About Space, Time & Energy in dense space or: Nuclear & Particle Physics (NPP) Version 2.1.0 Author: J. Albert Wyttenbach - independent researcher Abstract: In the following text we present a new model for nuclear & particle physics. The model is based and verifed on measured data and delivers a very good (up to 11 digits) correlation between experiment & theory. Key for understanding the new model of physics is the fact, that in dense space there is no independent time dimension. There is also no gravitating mass. All mass is given by rotating magnetic-fux or stored energy in felds. Time is co-linear with all space dimensions and occurs in the unit of the wave number. Seen from a mathematical point of view, there are at least 4 uniform independent rotating dimensions that can be expressed using SO(4) or SU(2) x SU(2) formalism. The outcome of this fact is that any fux of “matter” must follow, as close as possible, a trajectory that is “friction less”. A 4D hyper-surface that is conform with this precondition is the Cliford torus, that provides a surface of constant curvature. Simple examples like the magnetic moment of the proton confrm such fndings as the classic formula can be corrected by the radial metric change from SO(4) to SO(3) being square root of 2! The same relations can be found in mixed (4D/3D) coupled systems like the neutron orbiting a proton. The complete failure*****1 of 90 years standard model physics asked for a sound pathway to a new approach. Because many physical constants are derived by experiments, that fnally include some “standard model physics ftting”, we have to classify the quality of the experimental measurements/results. The most reliable values are measurements of masses e.g. the ones of Isotopes. Also many gamma levels are known with high accuracy. Other famous values that can be confrmed by closed form formulas [1] are the electron g-factor and the mass-ratio of electron/muon. On the other side, charge radii, most magnetic moments and many other constants are far less reliable and only can be used if we can confrm at least 4+ exact digits. The presented model is an “extension” of R. Mills famous GUT-CP[1]. The initial goals – the explanantion of the 4(6)D energy structure of Isotopes - could be attained by “reverse-engineering” the formulas from stable base values. The found nuclear 4(6)D quantum structure has been confrmed by the calculation/matching of a large number of nuclear gamma levels. The structure alone already explains many known facts about stability and symmetry of certain nuclei. Further we are able to calculate magnetic moments of isotopes with low Z and core features of the neutron. Only recently we detected that also many particle masses can be explained (calculated) by the new 4D space curvature constants, together with Mills relativistic metric for magnetic mass. Even more exciting is the most recent fnding (chpt. 8.4), that is based on the magnetic-mass formula for the proton. We found a possible “alpha” quantization term that could explain many efects/spectra found in LENR experiments. This needs more experimental verifcation.
Thanks go to R. Mills for his outstanding theory[2] and its brilliant presentation and explanation. Without him/ “his theory” this work would never have happened. *****1(The biggest mistake physicist made (and still make today..) is the usage of general relativity to model dense space. There is a simple logical deduction, that space is not fully associative to the general space/time metric. E.g. if we model an electron we use at least a two dimensional rotating magnetic fux. Magnetic fux = mass already is at light speed and will not follow the traditional metric. Thus, in the electron case 2 – out of 4 - dimensions will not follow the world wide metric physicists use today to model dense space... Further, gravity is the weakest force we know. It simply is absurd to believe that this force is able to curve dense space/time. )
1
About the author: The author restarted to work for physics two years ago and decided, after one half year of evaluating GUTCP, to no longer look at “standard model” physics. The author started in Physics & Chemistry and fnally switched to feld of computer science (with phd.). His strengths are analysis of logic and structure of complex systems. This NPP 2.1.0 theory/model evolved during the last 12 months, after the completion of the frst LENR theory. We, here will make only few references to papers covering the old “standard” model.
2
1 Introduction/Overview About 26 years ago, Randall Mills published the frst part of a new GUT-CP[1] theory, that successfully covered a large part of particle physics. Therein he proposed a frst idea how standard SU(3, 1) symmetry group derived space (three space + one time dimension) can be replaced by curved 4 dimensional space [2]32.37. In 2016 R. Mills [2] published a much more detailed version of his work, that successfully explained the basic relations between particle (basically Leptons) masses. Thus, to better understand this paper, we recommend that you download the latest version of Mills GUT-CP. Mills deep understanding of the relativistic efects of magnetic felds enabled him, to provide us an excellent theory for calculating atomic and molecular orbits and the related energies. His theory/model is at least two magnitudes more exact than standard QM-theory, mainly because he correctly handles the magnetic energy. But Mills did not yet attempt to develop a new model for condensed matter. He stopped at the border of time, not realizing that behind this border time & space are uniform and as a conclusion the metric for time, he found, is also a metric for space! Further on he stopped at the border of 4D space and did not show how the needed operations can be generalized. In appendix C we present a short summary of Mills work. The algebra needed to model dense 4D space is based on the SO(4) group, which is 6 dimensional and allows to consistently express 3x3 and 4x4 rotations. Further on, for algebras/models based on SO(4) or SU(2) x SU(2), most likely quaternion logic must be used, which is covered by an other group SO(2, Q) . To avoid over complication, we here present the structure of the dense space based on 4D analogues. Nevertheless, the new constant 3FC, we introduce and defne mathematically, is already based on 6 dimensions. What we did so far: The frst two versions (NPP 2.0, 2.01) contained only the nuclear mass/quantum structure based on the new 4(6)D fux compression constants and some outlook to new physics. We also explained how to explain/analyze the gamma spectrum and we calculated some properties of the neutron. What is new: In this version we will dig a bit deeper. We will show the calculation of the magnetic moments of the proton and some light nuclei that are very exact. We also show some mass relations between neutral/charged pions/kaons. A possible calculation of the “exact” neutron halve-live is given and also some paths to deduce particle mass relations. We also show an example of the proton as a pure magnetic mass particle with a possible alpha quantization. Further we did put some emphasis on improvements to our explanations.
3
2 The true physical space SO(4) is far more complex to imagine than its related sub-spaces SO(3), SU(2) and all their derivations, because you cannot separate the time dimension. Thus you must be able to think in (at least) 4 real, uniform space dimensions. Things become even more complicated as the common center of mass is a 4D surface known as Cliford torus, that is single sided. Thus, in any projection to a 3-D space, you must be aware of the front/back side nature of fux.
(1) SO(4) = SU(2) X SU(2) This topological equation shows one connection to existing physics and already explains why the existing models for dense space fail. The cross product is not commutative, respectively at least the sign changes.
(2) SO(4) =
The Cliford torus is the “topological equivalent” of SO(4) namely the connection of two circles (staying in independent dimensions) with a 4 dimensional bundle of tangents.
(3) (wiki) This is one possible representation of SU(2) as a 2x2 conjugate complex matrix.
(4) curvature of Cliford Torus: F''(X1,X2,X3,X4) = const (5) Radial norm: x21+ x22+ x23+ x24 = 1
Graphical representations of Clifford Torus from wikipedia:
4
Or topologically: SO(4) = SU(2) x SU(2)
Any projection of SU(2)xSU(2) to SO(3), SO(3)R, S(3) etc. leads to a radial change of measure: (6) R4 → R3 : r3 = r4 * (1/2)1/2. If two radii are involved, the the factor becomes ½.
2.1 Energy in SO(4)
Fig 1: 4He nucleus as torus projection In dense space most matter/energy is represented by rotations. In SO(4) we have 4 independent rotations, that can be mapped to two disjoint 3D tori where each rotation is represented by the two torus individual base radii. If we map everything to one single 3D torus then two rotations are given by the surface fux and two by the whole body rotation (green, black axis). This kind of simplifcation is only appropriate for highly symmetric nuclei like 4He. Further this picture can only be used for scalar quantities like mass/energy of the nucleus. The 4 rotations energy structure of dense space is new, albeit it forms the core of any nucleus. Even more complex to understand is the 3D/4D fux of mass. In any 4D space you have a 3D subspace. This subspace contains the well known mass we know from a proton but it performs one more rotation. This form of mass (the 3D/4D fux of mass) is new and shines up because time is becoming a uniform space-dimension. To imagine this movement just draw a proton (mass-fux represented by two spherical rotations) and add one more rotation given by the 4 th dimension. This three times rotating proton (in fact the three mass/charge waves) is now fowing along the Cliford torus (touching red line Fig.1 ) surface of SO(4).
Fig. 2a. 3D/4D fux of mass
Fig. 2b. Field
In Fig. 2a the red line indicates the Cliford torus surface. The surface has two sides in a 2D projection thus the orthogonal (to Cliford torus surface) wave drawn as black circle is counter rotating on the front/back
5
side. In addition we indicate the other two rotations as full body rotations. If we associate charge with one radius, Fig. 2b, what is logical given the magnetic moments, then we notice that in a perfect symmetric confguration (as in 4He) the magnetic felds vanish (at least macroscopically!) - green front/back arrow. We also can conclude, if charge(-density) has the same property as in 3D space the two counter-fux charge waves must be attractive if they run in the same plane. A change in the angle between front/back-fux could be the origin of the third fux compression constant we found.
2.2 Properties of 4D space In a rotating system the base line is the equivalence “point” of forces/masses. In SO(4) this point is not the common center of mass it is the entire surface of the Cliford torus. In a perfectly balanced system the sum of back/front side mass/rotations must be equal. Expressed in mathematics: For a perfectly balanced system the quotient of front/back fux must be equal at any point of the surface. For the 4D rotations this implies that all radii must be equal. For the 3D/4D rotation fux a system is “balanced” if the resulting SU(2)XSU(2) quotient = 1 All perturbation is measured as deviation from 1! 4D space has the following metrics: (normed for r=1) 4D hyper volume = ½ π2. 4D hyper surface = 2 π2. Internal 3D volume = 16/3 π. Internal 3D surface = 16 π.
2.3 Motion in 4D(1,3) space The natural motion in curved space is rotation. A general rotation motion of a mass in 4D(1, 3) has 1 radial and 3 spheric components. 4D(1, 3) space has 16 hyper-quadrants. To walk/move through all 16 hyperquadrants you have do make 16 complete (1, 3) half – rotations ( 3 curved dimensions), where always one dimension builds the radial component. Table 0 gives the complete boolean rotation matrix for a full walk through all 16 4D hyper-quadrants. Dimension 1 5 7 11 x: 1 1 0 0 1 1 0 0 1 1 0 y: 1 0 1 0 0 1 0 1 1 0 1 z: 1 0 0 1 0 1 0 1 0 1 1 a: 1 0 1 0 1 0 0 1 0 1 0 Table 0 Boolean matrix for all 16 4D rotations
0 0 0 1
1 0 1 0
1 1 0 1
0 0 1 1
15 0 1 0 0
One basic rotation includes a movement between (0,1 → direction 1) and three 180 degree turns. There are shortcuts to get faster back to the origin. E.g. with (2 x) 4 or 12 rotations. This corresponds to possible projections.
6
2.3.1
Asymmetry
Because nature never is perfect, we have to explain the efects of an unbalanced system. For the 4D rotations diferent radii will imply eccentricity, what is commonly (in 3D,t) understood as Larmor precision, but with more (3) degrees/axes of freedom. Because eccentricity is equivalent to a radial oscillation we can also associate this energy with a potential. We will see that these potentials usually are small compared to the main 4D and 3D/4D mass/energies compression factors. 3D/4D mass/energies occurs in various packets (quanta) sizes. In fact the three waves (rotations), we imply for one proton equivalent 4D mass (-wave), can be split in “any” integer number of waves that may fow around the (Cliford) torus. As we will see in the magnetic moment of Lithium 6 section, some individual waves can be restricted to one SU(2) subsystem and just rotate around a 3D sphere/torus! But asymmetric rotating/fowing 3D/4D mass/energy usually is the smallest part of the nuclear mass, at least for nuclei with higher Z.
2.3.2
Mass-relations between new 4D - and old 3D/time model
Eccentricity = perturbation is classically expressed by the reduced mass. (7)
(8)
In SO(4) physics we generally express (do norm) perturbation as deviation from 1. This allows us to do complex calculation of independent perturbations and derive the fnal result by a multiplication (division). For concrete work it is important to know, whether 1,2 or 3 dimensions are involved.
3 Magnetic moment of Proton As a frst illustrative sample we will calculate the magnetic moment of the proton. For that purpose we will use a simple 3D physics formula for a magnetic moment. (9) (10) (11)
7
The only parameter of interest in this example is the radius (a o) which is given by the latest measurement. Magnetic moment of Proton Measured µp 3D µp direct calc from exp. Charge radius µp= rp*c*e/2 corrected 4D-->3D Metric change is 2 (1/2) First error ratio µp mes . /µp calc calculated moment Error(1/3) of one dimension 4D correction : 3FC*2FC*(1FC) absolute error meas -clc relative error
Exper. chg. Radius 0.84087 fm. 1.4106067873 2.0194353567 1.4279564349 1.4142135624 0.9878500162 1.4106069281 0.9959334913 0.9959335244 0.0000001408 0.0000000998
Table 1. Proton magnetic moment and perturbation Because the proton has a magnetic moment, in average charge must fow on one radius, that is the 3D projection of the measured 4D radius. If we use the measured radius the moment will be to large because in the 4D torus (see Fig.2) the efective radius is ½ of the classic radius. If we stick to the 3D model, then we have to divide the result of formula (11) by 21/2. The other way round is a bit more complex to understand. If we use ao/2 as the input the we must multiply the result by 21/2. The uncorrected result is only 98,9% exact because the proton is highly perturbed by its own magnetic feld that is fully expanded to 4 dimensions. Because, the proton can only acquire 3D/4D fux energy the number of involved radii is 3. According to our method we calculate the perturbation for one radius that is 0.99593349. The big surprise is that the perturbation is the exact product (0.99593352) of the well known 3D/4D fux compression constants. After applying the correction the result is far below the precision of the radius measurement. There are other possible corrections based on slightly diferent factors like the relativistic rest-mass of the E-feld! Time will show the truth. Later we will explain that the correct proton de Broglie radius is 0.8412356405 fm and also that other methods can be use to calculate the moment.
