Comparison of Atomic Theories to Hydrogen Balmer Data

[sb635]

Here is the abstract to a paper I wrote:

 

Abstract

A Balmer series of observed hydrogen data was compared to two geometric levels of atomic theory and modeling. The first theory compared was the Euclidean‑based, special relativistic Dirac theory, with QED corrections added. The second theory applied was a non‑Euclidean electromagnetic Kerr field theory. Each model was used to predict the Balmer series transition wavelengths, and then compared to the observed data. The statistics for the model performances were computed, and show a noticeable increase in accuracy and precision of the model predictions using the non‑Euclidean Kerr field theory compared to Euclidean Dirac theory with QED. These results suggest Euclidean Dirac theory is too restrictive/special and does not incorporate an important relativistic contributor. According to non‑Euclidean field theory, the time dilation the electron experiences is a function of not only its velocity (as in Dirac theory), but also a function of its position in the “generalized” electromagnetic Kerr field of the hydrogen atom. The time dilation the electron experiences is then stronger than in Dirac special relativity. The introduction of these added non‑Euclidean relativistic effects produces predictions in better agreement with the observed hydrogen Balmer data.

 

The paper describing these results is at

 

http://www.sb635.qwestoffice.net/sci_forum_post.pdf

 

 

 

 

[sb635]

The "relativistic regime" described by hydrogen's electromagnetic Kerr model can be quantified by using hydrogen's electronic Schwarzschild (Sch) radius, which equals ~10^-15 m. Hydrogen's ground state radius lies at ~10^-11 m, which is ~10⁴ electronic Sch radii out from the proton. This is the "relativistic regime" needed to bind orbiting bodies along closed (e.g., circular) geodesics when they have about 1%c orbital velocity, which is about the velocity of the electron in hydrogen's ground state. This distance out, ~10⁴ Sch radii, is actually independent of scale, and holds for macroscopic as well as microscopic Kerr fields. For example, our galaxy is now known to host a 4 million solar mass black hole (bh) at its center. The gravitational Sch radius for 1 solar mass is about 3 km, so 4 million gives 12 million km for our black hole's Sch radius. The mass of the bh was obtained from observing the orbits of close stars (using a Keck scope). A typical orbital stellar radius is about 9 light-days. This is about 10⁴ gravitational Sch radii distant. Simple Newtonian theory predicts about 0.5%c for this distance, and there are stars that loop in even closer, with closer to 1%c for their orbital speed. This identity in non-Euclidean scaling is remarkable, but likely simply a coincidence. It is interesting, though, the stars around our bh and the hole itself, can be "scaled down" and end up in the same "relativistic regime" as the hydrogen atom.

 

These equations suggest a simple unification of electricity and gravity, and their magnetisms, for two body systems. The very small rest masses of the electron and proton are not zero, and these two bodies gravitationally interact. The force of this gravitational attraction is many orders of magnitude smaller than the attractive electronic force produced by the two charges. Both though, can be non-Euclidean described, and brought into a "total" gravitoelectromagnetic (GEM) metric structure of a "unified" Kerr field, through the use of the geodesic equation. Here the singular use of "magnetism" in GEM refers to both types, gravito- and electro-. To best describe what is meant here, the gravitational theory should be described first, I think. I personally adhere to Weinberg's basic physical interpretation of the geodesic equation of GR. Here is an excerpt from one of his famous books:

 

http://www.sb635.qwestoffice.net/wein.pdf

 

For implementation of basic GR orbital theory on a computer (try it, you'll like it <g>), all tensor algebra computations are performed as matrix algebra computations. For implementation on a computer, It is best to jump to matrix algebra for the theory also, instead of using the "scalar looking" tensor algebra. A matrix algebra representation of Kerr field theory can be found at:

 

http://www.sb635.qwestoffice.net/unified/matalg.pdf

 

