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Titius Bode Rule is a Balmer Rydberg rule Chapt16.16 deriving BalmerRydberg from Maxwell Equations #1479 ATOM TOTALITY 5th ed
Now on page 1113 of Halliday & Resnick's, Physics, part 2, extended
version, 1986, we see H&R discussing the Balmer Rydberg formula of this: 1/y = R(1/m^2 -(1/n^2)) So let us see how all of Spectral Physics is beginning to be all derived out of the Maxwell Equations. This should be the case since both the Schrodinger and Dirac Equations are derived out of the Maxwell Equations. When the Maxwell Equations are the axioms over all of physics, then everything in physics is directly tied to the Maxwell Equations. Alright, these are the 4 symmetrical Maxwell Equations with magnetic monopoles: div*E = r_E div*B = r_B - curlxE = dB + J_B curlxB = dE + J_E Now to derive the Dirac Equation from the Maxwell Equations we add the lot together: div*E = r_E div*B = r_B - curlxE = dB + J_B curlxB = dE + J_E 
________________ div*E + div*B + (-1)curlxE + curlxB = r_E + r_B + dB + dE + J_E + J_B Now Wikipedia has a good description of how Dirac derived his famous equation which gives this: (Ad_x + Bd_y + Cd_z + (i/c)Dd_t - mc/h) p = 0 So how is the above summation of Maxwell Equations that of a generalized Dirac Equation? 
Well, the four terms of div and curl are the A,B,C,D terms. And the right side of the equation can all be conglomerated into one term and
the negative sign in the Faraday law can turn that right side into the negative sign. Now in the Dirac Equation we
need all four of the Maxwell Equations because it is a 4x4 matrix 
equation and so the full 4 Maxwell Equations are needed to cover the 
Dirac Equation, although
the Dirac Equation ends up being a minor subset of the 4 Maxwell Equations, because the Dirac Equation does not allow the photon to be a double transverse wave while the Summation of
the Maxwell Equations demands the photon be a double transverse wave. And the Dirac Equation never has the magnetic monopoles of north and south always attracting which the Maxwell equations never has any repulsion of magnetic monopoles. But the Shrodinger Equation derived from the Maxwell Equations needs only two of the Maxwell Equations, the two Gauss laws.
The Schrodinger Equation is: ihd(f(w)) = Hf(w) where f(w) is the wave function The Schrodinger Equation is easily derived from the mere 2 Gauss's laws combined: These are the 2 Gauss's law when no monopoles are expected : 
div*E = r_E 
div*B = 0 Now the two Gauss's law of Maxwell Equations standing alone are nonrelativistic and so is the Schrodinger Equation. div*E = r_E div*B = 0 ____________ div*E + div*B = r_E + 0 this is reduced to k(d(f(x))) = H(f(x)) Now Schrodinger derived his equation out of thin air, using the Fick's law of diffusion. So Schrodinger never really used the Maxwell Equations. The Maxwell Equations were foreign to Schrodinger and to all the physicists of the 20th century when it came time to
find the wave function. But how easy it would have been for 
Schrodinger if he instead, reasoned that the Maxwell Equations
derives all of Physics, and that he should only focus on the Maxwell Equations. Because if he had reasoned that the Maxwell Equations
were
the axiom set of all of physics and then derived the 
Schrodinger
Equation from the two Gauss laws, he would and could 
have further reasoned that if you Summation all 4 Maxwell Equations, that 
Schrodinger would then have derived the 
relativistic wave equation and thus have found the Dirac Equation long
before Dirac ever had the
