sb635

I cannot find my past posts on this topic in the Quantum Physics forum. I fully anticipated on my very first post on this topic, that my posts would be moved into the Speculations form. I have searched the Speculations forum, and cannot find my past posts anywhere. Perhaps I have simply missed seeing something, but I looked fairly well in these forums, and for significant times in the past, and I do not see my posts describing this geometric revolution in atomic modeling. Perhaps the quantum physicists list managers reading my work, who are undoubtedly "hard core" QM physicists, are afraid. The physical truth is deterministic chaos, not white noise QM. This probably intuitively instills a great fear in QM physicists. Their guts tell them that QM is fundamentally incorrect. But any data suggesting this is true will be dismissed, because of their fanatic "religious" belief in QM. Any theory that states dead people can come back to organic life after 3 days of death, with a nonzero probability of that occurring, obviously allows miracles "in theory." Any theory which allows physically disallowed miracles to occur with nonzero probability, is not a scientific theory. The essence of QM as envisioned by the "priests" of QM simply cannot be incorrect. QM physicists have effectively a "religious faith" in the validity of QM. This must be so, because virtuality can only be a "belief." It cannot ever be observed. Have I been effectively banned from these forums, even the Speculation forum? I was hoping the Baltic/Slavic/Russo atomic physicist, who to me have a much more pragmatic view towards atomic modeling, would have viewed my deterministic ideas as at least interesting. With not one response, for over 700 views, I feel my theories are dismissed by everyone, which I find very strange. All readers of these forums, I bet, consider themselves to be "good" scientists. I have proven my theories perform better than the best QM theory to date, namely QED. Does anyone dispute that? If you do, please provide as much theoretical and experimental proof as I have presented, for your hypotheses. I challenge all QM physics: Formulate a better mathematical model for hydrogen than I have done. Describe your theory, and compare it to hydrogen’s Balmer data, and prove me wrong. My theories heralded a revolution in atomic physics. Prove me wrong with theory compared to data.

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 4th 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.

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>.

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.

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.

The masses of the electron and the proton's quarks are theoretically represented now, I suppose, by some type of Higgs mechanism, using the Higgs boson as the virtual field particle. In the hydrogen models I have used, the reduced rest mass of the electron enters the equations, and then gets time dilated (made bigger) in relativistic theory. This increase in mass contributes partly to the increase in the attractive binding energy. The classically-deterministic relativistic energy then gets "blurred" when all of the probabilistic aspects of QM are incorporated, usually as energy perturbations (such as the Darwin term and QED effects). Given Einstein's E = mc2, each of these energy perturbations (which include the "non-local" aspects of the electron) could be transformed into some type of "mass perturbation" based equation, but you would then not include the energy perturbations. Just stopping at energy perturbations incorporating the electron's "non-locality," I think answers your question as yes.

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 nS1/2 and nP1/2 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.

The scaling in the UP is indeed sometimes small, but not that small for understanding the two slit experiment, which is really the interesting setup, not the interferometer. If I understand the two slit experiment, the impacting of a photon in a pixel of the observatory screen also stops a clock. The clock was started (t = 0) when the photon was generated on the other side of the plate with the two slits. Position and time are measured at the observatory screen. If the observed time is used to tell which slit the photon went through, then the ideal situation is wide apart slits with large path length differences, with path times which are much larger than the error in the clock. But a wide apart slit configuration shrinks the distance between the interference fringes, which is like using a gigantic lens which makes really small diffraction patterns of star images. The slits can get far enough apart, where time gets "real good" at telling which pathway was taken. The delta-time differences can get very large, with well separated slits, but the interference fringe separation gets very small, where eventually, photons from two separate fringes get inside one pixel with high probability. At this point, accurate measurement of position has broken down. Let's say the clock error is gross, and can only time the pathways within 1 sec. In any lab experiment that also produces an interference pattern, with that level of a "sloppy" clock, you essentially have no path length information, and the interference pattern appears. Now start using a more a more accurate and precise clock. Eventually, according to the math of the UP, the timing error can get so small, the "error" in position at the observatory screen (and hence which slit was traversed) gets gigantic, which means the interference fringes overlap, and the pattern is "destroyed." The UP math goes something like this. In the UP, the "error" in position is called delta-x. The error in time is called delta-t. QM is confusing in that it does not matter what is the actual source of any of these observable errors, be they measurement errors or something that nature itself (in a manner) "jitters." The product of the errors in your experiment is [math]\Delta x\Delta t[/math] The energy time variant of the UP shows that approximately [math]\Delta x = {v_G}\Delta t[/math] where [math]{v_G}[/math] is the "group velocity" of the wave(s) that is (are) interfering at the observatory screen (see p. 252 of the Cohen-Tannoudji text). The position-momentum variant of the UP states that errors in these "observables" in QM must adhere to [math]\Delta x\Delta p \ge \hbar [/math] The UP does not state that you can't concurrently measure both position and momentum (or energy and time), but rather there is a mind-blowing lower limit of the product of the errors in these observables. And equally mind-blowing, all changes in the product of these deltas must come in integer quantized steps of [math]\hbar [/math], regardless of scale, macroscopic or microscopic, all the way down to Planck scale, where things get really strange. From these equations, the following inequality can be formed [math]\Delta t\Delta p{v_G} \ge \hbar [/math] The above inequality drives the logic of what happens in an experiment. The factor [math]\Delta p{v_G}[/math] is equal to [math]\Delta E[/math] (see the C-T text), and hence [math]\Delta E\Delta t \ge \hbar [/math] This is the energy time variant of the UP, and the mathematical path way shows how measuring time is effectively the same as measuring energy in QM's UP (go backwards in the math). Measuring energy is "the same" as measuring the momentum of the plate, which links your time measuring experiment back to the plate-on-springs momentum experiment in the C-T text. They are effectively the same. The energy time variant of the UP says as "error" in time gets smaller, the increasing "error" in the energy and momentum of the plate translates to "error" in position at the observatory screen itself, which must increase as the "error" in time decreases. The increasing "error" in position eventually destroys the interference pattern at the observatory screen, as the timing "error" gets smaller.