3.1 Second proof of the SO(4) → SO(3) metric change Based on measured magnetic moments and charge radii we construct a virtual 3D system based only on magnetic fux energy. We use one possible 3D! formula to calculate the stored energy in a neutron/proton and neutron/neutron orbiting system. After doing this we build the quotient of the involved systems.
(12) Sample formula (12) used for 3D stored magnetic energy!
Deuterium
r=
Emag: µneutron/µProton µProton µneutron Emag Neutron/Neutron
1FC = 1 -16*(α/2π)2 (1+1FC)^3
2.1415 half of R deuterium 18953748.9627837 R Proton E 4D/3D = x:1 1.4106067874 µneutron/µProton -0.9662365000 R factor (1.07075/0.84087..)^3 26806381.9089833 E Ne-Ne / Pr-Ne Dividing by 2^(1/2) Residual factor
1.07075 0.84087778850000 0.68497933558150 2.06474111785991 1.41430499905948 1.41430499905947 1.41421356237310 0.99993534867908
0.0000215569 works at radius (1+1FC')^3 = 1.0000646721 Residual factor * (1+1FC')^3
1.0000646721 1.0000000166
Table 2 virtual 3D Deuterium.
8
The resulting system is the 3D “deuterium nucleus”. In our example we use the real (internal n-p) charge radius of the Deuterium which is halve (1.07075) the measured one. The neutron radius is based on the measured proton radius. We use the point where the coulomb potential, used in the neutron 4D excess mass calculation (see chpt. 6), is normed to 1. Independent of such corrections the result of the leading frst 4 digits is always the same. The re-normed quotient is exact for the frst 4 digits. The meaning of the residual perturbation is only interesting, when you will fnally understand the Deuterium mass calculation we present in chapter 5. Keep in mind that the fnal result is independent of the formula used, because all unspecifc factors cancel. The intermediate result is just based on (Rd/Rn/p)3 * µn/ µp. This is impressive as we use 4 independently measured quantities! This works, because the proton is a 3D mass particle – only the moment is 4D perturbed – and the neutron is a 4D excess energy particle. Thus we build a quotient between a 3D and a 4D system. (There seems to be also new experimental proof [13] for for the 1.4143.. re-norming factor. In [13] the author shows that all mass of 4-He must be of electromagnetic nature and the measured relation between potential (electrostatic) 3D energy and magnetic (4D) energy is 1.44.)
4 The 4(6)D fux-compression constants There are three (1FC,2FC,3FC) fux-compression constants than can be related with the nuclear mass build up. We did choose to number them with the starting number of rotations prior to compression. 2FC, 3FC can be related to the classical nuclear force. However, in homogenous 4D space there is no classical potential to be associated with 2FC/3FC as all (most all) energy is contained into rotations. As we will see, there exist other relevant fux compression constants e.g for the absorption/emission of a massive photon.
4.1 The 2FC Flux capture constant The constant called 2FC is well known in QED and is also consistently explained in R.Mills famous work [1,2]. Mills shows that 1 +/– (α/2π) factor is proportional to the energy added/released by a magnetic quanta (fuxon). The true origin of the factor is the exact relativistic derivation of the mass gain/loss ( 2π) in a central feld for a rotating body going from v → c, the speed of light. “ α” is the length contraction associated with with a magnetic mass rotating at velocity = c. We associate 2FC with the energy released when the two dimensional surface fux is entering one more dimension (+ one rotation) an becomes the so called 3D/4D fux. 2FC = 1 – (α/2π) ; 2FC' = (α/2π) In fact Mills frst explained that 2FC applied [2; formula 39.42] to a proton and a neutron may explain the deuterium mass reduction. He also thought that 2FC is caused by the so called strong force, what is not accurate. (13) Mills (formula 13) applied 2FC only to the nuclear mass and avoided the electron, what is wrong but gave him a bit more precision...The fact is that the electron mass must be added. Whether in reality the
9
accounted mass is the coulomb feld energy or the so called electron rest-mass is a philosophical discussion, but will be important, if we go to more than 7 digits precision.
4.1.1
The physical explanation of 2FC
(14) (15) (16) The formulas 14, 15 are well known and are given (14) with electron Volts as the result. Formula 15 is the so called reduced de Broglie radius, what is the correct analog for a central feld 4D proton radius. But in 4D space all charge radii are (Cliford-) torus based. Thus we have to account for in/out-side fux and two radii, what increases the path length of the “mass-wave” by a factor 4. Thus the correct 3D equivalent De Broglie/proton radius is 0.8412356405 fm! (17) Formula (17) shows the mathematical identity between the proton fux loss and the De Broglie radius Coulomb potential. Thus we can conclude that in the frst build-up phase of nuclear mass the potential energy (at de Broglie radius) is released! (Remind that in the rightmost quotient of (17) 4Dr Dbr the 4 is part of the radius name and not a factor!)
4.2 1FC a proton/charge bound force? 1FC is a “potential” term. 1FC = 1 -16*(α/2π)2 This term 1FC' looks like the two dimensional dot product of 2FC' taken over all 16 hyper-quadrants of the 4D space. In the later on following nuclear mass calculations this term can be attractive or repulsive. But the exact rules for the sign are not yet known. From the mathematical point of view it is just a second order correction. In the Helium-4 mass calculation there is no 1FC occurring. In our virtual Deuterium model 1FC also shines up as a radial perturbation. 1FC always shines up if charge is not 4D symmetrically distributed.
4.3 3FC, the true nuclear “force” constant 3FC is based on Mills idea of mass-energy equivalence of gravitational/magnetic mass. (18)
Mills [2]36.3
(19)
Mills [2]36.4
10
Mills famous GUT-CP formula was of by a small factor he called Sec. Mills still thought, that time is a true factor, albeit he already found a more or less homogenous 4D metric. Thus in Mills terminology time somehow (proportional to the universal mass released as photons) gets slowed down what reduces the mass. This argument is OK in respect to universal space dimensions but not for dense space. But again this is a philosophical discussion because time and space are homogenous in dense space. The drawback of Mills defnition is the fact that there are diferent sec values for e.g. the neutron and the electron, for what he had only a intuitive explanation. But astonishingly (no longer for us!) he could form quotients of the mass-equivalence formulas and got ( Mills [2]36.20,..,22) very exact (up to 7+ digits newest CODATA 8 digits) particle relations. In the formulas on the left side the “sec”- factor has disappeared, what leaves it to us to fnd an explanation for the “sec” factor. For us 3FC is an independent “sec”- factor that works for all nuclear masses. 3FC is a pure mathematical constant that accounts for the mass compression and the eccentricity of 4(6)D space. Fig.3 Lepton mass relations from [2] 36.20,..,22
4.3.1
The eccentricity of dense space
(20) Ex4D' = (1.6180339887 – 1.6)/2π = 0.00287019845321 A force/acceleration free 4D movement is only possible if a mass/fux exactly stays in the 4D hyper-torus surface. This is never 100% possible, otherwise energy would get an infnite density. (Or we have to move into 6 space dimensions!) 4D space has 16 hyper-quadrants and a wave needs 2x8 180 o turns to fow once around the inner surface. The harmonic sub-waves, that form out (in a stable state) seem to couple at all minimum points or all ( ω = 90o, 270o cos(ω)=0 )degrees. A fow of matter is defned by the area it fows through. This holds for all known physics and conservative central forces in all spaces. If we want to double/half the fow, what is equivalent to double/half the energy, then we must divide/multiply the area the fow (constant feld density!) is passing through by a factor of 2. The only, mathematical structure which allows a consistent progressing division/multiplication of areas is the (21) golden ratio = 1:1.6180339887... Such a division allows to retain the shape (proportions) of the fow. The quantization of 4D(3,1) (or 6D(4,2)) space always impacts a radial dimension, that e.g. will double. If energy is split according the classical rules, then the relative length in 4D hyper quadrants is 16 and and the energy stored in one quadrant is 1/16 normed to 1 ! If you do the same splitting according the golden rule then the result of 16 length units is 1/16 → normed to 1 * 1.0180339887. This means for natural quantization all fux paths will become a little bit longer than the classical paths. (Classical related work using the golden ratio can be found in [12]. They also describe n-dimensions modulo 6 occurrence of the golden ration quantization.) Thus we defne (formula 20) a new constant for the 4D eccentricity of space, that is normed for one curved dimension. The following formula is given to explain the structure of 3FC. In 6 dimensions maximally 5 rotations are
11
possible. Thus the maximal compression “Z” with 2FC is 2FC5 . (22) Z = 2FC5 = (1 - α/2π)5= 0.9942064244067 Now we defne 3FC as the relation between Ex4D' and “Z”. (23) Ex4D'/(1 - 3FC) = 0.9942064244067= (1- α/2π)5 = Z Finally we get 3FC / 3FC'. (24) (1 – 3FC) = 3FC' = 0.00288692406602 If we use 3FC = 0.9971130759339820 in the Mills formula (25 below) for reverse Neutron mass-calculation then the diference between 3FC (3FC reverse neutron mass = 939565488.02 eV) and the measured ( 939565413.71 eV) neutron mass is 74.3eV or much less than one ppm. The reverse calculation of the gravity constant is not feasible, but doing so shows, that it's infuence on the particle mass (on precision) is low. (25)
An other important deduction, that we can make from our 4D(6D) understanding of space, is the natural explanation of the Zitterbewegung. Because almost all nuclei are slightly asymmetric they must compensate their toroidal orbit by a slight eccentricity. It looks like 4-He could be one exception, because of its almost complete symmetry. Also important: Dense space has only one freedom – eccentricity - to compensate for extra energy, it looks like otherwise the waves, that are carrying the fux energies, cannot acquire all needed frequencies, with the same probability.
4.4 Introduction to magnetic flux compression in 1;2;3 Dimensions.
a)
b)
c)
Fig. 4 N-P fux reduction “bonds” between protons and neutrons The term bond is wrong as in reality the magnetic fux is unidirectional. Thus double arrows are only illustrative. If we, in the following text talk of a 3D/4D wave, then we mean a wave, that is “equivalent” to a 3D mass, but traveling/rotating along a 4D surface in 4D space! In 4D space most energy is stored in fux, what is a synonym for compressed magnetic feld lines. 3D/4D fux is a bundle of magnetic feld lines with 3 rotations that stays in 4D space. 4D fux makes 4 rotations and 2D/4D ( +,-) fux-potential seems to (radially?) balance the frst two. The base particles, electron and proton, make only two rotations. Because a large part of their disposable
12
energy is stored in the radial feld, in the 4D world, radial energy is converted into rotational mass/energy or will be disposed. Deuterium Fig.4 a) is only able to exchange 3D-3D/4D fux in one dimension (through one plane!). Two deuterium Fig.4 b) that stay in the same plane in 3D(3, 1) space, can only build up 4 nodes of fux exchange. (2 x 2D wave =4 nodes , 2 planes). To further double the number of connections, we need at least 4 uniform space dimensions, where we can get up to 6 disjoint planes (4 disjoint planes are needed), that can be used for 3D-3D/4D fow exchange. (If right/left associative math is used, then the number of hyper-planes (halveplanes) - potentially can double.) In 4D space Helium-4 builds out 4 more connections, than possible in 3D space, with magnetic fux going through in total 4 disjoint! planes. The resulting 3D/4D wave on a 4D curved surface releases 8 3D/4D (2FC) fux exchange quanta, (in total 18735.768 mamu), because it acquires one more degree of rotational freedom. (The surface charge motion of a standard 3D particle -proton/electron - can be modeled by two spherical harmonic waves, what corresponds to 2 rotations. In 4D space you need at least 3 hyperspherical harmonics.)
4.4.1
Compression in 4 dimensions
It is easy to understand, that the surface fux of a proton, that makes two rotations acquires one more degree of freedom. But in 4D space the 3D/4D, three times rotating mass wave forms out a new 2D/4D (charge like ? ) wave running very close along a 4D hyperplane of constant curvature. As an analogy for thinking in 4D space (in the reference frame of the 2D/4D wave) we may use a 2D wave that runs on a 3D torus surface. Looking at a torus surface we can directly see, that two out of the 4 waves can run orthogonally. (See. Fig 1) The other two rotations can be projected as rotations made by the torus itself. This new “2D”/4D wave has the potential to live in SO(4) conform space. Seen from the reference frame of the wave it behaves like a 2D/4D wave with two rotations. But from the outside, because the inner surface has a constant curvature, the wave-space makes an additional 2 external rotations (see Fig.4) 4 He releases the frst time a new fux-quanta (11642.907 mamu) of weight (3FC' * “particle mass”). It looks like all nuclei frst release energy that is proportional to Z div 2 times the energy release of 4He. The basic 4D energy released is calculated by (1-3FC)* (base particle masses). Seen from this model 4-He is the frst true regular 4D-nucleus in the periodic system. (3-He and even the neutron – see chpt.7- can be modeled by 4D fux physics, but both still have parts that behave 3D particle like.)
