Re: New Explanation of Hydrogen's Fine Structure


"Igor" <thoovler@xxxxxxxxxx> wrote in message
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On May 28, 12:10 pm, "Steve Bell" <sb...@xxxxxxxxxxxx> wrote:
"Igor" <thoov...@xxxxxxxxxx> wrote in message

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On May 24, 2:51 am, "Steve Bell" <sb...@xxxxxxxxxxxx> wrote:





"Igor" <thoov...@xxxxxxxxxx> wrote in message

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On May 23, 4:11 pm, "Steve Bell" <sb...@xxxxxxxxxxxx> wrote:

Originally, I had thought the electronic Kerr frame dragging effects
would
play an important part in producing hydrogen's non-relativistic
spectrum.
I
decided to up the degree of frame dragging in my electronic Kerr
chaotic
orbit hydrogen simulation and see what effects this would produce.
With
no
frame dragging (electronic Schwarzschild field) and starting off from
the
radius given by the electronic Schwarzschild equations (see eqs. (18)
and
(19) athttp://sb635.mystarband.net/unified/res_2.pdf) and using no
fracturing (no in/out-of-plane velocity perturbations), and starting
with
a
0 deg inclined circular orbit at this radius, the simulation
deterministically produced a nice always-circular equatorial orbit.
Upping
the frame dragging effects causes this equatorial circular orbit to go
slightly elliptical and to start slightly precessing. I turned on the
level
of fracture (in/out-of-plane velocity perturbations) that I think is
correct, and I did a monte carlo search for that amount of frame
dragging
that raised the initial radius given by the electronic Schwarzschild
equations to Bohr's radius as an apogee value. I used many different
seeds,
and an average of all the runs gave Bohr's radius as an apogee
distance
very
nearly exactly. Of course, I am forcing this here, but for a
"calibration"
to next see how the n = 2 results come out; see below. In this
scenario,
there is a "selection rule" that states an electron cannot jump out of
(or
into) the n = 1 shell unless at an apogee transfer. With the degree of
frame
dragging introduced, the electronic Kerr metric produces an
ellipsoidal
charge-based curved space surrounding the proton, but only very
slightly.
The fracturing of the electron's orbit causes the electron to follow
an
attractor that is actually slightly ellipsoidal in shape, but due to
the
"apogee transfer selection rule," the spectra will only show a
spherical
shell residing at Bohr's radius (the apogee distance of the actual
ellipsoidal shell), in agreement with observation.

I next went to the n = 2 shell. I used the same level of frame
dragging
that
"calibrated" the n = 1 shell correctly. The starting radius was the
electronic Schwarzschild-equation-based radius given by eqs. (18) and
(19)
with n = 2. With the degree of frame dragging used, this shell also is
slightly elliptical (technically, any amount of frame dragging
produces
an
ellipsoidal shell, but even in the amounts introduced here, these
shells
are
very close to spherical). At the end of many monte carlo runs, the
average
apogee distance was once again non-relativistic, at essentially
exactly
four
Bohr radii. The perigee distance was equal to the beginning
Schw-equation-based distance. The difference between these to radii in
terms
of energy was 4.5 x 10^-5 eV, essentially exactly what is observed for
the
fine structure of hydrogen's n = 2 shell. There would be a transition
rule
for this shell, that would only allow jumps out of the shell at the
apogee
distance (non-relativistic), and only allow captures into this shell
at
the
perigee distance, which is most certainly driven by "significant"
relativistic effects, not only special, but all the way to Kerr. It
would
be
amazing, wouldn't it, if after launching a billion-dollar GB-P
spacecraft
to
observe frame dragging effects, they are in operation all around us,
in
the
very atoms that make us up. In certain ways, this dual differential
geometry between the world of the big and the world of the small looks
almost designed. The principle hint at unification was allowing us to
see
F
= (1/4*pi*eps)*e1*e2/r^2 and F = G*m1*m2/r^2, the exact same
functional
form
between mass-based and charge-based forces. Following the lines of
reasoning
here, there is a purely-particulate-based unified field theory, but
the
only
fields that need to be unified are gravity, electricity and magnetism
(frame
dragging in both). These are probably the only actual characteristics
of
matter that truthfully physically exist.

Steve Bell

Then maybe you could clarify for us as to why gravity as pictured in
GR is geodesic-based and electromagnetism isn't.

There are actual metrics in GR that have the amount of central charge
contribute to the geodesic motion of an infinitesimally small test
particle.
For a reference, please see Wald's "General Relativity" that describes
the
Kerr-Newman metric. Along with this metric is "tagged along" a
relativistic
Coulomb's electromagnetic field that is "extended" above just special
relativity by the inclusion of the full Kerr-Newman dt/dtau in the
electronic equations. From a practical standpoint, this electromagnetic
vector potential needs to be tagged along to get the correct total
acceleration from gravity and electromagnetism, because the way Newman
included the effects of the central charge produces a pathetically small
"curved spacetime-based" acceleration from just the Kerr-Newman
equations
of
motion. And there is a logical problem with these metrics. Even if the
charge of the test particle is neutral, if the central charge is not,
the
test particle coasts on a geodesic that is different as compared to if
the
central body has no charge. The neutral test particle interacts with the
charged central body, which is logically incorrect. I went a different
route, and used a scaled version of a "pure" Kerr spacetime (without the
Newman part) to model the coasting motion in hydrogen as a true geodesic
in
the electromagnetic Kerr field generated by the proton.