Since no "apertures" (slits) are involved, yes an interference pattern will (eventually) be observed at detector 2. Your above device is an interferometer. Usually, a gazillion laser photons are generated, and 50% bounced "to the left" along some distance that has been otherwise very accurately determined, and bounced back by your "left" flat mirror, and "interferes with itself" at detector 2. I think this is the basis of LIGO, the gravity wave detector. Any slight shift in the accurately-known distance "signals" a potential gravity wave passage (hypothetically changing the distance the laser light travels), as signaled by the slight shift in the interference pattern. You can set the "last wrap" of the "10 m" distance to a very high degree of accuracy by looking at the interference pattern at detector 2. Sit there and look at it after it is "calibrated" and see if a gravity wave has passed through (or a passing train, giggling the detector).

Considering time "absolute," a single "run" of your above device always produces the first photon impact at detector 1, which is theoretically exactly the same delta-time from t = 0 (photon pair generation event and no "clock error" anywhere) from run to run. For a single run, a second impact of either double that time or longer occurs at detector 2. If this second impact time is twice the first impact time, the shorter pathway was taken for that photon. If it was longer, the longer pathway was taken. Yes, you can tell which path one of the photons took.

With regard to your asymmetrical double-slit experiment, a QM physicist would agree classically, there exists a nonzero time difference because of the different path lengths between going through the two different slits. But in QM, the math of the double-slit experiment shows how classical thinking is apparently flawed, which is also what experimentation has shown up to now. If timing is observed, the observation of the time consumed along a pathway must be obtained at the same instant (by a clock) at which the position of the “focused” photon impacts (and is determined) on the observatory screen. The position on the observatory screen can only be physically measured within a delta-x (within a pixel, say). The time of photon impact can only be measured within a delta-t, the measurement error of the clock. (How fast we can “take pictures” is extremely important at the LHC.) If the “slop” (measurement error) in either (position or time) is bigger than what the QM uncertainty principle (UP) relations dictate, the diffraction pattern is destroyed. All experiments that have adhered to these extremely “tight” measurement error constraints have always shown, when and what degree of measurement error in any “observable” of QM destroys “entanglement,” which is really what’s going on between photon generation and (later) observation, given absolutely no information is gathered about “the path way” in between. The “information” about the path way can be either the time spent (as you see) or energy induced on the plate. Your “measure the delta-t” setup can be recast as a “measure the plate momentum” experiment which is described in Cohen-Tannoudji’s extensive textbook: “Quantum Mechanics, Vol 1,” p. 50. The QM UP math on their p. 252 shows how one would interpret your time measuring experiment as one that puts the plate on springs (in your diagram, on the left and right) so the plate can move when a photon goes through. The differing classically- induced momenta should allow for path way determination, just as does your time measurements. But measuring the plate’s momentum (or the time spent during “flight”) destroys the diffraction pattern. Time and energy, and position and momentum, are all wrapped up and correlated in the UP of QM. The UP itself serves as one the bases of QFT/QED, where time and energy are actually allowed to go “completely non-classical,” and for short delta-t’s (that can even be “backwards in time”), deterministic conservation laws themselves are violated. And it’s not that they are “allowed” to be violated. Apparently, they are violated, given the equations that follow from the allowance of the violation, and the agreement with experimentation. The agreement implies these mind-blowing violations do occur. An interesting aspect of “timing of measurements” can be used to try and refute the UP. Put the plate on springs, and classically it moves “to the left” or “to the right” given the different photon path ways. If the actual determination of this plate motion could be obtained substantially after the photon impacts on the observatory screen, then according to QM, on face value, the diffraction pattern should