13
5 Some simple isotope masses As a starter we present the basic rules to calculated the masses of 2H, 4He, 6Li and 7Li. How is mass = energy stored? All basic physics entities like photons, electrons, protons & nuclei can be distinguished by the number of rotations and the potentials/kinetic energy that constitute their (magnetic) mass/energy. We usually count number of rotations and the efective dimensions (planes) that the rotations fow in. If we write 2D/3D particle then the frst number denotes the rotations and the second the space dimensions it flls. If we write just 3D particle then we only refer to the total of its space dimensions. Thus a standard photon has one rotation and one kinetic dimension. It is a 1D/2D particle. The electron and the proton have two rotations and one kinetic dimension thus we call them 2D/3D particles. This makes clear that if a photon, respective its energy, that enters/exits a three 3D particle has to acquire/release rotational energy. This fact is well refected within the Mills[2] formalism. The point is that dense mass lives in dense space and that not only energy must be converted. The space needed to store the added quanta (given in 3D equivalent energy) undergoes a contraction that is “proportional” to the mass of the host particle and the quanta added. This factor has been found by Mills and is called γ*. Using standard formalism this is the inverse relativistic (using Mills metric) correction of the mass. Or more general and somewhat simplifed: If you add mass(=energy) to mass then the average space to store the mass shrinks (at least up to 64Ni).
5.1 Calculating Deuterium mass from particles: First a general remark: In our samples all calculations of nuclear masses start from the “proton + electron”= hydrogen and the neutron base particle masses. R. Mills eq. 39.42[2] frst detected that using 2FC on the sum of the neutron and proton mass (total 2016489.955 mamu) closely estimates the nuclear mass of Deuterium. By using the 2FC only you get a Deuterium mass of 2014149 mamu's, which is quite of a large factor compared to what is possible now. Mills didn't know about the 1FC compression. 2FC works on 2D/3D particles, that join to form a new 3D/4D particle/nucleus. This process of fusing, typically between a neutron and a proton, works as defned by R. Mills. It its in average the minor part of nuclear energy release, but it is dominating the gamma ray resonances. In the neutron/proton spinning model we presented in chapter 3.1, we could identify that 1FC is the radial perturbation. Now we will use it to refne the mass calculation. 1FC is an emerging radial force acting between the neutron and the proton, that causes an energy release. If we additionally use 1FC to calculate the Deuterium mass, then we get 2014104.464 mamu instead of the measured one 2014101.778 mamu. (This cumulation of energies is possible, because 1FC and 2FC work in diferent fux reduction dimensions. 1FC is radial only where as 2FC is working on the rotation only!) The absolute error is still about 2.7 mamu's. (See table 3 below) If we do a second order correction by calculating the induced (added) 2D/3D - 2D/4D fux on the new joint released 3D/4D fux, we get an additional 2.77 mamu, more or less “exactly” what is missing! This efect is difcult to understand. Only later, when we will explain the gamma spectrum of a nucleus, you will see that in fact also the fux-hole = energy released will be compressed and because of the symmetry the same amount of energy must be released. Deuterium mass Summary: (2FC) 2D/3D-3D/4D Flux captured between neutron & proton = 2341.971 mamu. (1FC) 2D/3D--> 2D/4D Flux captured = 43.520 mamu – gets added to 3D/4D. Fine-tuning correction: New Sum fux released = 2385.491 * 2FC = 2.771 second order correction. The diference between the measured mamu value and the calculated one is now 0.084mamu! Or the precision is 8 digits.
14
Deuterium calculation Neutron Proton + electron Sum particles Sum first order adjustments Correction by 2FC on the Induced flux calculated difference measured difference Calculated Deuterium mass Deuterium mass measured
mamu 2FC 1FC 1008664.923 0.0011614097 0.0000215820 1007825.032 Reduction amount 2FC Reduction amount 1FC 2'341.971 2016489.955 43.520
2'385.491 2.771 2'388.261 2'388.177 2'014'101.694 2014101.778
2.771
0.0505443282
relative error absolute error relative error
0.0000353391 0.084 mamu 0.0000000419
Table 3 Deuterium mass-calculation Of course there will be a higher order correction, but as long as we have no exact mathematical model, this would be speculative work. The second order correction (fux of fux) will also be used in the gamma line calculations. Thus this value/method is confrmed.
5.2 Calculating Helium (He4) mass from particles Now we are ready to enter deeper water. The calculation of nuclear/isotope masses is a game that fascinated hundreds of researchers. (We played it too...) But up to date there still exist only heuristic formulas with no real value. Now, with the presented modeling approach, we can show how it works – at least for simple nuclei. For the calculation of the correct helium mass, we only need two constants, the 3FC and 2FC. Because of the high symmetry there is no radial 1FC force. Further, in 4-He, there is no free 3D/4D fux! This explains why 4He has no (low energy) gamma tot. micro amus α/2π * 8 2D/4D flow c. levels. 4He, the frst time, forms out 2 1'008'664.923 9'371.786 Amu Neutron 2 1'007'825.032 9'363.982 Amu Proton + electron the base resonance 4D wave 4 4'032'979.910 18'735.768 Amu sum(particles) / tot. bound flux structure, what leads to a signifcant 3FC (use 1 – 3FC) 0.9971130759 3D/4D flow c. mass-reduction of 11642.907 mamu Used 4D He4 quantas 1 11'642.907 0.0028869241 (mamu = 10-6 amu = atomic mass Amu He measured 1 4'002'603.250 30'376.660 Delta mamus measured unit). In general for each Z div 2 one Delta mamus calculated 30'378.675 30'378.675 base 4D quanta is released. Absolut error Relative error total mass
-2.015 0.0000005035
Table 4 Helium mass-calculation To get the correct Helium mass only three steps are needed. 1: Summing of particle masses see line 3) Fig.3. 2a: Apply the 3D/4D - 4D Flux-capture (3FC) constant. 2b: Apply the 2FC fux-capture constant for two dimensions for each possible n-p pair! (8 bonds) 3: Make the sum. There is a small (2 mamu) diference occurring. In general, the expected precision, without ftting is at least 6 digits. The main contribution to this diference, in the 4He case, is given by the internal de Broglie radius expansion of the neutrons. Neutrons are carriers of 4D excess-energy that inside a nucleus can be shared with other protons.
15
5.3 Lithium 6 Helium base calc mamu Neutron mamu Proton + electron mamu sum(particles)
tot.
3FC (use 1 -3FC) Used 4D He4 quanta newly added particles mamu Neutron mamu Proton + electron Total Li6 particles sum Additional flux quanta released (5/3) mamu Li6 measured Charge correction by 1FC Delta mamu measured Delta mamu calculated calculated mass Absolute error Relative error total mass
micro amus
α/2π * 8 2D/4D flow c. 9'371.786 9'363.982 18'735.768
2 2 4
1'008'664.923 1'007'825.032 4'032'979.910
1
0.9971130759 3D/4D flow c. 11'642.907 0.0028869241
1 1 1.667 1 3
1'008'664.923 1'007'825.032 6'049'469.865 2'341.971 6'015'122.281 1'007'825.032 34'347.584 34'347.213 6'015'122.652 0.371 0.0000000617
3'903.285 65.253 34'347.213
As said before, He4 the frst time forms out a closed 4D orbit (two orthogonal waves on a 4D surface with constant curvature). The frst 8 NP fux release bonds form out one new rotation and fnally build the core energy structure (with 4 rotations), that is the base of any stable isotope. (First part in Table 5) This 4D core wave is able to couple in one plane with an adjacent wave. Whether all core fux goes into a 4D orbit or a coupled 3D/4D orbit coexists is an open point
Tab. 5 Li6 mass-calculation The added (to 4He core) neutron and proton in Li6 is not able to enter the 4D orbit. It forms out new fuxrelease bonds and goes into a 3D/4D three rotation state. This part of the energy (5/3 waves) we name free 3D/4D fux. The free 3D/4D fux in Li6 it consists of one complete N-P bond and two 1/3 bonds of either N/P to the core (bound fux) wave. Because in Li6 each of the two added particles can only attach to one of the three core waves, they only release 1/3 of a “FC fux quantum.
z
The second component of Tab. 5 above is captured 2D/4D fux that needs to be released as already seen in the Deuterium case. The nature of this part is not yet fully understood. But for nuclei with N=Z it is directly related to unshielded charge. (He4 + H + n → Li6) In Table 5 above we also see, that the core He4 wave is counted in unchanged. Li6 forms out one new virtual Deuterium bond (2FC) and two week (1/3) one wave 2FC connections to the base He4 attached 3D/4D fux.
x
y
x
Fig. 5 The structure of Li6
y a
5.3.1
Lithium(6) flux bonds calculation
In Li6 we see one added Deuterium “bond” (Fig. 5 in plane, fux through plane), which counts for 3/3, and two additional bonds (Fig. 5 in plane red arrows), which count for 2 *1/3 = 2/3. Thus, Li6 releases in total 5/3 3D-3D/4D fux compression quanta. The weight is 1/3 because only one wave of the three rotating ones can interact with the core fux. We draw two helium structures (one translated) just to illustrate the wave character of the mass.
z
x
y
x
Fig. 6 The structure of Li7
5.3.2
Li7 flux/mass calculation
New in 6Li → 7Li green neutron. The calculation for released Li7- free fux looks as following: 2 * 3/3= 6/3 free fux bonds between 2N and one P. One (existing N-P - He) Li6 bond unit = 2 * 1/3 = 2/3 for one
16
y a
P-.N pair. One new – added neutron- Li6 like bond unit plane = 1 * 3/3* 1/3 = 1/3, that we can draw without moving the neutron to a second position. Two new fux units, plane, between the neutron 4D orbit and the core He4 4D orbit that occupy the same space (= 2 * 3/3 = 6/3). (Whether this factor 2 originates from two diferent bonds or from one with double the strength, needs to be sorted out) Total 3D/4D free Flux quanta released in 7Li: 15/3. People not used to think in higher dimensions can use the following rule. For any N-P pair you can freely choose one out of 6 possible interaction planes (a,x,y,z – coordinates). For direct (full) interaction with a (np)(n-p) -He4 core orbit a neutron can only choose the one remaining plane He4 is not using for his own fux fux exchange because the other remaining one is the plane the 4D objects stays in! In our sample picture (Fig. 6, the added neutron to Li6 → Li7 choses the plane to exchange fux with the helium core, where it forms 2 “bonds/nodes” with the He4 protons and the other new N-P bond to the core is in the remaining plane the other bond (1/3 weight) can choose the other two dimensions.
5.3.3
Lithium 7 mass calculation table
Helium base calc tot. micro amus α/2π * 8 2D/4D flow c. mamu Neutron 2 1008664.923 9371.786 mamu Proton + electron 2 1007825.032 9363.982 mamu sum(particles) 4 4032979.910 18735.768 3FC (use 1 -3FC) 0.9971130759 3D/4D flow c. Used 4D He4 quanta 1 11642.907 0.0028869241 newly added particles mamu Neutron 2 2017329.846 mamu Proton + electron 1 1007825.032 Total Li6 particles sum 7058134.788 Additional flux quanta released (15/3) 5 11709.855 2'341.971 mamu Li7 measured 1 7'016'004.049 Charge correction by 1FC 2 1007825.032 43.502 Delta mamu measured 42130.739 Delta mamu calculated 42132.032 42132.032 calculated mass 7'016'002.756 Absolute error -1.293 Relative error total mass -0.0000001843
In Tab. 5 you may notice, that, contrary to Li6, we need only to compensate for two charges. In general one neutron “entering”/connecting to the 4D orbit compensates one charge fux efect. Because this is a weak efect, its nature needs more deep investigations. One possible reason for this efect is the fact, that charge “fows” on the 4D 4 curved dimensions surface and the neutron splits again in a proton and an electron. Thus neutralizing/shielding its charge.