Eq. (2) of the above document gives the proper time accelerations, the "equations of motion," that need to be integrated to map out GR geodesic motion. I should note, all of this is "pure, no gravitational radiation" theory, which certainly is only "approximate" for that simple reason. But instructive. The route to gravitoelectromagnetic unification is through the use of the proper time accelerations, the Kerr equations of motion, which are quadratic forms with central Kerr Christoffel matrices (eq. (2)). The authors MTW in their book "Gravitation," describe "nonlinear superpositions." If anything superpositions in nature, it's accelerations. I personally believe nature is "built from the ground up," and nature superpositions, no matter how we define the "nonlinearity" of our field mathematics. Assuming subaccelerations do add (superposition), the centrality of the Christoffel matrices (in the quadratic form, eq. (2)) comes into play. Assume the coordinate time frame is the "laboratory coordinate spacetime frame" as described by Weinberg, which can be assumed to be Euclidean-Cartesian. Such is possible given Weinberg's words "what we will" for this "laboratory frame." The Christoffel "connection coefficients" do in fact "connect" accelerations between the laboratory frame, and the attached frame of a "freely falling/acceleration free" geodesic body, which "falls" along a curved pathway in the laboratory, as directed by the proper time accelerations given by eq. (2).

 

Now quantify a completely gravitational/mass gravitomagnetic Kerr model for hydrogen. The very small rest mass of the proton is "spinning" and sets up a very weak gravitomagnetic Kerr field, through which the electron orbits. If that was all holding (binding) onto the 1%c electron, it would fly right out of the atom. None the less, gravity, like electricity is "absolute" and there must exist the small gravitational attraction between the proton and the electron, even in hydrogen. Work up all of the "sub" gravitomagnetic Kerr Christoffel matrices in the laboratory frame. These equations have Newton's G in them, and the gravitomagnetic metric structure is very nearly Euclidean. The Kerr gravitomagnetic spacetime is very nearly flat. (But it is not absolutely flat, and completely Euclidean, and this itself indicates Euclidean special relativity is incomplete.)

 

Now consider the electromagnetic Kerr model for hydrogen. If you follow the equations, there is a completely "G-free" final electromagnetic Kerr field representation. There are completely electromagnetic Kerr Christoffel matrices which are then described by the equations, which in theory, are completely independent of the gravitomagnetic Kerr Christoffel matrices. The use of quadratic forms now becomes apparent. For an electron's given coordinate time position and velocity in laboratory spacetime, compute the "sub" gravitomagnetic and "sub" electromagnetic Kerr Christoffel matrices. Then add them together. Then compute the "total" GEM Kerr acceleration quadratic form (a scalar) using this "total/unified, summed" gravitoelectromagnetic (GEM) Kerr Christoffel matrix. This single total GEM Kerr Christoffel matrix represents the "GEM unified Kerr field" for hydrogen. No gravitational radiation losses have been incorporated, but that too is possible, incorporated as a perturbation. Of course, for hydrogen, this is exponentially less than even a "nit of a nit of a nit, etc" for the amount of gravitational radiation which is deterministically emitted by hydrogen. (And here is a question: Does this theoretically ever present gravitational attraction between the proton and the electron, continuously "actualize" the electron "into reality"?)

 

These ideas seem to me, to suggest a type of "unification of GR and QM," at least on the atomic scale. It also may be that a lot of basic Euclidean Dirac special relativistic theory needs the QED corrections, which are really attempts at accounting for the stronger field induced time dilation this (G)EM Kerr theory says the electron is experiencing. The agreement between the Balmer hydrogen data, and the EM Kerr theory predictions, suggests this is true.

 

 

[sb635]

I revised my paper on the EM Kerr hydrogen model. I eradicated the use of the "anomalous frame dragging g-factor" and evaluated the EM Kerr theory with this factor equal to 1, as it should be. I also introduced the Euclidean Dirac QED effects into the non-Euclidean EM Kerr theory. The EM Kerr model with Euclidean QED now gives the correct prediction for hydrogen's observed 2S_1/2 <-> 2P_1/2 (Lamb) transition. In the original version, this was quite a bit off. The new revision of the paper is at

 

http://sb635.qwestoffice.net/sci_forum_post2.pdf

 

I added a title, and equation numbers, etc., and the equations for including the dominant Euclidean QED effects. The basic conclusion stands: The Balmer series data supports the hypothesis of non-Euclidean field effects on the electron's time dilation in hydrogen. If this is the physical truth, modern QM/QED-based atomic theory has missed an important relativistic effect in all atoms, equal to introducing special relativity itself. Of course, the probability that being true is low, but the data analysis speaks for itself, at least for hydrogen's Balmer series. Since these results suggest modern QED has "missed something" for simple hydrogen, I seriously doubt these results will ever be publish in any refereed journal.