appear. No information about path way or plate movement is determined during the course of the experiment, up until photon impact on the observatory screen, and the diffraction pattern should appear. How could it not, if the plate motion measurements are taken after the diffraction pattern theoretically should appear, given the finite distances of photon travel to the observatory screen? The plate motion observations conceptually could be delayed for any amount of “time later,” seconds, months, years, millennia, etc. How would such a “delayed plate motion” observation be obtained? The answer is rather simple, using gravitational radiation. Especially given your asymmetrical plate slit arrangement design, “straight in” and “off to the side.” Say the plate is on springs, and moves “to the left” at photon passage. Since the plate has mass, this sets up a specific gravitational wave of nonzero strength and phase emanating from the plate. If the photon passage is through the other slit, the gravitational wave emitted is different. A gravitational wave detector could be placed light-years (gravitational-wave-years) distant, and these “post diffraction pattern present” data could be used to determine photon path way. There is an interesting “gigantic delta-t” aspect to this “post plate motion observed” thought experiment. The delta-t can be gigantic (time to gravitational wave detection, long ways away) , requiring a very small delta-E, according to the UP. This means the gravitational signal is faint far away, but technology is here assumed to “raise the signal above the noise.” If you want to wait long enough, using gravity waves, you can theoretically determine to a high degree of “accuracy” which slit the photon went through. To determine it “absolutely” would require the gravitational wave detector to be infinitely far away, and infinitely “sensitive” and would require an infinite amount of time for the gravitational wave to “reach” the gravity wave detector infinitely far away. In practicality, nothing can be determined “absolutely” in our discretely quantized and finite universe, but the very fact (if true) that it could be determined in limit, might be of significance.

Here is the abstract to a paper I wrote: Non-Euclidean Electromagnetic Kerr Model for Hydrogen 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 (Minkowski metric) special relativistic Dirac theory, with QED corrections added. The second theory applied was a non Euclidean electromagnetic (EM) Kerr field theory with Euclidean QED corrections added. Each model was used to predict the Balmer series transition wavelengths, and then compared to the observed wavelength data. The statistics (sample averages, standard deviations) for the model performances were computed, and show a noticeable increase in accuracy and precision of the model predictions using the non Euclidean EM Kerr field theory with QED, compared to Euclidean Dirac theory with QED. These results suggest Euclidean Dirac theory is too restrictive because of its special geometric nature, and does not incorporate an important “beyond special/non Euclidean” 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 the electron’s time dilation is 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, and increases subshell energies. This causes a “compression” of the probabilistic hydrogen subshells towards the proton (on average), even more so than the introduction of special relativity. The modeling of these added non-Euclidean relativistic effects produces predictions in better agreement with the observed hydrogen Balmer data. The paper can be found at: http://sb635.qwestoffice.net/sci_forum_post4.pdf I hope relativity theorists find the idea and theory interesting. The results suggest modern QED has missed modeling an important contributor to atomic time dilation. The better fit of the EM Kerr model suggests the electron's time dilation in hydrogen is not just a function of its velocity, as in Euclidean Dirac + QED theory, but the electron's time dilation is also a function of its position (radius) in a generalized EM atomic-sized Kerr field, which includes "magnetism," that is, "frame dragging." The theory and modeling strongly suggest a simple route to the unification of both "magnetisms" in nature, both gravito- and electro-.

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?

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 2S1/2 <-> 2P1/2 (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)rS to 2rS. 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 rS, considered here to be a physical impossibility.

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.