Table 6 Li7 mass calculation
5.4 First rules for mass/4D quanta -calculations For simple nuclei (e.g. 9Be) with low Z it is possible to draw the wave pattern that forms the free fux. But for practical reasons it is much easier to derive the 4D quanta structure by analyzing the diference between base particle mass and measured mass. There are two (Step 1,2 below) fx rules given by the above presented frst fndings. The number of released 4D quanta (11642.907mamu=Q3FC) defnes the total nuclear orbit number. For each He4 quanta locked in into 4D bonds, there exist 8 3D/4D bonds that we call bound 3D/4D fux. The new step 3) is the determination of excess 4D fux. As soon as the released free 3D/4D fux is greater than one 4D quanta, an additional (4D-) quanta is generated. Normally the free fux cannot be greater than Q 3FC , But in general nuclei with 0 or one single 1/3 free- fux wave are not stable as e.g. 8Be. Steps to defne the 4D nuclear quanta structure: The “formula” below is reliable for the 4D quanta down to the remaining free fux. But with larger Z efects of the 5th,6th dimension emerge and lead to additional compression. Further, more neutrons than protons get added, that obey to additional rules. Quanta for abstraction: (Q2FC = (1-2FC)*(n+p+e)) ; Q3FC = (1-3FC)*2*(n+p+e) )
17
0 Take measured isotope (Z,N) mass and calculate the sum of Z*(p+e) + N*(n), build diference M* = total measured fux released. 1 Base 4D quanta = Z/div 2 ==> B; BF (Base 4D fux released) = (Z div 2) * Q3FC 2 Bound 3D/4D fux locked into Base 4D quanta F = B * 8 * Q2FC 3 Number of excess 4D quanta E = (M* – BF – F) div Q3FC. 4 Free fux in 1/3 units: L = (M* – F – BF – E* Q3FC) * 3 /Q2FC. 5 Charge correction: C = (M* – F – BF – E*Q3FC - L* Q2FC/ 3) div (Q1FC) ; (For larger nuclei only approximative..) (6,7) The Neutrons can release or accept Excess 4D fux. (These rules are more complex, see******)
Abs. rel error base addit. tot 4D flux free flux Chg. Isotope Z N Sum base particles Measured mass excess flux calculated excess Error “10e-6” 4D q. 4D q. 4D q. released in“1/3” free 3D/4D flux3D/4D flux comp. 1D/4D flux Li6 3 3 6'049'469.865 6'015'122.281 34'347.584 34'347.267 0.317 0.053 1 1 11'642.907 5 3'903.285 18'735.768 3 65.307 Li7 3 4 7'058'134.788 7'016'004.049 42'130.739 42'132.068 -1.329 -0.189 1 1 11'642.907 15 11'709.855 18'735.768 2 43.538 Be8 4 4 8'065'959.820 8'005'305.094 60'654.726 60'670.275 -15.549 -1.942 2 2 23'285.814 0 0.000 37'471.537 -4 -87.076 Be9 4 5 9'074'624.743 9'012'182.135 62'442.608 62'449.278 -6.670 -0.740 2 2 23'285.814 2 1'561.314 37'471.537 6 130.614 B11 5 6 11'091'114.698 11'009'305.466 81'809.232 81'811.679 -2.447 -0.222 2 1 3 34'928.720 12 9'367.884 37'471.537 2 43.538 C12 6 6 12'098'939.730 12'000'000.000 98'939.730 98'942.596 -2.866 -0.239 3 3 34'928.720 10 7'806.570 56'207.305 0 0.000 C13 6 7 13'107'604.653 13'003'354.838 104'249.815 104'253.171 -3.356 -0.258 3 1 4 46'571.627 2 1'561.314 56'207.305 -4 -87.076 C14 6 8 14'116'269.576 14'003'241.988 113'027.588 113'036.319 -8.731 -0.623 3 1 4 46'571.627 13 10'148.541 56'207.305 5 108.845 N14 7 7 14'115'429.685 14'003'074.005 112'355.680 112'342.737 12.943 0.924 3 1 4 46'571.627 12 9'367.884 56'207.305 9 195.921 N15 7 8 15'124'094.608 15'000'108.898 123'985.710 123'963.875 21.835 1.456 3 2 5 58'214.534 12 9'367.884 56'207.305 8 174.152 O16 8 8 16'131'919.640 15'994'914.622 137'005.018 137'017.355 -12.337 -0.771 4 1 5 58'214.534 5 3'903.285 74'943.074 -2 -43.538 F19 9 10 19'157'074.518 18'998'403.205 158'671.313 158'676.547 -5.234 -0.276 4 3 7 81'500.347 3 2'341.971 74'943.074 -5 -108.845 Ne 20 10 10 20'164'899.550 19'992'440.176 172'459.374 172'408.148 51.226 2.562 5 0 5 58'214.534 26 20'297.083 93'678.842 10 217.690 Mg24 12 12 24'197'879.460 23'985'041.898 212'837.562 212'845.006 -7.444 -0.310 6 2 8 93'143.254 9 7'025.913 112'414.611 12 261.228 Mg26 12 14 26'215'209.306 25'982'593.040 232'616.266 232'616.350 -0.084 -0.003 6 4 10 116'429.068 5 3'903.285 112'414.611 -6 -130.614 Si28 14 14 28'230'859.370 27'976'926.533 253'932.837 253'933.548 -0.711 -0.025 7 3 10 116'429.068 8 6'245.256 131'150.379 5 108.845 Si29 14 15 29'239'524.293 28'976'494.719 263'029.574 263'038.563 -8.989 -0.310 7 4 11 128'071.974 5 3'903.285 131'150.379 -4 -87.076 S32 16 16 32'263'839.280 31'972'070.690 291'768.590 291'768.848 -0.258 -0.008 8 4 12 139'714.881 3 2'341.971 149'886.148 -8 -174.152 Tc87 43 44 87'717'732.988 86'936'530.000 781'202.988 781'200.274 2.714 0.031 21 12 33 384'215.923 5 3'903.285 393'451.138 -17 -370.072 Pb207 82 125 208'724'767.999 206'975'880.605 1'748'887.394 1'748'901.462 -14.068 -0.068 41 43 84 978'004.168 4 3'122.628 768'166.507 -18 -391.841 U238 92 146 239'984'981.702 238'050'782.583 1'934'199.119 1'934'205.782 -6.663 -0.028 46 46 92 1'071'147.422 2 1'561.314 861'845.350 -16 -348.303 Cm252 96 156 254'102'931.060 252'084'870.000 2'018'061.060 2'018'053.025 8.035 0.032 48 48 96 1'117'719.049 2 1'561.314 899'316.887 -25 -544.224
Table 7 some examples of calculated fux But “nature” is not that simple. There exist only a few nuclei that are highly symmetric (like carbon, Mg24, sulfur) and exactly behave as expected. This is a small island.
5.5 Main nuclear quantum numbers Here we give a short outlook of the physical implications given by the new 4D nuclear quantum numbers. We already mentioned that 4He has no free fux, what fully explains the absence of gamma ray resonances. The analysis of the nuclear gamma spectrum shows, that the total sum of 4D quanta released and the allocation of the 4D quanta into orbits is defning the fne-structure of the nucleus gamma levels. We can see gamma line resonances, corresponding to classical fne-splitting, given by the active (last flled) 4D quanta orbits. Individual nuclear Q3FC orbits are flled by following the frequency doubling/add rule. (1), (1,2), (1,4), (1,2,4). The rules how the orbits get flled are not straight forward to explain. Later we will show some fndings. Gamma ray analysis shows that a paired orbit like (7,0) is not allowed and we see in fact (5,2) or (4,3) . Remind that (7,1) means (1,2,4;1,0,0) and (5,2) means (1,0,4; 0,2,0) and (7,4) means (1,2,4;0,0,4). Lead is the last stable nucleus in the periodic system. It has 6 complete 2 x ( 1,2,4) fux fow attached Q3FC waves, with the following structure of (7,7);(7,7);(7,7);(7,7);(7,7);(7,7); (= 84 4D quanta) This corresponds to the six independent ( 12 halve hyper-planes – back front normal to the Cliford torus single surface) planes found in 4D space. Thus we can defne the 4D nuclear quantum structure based on the amount of released 4 quanta. 4D nuclear orbit numbers, are only based on the number of full Q3FC quanta released. The gamma spectra analysis of all nuclei with 7 and 2 x 7 complete, fux units show the same gamma line (level) fne splitting.
18
Uranium 238 is the last and most stable meta stable nucleus, that has managed to fll one orbit with a higher (8) quantum number to reach a (15,7);(7,7);(7,7);(7,7);(7,7);(7,7); quantum structure. Here again the gamma ray main response shows a dominant coupling to 15 units of 4D bound fux.
5.5.1 Fractions of 2FC fux quantization Any proton/neutron not locked into 4D fux structure can build out free 3D/4D fux. These fux components (the holes left behind) form the base resonators for gamma rays. In our frst sample calculation given above, we only used 1/3 quantization of the so called free 3D/4D fux. But gamma-ray analysis shows that the free fux can also split according to the weight of the last flled Q3FC orbits. Whether this splitting is only active in a transient state or already can be used for the more exact mass-calculation has to be shown. In general free 3D/4D fux ( one Q2FC ) is represented by three “individual” coupled waves. In the ground state all three waves carry the same amount of fux = energy. A full symmetric coupling of two 3D/4D three wave packets is only possible if all “paired” waves doing the coupling have matching frequencies (wave number). Sometimes a locked in wave, of e.g. a proton, that already has a full 3/3 fux connection, can not present all waves for additional fux exchange. Already with Li6 we see 1/3 quantization of 3D/4D N-P free fux. With 9Be an other efect comes into play. 9Be having the (0,2,0) quantum number allows a two times stronger coupling than the basic 4He wave. In the 9Be spectrum we see 2/3 of free fux quanta splitting into 6/8 of free fux quanta (the 1/3 waves split into 3 waves).
5.5.2 The role of neutrons The true nature (fux add/release) of the neutron is not yet fully understood. In the following chapter 6 we will present the 4D excess energy model of the neutron. According to the new neutron model the neutron is either able to release 4D excess-energy or to accept additional 4D energy to fll incomplete orbits. Isotopes with N>Z show many diferent forms how a neutron is integrated into the base and free fux. Because the neutron has a 4D structure it is much more fexible and can also directly couple with the core 4D waves.
5.6 Magic 28Si Mass
Fig.7a
Fig. 7b
All nuclei are consisting of fux that is running along/inside a torus. We will see in the gamma-ray calculation chapter that the energies can be modeled with mechanical analogues of the moment of rigidity/inertia. In our drawings we always use an open torus. In reality the radii are equal and there will be no hole! If both torus radii are equal then for Fig.7a the moment of inertia factor is 9/8 * r 2. In the more energetic case 7b it is 7/4 * r 2. The case 7b is much more natural. The rotation and the fux is in line with the movement of fux! 28 Si has 11 4D quanta what is exactly the magic sum of 4 + 7 seen in sample 7b. In the following we present
19
four diferent mass-calculations for 28Si. On top of table 8 you see the standard mass split with the base 4D quanta. For nuclei with even multiple of 4He we usually expect only 4 charges to account for, but 5 are needed for a perfect ft. But this is an efect working at the 7 th digit of precision. Then we look what nature is doing with our constants (2FC/3FC) and form 28Si based on 4He, 14N, 14C. Si 28 measured from particles
From He-4 From N-14 From C-14
mamu's 3FC 2FC 2FC 27'976'926.533 delta mamu 4D flux Bound 3D/4D flux free 3D/4D flux 28'230'859.370 253'932.837 116'429.068 131'150.379 6'245.256 charge flux 1FC calculated flux r. delta -0.620 108.754 253'933.457 28'018'222.750 27'976'926.533 28'006'148.010 27'976'926.533 28'006'483.976 27'976'926.533 2FC * 2FC =
41'296.217 3FC 29'221.477 29'557.443 0.9976785294
11'642.907 11'642.907 41'296.217
40'864.384 41'200.3498 41'200.3490
Table 8. 28Si diferent mass-calculations What we expect out of a comparison between 14N , 14C is the verifcation, that the neutron compression works diferent, than the n-p compression. In fact we directly see from the measured mass of 14N, 14C that 14 N does a better job on particle compression. What we also see is that the uncompressed fux diference between (2 x ) 14N, 14C (29'557- 29'221 = 336 mamu) is exactly the neutron 4D fux hole we present in the following chapter. How extremely well 2FC & 3FC ft we see in the following comparison. If we subtract 7 x 4He from the 28Si particle mass then 41'296.217 mamu's are left for further compression. 14C already does a higher compression than 4He thus we have to add one 4D quanta to make the result comparable. This leaves 41'200.349mamus for further compression. The compression of 7 x 4He is uniform and only n-p based. In the case of 14C the resulting fux contains only 6 x 4He compression (- 1 we add again) and two time neutron base 4D compression. The key fnding is: If we apply 2FC twice to the remaining 4He uncompressed fux, then both quantities are absolutely equal. (Because in SO(4) physics is quotient based diferences are much more exact than absolute values! See also Mills Lepton quotients!) Conclusion: For highly symmetric nuclei the constants 2FC & 3FC seem to exactly describe the mass relations between diferent amounts of fux. Exact means we here have the base weight of three isotopes given with up to 11 digits and hydrogen/neutron. We have 2FC/3FC and a relation that is exact for 11 (known) digits. Similar coincidences can be found for 56-Ni, 56-Fe and 84-Kr (more complex).