 

If these atomic-sized non-Euclidean field theories are right, this might suggest the structure of the nucleus itself also involves non-Euclidean field theory. The simplest nucleus is the proton of hydrogen, and preliminary theoretical results show if a non-Euclidean field theory is to be used, the outer orbitals of the partons inside a proton must be near the required Schwarzschild radius of a "strong force" Kerr field, in the range of (3/2)r_S to 2r_S. Then, this "is it." All non-Euclidean fields for some "internal" structure of the proton's internal partons would require orbits underneath the non-Euclidean field's event horizon, i.e., less than r_S, considered here to be a physical impossibility.

 

[sb635]

I revised my paper again. I had always thought by studying MTW's "Gravitation" text book, that coasting gyroscopes in non-Euclidean fields did not experience a Euclidean Thomas precession. From that logic, the usually introduced Thomas precession value of 1/2 for the spin-orbit delta energy should not be introduced in this generalized theory. My previous papers have this 1/2 factor in their results. I decided to eliminate this Thomas precession, based on its nonexistence for non-Euclidean geodesic motion. The new results are in the paper at:

 

http://www.sb635.qwestoffice.net/sci_forum_post3.pdf

 

The same basic conclusions are maintained. The equations of this theory are those which are basically already known, for the most part, in the macroscopic General Relativity domain. As such, I would like to cross post to the relativity forum, but I don't want to simply duplicate posts. Is there a way to easily post at once in both forums?

 

 

[sb635]

I apologize for the revisions, but here is the latest version of this paper:

http://sb635.qwestoffice.net/sci_forum_post4.pdf

In this version (which should be the last for a while), the inner main shell/subshell energy differences were predicted/modeled by basic Euclidean Dirac + Euclidean QED theory. So now, the EM Kerr model gives correct predictions for all "interior" subshell-to-subshell energy differences, such as all Lamb shifts between the nS_1/2 and nP_1/2 subshells (same n). The specific EM Kerr frame dragging "characteristic length" a can be exactly derived by equations for the hydrogen atom, to model these interior Euclidean QED effects as a type of non-Euclidean frame dragging magnetic perturbation. The EM Kerr model as before suggests the overall spacetime contraction of the hydrogen atom is more "compressed" than predicted by all previous theory.

The main equations are presented in this latest version of the above paper for EM Kerr hydrogen theory, along with the observed data for comparison to the theory's predictions, to establish the relevant statistically significant results supporting the geometrically extended atomic theory above and beyond Euclidean Dirac theory. Any interested person should be able to reproduce these results essentially exactly.

Let us assume the probalistic compression of the hydrogen atom is greater than current Euclidean Dirac field theory predicts. As compared to the non-relativistic Bohr model, Euclidean special relativity Dirac theory dictates all mean/expected subshell radii compress towards the proton. This is the first major relativistic compression, beyond Bohr. The non-relativistic Bohr hydrogen atom is more "inflated" compared to Dirac's (or Sommerfeld's) special relativistic hydrogen atom. Perhaps counter-intuitively, the relativistic "collapse towards the proton" for average radii (and variances), produces smaller overall transition delta-energies with longer transition wavelengths.

The counter-intuitive result is that the stronger non-Euclidean relativistic effects generally increase the transition wavelengths (translating to less transition energies), due to the greater compression, due to the EM Kerr relativistic effects throughout the entire hydrogen atom. The first special relativistic compression was predicted by Dirac and Sommerfeld. The next equal in strength compression presented here using generalized geometry, is perhaps introduced in the only next "geometrical way" possible. The link from macroscopic to microscopic electrical and gravitational fields is through the use of the "curvature parameter chi," which fixes the “scale (or gauge)” of the basic electronic atomic sized Schwarzschild spacetime metric structure. And it seems to work better than the best current QM/QED theory. Of course, the EM Kerr theory now relies heavily on the current theory, but only for interior-main shell subshell energy differences. These are “offset” from the compressed “deeper in” EM Kerr energies. Predictions of the hydrogen Balmer series still show smaller errors than the best current Euclidean Dirac atomic theory.