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

I was wrong, the text book that describes this plate-on-springs experiment states the diffraction pattern is destroyed. But still the logic why is flawed, to me. Let p1 be the induced plate momentum if the particle goes through slit 1, and p2 be the momentum induced if the particle goes through slit 2, which will be different. The text then states "the uncertainty [math]\Delta p[/math]" in the momentum of the plate must be sufficiently small for us to be able to measure the difference between p1 and p2. It is clear to me, this "uncertainty" (which is the uncertainty in the UP itself) is just the measurement error in determining the plate's momentum using a (necessarily) flawed momentum observing machine. And of course, the measurement error in determining the plate's momentum should be much smaller that the actual physical momentum of the plate, otherwise, this momentum will be "lost in the noise" of the measuring device. The is clearly implied in the text book by stating the requirement that [math]\Delta p < < \left| {{p_2} - {p_1}} \right|[/math]. I certainly agree with that, but only if I interpret [math]\Delta p[/math] as an observatory machine error. This measurement error, to me, is completely independent of whether or not the electron is a particle or a wave when it "went" through the plate. What if the momentum observations were never taken? Does the diffraction pattern then appear?

Does the matter of the plate (which has the slits cut in it) "observe or detect or interact with" the electron as it passes from one side of the plate to the other side? If so, this would seem to "force" the electron through one of the slits, not both, at that instant of interaction, which is before it impacts on the observing screen. Also, the double slit experiment can be made more interesting if the plate is put on springs. The plate then moves at the instant the electron goes from one side to the other. The electron itself is not observed to tell which slit it went through. The momentum of the plate is observed, which is different if the electron went through slit A compared to slit B. Supposedly, even if the plate's momentum is observed for each single electron sent to pass through the slits, this still does not destroy the diffraction pattern, but the logic behind that conclusion is flawed to me. The logic clearly shows the delta-momentum (in the UP) is actually the measurement error of the momentum determining/observing machine, which has nothing to do with the nature of an electron. Also, conceptually it seems that after the experiment has been performed, and a diffraction pattern has been produced, a person could still figure out the which slit the first electron went through, and then likewise for the second, third, etc. electrons. A gravitational wave detector could be setup a farther distance away than the observing screen. For each electron sent through, the gravitational wave the plate emitted (due to its motion after acquiring some momentum from the electron) could be observed by a gravitational wave/radiation detector after the electron hit the observing screen. The gravitational radiation could be then used after the diffraction pattern is produced to determine, with a very high degree of confidence (by using a very accurate and precise gravitational wave detector), which slit each electron went through. It is also stated that a single experiment cannot determine both the particulate and wave characteristics of an electron. A single electron is sent to the plate containing the two slits, and a single electron (particle) is observed to impact on the observing screen. That seems to say an electron is a particle, at least when it impacted the observing screen. Many electrons are sent through one at a time and many single particle impact locations are produced, building up the diffraction pattern. Isn't that observing both the wave and particle characteristics of an electron in the same experiment?

To expose the field contribution to the electronic Schwarzschild time time dilation, set [math]\theta = \pi /2[/math] for an equatorial orbit. Then the general matrix algebra simplifies to [math]\frac{{dt}}{{d\tau }} = {\left( {1 - {{\left( {\frac{v}{c}} \right)}^2} - \frac{{{r_S}}}{r}} \right)^{ - 1/2}}[/math] The dimensionless ratio [math] - {r_S}/r[/math] is the nonEuclidean contribution, and subtracts more from 1, increasing the time dilation beyond special relativity. A neutral clock placed in an electronic field obviously would not electronically time dilate. But what about a charged clock? The electron can be considered a type of charged clock. Does a charged clock run slower in an electronic field, even if it is not moving through this field? Then v = 0, but the nonEuclidean term is still there, producing a non-unit time dilation. There has already been set the precedent of charge curving spacetime. I think it was back in the 60s, the charged Kerr metric was derived, although introducing charge into GR has been going on for decades. In this final statement of the union of gravity and electricity, the amount of central charge enters the metric and contributes to the Schwarzschild radius, and produces a different curvature if assumed nonzero compared to neutral. The nonEuclidean Kerr time dilation is technically different, depending on the charge or neutrality of the central body. In other words, charge itself "curves' or dilates time according to this well-accepted metric. There is no logical reason why the charged Kerr metric could not be applied to the field surrounding a proton. If it is, the contribution to the total field curvature is pathetically low, and does not produce the degree of curvature to bind a 1%c orbiting body. This why the electromagnetic field equations are always "tagged along" as auxiliary. But even in these relativistic Lorentz equations, where time dilation is also represented in the mathematics, the time dilation is not as in special relativity, because the overall curvature of spacetime is not flat if any central mass or charge is present. The effects of a much more strongly curved spacetime resides in the auxiliary electromagnetic equations, not in the metric itself. In the charge Kerr metric, in the actual metric itself, electricity is as "weak" as gravity. Application of the charge Kerr metric would simply produce essentially special relativistic predictions, using the auxiliary electromagnetic equations just as they are in special relativity. In the nonEuclidean atomic mechanics presented here, all of the force of binding comes entirely from the metric structure of the Schwarzschild spacetime. No auxiliary electromagnetic equations are need. There also exists an unrealistic nature to the charged Kerr metric. If the central charge is nonzero then, say, a particular geodesic pathway is produced. If the central charge is simply turned off, a completely different geodesic results. The body coasting on the geodesic could be neutral, and yet it would travel on different geodesics, which is in fact an electronic interaction that should not be there. Neutral and charge bodies should not interact in the theory. Note in the nonEuclidean theory presented here, if either the central or orbiting charge is zero, the entire electronic metric structure goes flat. There are no electronic interactions, as there should not be.