20
6 The Neutron The neutron is a 4D excess Energy particle. This is obvious as the source of all neutrons is the nucleus where they “live” in a 4D environment. A combination of an electron and a proton is only possible with maximally two coupling rotations. The so called 4D-excess-energy part of the neutron is calculated by 3FC' applied to the neutron mass. This gives a value for 4 rotations. According to Mills we can reduce one dimension by applying the above eV mentioned γ* factor. The result, by Tabulated neutron excess mass 782'353.51 Neutron mass in eV 939'565'413.21 applying the factor twice is the so called Neutron mass * 3FC * = excess 4D flux 2'712'454.00 “electron sec factor” that can also be compensation for electron excess calculated by using the Mills formula for ** (1+PI()*D 2^2)^2 : Mills 36.15 3D → 2D 1.0003346161 mass equivalence. The efective neutron 3FC** charge normalized by* 4D--> 2D 0.9974467260 4D excess flux gained by neutron-mass * 3FC** 2'398'967.91 4D excess mass has the same density as Corresponds to electron 4D->2D/3D flux loss (M:36.4) 313'486.10 the electron and is 2'398'967... eV. Table 8. The neutron 4D energy The values of table 9, below, are calculated as 3D externalized energy amounts of the neutron decay. If a neutron decays the potential energy 1.7MeV must be built up again. The potential is calculated at the limit of the experimental proton radius. After this step about 686505 eV of 4D energy remain. The fux captured by the electron can be calculated according to Mills formula as rest-mass of electron divided by “2π”. During the decay one spin of a down quark is fipped. This energy has been calculated by Mills. Further the de Broglie energy of the neutron changes to the proton's. This are the terms marked green. They together constitute the so called kinetic energy terms and are, in their sum, exactly the ones measured in the aSPECT experiments[10]. The green marked energies are directly coupled with the e-p bond. 4D excess flux gained by neutron-mass * 3FC** 2'398'967.91 The blue marked energies are the Corresponds to electron 4D->2D/3D flux loss (M:36.4) 313'486.10 3D/4D and 4D excess energy parts of exp proton charge radius in fm. 0.8408739000 the electron. These energies stay in 4 electron potential at exp p-radius 1'712'461.92 dimensions. Summed up, the neutron + (4D flux gain) – (potential to overcome) 686'505.98 excess energy is (5 digits) correctly Freed excess electron flux of neutron e 0/2pi() 81'328.01 calculated. There is a small error range Freed excess electron flux 3D/4D (2FC) induced 94.46 given by the somewhat to large radius Freed excess electron flux 4D (3FC) induced flux 234.79 used and the missing 1FC correction. If Spin flip energy N-->P (Mills: 39.7) 15'691.94 we use the radius we found in the (less gain) – de Broglie wave correction Rn--> Rp -1'502.11 proton magnetic moment (→ E-kin = Neutron kinetic excess mass 4D--> 2D/3D 782'023.82 782'015.71) section then the match with Missing to measured Neutron excess 329.68 aSPECT is even better and the 1FC Adding 3D & 4D flux to 81238.01 eV e excess 329.24 correction can be added.
Table 9 Neutron 3D/4D excess-energy parts mamu Neutron excess in mamu Neutron 4D hole Freed energy neutron->4D
eV 839.891 336.541 503.350
782'353.507 313'486.098 468'867.409
Table 10 Relevant amounts of neutron energies. Table 10 shows the two junks of energy we must take into account if a neutron stays inside a nucleus. The neutron 4D hole consists of two missing waves. Thus we may see also cases (14-C, 10-Be), where halve of the hole – one wave - gets flled.
21
6.1 The neutron halve live In general the halve live of a state is calculated by the well known energy/power formula. In reality halve live is an exponential formula of the e -kt kind. In dense space time and space are uniform and thus the metric for a decay, which usually is one dimensional kinetic nature, has to be corrected by the 4D → 3D form factor of 21/2. If we do “exponentiate” the classical 3D power quotient we get the corresponding 4D energy (power) that is responsible for the power part of the decay. The energy part of the neutron halve live formula is simple to Live-time = energy/power derive and is given by the freed kinetic energy. The power factor Energy = Excess energy 782'023.824 must be delivered by the origin of the decay. A neutron stops to halve live in seconds 881.500 exist as soon as one quark node fips its spin. Thus the prime derived 3D power quotient 887.151 energy associated with the decay is the “quark” spin-fip-energy. applying 3D--> 4D mapping 1.414 corresponding 4D power 14'760.405 Directly tied to the spin-fip is the change of the de Broglie Spinflip corrected 15'600.820 energy from n → p. The other transient energy that immediately De Broglie correction -1'502.111 is lost is the electron 3D/4D and 4D excess energy. The only 2* electron flux correction 659.365 interesting point is the fact that we must count the 3D/4D and Sum acting power 14'758.075 4D excess energy twice. This must be due to the fact, that each reverse halve live 881.598 3D/4D and 4D (excess) energy amount always occurs as a pair of energy/energy hole. Further we converted the Mills 3D quark spin-fip mass/energy to its 4D equivalent. Table 11 Neutron halve live energies The above calculation is a “frst try” example to show that some consistent mapping from 3D → 4D physics is possible. To get a more deep understanding the two 4D-wave coupling of the e-p system must be modeled.
7 Some more magnetic moments It is well known that also some even Z+N nuclei have a magnetic moment. In the 4D physics model it can be shown if all charge is shielded – running on the Cliford torus 4D orbit – then there is no magnetic moment. In nuclei With N-Z = 1 the charge of the neutron is responsible for the magnetic moment.
7.1 The Lithium magnetic moments The Lithium-6 nucleus consists of a 4He core and a quasi bound Deuterium wave. It is impossible to fnd a 4D symmetric confguration for the charge. In fact you can imagine that the shape of the “Deuterium wave” has the form of a 3D torus that fows around one base circle of the Cliford torus. The consequence is that the third electron runs just on one 3D torus radius. Further we know that for a 3D torus in 4D space (“=” 4D sphere) three symmetric waves produce a homogenous cover of the surface with no resulting current. Thus for the 6Li magnetic moment only 2 out of 5 waves are responsible. Thus the weight of the moment generating charge is 2/5. Formula (25). Fig.7 Lithium-6 outer charge orbit
(25)
22
6Li radius (russian data!!) 4He radius Difference (eff chg. Radius = ½ of diff.)
μ6Li in Magneton units Nuclear magneton
effective μ6Li moment calculated moment 2 off 5 waves relative match 4He 4D flux compression measure (N155-4*(1-H147))1/2 corrected moment correct by 4 He compression ratio
2.5432 1.6755 0.8677 0.8220566700 0.5050783699 0.4152030428 0.4167740695 0.9962305077 0.9962268500 0.9962265992 0.4152015184 0.9999963284
For the calculation of the 6Li magnetic moment we use the diference between the 6Li radius and the 4He radius. The efective torus radius is ½ of the diference. This frst approximation 99.6% exact. If you look at fgure 10 then you note that the two 1/3 waves that cause the moment are bound to the 4He core wave. If we take the 4He fux compression factor (third last line, for one dimension) as the perturbation then the moment is exact for 5+ digits. In Fig. 5 you can see that the two 1/3 waves, that produce the moment, directly couple to the core.
Table 12 6Li magnetic moment calculation
7Li radius (russian data!!) Measured 7Li moment 7Li is a 4D nucleus standard moment! Using 0.2 for 2 4D waves asymmetry 4 → 3D normalized
First relative precision μcalc/μmeas.
2.4173 For the calculation of the 7Li magnetic moment we use 1.6447507398 the measured 7Li radius because the free-fux is 0.2*radius 7Li*e*c/(2*2) 2.3221573312 equivalent to a 4D quanta. Because the moment runs 1.6420131959 on one 4D radius we see a 1/21/2 factor correction. 0.9983355873 7Li has 15/3 free fux. It looks like 4 out of 5 3/3 fux
Mass ratio (proton+electron/neutron) square of mass-ratio (2 dimensions) radial error 7Li = 0.9983355873^(1/2) calculated μ 7Li Relative error
0.9991673459 0.9983353852 0.9991674471 1.6447510729 0.0000002025
waves are neutral and only one (1/5 charge) is responsible for the moment. The frst calculation is 99.8% exact. The perturbation is given by the 4D orbiting masses namely the relation of the masses given by the proton/neutron mediated electron.
Table 13 7Li magnetic moment calculation If we take (p+e)/n mass ratio factor ( for one dimension) as the perturbation then the moment is again exact for 5+ digits. (**** One word to “Russian Li radius data”. The US still forces IAEA to publish wrong data for Lithium, because the knowledge about the Lithium (Hydrogen-..) bomb is still undisclosed. The US also fakes (dilutes 6Li) in all US-sold Li containing chemicals.)
7.2 Helium-3 mass and moment Helium 3 base calc tot. mamu Neutron mamu Proton + electron mamu sum(particles) Number of 3D/4D waves Neutron 4D mass released Charge correction by 1FC Sum calculated mass release Measured mass He3 calculated mass He3 Difference Relative error total mass
1 2 3 10 1 -1
In the 3He mass-calculation we see the frst time the Neutron 4D excess-mass release factor we mentioned in table 10. Contrary to Deuterium we did no second order ftting. In total we see 10+1 3/4D fux waves. Here too it looks like two 3/3 3D/4D free fux waves are charge neutral.
micro amus 1008664.923 1007825.032 3024314.987 1- α/2π 2D/4D flux calc. 3024314.987 7'806.570 503.350 1007825.032 -21.751 4032140.019 8288.169 3'016'029.310 3'016'026.818 2.492 0.0000008263
Table 14 3He mass calculation He3 Nuclear radius µHe3 exp. in N units µHe3 exp effective 2D wave 3/3 harmonic 5/11 flux perturbed ratio one Dimension First perturbation correction 3D ½ electron+proton/Neutron Rest error after first correction Calculated corrected moment
He, as Deuterium, is still a 3D nucleus and the moment has no 2 1/2 factor correction. Two 3/3 fux waves (back/front) are electric neutral so the remaining 5 3D/4D free fux waves are the weight to calculate the perturbed 3He moment. The frst perturbation is the standard 4D reduced mass factor of one electron shared between two protons. Because the radius is only known 4 digits exact the result is within the measurement error. 3
1.9664 -2.127625306 1.0746175213 1.0732979169 (5/11)*1.9664*e*c/(2*2) 0.9987720241 0.9988954123 0.9998764754 1.0744847796
relative error
0.0001235246
Table 15 3He magnetic moment calculation
23
The moment for Deuterium can be calculated with the same method/precision with the weight of 1 wave. Tritium has a higher (4D-) symmetry with 12 4D fux waves that need a 2 1/2 factor correction. The tritium waves that generate the 3H magnetic moment shows a perturbation that is based on the fne-structure constant. The magnetic moment of larger nuclei have complex relations to the internal structure. It looks like larger nuclei are built by nested layers of SU(2) x SU(2) systems. Some moments can be reasonably approximated by a radius given by the diference of the stable core substructure and the isotope radius. Some isotopes (e.g. C-13) with N-Z=1 show a moment that is based on the proton radius. Other moments like that of O-17 are based on a combination of the proton radius and the stable C-12 core radius. There a is lot of work waiting!
8 The Mills metric for mass and particle relations From Mills 1.265 to 1.281
Fig.8a Mills gamma
8b) Mills g(uv) metric for cosmic calculations
As already explained in the introduction, magnetic mass, due to it's inherent speed of light, is not able to follow further speed-up. The consequence of this fact is, that in the radial (inside) direction of a central force system there never can be time dilatation – only length contraction. The other consequence is that the rotating maximal possible relativistic (moving inward) mass is fnite and can be given as 2π*m at rest. This fact has been successfully used by R. Mills to enhance the precision of nuclear orbit calculations and to exactly calculate the electron g-factor! A simple experimental proof can be given by looking at neutral Pion/Kaon to charged Pion/Kaon masses.
8.1 The Kaon mass difference If we simply add the Mills electron mass factor to the charged kaon we already get a very good Kaon + 493'677'000.000 approximation 99.85% of the neutral Kaon Adding Mills 2*π*me (Mills 1.281) 496'887'530.189 mass. If we account for the additional 4D uncorrected match 0.9985461137 excess mass for the two dimensional 4D expansion in 2D 3FC^(1/2) 497'606'325.178 coupling wave then the calculated mass is corrected match (inside measurement) 0.9999906055 within the measurement error. Kaon 0 497'611'000.000 Table 16 K+/Ko mass diference calculation
24
8.2 Pion mass difference Pi 0 Adding Mills 2* π*me (Mills 1.281) uncorrected match Experimental correction: µproton renormed by 1/ 1.41421...*(1FC^3) removing radial perturbation → /^4 Pi+-
134'976'600 138'187'472 0.9900930983 1.4106067874 0.9975142085 139570074 139570180
If, for the Pion, we make the same calculation as above with the Kaon, we get a 99% match for the mass. The Pion is a particle with a highly asymmetric wave of a 4D relativistic electron coupled with 1/7 of a proton mass. We found one (perfectly matching) possible 4D perturbation r4 that is based on the proton magnetic moment reduced by the radial (1FC) perturbation.