[sb635]

I think I see a way to generalize the Euclidean-based Dirac/QED theory. Please see the document at:

 

http://hitoshi.berkeley.edu/129A/QED.pdf

 

Immediately below (1) is shown how special relativity and electromagnetism have classically been unified. Note the metric tensor is assume special in form (diag +1, -1, -1 , -1 (Lorentz signature)). The special relativistic tensor elements are simply multiplicative +/- 1 unit factors applied to the elements of the electromagnetic tensor F. In the generalized EM theory, the metric tensor elements are EM Kerr. For example, the EM Kerr metric tensor elements are given by equation (4) at:

 

http://sb635.qwestoffice.net/sci_forum_post4.pdf

 

(The above is also the latest version.) For any subshell, the EM Kerr metric tensor elements are given, and each element is not +/- 1, as assumed in the Hitoshi paper (see twice above). The degree “not unit” shows the increase in binding strength above and beyond Euclidean Dirac theory. This basically translates to a simple > 1 multiplicative factor to “generalize” all Euclidean QED theory, such as the derivation of the Lamb shift given in the Hitoshi paper.

 

It looks like all that is needed to compute “fully non-Euclidean” EM Kerr QED effects is to simply multiply the Euclidean QED value (for example, the Euclidean electron’s self energy) by a value greater than 1. This effectively slightly increases the “strength of the virtual background.” I hope to compute these types of results in the future, but I suspect, since the QED effects are relatively small anyway, when increased slightly, not much difference (improvement of model fit) will be seen. The model fit of the non-Euclidean EM Kerr field theory is impressive, to me, as it stands

 

After a few hundred views of this thread, I am surprised no one has objected to the new theory. I am aware of how “grandiose” it is to claim these results are better than QED. But I followed strict statistical testing to support this grand statement, and I hope Sagan would approve: Extraordinary claims require extraordinary proof.

[sb635]

Looking at the length scale at which the electron's self energy is closed-loop virtually produced, it appears to be at about the Planck scale of length. The self energy length scale size is given in Hitoshi’s paper by eqs. (52) and (53) (please see past posts for the paper’s link). Computation shows the length scale to be about the Planck length scale, which is about 10^-35 m. I interpreted Hirotishi’s eq. (52) as the mean radius of the self energy, and eq. (53) as its variance. A virtual photon the electron is “emitting or absorbing” is “coming and going” in an extremely small “virtual cloud” around the electron, with the “bare electron” at the center. This length scale, compared to the “size” of the EM Kerr field I’ve proposed for hydrogen, is essentially “differential” in scale (hydrogen’s “size” in all models is about 10^-11 m, 24 orders bigger). Such a small volume of spacetime can be considered essentially Euclidean, given the “macroscopic” size of hydrogen’s EM Kerr field. As such, all specially relativistic Euclidean-based QED equations are essentially completely sufficient. But if the EM Kerr theory is physically correct, the virtual background in all of QFT/QED is not Minkowski/Lorentzian and “totally flat” as usually assumed. It still has a small “curvature” even at Planck scale. But for modeling of the entire hydrogen atom as need for a Balmer series prediction, there is no need to generalize the known Euclidean electron self energy equation to a more generalized spacetime, except for pure mathematical modeling interests of getting “closer to the truth.” The hydrogen Balmer series EM Kerr results I have presented do not need to be modified. In fact, by taking the “short cut” of using completely Euclidean Dirac theory for a main shell’s sublevel energy differences (which, btw, reintroduces the Thomas precession effect), I see I was assuming Euclidean structure at a level “way above” the electron’s self energy scale. Immediately, I should have accepted the Euclidean self energy equations as geometrically sufficient, justifying the use of the specially relativistic Lorentz signature in Hitoshi’s paper.

 

 

This model is decidedly a step “backwards” towards “determinism.” It completes the deterministic route started by Sommerfeld. He formulated a “Newtonian plus special relativity” model, which is easily done in the mathematics. But Newton’s mechanics made only specially relativistic is not generally relativtstic. Sommerfeld’s route could never include magnetism. There is no entirely geometrical (entirely metric-based ) way to generalize Newton’s mechanics to include general relativistic effects (including “magnetism”), except by generalizing the entire spacetime to that of Kerr with frame dragging. This could complete the last atomic relativistic step, and eliminate the need for “tagging along classic” Lorentz EM equations in the full model, like in the final 4-D gravity/EM unified charged Kerr metric. To note, Einstein’s route to unifying gravity and EM was not 4-D. It was “pseudo” 5-D Kaluza theory, beginning the path to 11-D string theory. I believe Einstein was wrong here. The theory I’ve presented is all 4-D, and is similar to the last attempts at 4-D unifications.