idea of finding a relativistic wave equation. So, now, how does the Maxwell Equations of just the two Gauss laws with magnetic monopoles derive the Balmer-Rydberg formula? Very easily is the answer because when you have magnetic monopoles in the two Gauss laws, you have in effect, two inverse square laws and thus you have the 1/m^2 term and the 1/n^2 term in a Summation of the two Gauss laws: div*E = r_E div*B = r_B Those two laws can be translated into two Coulomb laws: F1 = K1(1/m^2) K2(1/n^2) = F2 Now Summation of those two Coulomb forces gives this: F1 + K2(1/n^2) = F2 + K1(1/m^2) which yields this F1 - F2 = K1(1/m^2) - K2(1/m^2) now the F's are consolidated into a 1/y and the K's constant terms merge into one consolidated constant of R, Rydberg constant. So in the above I have outlined how the Maxwell Equations is all of Spectral Physics, is all of Quantum Mechanics and even more than Quantum Mechanics. So that when physicists and astronomers see something like the Titius- Bode Rule, what they are in fact seeing is a law of Physics as the stars, galaxies, planets and moons are atomic physics writ large. -- I post this also to misc.legal for maybe a lawyer can tell me why AP is receiving this Google discrimination? Why is it that the author- archive of AP has become broken since May of 2012 where 90 percent of my posts are missing. And where Jeff Relf claims "Google Groups is 100% uncensored, so it isn't fully indexed. Were Google Groups fully indexed, it'd be used to game the system;.. " Yet anyone looking at another poster, David Bernier has a full intact author archive up the latest hour of posting. So someone is discriminating against Archimedes Plutonium by destroying his Google author archive. If David Bernier and others have a full Google author-archive, no excuse for AP to have the same. Only Drexel's Math Forum has done a excellent, simple and fair author- archiving of AP sci.math posts for the past several years as seen he http://mathforum.org/kb/profile.jspa?userID=499986 Archimedes Plutonium http://www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies |
#2
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binary stars collectively follow a Titius Bode rule? Chapt16.16deriving Balmer Rydberg from Maxwell Equations #1480 ATOM TOTALITY 5th ed
On Apr 8, 11:41Â*am, Archimedes Plutonium
wrote: Now on page 1113 of Halliday & Resnick's, Physics, part 2, extended version, 1986, we see H&R discussing the Balmer Rydberg formula of this: 1/y = R(1/m^2 -(1/n^2)) So let us see how all of Spectral Physics is beginning to be all derived out of the Maxwell Equations. This should be the case since both the Schrodinger and Dirac Equations are derived out of the Maxwell Equations. When the Maxwell Equations are the axioms over all of physics, then everything in physics is directly tied to the Maxwell Equations. Alright, these are the 4 symmetrical Maxwell Equations with magnetic monopoles: div*E = r_E div*B = r_B - curlxE = dB + J_B curlxB = dE + J_E Now to derive the Dirac Equation from the Maxwell Equations we add the lot together: div*E = r_E div*B = r_B - curlxE = dB + J_B curlxB = dE + J_E 
________________ div*E + div*B + (-1)curlxE + curlxB = r_E + r_B + dB + dE + J_E + J_B Now Wikipedia has a good description of how Dirac derived his famous equation which gives this: (Ad_x + Bd_y + Cd_z + (i/c)Dd_t - mc/h) p = 0 So how is the above summation of Maxwell Equations that of a generalized Dirac Equation? 
Well, the four terms of div and curl are the A,B,C,D terms. And the right side of the equation can all be conglomerated into one term and
the negative sign in the Faraday law can turn that right side into the negative sign. Now in the Dirac Equation we
need all four of the Maxwell Equations because it is a 4x4 matrix 
equation and so the full 4 Maxwell Equations are needed to cover the 
Dirac Equation, although
the Dirac Equation ends up being a minor subset of the 4 Maxwell Equations, because the Dirac Equation does not allow the photon to be a double transverse wave while the Summation of
the Maxwell Equations demands the photon be a double transverse wave. And the Dirac Equation never has the magnetic monopoles of north and south always attracting which the Maxwell equations never has any repulsion of magnetic monopoles. But the Shrodinger Equation derived from the Maxwell Equations needs only two of the Maxwell Equations, the two Gauss laws.