Table 17 Pion+/ Pion0 mass diference calculation
8.3 Muon, Pion, Kaon – proton mass relations In chapter 5.6 we did show that the momenta of inertia of a 3D torus with equal radii are given by 7/4 and 9/8. In the 3D projection of the 4D model the torus volume is the containment of the total magnetic mass fux. Further we know that stable quantization happens with integer numbers. Thus a proton mass can be divided either by 7 or 9 to form equivalent sub-waves that are conform with his rigid mass momentum. The following is experimental and given with no further/deeper explanation. As a rule we know from the neutron is: All unstable particles are carriers of 4D excess energy. Pion mass from Proton One Proton torus wave (mp/7) 4D expansion by 3FC magnetic moment correction one D 1/3FC*2FC*1FC absolute error (eV) Pi 0
eV 134'038'869 134'426'949 134'975'825 775 134'976'600
If we take 1/7 of the proton mass and form the excess mass with the known factors 3FC and 3FC*2FC*1FC (the proton moment radial perturbation) then the resulting Pion mass is “exact”.
Table 18 Pion mass from proton 1/7 wave Muon mass Torus 1/9 Adding one electron rest expanding by 3FC^3 relative precision Missing mass One (3D/4D wave) spin flip
105658375 104252453 104763452 105673407 0.9998577481 15032 15692
The muon can be based on the 1/9 proton mass to wave quantization. The perturbation factors are the same ones found in the proton magnetic moment without 2FC/1FC. The remaining diference “corresponds” to the energy Mills calculated [2](39.7) for a quark spin-fip what we call a 3D/4D wave-node immersion.
Table 19 Muon mass from proton 1/7 wave Kaon + Kaon 0 Kaon sum Minus 1 quark 3D mass Minus 4D energy minus electron mass Excess
493677000 497611000 991288000 941511120 938793049 938282050 9969
The Kaons are formed when we add the relativistic magnetic-rest mass equivalent (according Mills) of one quark to a proton. If we just subtract the quark mass from the grand total and reverse the 4D expansion we are already in the ball-park! This calculations looks absolutely sound.
Table 20 Kaon mass from proton
8.4 Experimental calculations The formula (26) below can be derived for the exact electron mass, by change of constants by starting from E=mec2. In the electron formula the radius to use is r = “electron de Broglie radius”. In the proton case we use the 3D equivalent 4D radius derived from 4-He. Keep in mind that the efective radius in 4D is ½ of the 3D equivalent.
25
(26) (eV) = µp2*4* π * 100000/(α * π* r3*e) (See also magnetic mass formula from Mills [2]32.32b. ) In formula (26) 4* π * 10000 stays for µo. According to Mills relativistic treatment you have to increase the energy by π/ 2*α. This Corresponds to the 2FC factor for added mass gaining one rotation! Because the Protonmass from moment and 4D radius magnetic mass stays in 4 dimensions we use the 4D radius µproton 1.4106067873 for the proton as a base to calculate the magnetic energy. 3D/4D radius from 4-He (fm) 0.8376530063 magnetic energy uncorrected 926'603'086.79 To the intermediate result we apply the same perturbation correcting with µp perturbation 937'999'675.21 correction we found for the exact 3D calculation of the Alpha quantization for 3D/4D proton magnetic moment, namely: (3FC*2FC*1FC)3. It is (1-(alpha/(PI()*16)))^2 0.9997096686 Mass corrected by 938'272'085.01 obvious that a formula that follows the magnetic moment proton mass 938'272'081.30 has its perturbation. The frst correction is already close to mass difference 3.71 the known proton mass. relative error 0.0000000040 Tab. 21 proton magnetic mass-calculation The second perturbation we found is similar to the proton Bohr level(s). It's the relation of alpha to the whole 3D/4D surface (4 spheres) of 4D space. The result is far to good to be true. Thus we have to discuss the 4D radius of the proton. Formula 26 b) is the fnal proton magnetic mass formula that shows an αquantization. (26 b) (Mass proton in eV) = µp2*4* π * 100000/(α * π* r3*e*(3FC*2FC*1FC)3 *(1-(α /(π*16)))2) The frst fve (unperturbed) levels of the proton quantization are the following: ( 2'002.34, 4'034.33, 6'096.64, 8'189.95 ,10'314.96 eV). In [15][16] the experimenter found that at 1keV particle (electron) stimulation energy strange resonances do occur. The cut-of of the spectrum seems to ft the quantization. Please note that in experiments most deep orbit efects occur with particle stimulation not by em-waves!
8.4.1
Radius discussion
In the frst column we see the measured values for the 4-He compression (volume and radial) from particles. Our frst assumption was that 4-He is a 4D nucleus that directly can deliver the correct 4D compression for a magnetic proton radius. But then we detected that a neutron can accept/release fux, 503.3498458035 what corresponds to a hidden fux compression mamu He4 4'002'603.25 4'002'351.58 He4 from particles 4'032'979.91 4'033'231.59 silently happening in 4D. Because we know the fux compression ratio (CR) 0.992468 0.9923436058 quanta of the neutron (see table 10.) we torus area r*r → r * CR(1/2) 0.996227 0.9961644472 measured He4 chg radius 1.67530000 1.6753060138 symmetrically added halve the value to the total half of He4 radius 0.83765000 0.8376530069 particle sum and subtracted it from the measured Measured proton radius 0.84087000 0.8408777885 compressed proton radius 0.8376972714 0.8376525573 (compressed) 4-He value. This gives us the correct relative error 0.0000564301 -0.0000005367 4D particle compression ratio (0.9923436...) Tab. 22 4-He compression from particles The radius in red (Tab. 22) is the neutron base (potential free) radius that is active “inside” a p-e-p (n-p) bond. Whether this radius is a physical reality or not must be shown. We already used it for the 3D virtual Deuterium model. If we are using known/measured values for the proton radius we see a uncertainty of 1020keV The ftting constant we used for calculating the new 4-He radius was 0.9941929513 =1-5*α/(2*PI()). This corresponds to a 3D/4D surface fux compression in fve dimensions. The reason to use this values was our detection that the ratio between 4D-radius/3D-radius is exact when 0.9941929513 = (R4/R3) 1.51571.. where 1.5157165665 = 2(3/5). The helium/proton radius compression work has been completed three months before the proton magnetic mass-calculation! We just took the data and used it.
8.4.2
The electron g-factor (Mills [2].1.228) (27)
26
Formula (27) is one key (calculation & verifcation) of Mills work, that explains how magnetic energy works. It is correct for about 9 digits with the actual CODATA values. We made the following logic deduction: If the electron and the proton just behave complementary then we can fnd the 4D correction of Mills formula. The frst guess was easy and also the last. We took the complement of 1FC*2FC*3FC = 1FC'*2FC'3FC' we used the weight 4 for 4 dimensions and subtracted it from the above value. Now the calculated electron g-factor is 11 digits exact... Why just the 4D inverse perturbation of the proton?
(28)
- 4* 1FC'*2FC'*3FC'
Again we have to inform you that this is a logical guess and not a totally funded derivation. But it is interesting to note, that the factor exactly has the right dimension and we had no other known choice to make an improvement.
9 Li6, Li7 Gamma lines The Li6 fux structure looks diferent than the He4 one, because single pairs of neutron/proton cannot exchange (reduce) fux with a basic He4 4D quanta. Added mass/fux can only couple with the He4 (or core) bound 3D/4D-fux. The remaining unbound fux (see Table 5 5/3 of one 3D/4D fux unit) that couples to the 2 x 4 p-n bonds is called free 3D/4D fux. We call it free, because it seems not strongly coupled to 4D bound fux. This understanding is crucial. The prime coupling for gamma wave resonances always (if available) goes over the amount of free fux and the related energy hole(s) of released fux. γ quantum
Gamma energy
Reduced by γ* = 1/(1+πα2)
Reduced by activation energy
Flux hole + activation energy Energy (2FC') Flux hole
Reduced gamma = activated flux hole
Fig.9 Gamma energy matching How is gamma-ray energy exchanged? In fact, a gamma quantum must match a certain amount of energy that is equivalent to prior (during nuclear build-up) released 3D/4D fux energy. Further we know that a photon makes only one rotation and all mass that is nucleus bound makes at least two rotations. Mills found the factor that converts the photon 2D/3D energy to 3D/4D particle energy. He called it γ * = 1/(1+πα2) = 0.9998327339.. (Box 2 Fig.9) On the other side all energy of a 4D nucleus makes at least 3 rotations. Thus we have to increase the fux holes mass ( in fact the mass of the energy hole second box from right Fig.9) by the released compression energy! Basically we calculate the equivalence of gamma-ray energy and nuclear cavity by increasing the nuclear 3D/4D energies by 2FC and by decreasing the photon energy by γ*. The needed energy to increase the weight of the cavity must be delivered by the gamma quantum. (3rd step middle of Fig.9) This process is easy to follow because we, up to now, always tabulated the fux released not the energy of the 3D/4D wave. The maximum unit that can directly accept incoming fux is one n-p fux hole bond. But the fux holes can go into resonance with other holes what leads to splitting.
27
9.1 The frst Li6 gamma Line Li6 2186 line
1:1 full coupling
measured line Needed Flux calculation Full coupling free flux mass 3/3 - of 5/3 Flux hole weight coupling rotator mamu Rotator Flux to provide = mamu CME (1-2FC)/2FC Rotator full weight without flux rotator plus flux energy one base unit
The frst Li6 line represents the most simple gamma coupling we can encounter. In Li6 only one subset of the free N-P bond (cavities) is responding and thus the gamma energy does 2'536.599 factually not interact (No 4D coupling) with the 2'181'532.212 2'184'068.811 core nucleus (bound fux). On frst sight we can 2'184'068.811 say that the frst 6-Li line corresponds to the 2'184'068.811 3D/4D binding energy of the n-p bond. eV 2'186'000.000
2'341.971 2.723
Full base couples Couples 1/1 ! Base rotator split any (x,y,x)
( An other simple case is the frst Be9 line where the full free
Line relativistically corrected by Mills γ*
2'185'834.295 fux couples, is presented in chpt. 10.) 2'536.599 2'183'297.696 -0.00035319 -771.115
Line reduced by one flux quantum given to rotator relative error absolute error
Table 23 Li6 base gamma line calculation A more sophisticated way to calculate frst gamma line of Li6 is the model (explained in chpt. 10), of the 3 axes symmetric, force free rigid rotator. This works fne because the free 3D/4D fux splits into three independent hyper- harmonical, waves that carry all the (electron magnetic mass-) energy! Further on there is one crucial feature of 4D space: In 4D space there is no time. We only can count wave numbers and they usually must couple with a natural number relation! In the base state we assume that all the frequencies are equal
9.1.1
One more way to calculate the first Li6 line:
In Li6 the rotator (= sum of free fux hole = 5/3) moments of inertia are split 1:3:1 and thus the middle rotator (wave(s)) is equivalent to 3/5 of the free 3D/4D fux energy. The simple rotator only gamma coupling between neighbor bonds usually happens when the Li6 base line 1:1 full coupling eV acting fux hole will accept exactly the amount of all measured line 2'186'000.000 own fux lost during the nuclear binding phase. Needed Flux calculation Full coupling free flux mass 3/6! - of 10/6 mamu 1'170.986 no coupling 0.000 Flux hole weight coupling rotator mamu 1.362 Rotator Flux to provide = mamu CME (1-2FC)/2FC Rotator full weight without flux rotator plus flux energy one base unit 3/6 (of 10/6) 3/6 base couples Couples 1/1 → !2:1 Base rotator split any (x,y,x) Resonance of full rotator Line relativistically correct by Mills PC2 Line reduced by one hole activation flux quantum relative error absolute error
1'268.299 1'090'766.106 1'092'034.405 1'092'034.405
The precision for the line is excellent and the error at/below measurement. Here we use a factor of 2 to convert 5/3 into 10/6.
2'184'068.811 In this case the free fux wave energy (in 10 th) is 2'185'834.295 2'184'565.996 0.00022759 497.185
distributed 3:4:3. One wave (3/10) makes a 1:1 resonance = frequency doubling that is far better than the measurement.
Table 24 Li6 gamma line calculation based on frequency doubling Summary: A gamma quantum always adds energy to the rotator/wave cavity ( we use fux hole = cavity as synonyms). To make the energies comparable, we must transform the gamma energy and the cavity energy into the same state - in our case, free 3D/4D energy. In a stable nucleus all energies are free of the original 3D excess fux. Thus, we must calculate the amount of fux needed (once given away fux) to lift the rotator cavity (at least the part that receives the gamma quantum) back into the nucleus creation state. Further on a gamma quantum is a 1D/2D-3D form of energy, that must be relativistically corrected for the reference frame of 3D particle creation. This is done by lowering its energy by γ* see Mills [2]36.15. In gamma lines, where more (or much less) energy is added, than the matching base rotator (wave) contains more sophisticated coupling does occur. As shown, there are usually several possible modes a nucleus can go into gamma resonance. This could be one reason, that the measured energies have a certain distribution.