 

[sb635]

The success of the EM Kerr theory in predicting hydrogen's Balmer series leads me to believe an atom is more deterministic than previously thought, which would be an apparent fundamentally new result if true. The only way to 4-D unify electricity with gravity, in the way I have described here (through an extension of Einstein's EP to include electricity), is to take the dominant clue from gravity, and assume electricity is at first as deterministic as gravity. The electron in hydrogen then becomes Einstein's "freely falling man in an elevator." As far as what this observationally isolated (with nonzero mass) electron can "tell," there could just as well be a neutral central mass at the proton's location binding the electron. The extended EP then shows the route. Simply equate the actual electronic forces in hydrogen to an "effective gravitational force model" which is at first, Schwarzschild in structure. As I have proven, there exist a simple gauge transformation unifying the tensor-only representation of gravity and electricity, including their magnetisms, for bipolar two-body systems. The fact that the extended theory generally includes gravito- and electo- magnetisms in a single metric structure (which was in fact Einstein’s wanted goal) is a strong indication that a truly non-Euclidean unification has been accomplished (at the atomic‑sized level) by these EM Kerr field equations.

 

Potentially all gravitoelectromagntic spacetimes in the universe are simply differently scaled (gauged) 4-D Kerr geometries. A curious thing is that the extension of non-Euclidean spacetimes into the atomic world seems to demand a type of "bipolar" structure to the spacetime, decidedly different than the "monopole" character of gravity. That is, in a gravitational Schwarzschild model, the curvature of the exterior spacetime is completely defined by the mass (and only the mass) of the central body. The orbiting body's mass (in the small limit) in no way contributes to its motion along a geodesic, as in Newtonian theory. The equations I have developed show, for an extension of differential geometries into the electrically bipolar atomic world, this "central body only" structure in the mathematics cannot be maintained. The only way I can see to "set the correct gauge" is to allow the non-Euclidean mathematics (per the extended EP) to include the electron's own invariant rest mass and relativistically invariant charge, which then both dictate the entire metric structure of the whole spacetime (across the physical size) of the hydrogen atom, but “dynamically above and beyond” mass-based GR. Each and every subshell in hydrogen has its own completely different metric structure, a “shifting EM Kerr” structure, as the frame dragging shifts as needed if geometric magnetism is to fundamentally reside in a (needed) “frame dragging dynamic” metric. Please recall, this new theory has “all electron binding forces” explicitly due to the curvature of the EM Kerr spacetime, and nothing but that. This formulation is decidedly different than the accepted charged Kerr-Newman 4-D unification.

 

With a smile on the lips, the “force symmetric” reverse is also true. For example, an "effective electronic force model" can be defined for the Sun-Earth two body system. If the Earth had -1e of charge like the electron, and also had its known rest mass, an observationally-isolated Earth “would not know” what was the character of the matter at the center of its orbit. The central body (the Sun) could have positive charge, and no mass, since in this weird assumption, the Earth has -1e, equal to the electron’s charge. This strange model’s Earth charge-to-mass ratio (using the electron’s charge and the actual rest mass of the Earth) can be computed and used in the computation of the curvature parameter I describe in my paper. This curvature parameter “chi” has the Planck charge-to-mass ratio as part of its definition, which it must, if gravity and electricity are to be completely metrically unified through a simple gauge, i.e., through a simple “ruler” whose tick marks are as compressed as needed. The inverse of this gauging parameter is then multiplied by the actual rest mass of the Sun, which then computes an amount of “effective positive central charge” for the Sun. This amount of central charge then electrically binds the “oppositely charged” Earth exactly as does its central rest mass in the usual GR gravitational model. Completely “electronic Schwarschild” orbits can be defined for the Earth, and they are exactly the same as in gravitational-mass-based GR, and predict exactly the same amount of orbital precession, etc., and Kerr frame dragging, assuming the correct “spin” of the “central charge.” Complete gauge symmetry can be accomplished, but only if the gravitational Einstein equations (Kerr/Schwarzschild specific) are forced to be bipolar. Then the simple ~10³⁹ strength-of-gauge difference between these two fundamental forces makes for a simple bipolar unification of gravity and electricity via the use of the curvature parameter chi, and its inverse.