Yes, strictly speaking, the electron cannot be orbiting on a smooth Bohr-like orbit. But if you want to associate a "velocity" with a shell, both nonrelativistic theory and relativistic theory (even this more general theory) predicts the electron's "velocity" in ground state hydrogen is about 1% the speed of light. Schroedinger's theory is completely deterministic (no random variables) up the derivation of the wave equation solutions, like the radial wave equation solution. From a deterministic standpoint, the electron is viewed as "everywhere in configuration space at once," with the amplitudes of the electron's deterministic standing "matter-wave" over this space, defining "how much" of the electron is "here or there." Of course, this is an extremely difficult mental picture, so probability is introduced. Born interpreted the deterministic amplitudes as proportional to the probability of the electron "being" at the position (location) part of configuration space. The introduction of probability theory demands actualizations occur. After all, what's the point in deriving a pdf if then no "draws" are ever made from it. So probability actually demands the electron sometimes "takes on" a physical presence. But where was it when it was going from the physical "here" to "there"? It looks like (to me) Feynman decided it is traveling along a "virtual path integral," which if it were real, is a type of very "fractured, jittery" motion. The analog in the physical world is a white noise 3-D Weiner stochastic process. Deterministic orbital theory cannot be absolutely correct for an atom. The primary obvious reason, to me, has never been mentioned in any text book I've read. Say an electron did in fact reside in a classic orbit. It would always stay in the plane of this orbit, until disturbed. That would mean hydrogen would be extremely flat, and show no 3-D structure. We know this is not true, atoms are 3-D. I personally believe the Feynman path integrals are physically true, and the electron is always "here" undergoing some type of deterministically nonlinear chaotic and fractured motion when in a shell. The deterministic orbit theory sets the deterministic characteristics of the shell, while nature "fractures" it. This "fracturing" process pushes the electron out of its current orbital plane, and causes it to stochastically wander around in the 3-D shell (but not jump shells), all the while amazingly maintaining exactly what the deterministic theory dictates for its orbital energy.

Since the time of Bohr, physicists have known the speed of the electron in, for example, hydrogen's ground state is about 0.7%c, about 1% the speed of light. Only a percent dictates, perhaps, a statement of "low relativistic effects," and that is true. Nonrelativistic Bohr theory does remarkably well given its simplicity, when predicting hydrogen transition frequencies. But as well know, it fails miserably for more complex systems (atoms). The electronic [math]{r_S}[/math] for hydrogen equals ~10-15 m, about the size of the proton. (This is probably just coincidence, but maybe not.) A Schwarzschild geometry is "parametrized" or "fixed in metric structure" given a value of the geometry's Schwarzschild radius. The ground state radius is about 10-11 m, or about 104 electronic Schwarzschild radii from the center of the field. This is also a "low relativistic effect" region for any Schwarzschild field, macro or microscopic. The electronic Schwarzschild field described here is an atomic-sized "tightly curved" spacetime, at least "tightly curved" enough for closed-loop-binding of a 1%c orbiting body. An important product has emerged in the equations, the quantity [math]G4\pi {\varepsilon _0}[/math]. This is the square of the Planck charge-to-mass ratio, which is [math]{e_P}/{m_P} = \sqrt {G4\pi {\varepsilon _0}} [/math]. A "particle" with the Planck mass [math]{m_P}[/math] and the Planck charge [math]{e_P}[/math] has this charge-to-mass ratio. I don't think any observed, nor theoretical particle, has this charge-to-mass ratio, but two of these (identical) particles interact in a most force-symmetric way. The gravitational force a distance r apart, is [math]{F_g} = G\frac{{m_P^2}}{{{r^2}}}[/math] Given the Planck charge-to-mas ratio, the square of square [math]{m_P}[/math] equals [math]m_P^2 = \frac{{e_P^2}}{{G4\pi {\varepsilon _0}}}[/math] Substitution into the gravitational force produces [math]{F_g} = G\frac{{m_P^2}}{{{r^2}}}[/math] [math] = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{e_P^2}}{{{r^2}}}[/math] [math] = {F_e}[/math] In this two-Planck-body system, the force of gravity exactly equals the force of electricity. In a general n-Planck-body system, the gravitational contributions to collapse exactly equal the positive and negative electronic attractions and repulsions (assume a mix of positive and negative charges). In this type of Planck particle system, gravity is an "equal partner" and has been "unified" with electricity in terms of field strength.