28
9.1.2
Li-7 Gamma lines
The Tab. 25 shows that the 7Li free 3D/4D fux is a little bit greater that one 4He 4D base quanta. This nucleus is thus highly perturbed and shows Li7 base line 1:1 full coupling eV strong wave coupling, because it would like to measured line 477'612.000 release on 4D quanta. Investigations show that Needed Flux calculation Full coupling free flux mass 1/3 - of 7/3 780.657 three possible confgurations exist. The most Couples with 2 3/3 bonds Rotator total 6/3 + 1/3 5'464.599 demanding is the case, where all fux is added 6.354 Flux hole weight coupling rotator mamu 5'918.730 to the existing 4D fux, what would lead to a Rotator Flux to provide = mamu CME (1-2FC)/2FC Base rotator full weight without flux 727'177.404 rotator plus flux energy 733'096.135 virtual Be8 confguration, that is known to be one base unit 1/14 52'364.010 unstable. In that case only about 162'461eV of 471'276.086 free fux would remain available ( but here a Full base couples Couples 9/14 Base rotator split 5:4:5 two waves 5:4 evolve 2D/4D correction would be crucial). 162'461eV Line relativistically correct by Mills PC2 477'532.098 471'613.368 is more or less exactly 1/3 the amount needed Line delivers flux to coupled rotators flux hole cavitiesy relative error 0.00071517 for the frst gamma line. absolute error
337.281
Table 25 Li7 resonance between two n-p bonds coupled with 1/3 N-P bond. In Tab. 25 we present a possible calculation for the frst 7Li gamma line. In this case, where the gamma line energy is much smaller than the “total free fux cavity”. We assume that only a part of the nucleus 3D/4D free fux cavity is responding. The splitting of 1/14 is natural, if we assume, that one out of the 15/3 wave is the core of interaction (receiving the gamma energy) and the remaining 14 others are only in resonance. Further on 7Li carries enough free fux for a ”virtual” 4D quanta which potentially can generate an additional 2D wave splitting. The simplest assumption we can make is: The base rotator splits symmetrically into 5:4:5 and two out of three waves are acting = are flled by the incoming gamma energy. (Keep in mind if we talk of bonds, – in case of line resonances – then always the fux hole is meant!) During our investigative work we usually found good matches (exact at about 4 digits) for all measured gamma lines of a nucleus. The number space to look at is wide. We restricted our search to the most obvious rotator solutions, - the solutions (see chpt 10.) for sin(90), sin(45) degrees. 45 degrees leads to an unstable inharmonic rotator, which usually catches some unexplainable higher gamma quanta. In the inharmonic case, we have to count in many additional scenarios, what should be done by writing some software.
9.1.3 Li7 second line The second 7-Li line shows a resonance with 7/14 base resonator coupling at 59/14. The full fux, the total cavity can absorb, – without frequency Li7 4630 line 1:1 full coupling eV doubling - is 70/14 (See Table 26. 5/2 2FC fux measured line 4'630'900.000 reduction holes). The coupling happens Needed Flux calculation between a (½) n-p fux hole and two Full coupling free flux mass 1/2 - of 5/2 1'170.986 Couples with rest of free flux 6/3Rotator total 5'854.928 neighboring (coupled) n-p fux holes. The base 6.808 Flux hole weight coupling rotator mamu 6'341.497 cavity splits 1:2:1 where either the inner or the Rotator Flux to provide = mamu CME (1-2FC)/2FC Rotator full weight without flux 1'090'766.106 two outer wave can couple. The base rotator plus flux energy 1'097'107.603 resonance energy is calculated as sum (fux one base unit 1/14 78'364.829 4'623'524.898 hole ½ n-p bond fux hole) of the reacting Base – 2 waves - couples Couples 59/14 cavity plus the weight of the energy needed to Base rotator split 5:4:5 coupled rotators 5:4:5 activate the all the cavities in resonance. See Resonance: base 5:4:5→ 10:8:5; 4 coupled fill: 5:4:0 Line relativistically correct by Mills PC2 4'630'125.278 table 23., rotator full weight. Line delivers flux to coupled rotators flux hole cavities 4'623'783.781 If we add more than 4Mev the dynamic mass relative error 0.00005599 7 absolute error 258.883 of Li is large enough to produce a second 4D quantum, so we see the additional factor 2. Tab. 26 7-Li second line
29
See Fig.10 below. First the base cavity – the primary acting fux hole - is fully flled and gets 14 units (1'097'107 eV). Then two out of three waves double the frequency which gives in total 23 units that are assigned to the base cavity. The remaining 36 units go to the other 2 active rotators that show the identical wave pattern where the same waves/cavities (4:5 couple ) and get flled. 4 x 9 = 36. This is a typical 2 wave coupling, where waves with equal weight evolve.
Activated base cavities
1: Filled base (14) 2: 2 x Resonate base waves (9) 2: 2 x Resonate coupled waves (4 x 9 = 36)
The model with the three dimensional coupled force free rotator basically allows any symmetric (1:1:x) relation between the 3 coupled masses (waves). But quantization forces the relation to be based on a natural number quotient (here 5:5:4). The number of the maximal splitting is given by the number of maximal possible involved waves. Further the resonant (neighbor) waves must have the same frequency( mass) here 4,5. There is no surprise as both 7-Li lines show 1/14 quantization.
Fig.10 7Li seconds line energy distribution between coupling waves.
10
More about gamma lines
Our simple modeling of nuclear masses and gamma lines – using the free and bound 3D/4D mass (holes!!) only, shows that three evolving waves/cavity already can explain many phenomenas. Because of the quantization rules, the intrinsic energies of these waves (at least in a stable state!) must follow a natural numerical, rational relation. (In excited states or under stress condition we also found waves with rational quotients. More later.) In our frst modeling approach for gamma lines, we successfully used the equivalent of a three dimensional force free symmetric rigid rotator to model[4] the energy of the gamma waves/resonances. A typical energy relation for the 3 independent rotation axes, found for 6Li is 1:3:1. Each wave, that couples to the bound 3D/4D fux (-hole), carries one unit of energy and the middle one carries 3 units. This simple 1:3:1 is just a proportion relation. In realty this can also be 5:15:5 units.
10.1
The standard gamma-ray matching process
As explained in chpt. 9 (Fig.9): In a nucleus the 3D/4D fux holes are responding to ( and releasing) gamma ray radiation. A fux hole is an empty cavity that can be (re-)flled by the gamma energy. Energy can only be compared if the involved energies are measured within the same dimension/state. Thus 3D/4D cavity can only accept energy, if the hole enters a 3D energy corresponding state. We treat the 3D/4D fux hole as an independent object, that, after adding 2FC fux, is ready to interact with normal 3D (particle) energy. The gamma ray is an external 1D/2D-3D form of energy, which must be converted to internal 3D energy, by using Mills γ* = 1/(1+πα2) . For optimizing our matching process, we compare the normalized gamma energy minus the initial fux needed to activate the cavity with the possible ratios all cavities can respond. The usual entry points for a gamma-rays into a nucleus are the bonds (cavities) between one neutron and one proton. The so called “base rotator weight” is the maximal fux the acting cavity can absorb + the fux that was needed to activate it. Because the base rotator consists at least of three waves, which must have the weights (x:y:x) x,y positive integer numbers >=1, at least one rotator/wave must be completely flled to get a match. Such a single rotator wave can be modeled by the matrix (Fig. 11) given below. The model we frst used for the calculations of gamma lines (like the measured ones for Li6), was an
30
mechanical analogy to the three dimensional force independent symmetric rigid rotator. Below the solution matrix for the momenta of inertia for all three dimension is given.
Fig. 11 From [4] . The moment (M) of inertia Matrix The trivial solution can be found by setting cos = 0, what leads to the following relation: 1:1:M1/M3 where the numbering of the dimensions is not important because of the symmetry. This, in general (in 4 independent dimensions) leads to the following two possible symmetric energy (proportional to momenta of inertia) distributions: x:y:x or y:x:y. As a conclusion of this, we see that the free fux always occurs in quanta of 1/3 (there are always three rotators = waves and 1:1:1 is always a solution). Any addition of a 1/3 excess quanta leads to a stable simple 3D/4D rotator! Only for very simple nuclei like Li6, Li7, Be9 we are able to exactly predict a line, based on the known coupling mass/fux. The less trivial solution cos/sin(45) of Fig. 10 Matrix M, leads to a rational relation of the three rotators. This relation is important in cases, where the remaining free 3D/4D energy is lower than one quantum (3/3) or 2'341.971 mamu's!, or in cases of very high energies. In our frst search we ignored lines, that match in a rational number relation. Only a low percentage of all gamma ray (= nuclear gamma levels) levels can be assigned to simple free fux only coupling. Most lines or higher harmonics of basic lines occur in a combination of free fux and coupling free/bound fux. If a nucleus has two basic He-4 4D quanta released, then the coupling force, in (most times found) two dimensions, has double the strength, leading to a split of matching wave number from eg. 1/3 → 1/6 or 2 2 → 1/12 of the base rotators. If in a nuclear orbit all 3 sub waves spaces are used, (1,2,4) orbits = 7 4D quanta were released, then the splitting can be even fner. Usually it goes further from 2 → 4 and for 7 it goes to 7 2 . This means resonances interacting with bound fux are split by x*1/49. Usually the denominator is given by the prime factors (2,3,4,5,7) x (2,3,4,5,7) which are given by the nuclear quantum numbers. If more than one 4D (1,2,4) orbit has been flled, then also the sum of primes of two adjacent orbits can occur in the denominator. Sample orbit number (7,4) leads to 1/11 split. The splitting of is dominant because this is the only orbit pair with equals numbers of quanta!
10.1.1
4D coupling
The simple solution we present above only covers three dimensions of fow interaction. To model a general 4D rotator, we must expand the matrix (Fig.10) above to a 4D tensor of rank 3. The simplest coupling method we tried is linear 1:1 fux fow with rational coupling terms of one base rotator with 3 coupled rotators. (Covering 1 quadrant of interaction) With this method already a few hundred lines could be reproduced, that usually cover at least 2/3 of all gamma lines of one nucleus. The most exact results we got with multiplicative 4D coupling, where the weights of all four dimensions are multiplied and the coupling strength is used as a new input to adjust the rotator weight. Such matching can agree up to 7 digits for exactly known wave energies. But a flter based on this method is no longer linear and requires much more manual work. A simple 4D 3 → 3 + 3 x 3 coupling looks as following:
31
Base rotator BR splits: 1:2:1 (a:b:a) couples with 3 associated rotators AR typically also splitting 1:2:1. In principe rotators may assume any valid (x:y:x) split, but all three associated AR's must have the same (x:y:x) substructure. One base rotator part (a,b) must at least match one out of x:y. Usually the coupling is from the inner BR(,b,) rotator to the outer rotators (x,,x) of AR or from the two outer BR(a,,a) to the inner AR(,y,). For the more complex multiplicative coupling any amount of fux or energy, that must be added to the acting base rotators is in the form of base-energy * (coupling constant) 3.
10.2
The methods to match a gamma line
Repetition: The inverse logic of energy holes is crucial for the understanding of gamma ray resonance. Principally a gamma ray can only add energy to a nucleus if there is a hole equivalent of energy. The hole in the given samples of Li6/Be9 (below) involves only the free fux holes for the gamma ray bulk energy. But this is only the core of the understanding. A hole can only come into resonance when it too carries free fux!! Only matter – holes included - that is equivalent to 3D matter is able to interact. Thus, in a frst step, we always must calculate the free fux equivalent of the acting (sum of) hole(s) (“decompressing the hole!”. After adding this fux to the holes they are able to interact. This is the point where the holes act like individual substructures. In our frst modeling approach we subtract this hole-fux needed from the incoming gamma energy to get a match and add its energy to the rotator mass. Physically it could also be possible that the hole itself delivers this energy as a reaction fow with the gamma ray. This is one detail, which only can be answered after we will have analyzed and fully understand all 3D/4D coupling models for resonant waves. Thus the steps for calculating a gamma ray are as follows: 1: Build a rotator with (matching parts of) the free 3D/4D fux. This is called the BR – base rotator. For the analysis, this rotator can potentially split in to (x:y:x) and for large nuclei further in (2*2*)3*3*4*4*5*5*7*7 sub quanta, plus the allowed (involved 4D quanta) sums of two out 1,2,3,4,5,7. 2: Calculate the rotator 3D/4D hole fux (RF), that is needed to make the rotator equivalent to a 3D mass. Add the fux RF to the BR mass. 3: First you must reduce the mass of the incoming gamma line by Mills γ* which relativistically transforms a 1D/2D-3D mass(energy) to a 3D mass(energy). Then the mass of the incoming gamma quantum must be reduced by RF (point 2 above). This method avoids re-weighting of fux of fux (second order ftting). 4: If you want to try advanced 4D matching, then you must calculate the activation fux for all involved fux cavities and add it to the base rotator weight. 5: Now you have to make some reasonable guesses for the quantization (denominator fraction of the base rotator) and then just walk through the quantum numbers. Usually if you get a 4 digit match then result is sound.
10.2.1
Other possible methods
In principe we could also model a matcher doing a 3D/4D match, where the incoming gamma energy fnally again releases 3D/4D fux energy and the quantum is added as a temporary “additional bond”. On the other side a complete 4D (6D) model built on three/four coupled hyper-spherical harmonics could allow to narrow/predict the possible frequency space. But this work is hardcore math to be done, by people with extended experience. Anyway the presented methods do not yet cover efects caused by involved neutrons, that couple to 4D fux. There are clear indications, that certain lines exhibit an inverse alpha quantization, but this is future work.
