized. When it is not ionized, the
electron falls to the lowest level basically resting on the proton. The
quanization is not due to some magical something that forces the electron into
fixed sized orbits, it is space itself which does the quantization. A concept,
which I think is much easier to accept. Balmer himself could not justify how
electrons maintain their stately orbits around the nucleus, but this derivation
solves that problem by forcing the electron to only exist at fixed distances
away from the nucleus for short periods of time due to the granular nature of
space itself.

The derivation of the Balmer formula
is based on the Cubic Atomic model which can be found at : http://franklinhu.com/atmpics2.html

This is part of my Theory of
Everything which can be found at: http://franklinhu.com/theory.html