 

But then, there exists the obvious "jitter" of particles in the atomic realm ruled by electricity, as proven by Einstein's statistical Brownian motion analysis. Assuming as probably did Einstein, if this fundamental microscopic "jitter" is in fact not truly white-noise stochastic, then the only logical alternative modern theoretical route is deterministic chaos. According to deterministic Chaos Theory, there are in fact physical "hidden variables" at work in an atom. Perhaps my small step back to determinism might shed some light on the deterministic chaotic pathway to come.

 

On an interesting (and related) closing note, I contend that any and all “Monte Carlo” computer simulations run anywhere on the Earth using finite digital computers, are in fact deterministic chaos simulations. These “stochastic” Monte Carlo simulations can serve as perhaps the best example of what a deterministic chaotic process looks like, as signaled by their extreme sensitivity to initial conditions. Change the input “seed” (a “seed” is necessary with deterministic finite sized computers, running deterministic “random” number generator algorithms), and then usually widely different future outcomes are produced when all geodesics across integrated proper time are (numerically deterministically) computed. There exists a strong deterministic future dependency upon small changes in the initial “seed” conditions, signaling a chaotic and “non-random” process. All Monte Carlo computer experiments are fine examples of deterministic chaos. If many QM “stochastic” Monte Carlo simulations are run implementing these “pseudo random number generators” on finite digital computers, in my interpretation, these are in fact deterministic chaos results <g>.

 

 

[sb635]

I hope this post is not too long. If it is, I apologize to the list managers. If this chaotic deterministic approach is correct, one of first casualties should be the radial pdfs of QM. I have always thought the very detailed structure of hydrogen’s spectrum (the fine and hyperfine splittings) imply relatively exact electron radial distances. Yet the radial pdfs of QM predict relatively large variances/standard deviations (second order moments) in this radial state variable. The angle out along a radius is 3-D, 360 degree, directionally uncorrelated “white noise” according to QM. This 3-D directional white noise destroys any deterministic motion of the electron. The pdfs demand “actualizations” (why else postulate a pdf?) so that at an instant in time (measured or not), the electron is real. At some point in physical time, it must actualize into reality if probability in introduced. Along with the complete white noise directionality of an electron’s actualization, the electron (to me, according to QM) “sparkles in and out of reality and virtuality” when in a hydrogen subshell, with the instantaneously real radius values being “drawn” from a QM radial pdf. The direction (angle) pdfs specify any spherical 360 degree direction of the radial vector is possible at an actualization. Once an electron actualizes, the next direction of an actualization is not at all dependent on the last past one, or any past direction of “sparkle.” This is true QM “white noise.” Mathematically, this complete non-correlation of radius magnitude with the direction of the radius vector, is expressed by the separability of the basic Schroedinger equation. Complete separation of radius length with direction (yielding three separate radial, theta and phi uncorrelated pdfs) demands the electron “sparkles in and out of reality” in a completely uncorrelated manner, and all deterministic motion is destroyed.

 

 

A recent science show entitled “How Small is the Universe?” showed “wavy” electron orbits. Of course, a knowledgeable QM physicist would say this is just a “depiction,” and the electron must “sparkle” completely 3-D “randomly.” The electron actualizes creating a real “cloud” of actualized real locations over a very small amount of time. If the radii of these 3-D uncorrelated locations were plotted, the subshell’s radial pdf (which is really just a scaled diffraction pattern) would be mapped out. It is the width of these probabilistic shells which seems to me, to be at odds with the “exact” fine and hyperfine lines of hydrogen’s spectrum.

 

 

Even if the science show presented only a depiction, what was depicted is not what I think how the electron moves, even if a deterministically disturbed type of motion is contemplated. The waviness as shown in the show can be easily accomplished in a Monte-Carlo deterministic chaos simulation of the subshells (suborbitals) of hydrogen on a computer. To produce this “wavy” motion, a perturbation of the instantaneous orbital plane can be used. A quantized "flip” of the orbital plane (up or down) relative to the past orbital plane, can be introduced after each numerical integration step. The directionality of the flip (above or below) comes from a uniform white chaotic random number draw, with a 50:50 ratio of “above” and “below” in the chaotic limit. If the magnitude (degree) of the orbital plane change is “small,” the wavy pattern is produced. Here is a link to a “wavy" electron orbital plot for hydrogen’s ground state:

 

 

http://sb635.qwestoffice.net/orbit.pdf

 

 

The distance units along the x,y,z axes are in terms of the electronic Schwarzschild radius for hydrogen. (Note the relativistic scale, about 10⁴ EM Sch radii from the proton, is about the same “relativistic regime” of the immediate stars around our galaxy’s black hole.) The 3-D plot is tilted towards you, and the subshell is actually completely spherical in shape. The radius out to the wavy lines is held completely constant, at the EM Kerr ground state radius. The orbit plots were produced using a 4^th order R-K integrator which integrated the full EM Kerr equations of motion for hydrogen’s electron, using about 10^-20 sec coordinate integration time steps. Here, I numerically “chopped up” a single orbit into about 1000 time steps in coordinate time, as necessary on a digital computer. There is an interesting link between the substeps performed within this deterministic integrator and “virtuality” which I’ll talk about later.

 

The wavy pattern shown above is very similar to the science show’s “deterministic” orbit plots. Of course, all of these deterministic plots are just inaccurate depictions, according to QM. The electron, according to the (decorrelating) separability of the Schroedinger equation, demands real to real states are “all over the place” in direction. Could the show have shown “the truth”? To me, yes, easily so. Just do the graphics which shows a “randomly sparkling” electron, instead of a deterministic wavy pattern. This may just be picking nits, but maybe not. Continuing with an assumed chaotic deterministic “jitter,” here assumed to be introduced by a rapid white noise (in the chaotic limit) orbital plane change, it can be shown the smallest angle of plane change must be a 45-deg angle, “up” or “down.” The proof is based on the amount of the SEDS (Stochastic Electrodynamics) real EM background EM magnitude, also shown to be the same value according to QM (their common “zero point energy” of the background). I basically adhere to the SED’s view, except I believe the background GEM radiation washing through any hydrogen atom is actually deterministically chaotic, and extremely complicated in its components, which are made up of all photons of essentially all frequencies the exterior charged and massive matter have “induced” in the Einsteinian volume of the atom.. In the background there are essentially always present photons of exactly ½ the required energy of a full subshell/orbital jump of the electron to another subshell. I conjecture this “almost jump” photon “jitters” the deterministic motion via a hypothesized quantized 45-degree orbital plane change, in accordance with the minimal real (G)EM background. The orbital plane of the electron “jinks” after some small delta-t amount of coordinate time (the smallest numerically accurate delta-t passed to the R-K integrator, about 10^-20 sec). The plane change is always (after an integration step) 45-deg shifted, with “up” or “down” given by a 50:50 decision from a (chaotic) draw of a (0,1) uniform random number generator.

 

 

The degree (such as 45 degs) of orbital plane change is an input to the orbit simulation. A value of only 0.45 degrees (0.01 zero point energy) produced the above wavy plot. Imo, this is not enough “fracturing” of an orbital as demanded by the smallest photonic value of the background. A “full strength” background-induced chaotic 45-deg, 50:50 orbital plane change was introduced in the integration after a full R-K state step. Over an extended amount of electron ground state orbital motion time, the following chaotic plot was produced:

 

 

http://sb635.qwestoffice.net/frac_orbit.pdf

 

 

This “directly above” plot shows 500 “orbits” produced in about 10^-14 sec. The hydrogen ground state is not filled, but becomes filled rapidly, mapping out “continental borders” along the way. The above depicted motion is “fractured” and occurs at an exact radius distance “on the mass shell.” To me, the smooth wavy motion in the show is too deterministic. In these above plots, the “wide” radial pdfs of QM are not assumed to be correct. The electron stays at the exact EM Kerr subshell radius, but is “plane change fractured.” The electron is as quantum bound as in all quantized theories, and does not radiate away energy away during the (short) plane change. The “before and after” total relativistic EM Kerr circular orbital energy is exactly conserved. The plane change energy is exactly supplied from the deterministically chaotic background. As I previously argued, the plots shown here are actually deterministic chaos plots. A nearly complete ground state is depicted at:

 

 

http://sb635.qwestoffice.net/frac2_orbit.pdf

 

 