Envision the electron in the ground state in hydrogen to be Einstein's "independent perceiving subject." Imagine a neutral atom-sized elevator somehow rigidly fixed with the center of its inside volume at a point along the electron's orbit. At first, think "classically, deterministically" here, and view the electron as coasting along its smooth Bohr orbit while inside this fixed elevator. The electron has a sub-atomic sized radar gun, and takes Doppler shift readings off the inside walls of the elevator while coasting through. Based on this data, the electron concludes its pathway through this fixed elevator was curved. The electron concludes there must be something in Einstein's physical "external" world that forced it along this curved pathway. The electron somehow knows the elevator was fixed, and discounts inertial-based accelerations to have caused the apparent curved pathway. The elevator did not move. The electron knows it has mass and charge, and their amounts. Based on the observed curvature of the orbit inside the elevator, the electron pinpoints the center of this curvature at a specific point "out there" in the external world. The electron now knows where the center of its orbit is at, but does not know the physical cause of the attraction. Since the electron knows it has mass, it maybe gravitational. Maybe there is a neutral central mass at the center, which produced gravitational field-induced accelerations curving the electron along its orbit. Or maybe the induced accelerations were electronic. Maybe there was an oppositely charged central body present, with no mass. Or maybe the central body has both mass and charge, and the total accelerations came from a combined source. The electron does not know, and cannot tell from the observed Doppler shifts. The electron assumes the physical source of the attraction is electronic. Using classic Coulombic theory and its known charge, mass and the observed orbital characteristics, the electron computes there must have been 1e worth of massless positive charge at the center of its orbit, identical to its charge, but opposite in sign. The electron then assumes the physical source of the attraction is gravitational. Using its mass (its charge is irrelevant, assuming the central body is neutral) and the observed orbital characteristics, it computes an amount of "effective central mass" which produces identical observed forces and accelerations inside the elevator. The computed value, in the mks system, is a whopping ~1012 kg. The electron is surprised, and concludes it must have been subjected to an electronic force, not a gravitational force, but conceptually, it cannot tell. How did the electron compute the required ~1012 kg for the "effective central mass"? Assuming the forces are electronic, they are (using absolute value) [math]{F_e} = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{\left| {{e_e}{e_p}} \right|}}{{{r^2}}}[/math] Set this proportional to a gravitational force (allowed by the gravitoelectronic EP) so that [math]\frac{1}{{4\pi {\varepsilon _0}}}\frac{{\left| {{e_e}{e_p}} \right|}}{{{r^2}}} = G\frac{{\chi {e_p}{m_e}}}{{{r^2}}}[/math] where [math]\chi [/math] is a proportionality constant producing equality of electronic and gravitational forces. This proportionality constant is a mass-to-charge ratio, and transforms the amount of central charge, computed from the electronic-only attraction, to an amount of "effective central mass" which produces the equality of forces. Modeling the forces as such is completely allowed by the extended gravitoelectronic EP. Solving for [math]\chi [/math] produces [math]\chi = \frac{1}{{G4\pi {\varepsilon _0}}}\left| {\frac{{{e_e}}}{{{m_e}}}} \right|[/math] For the hydrogen atom, [math]\chi {e_p}[/math] = ~1012 kg. Note the statement must be "for the hydrogen two-body system/atom." The electron's own charge-to-mass ratio partakes in the definition of how much "effective central mass" is needed to produce gravitational-electronic force equality. The product [math]\chi {e_p}[/math] is an amount of central mass. This central rest mass can now serve as the mass-value used to parametrize a nonEuclidean Schwarzschild geometrical representation of the proton's electrostatic Coulomb field. An electronic Schwarzschild radius can be defined as [math]{r_S} = \frac{{2G\chi {e_p}}}{{{c^2}}}[/math] [math] = \frac{1}{{2\pi {\varepsilon _0}}}\frac{{\left| {{e_e}{e_p}} \right|}}{{{m_e}{c^2}}}[/math] This Schwarzschild radius is completely electronic in form. The diagonal elements of a 4x4 electronic timelike Schwarzschild metric tensor G can be defined, all based on this electronic Schwarzschild radius for the "central body" of hydrogen. These diagonal elements are (in spherical polar coordinates) [math]{{g_{rr}} = - \frac{1}{{{c^2}}}{{\left( {1 - \frac{{{r_S}}}{r}} \right)}^{ - 1}}}[/math] [math]{{g_{\theta \theta }} = - \frac{{{r^2}}}{{{c^2}}}}[/math] [math]{{g_{\phi \phi }} = - \frac{{{r^2}}}{{{c^2}}}{{\sin }^2}\theta }[/math] [math]{{g_{tt}} = 1 - \frac{{{r_S}}}{r}}[/math] The off-diagonal elements are zeros. The electronic Schwarzschild total orbital energy is [math]E = \frac{{\mu {c^2}}}{2}\left[ {{{\left[ {\left( {1 - \frac{{{r_S}}}{r}} \right)\frac{{dt}}{{d\tau }}} \right]}^2} - 1} \right][/math] This total orbital energy equation incorporates a nonCoulombic Schwarzschild system potential. The time dilation is now generally defined as (using matrix algebra) [math]\frac{{dt}}{{d\tau }} = {\left( {\frac{{d{{\bf{x}}^T}}}{{dt}}{\bf{G}}\frac{{d{\bf{x}}}}{{dt}}} \right)^{ - 1/2}}[/math] where [math]{\bf{x}} = {(r,\theta ,\phi ,t)^T}[/math] (I put coordinate time as the fourth spacetime element.) When no central body is present, then [math]{{r_S}}[/math] is zero, and the electronic Schwarzschild metric tensor is Euclidean/Minkowski. Electronic special relativity, as now applied to hydrogen, is the special case. The above time dilation is then the familiar one as in special relativity, which is a function of only velocity. This more geometrically general theory predicts an added component to time dilation, given as a function of the position in the field, just as in gravitation. This is really the key, is that true, or not? I am sure I will get many "no's." <g> Quantization of this orbital theory can be accomplished by relying on relativistic de Broglie "matter-wave" relationships. The result is a quantized electronic Schwarzschild total orbital energy equation. This can be inserted into Schroedinger theory, and Schwarzschild radial wave solutions produced. These then go to the probability theory, and define Schwarzschild radial pdfs. This theory predicts stronger relativistic effects than special relativity, and the means and modes should should shift even closer to the proton than in special relativity. The shell shrinks, gets less variant, and becomes more tightly bound than in special relativity.