The Schrodinger Equation is: ihd(f(w)) = Hf(w) where f(w) is the wave function The Schrodinger Equation is easily derived from the mere 2 Gauss's laws combined: These are the 2 Gauss's law when no monopoles are expected : 
div*E = r_E 
div*B = 0 Now the two Gauss's law of Maxwell Equations standing alone are nonrelativistic and so is the Schrodinger Equation. div*E = r_E div*B = 0 ____________ div*E + div*B = r_E + 0 this is reduced to k(d(f(x))) = H(f(x)) Now Schrodinger derived his equation out of thin air, using the Fick's law of diffusion. So Schrodinger never really used the Maxwell Equations. The Maxwell Equations were foreign to Schrodinger and to all the physicists of the 20th century when it came time to
find the wave function. But how easy it would have been for 
Schrodinger if he instead, reasoned that the Maxwell Equations
derives all of Physics, and that he should only focus on the Maxwell Equations. Because if he had reasoned that the Maxwell Equations
were
the axiom set of all of physics and then derived the 
Schrodinger
Equation from the two Gauss laws, he would and could 
have further reasoned that if you Summation all 4 Maxwell Equations, that 
Schrodinger would then have derived the 
relativistic wave equation and thus have found the Dirac Equation long
before Dirac ever had the
idea of finding a relativistic wave equation. So, now, how does the Maxwell Equations of just the two Gauss laws with magnetic monopoles derive the Balmer-Rydberg formula? Very easily is the answer because when you have magnetic monopoles in the two Gauss laws, you have in effect, two inverse square laws and thus you have the 1/m^2 term and the 1/n^2 term in a Summation of the two Gauss laws: div*E = r_E div*B = r_B Those two laws can be translated into two Coulomb laws: F1 = K1(1/m^2) K2(1/n^2) = F2 Now Summation of those two Coulomb forces gives this: F1 + K2(1/n^2) = F2 + K1(1/m^2) which yields this F1 - F2 = K1(1/m^2) - K2(1/m^2) Sorry, I was typing too fast and should have an "n" where the "m" is: F1 - F2 = K1(1/m^2) - K2(1/n^2) which is further reduced to the Balmer Rydberg formula as seen on page 1113 of Halliday & Resnick. I corrected this in the original with a (sic) sign. Now I was thinking about stars, binary stars and wondering if we are able to plot their orbits around each other with any accuracy? Of course I suspect we cannot plot exoplanets orbits with any precision, but perhaps with nearby binary stars we can have precision. If so, I suspect that binary stars follow a similar pattern as the Titius Bode Rule of doubling of distances. So that one binary star pair would have a orbit like that of Venus versus Sun and another binary pair have an orbit like that of Earth versus Sun and a different binary pair have a orbit like Jupiter versus Sun. So in a way, or manner, we have quantized binary star orbits, that the orbits can be only according to a doubling pattern that we see in Titius Bode Rule. So where Tifft found quantized galaxy speeds (quantized redshifts), I am proposing that the orbits of binary stars are quantized as per distance of orbits and following a Balmer-Rydberg formula. Now if we cannot tell the orbital distance of star binaries with any sort of accuracy, then forget I wrote this. But if we can, then we have a great opportunity to see that the Titius Bode Rule is not just linked to the Solar System but throughout the stars of the Cosmos. now the F's are consolidated into a 1/y and the K's constant terms merge into one consolidated constant of R, Rydberg constant. So in the above I have outlined how the Maxwell Equations is all of Spectral Physics, is all of Quantum Mechanics and even more than Quantum Mechanics. So that when physicists and astronomers see something like the Titius- Bode Rule, what they are in fact seeing is a law of Physics as the stars, galaxies, planets and moons are atomic physics writ large. -- Google has stopped archiving all my posts and thus I am looking for a new forum where all my posts will be archived. A place like Drexel University's Math Forum. Only problem with Drexel's Math Forum is it is math related and many of my posts deal with other sciences. It would be nice if every science is hosted by a University. Only Drexel's Math Forum has done a excellent, simple and fair author- archiving of AP sci.math posts for the past several years as seen he http://mathforum.org/kb/profile.jspa?userID=499986 Archimedes Plutonium http://www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies |
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