The total integration time was about 10^-13 sec. This fractured motion can (in a sense) be viewed as an “always on the mass shell” constrained Feynman path integral, but here assumed to be physical in nature. I think given this radius-constant constraint, even the Feynman pdf paths (of their moments, means, variances, etc) “on the mass shell” “go through” deterministic virtual substeps. If numerical steps are used, this is when the actual deterministically propagating pdfs are integrated forward on average inside a R-K integrator (for example) using small virtual time steps between “real to real” quantum states. This is also in direct analog to what is done in these numerical orbit simulations. The steps interior to the R-K integrator are completely deterministic, with small linear substeps taken in coordinate time. Interestingly, the little straight line linear substeps inside the R-K integrator are thought/known to be completely physically inaccurate. If the motion was completely Euclidean/specially relativistic and straight line, what would be the point of using an integrator of accelerations? Assuming the physical motion is simply straight line and rectilinear and not bound, no accelerations are present, and gigantic state steps can be taken in time This would obviously not be correct for “bound state” propagation, which is obviously needed for hydrogen. I believe Feynman himself warned that the hypothetical linear propagation of the pdfs in his diagrams which include virtual substeps, should not be taken as “the truth.”

 

 

Also interestingly, the jump to a non-Euclidean field theory for hydrogen does not destroy the separability of the generalized Schroedinger equation. I proposed this equation as eqs. (15), (16) and (17) in my paper at:

 

 

http://sb635.qwestoffice.net/sci_forum_post4.pdf

 

 

For the spherical EM Schwarzschild orbitals, the special cases of (16) and (17) are still functions of radius and velocity as necessary in a nonlinear/non-Euclidean field theory which has position dependent time dilations, even when total field sphericity is on hand (no magnetism, Schwarzschild conditions). Then obviously, the simple special case circular orbit equations suffice. But given the “plastic” way magnetism is introduced in Kerr theory, that is, by a field warp (by introducing EM frame dragging), circular orbits can exist with “elliptical” (magnetic) effects along the circular orbit. The shape of the field shifts, not the circularity of the orbit, and the circular orbit equations are still correct even for “P” and higher magnetic subshells. This is a significant result, to me, perhaps the most significant aspect of “going nonlinear.” This leads to a simple pleasing result, where the special cases of (16) and (17) can be written as functions of only radius, given the exact one-to-one relationship between the radius and the circular speed (v) for that radius. The equations of motion are always “circular correct,” allowed because the field shifts to aspherical for magnetism, not the circular orbit. Then the EM Kerr potential function can be written as a function of only the radius for a circular orbital (with or without magnetism, i.e., with or without magnetic field warp). Hence the separability of the EM Kerr Schroedinger equation (15) is still guaranteed. According to the postulates of QM, even if this advanced field theory is true, the electron still “sparkles” in and out of reality. But not at exactly the same radii and energies as predicted by the Euclidean Dirac theory, even with QED. To stress again, this new result is completely supported by my hydrogen Balmer series analysis.

 

 

I obviously prefer the chaotic interpretation. There are no “hidden variables.” Chaotic deterministic motion is assumed as simply “the truth.” In an atom, this deterministic motion is rapidly fractured in time, due to the chaotic background, and only appears stochastic. But there are depressing aspects of “pure determinism.” On any scale, micro or macroscopic, the future real states are exactly determined by the present real states. If you are going to be dead by tomorrow’s sunset, there is absolutely nothing you can do about it today.

 

 

[swansont]

The electron actualizes creating a real “cloud” of actualized real locations over a very small amount of time. If the radii of these 3-D uncorrelated locations were plotted, the subshell’s radial pdf (which is really just a scaled diffraction pattern) would be mapped out. It is the width of these probabilistic shells which seems to me, to be at odds with the “exact” fine and hyperfine lines of hydrogen’s spectrum.

Even if the science show presented only a depiction, what was depicted is not what I think how the electron moves, even if a deterministically disturbed type of motion is contemplated.

 

 

pdf? scaled diffraction pattern?

 

The electron's motion is not described. The energy width of states is a result of the uncertainty principle; energy is an eigenvalue of the wave function. Position is not.

[John Cuthber]

"the subshell’s radial pdf (which is really just a scaled diffraction pattern)"

Nope, wrong units.

A diffraction pattern typically has units of reciprocal distance, but an distribution in space has units of distance (or proportional to distance).

 

Ouch! that's a lot of pages of wrong.