Steve Bell
But that still doesn't explain why the Lorentz force is a vector and
its equivalent in GR is not.

This depends on your interpretation of "force" in GR. I adhere to what
Weinberg has presented, that generally relativistic forces exist and have
a
general differential geometry representation. Please see Weinberg's text
"Gravitation and Cosmology."

Steve Bell

Surely forces exist in GR. True forces and their underlying
accelerations are tensors. Tidal forces are true forces. As is any
differential force. Or the interaction between two objects undergoing
geodesic motion. Geodesic acceleration, however, is not a tensor.
What I was asking is why geodesic motion seems to be fundamental in
GR, but not in EM theory. And certainly you can formulate geodesic
motion in GR under EM fields, but that's not what I was getting at.
My point is that GR and EM theory have entirely different basic
notions from the start. Any true attempt at unification should be
able to place them both on the same footing. Alas, that's also where
most fail.


Oh, ok, I see what you meant. There is actually a complete linear algebra
representation of the basic equations of Kerr GR. If you are interested, you
can see:

http://sb635.mystarband.net/matalg.pdf

I even derived all the nasty partial derivatives (checked with Maple):

http://sb635.mystarband.net/derivs.pdf

I derived these matrix algebra equations principally for computer
programming, but they do make a nice matrix algebra result of the tensor
algebra. I have always thought there is a significance to that. Exactly
what, I don't know <g>, although such ideas might be related your question
about unification, which I'm sure you see, I am actually not answering
<another g>. So, I ignored all the stuff about what I should not have done,
and tried to extend the orbit theory of Sommerfeld into a more general
representation. Reissner and Nordstrom set the precedence for thinking that
charge curves space and dilates time, but there are problems with their and
Newman's approaches. They may be "orthodox rigid," but they will never be
used to model a hydrogen atom, for example. The charged based curvature is
simply too weak, given the small charge of the proton. I ignored all that,
and parameterized a Kerr spacetime so that it would curve space enough to
bind an electron. This electronic Kerr representation can be modified to
have Sommerfeld and non-relativistic Bohr as special cases. It really is
rather easy to do, and admittedly results in a "cookbook" type approach, but
hey, you have to start somewhere. Sometimes, advances come by these types of
approaches first. There exists what I call a "curvature parameter," which is
nothing more than (e/m)/(G*4*pi*eps) where e and m are the charge and mass
(reduced rest mass) of the electron. If you look at the units of
(G*4*pi*eps), it's the square of a charge to mass ratio made out of these
fundamental constants. The square root could be called a "Planck
charge-to-mass ratio." I've always thought there is a significance to that,
but exactly what, I don't know <g>. I've got ideas, though. The curvature
parameter can be multiplied by the charge of the proton, and an amount of
"effective mass" results. For the proton, it's a whopping 3.79741875 x 10^12
kg. This mass can be used in the mass-based equations for GR, and get the
correct amount of curvature needed to bind the electron, and I mean exactly
like either Bohr or Sommerfeld if you want to use these special cases. There
is an electronic Schwarzschild representation when it is assumed the proton
does not rotate, that has actual closed form solutions to the radii and
velocities (quantized, of course) that can be written entirely without
Newton's G anywhere. This is a neat thing, by taking one last "jump into
only electronics," all of the ending equations do not contain G. There then
is a very nice unification of gravity and electricity, where the
characteristic lengths (e.g., the classic Schwarzschild radius in mass-based
GR) entering the Kerr metric are simply a function of the sum of this charge
and mass. In the hydrogen atom, the actual mass of the proton is so small
(as compared to its effective mass), you can forget it in the equations.
Also, an intriguing thing is that the classic mass-based Schwarzschild's
radius for 3.8 x 10^12 kg is about 1 fermi, about the actual size of a
proton. I've always thought that was significant, but exactly what, I don't
know <g>. Now, I don't think the proton is an actual little black hole or
anything like that. I've got my ideas about the internal construct of the
proton, and there are no black holes involved. Just regular old ordinary
matter possessive of only mass and charge. Another "plastic" thing about
this approach is that the charge-to-mass ratio of the orbiting body itself
partakes in the curvature of the space within which it coasts. For example,
when a muon orbits a proton, the curvature of the space "adjusts" by
defining a different effective mass for the proton. The adjustment once
again, nails the basic quantized structure of a muonic atom. You can see
more of the development at:

http://sb635.mystarband.net/unified/res_2.pdf

Steve Bell


.

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