I agree charge and mass are not the same "physical thing." Charge is charge and mass is mass. I am glad you mentioned the charged based coupling. The nonEuclidean model for the electronic field in hydrogen has a type of "coupling" in it. It is a very strange differential geometry, not in its identity, that is, the first model is pure Schwarzschild in form, but both the rest mass and charge of the electron themselves must partake in defining the curvature (the strength of the field) in the generalized spacetime mathematics. The electron's rest mass and charge themselves (actually the electron's charge to rest mass ratio) partake in defining the geodesic upon which it coasts.The electron's charge to rest mass ratio resides in the equations for the elements of an electronic Schwarzschild metric tensor. In the final representation of this Schwarzschild metric tensor, Newton's G does not appear anywhere. It is purely electronic in form. But it is for a system of two particles, (e.g., the electron and proton in hydrogen). When the orbiting body changes (has a different charge to mass ratio) like in "muonic hydrogen," the entire metric structure of the electronic Schwarzschild field shifts in accord.

Yes, sorry, those damn sign flips <g>. The correct derivation is [math]v = c{\left[ {1 - {{\left( {1 + \frac{{{\alpha ^2}}}{{{{\left[ {n - j - 1/2 + \sqrt {{{(j + 1/2)}^2} - {\alpha ^2}} } \right]}^2}}}} \right)}^{ - 1}}} \right]^{1/2}}[/math] This also can be expressed as (if I didn't make a mistake <g>) [math]{v_n} = c\sqrt {1 - {{\left( {\frac{{d\tau }}{{dt}}} \right)}^2}} [/math] I've subindexed in the above by the main orbital quantum n, also in the quantized time dilation equation. This shows the explicit fraction of the speed of light an electron has when in a main orbital. Recall the quantized radii equation: [math]{r_n} = {n^2}\frac{{4\pi {\varepsilon _0}{\hbar ^2}}}{{{e^2}\mu }}\frac{{d\tau }}{{dt}}[/math] These two "simple" equations are the special relativistic quantized radii and velocities, the relativistic extensions of Bohr's nonrelativistic equations. These two equations where time dilation is explicitly revealed, show the path to possible model development more general than just special relativity.

This topic is both gravitational and electronic in nature. It could easily be in the relativity forums, but also has significance (maybe) in the electronic world of QM. Einstein described his gravitational EP by envisioning a "man floating in an elevator." The man is at first floating because no accelerations are "present" inside the elevator.The man has a cop's radar gun, and at first, the radar does not register any Doppler shifts off the interior walls of the elevator. They "look" stationary, and do not appear to be moving either towards or away, because the radar sees no Doppler shifts. Suddenly, the radar does register a Doppler shift, and one of the walls appears to be moving towards the radar. One side is "blue shifted" and the opposite side is "red shifted." Some relative motion has been physically detected by the radar. The man is a good physicist, and ponders the "truth" behind the observations. He considers Einstein's quote: "The belief in an external world, independent of the perceiving subject, is the basis of all natural science." He realizes he is Einstein's "independent perceiving subject," and his radar observations, because they are observationally independent (isolated) from the "external world," will never be able to discern the actual "physical truth" of Einstein's "external world." It may have been that the exterior walls have rocket engines attached (that run *real* quiet <g>) and the walls actually, physically moved towards and away from the radar. Or maybe when the radar gun showed Doppler shifts, the elevator was actually sitting on the surface of a large solid spherical mass. The man understands that he and his radar gun have attractive mass, and then, it was actually he and the radar gun that physically experienced a "gravitationally-field-induced" acceleration towards and away from the interior walls of the elevator. Or even, the observed relative motion resulted from some combination of both of the two fundamental types of accelerations in the Universe: inertial and field induced. To me, there is an extremely important fact to walk away with here: There is always some assumed physical motion in Einstein's "external world" responsible for the observed nonzero relative motion. Otherwise, what was Einstein referring to by an "external world" that is "independent of the perceiving subject"? Now assume the floating man inside the elevator is electronically charged, either positive or negative, it does not matter. Assume the walls of the elevator are neutral, and do not electronically interact with the man and his also neutral radar gun. (But he is charged, and grasping the gun.) The radar gun sees a Doppler shift, indicating some "physical motion" has occurred, and he ponders what it was. Like before, perhaps some exterior electronically-neutral rocket engines inertially accelerated the walls. He is charged, but they are neutral, and the observed motion is not from electronics. Or perhaps, just as before, some big gigantic neutral mass is responsible. The man still has mass, so the neutral radar gun cannot tell. It could have been all gravitationally-induced motion, given the exterior "external world" is electronically neutral. What if it is not? Imagine a big "massless" but charged, exterior body. It will pull (or push, it doesn't matter) the charged man, just like gravity, and produce the observed Doppler shifts. Or maybe the observations are the result of a combination of all three: inertially-induced (rocket engine) accelerations, gravitational-field induced accelerations, or electronic-field induced accelerations. Assuming the interior body is charge, interior observations can't tell the difference between gravitational, electrical, or inertial accelerations. Or any combinations thereof. Hence electricity has been conceptually "brought iinto" Einstein's gravitational EP. The full mathematical development that Einstein produced after envisioning the Equivalence Principle, described an essential required nature of all field theory, quantum or not: The theory must be coordinate-frame/coordinate-system independent. The type of field mathematics that satisfies this requirement, and is most general, occurs when the field is modeled by a nonEuclidean differential geometry. From this, in the gravitational world, came the wealth of macroscopic orbit theory, first Schwarzschild and then Kerr. By bringing electricity up into the Equivalence Principle, creating an extended "Gravitoelectonic Equivalence Principle," the logic demands there must exist a nonEuclidean differential geometry representation of a simple spherically symmetric electronic Coulomb field, such as that which is generated by the proton in hydrogen, with all of the general time dilation characteristics of such a nonlinear field. A nonEuclidean description of a spherically symmetric Coulomb field can be formulated, and now the topic goes "new theory." The description is mathematical, and the forum managers can shift this thread/topic to wherever deemed appropriate. I assume I'll be able to follow the thread, if there are any replies.