32
In the case of 6Li we also could see (not shown here) that we can calculate in the perturbation of the magnetic moment to signifcantly enhance the precision of the line matching.
10.3
Some more sample lines
(We always use the term bond as a synonym for the associated fux hole = cavity.) Be9 2429 line
1:1 full coupling
measured line Needed Flux calculation Full coupling free flux mass 2/3 Flux hole weight coupling rotator mamu Rotator Flux to provide = mamu CME (1-2FC)/2FC Rotator full weight without flux rotator plus flux energy one base unit
eV 2'429'400.000 1'561.314 1.815 1'691.066 1'454'354.808 1'456'045.874 485'348.625
Table 27 presents one line, where only the base rotator acts, with one wave doubling its frequency. Here again the base rotators(1:4:1) get flled (6/6) and the middle wave/rotator doubles (1:8:1) the frequency.
2'426'743.123
Full base couples Couples 5/3 (10/6) Base rotator split 1:4:1 Resonance at middle (4) x 2 1:8:1 Line relativistically correct by Mills PC2 Line delivers flux to all coupled rotators flux hole cavities relative error absolute error
2'428'993.576 2'427'302.510 0.00023046 559.387
Table 27 Be9 second line C12 first line
1:1 full coupling
measured line Needed Flux calculation Coupling free flux mass 3/3 couples with 8 3D/4D bound flux Flux hole weight coupling rotator mamu total 27/3 Rotator Flux to provide = mamu CME (1-2FC)/2FC Rotator full weight without flux rotator plus flux energy one base unit 1/18
eV 4'438'910.000 2'341.971 21'077.740 24.508 22'829.389 2'184'068.811 2'206'898.200 2'206'898.200
Here one full free fux N-P bond reacts together with one He4 core cavity attached (8 N-P) bonds fux. As usual the total fux hole must be flled with his own fux to make it 3D mass equivalent. All carbon 12 lines have a very good agreement with this model.
4'413'796.400
Full base couples Couples 2:1 Line relativistically correct by Mills PC2 Line delivers flux to all coupled rotators flux hole cavities relative error
4'438'167.397 4'415'338.008 0.00034915
Table 28 Carbon 12 frst line
10.3.1
Sn the island of stability
117
Sn is an extraordinary set of nuclei. It covers a large range of orbital quantum number from 47 to 55 4D quanta released. Sn117 itself has 51 4D quanta released what leads to a special orbit structure of (7,7); (7,7);(7,7); (7,2). It has a long living (> 1 week!!) gamma state at 314keV. In our analysis, many gamma lines match multiple Sn117 1x7 1x7 1x7 2x7 2x7 2x7 2x7 2x7 times at various Final lines keV 13/49 5/21 20/49 5/6 29/49 3/5 7/49 1/3 6/49 4/3 13/49 5/6 24/49 6/7 43/49 1/3 158.562 0.092051 0.017940 0.017408 1.000474 -0.171169 -0.175421 -0.109274 -0.174201 primes/fractions. 314.58 1.000117 0.199061 0.198626 2.327705 0.040955 0.041349 0.025151 0.038445 The red marked 1004.53 5.015806 1.000025 1.000016 8.197049 0.979019 0.999956 0.619610 0.978816 felds show the 1019.92 5.105380 1.017892 1.017892 8.327971 0.999943 1.021339 0.632870 0.999792 1179.7 6.035341 1.203381 1.203480 9.687205 1.217182 1.243335 0.770536 1.217565 be st matc hin gs 1446.2 7.586441 1.512761 1.513025 11.954297 1.579518 1.613606 1.000152 1.580793 with at least 5 1468.6 7.716815 1.538765 1.539043 12.144852 1.609974 1.644729 1.019452 1.611323 digits precision. 1510.1 7.958355 1.586943 1.587246 12.497889 1.666397 1.702388 1.055208 1.667885 The blue matches 1578.25 8.355006 1.666058 1.666404 13.077635 1.759055 1.797075 1.113926 1.760771 2048.2 11.090238 2.211624 2.212260 17.075458 2.398004 2.450017 1.518834 2.401292 usually are lower 2128.6 11.558187 2.304960 2.305646 17.759414 2.507317 2.561724 1.588106 2.510873 grade, three digits 2280.4 12.441703 2.481185 2.481965 19.050763 2.713706 2.772633 1.718897 2.717770 matches. 2304.6 2367.3 2415.9 2515.8 2590.2
12.582553 12.947483 13.230348 13.811792 14.244820
2.509279 2.582068 2.638487 2.754462 2.840833
2.510073 2.582901 2.639351 2.755386 2.841803
19.256630 19.790014 20.203450 21.053290 21.686204
2.746608 2.831856 2.897933 3.033758 3.134913
2.806256 2.893371 2.960895 3.099695 3.203065
1.739747 1.793770 1.835643 1.921717 1.985820
Tab. 29 Sn117 4D coupling matches with expected 7x7 (=49) base line splits.
33
2.750754 2.836211 2.902450 3.038610 3.140014
Tab. 29 shows a small, but instructive subset of the Sn117 base-lines (lines that fall back to ground state) that we could match. The red matches usually are exact (line energy 6 digits) at the measured line energy. The blue indicated higher harmonics matchings are less accurate, but clearly indicated that the lines are connected by natural number quotients. Even more instructive is the matching at 1/7 (7/49 = 1/7 = highest splitting force) which shows(green) four higher (harmonic) lines connected by prime numbers! Usually, if we did fnd a good parameter set, we see multiple lines matching at the same set (e.g 13/49). The prime factors that show up in the nominator are built by summing up the weights of coupling rotators. The primes in the denominator are given by the coupling weight of the waves. Typically we see (1,2,3,5,7,11) 2 . 11 occurs if the fnal 4D orbits are (7,4). For Sn117 we also see many resonances with bound fux (= incoming fux releases 2FC, what lowers the base weight of the resonator.) fux coupling. These resonances need a slightly diferent modeling, what will be a next task.
10.4
First (20.210 MeV) Helium gamma line calculation
He4 20210 line
1:1 full coupling
5/6 base couples Couples 11/1 ! Sample base rotator split 1:3:1 → 2:3:2 CR rotator 24/36 must double e.g 1:4:1 → 1:8:1 Line relativistically correct by Mills PC2 Line reduced by one flux quantum relative error absolute error
eV 20'210'000.000
With the standard free/bound fux coupling method most He4 lines can be modeled. He4 is a special nucleus because it has no free fux. Thus at least two waves (rotators that go in 17'333.425 resonance with the other 6 Bonds) must be 1'817'943.510 involved. A splitting factor of 6 is natural (6 1'835'276.935 1'835'276.935 bonds out of 8 coupling) and the base resonator 20'188'046.286 involves no fraction, what usually confrms an exact match.
measured line mamu Needed Flux calculation Full coupling free flux mass 5/6! - of 6/6 1'951.643 Coupling with 3 x 2 x 3/3 N-P flux reduction cavities 14'051.826 Flux hole weight coupling rotator mamu 18.608 Rotator Flux to provide = mamu CME (1-2FC)/2FC Rotator full weight without flux rotator plus flux energy one base unit 5/6
20'206'618.987 20'189'285.562 0.00006138 1'239.276
Table 30 4-He gamma line
1 4 1 1 4 1 Fig. 12 a)
b)
c)
1 3 d)1
1 4 1
Fig. 12 a) shows the N-P bond structure of the original He4 3D/4D Flux base. After transforming to 4D fux, each N-P bond leaves behind its 3D/4D fux reduction cavity. In Fig. 12 b) energy is brought in by coupling to the red bond cavity. In Fig. 12 c&d we show the evolving waves (rotators) of the input coupling red and one set (3 out of 6) of the coupled 3D/4D cavities. There are other possibilities to represent the same facts, like joining two adjacent cavities, what would give 2:8:2 wave splitting for the coupled waves. How to interpret the fndings: The base rotator gets 5/6 fux units and the coupled 6 x 4/6 = 24 units. The coupled base resonant cavity gets in total 29 initial fux units. Then the coupled waves double the frequency. The coupled rotators gets once more 24 units and the base rotator doubles the frequency of the the two outer coupled rotators from 1 to 2, what gives 2 more units. In total we have 29 + 26 units added what is required by the resonance condition of 55/6 of the base (red arrow) coupling rotator. This is the typical standard linear coupling we see. Two adjacent 1:1 waves (of 1:3:1 to 1:4:1) couple and transport the energy to the neighbor (4) middle waves.
34
10.4.1 Doing it the wrong way He4 20210 line
1:1 full coupling
measured line Needed Flux calculation Full coupling free flux mass 6/6! - of 6/6 Coupling with 7 x 3/3 N-P flux reduction cavities Flux hole weight coupling rotator mamu Rotator Flux to provide = mamu CME (1-2FC)/2FC Rotator full weight without flux rotator plus flux energy one base unit 3/3 5/6 base couples Couples 55/6 ! Sample base rotator split 2:2:2 → ?:?:? CR rotator 55-BR must double Line relativistically correct by Mills PC2 Line reduced by one flux quantum relative error absolute error
eV 20'210'000.000
To illustrate the pit-holes of the matching algorithm, we show an other attempt. If you use 6/6 = 3/3 = one full N-P in resonance with all other 7 full N-P fux-bond cavities, then you get about the same 20'292.790 2'181'532.212 result but with far less accuracy. For judging the 2'201'825.002 quality of a match, we frst look at the ratio of the 366'970.834 “absolute error”/ “base resonator”, which is an 20'183'395.855 indication how the match compares to a random match.
mamu 2'341.971 16'393.797 21.785
20'206'618.987 20'186'326.197 0.00014516 2'930.342
Table 31 “Wrong” match for He4 20210 line. The resonance at 55/6 (see Tab. 31) is the same partition ratio, we needed in the frst sample (see tab. 30) to distribute energy to the coupled rotators. Further on, with the second match it is much more difcult to fnd a rotator/wave partition ratio that works. We can always fnd one, that matches, but much higher numbers of fractions are needed. At least we do get the same fractions (55/6), what confrms the frst coupling sample. There will always be a discussion about random matches claimed to be fndings. If one parameter set (see tab. 29) delivers multiple matching lines, then this can have two reasons. The waves are “linear” dependent or we had even much more luck. But the later can be excluded for most samples we found. The waves are dependent but these relations are complex and involve many prime quotients not just simple factors. Further on how big are your chances to simultaneously match a good dozen of measured line values with a narrow (single set for one column) set of parameters? - Only using the same primes. Further on with 117-Sn (like for most other lines too) we have many perfect matches, which are better than the measurement!
11
Physical implications of 4D space
(Discussion of some aspects of the fndings.)
Fig. 13 He-4 Charge/mass wave on a torus surface There exist quite many papers that deal with curved space orbits of particles. We just reference three samples [7] [8] [9] from diferent domains. A closed, self sustaining magnetic “body/feld” structure is also known under the term anapole feld. An anapole magnetic/electric feld structure is able to generate current that is coupled to a feld that again must generates the original current. One consequence of such an approach is the non existence of isolated charges. An other in-depth investigation of force free toroidal feld
35
structures is given in [14]. But all these papers deal with common 3D,t structured space. Paper [14] is interesting as it covers phenomenas like ball lightening and proves that already in 3D we can fnd force-free solutions for a self sustaining coupling feld/charge density with a torus topology. We did not yet fnd a concrete mathematic representations for a SO(4) conform space anapole feld structure that satisfes all conditions. But one analogy is obvious: Operation (analogous to 3D(3, 1)) that include curl will become (curl) 2 or f(curl,curl). An other possible consequence could be a splitting of the feld nature in a H-- & H++; H+-, H-+ (here “+ -” denote curl and the inverse operation!) and E--, E++; E+-, E-+. This makes it possible to express a neutral – non repulsive charge combination for two out of 4 dimensions. E+-, E-+ is exactly what we understand as a free wave or photon nature of charge. In SO(4) the charge fows on 2 circles that are two time (2D) orthogonal. This explains why there is no Coulomb stress in any nucleus. This also explains that that the general Maxwell logic must be adapted to one more dimension, because the classic curl operation would be co-linear (not orthogonal to!) with an existing fux of charge. We also might get felds that do not act on some types of charge charge (-density). Operation between pairs of (E+-, E-+.) will cancel in the acting dimension. Even more weird efects could make sense, like the combination of a potential and a rotation. But if nature is a kind of symmetric, then there must also be a rotation efect for the charge like feld. The same must happen for the H feld which should express a radial component. It is structurally obvious that H+- operation has a diferent efect that H-+. Whether the operations involving the above defned H/E felds are symmetric and behave (are isomorphic) according a standard Abelian group must be detailed out. We will frst try quaternion logic or left/right associative logic for basic operations. Fig. 13 shows the core 4D orbit of Helium-4, simplifed as a single torus, with four rotations of the fux. But keep in mind that latest after 8 complete (by 360 degree = 2*π) turns a waves must have once switched from the inner to the outer surface or vice versa. This also implies that the path length on a true 4D (Cliford torus like surface) is twice as long as given by the “sum” of the (4) base rotation operations. The blue and red circles represent the proton/neutron(electron!) nodes of the wave. Such a structure shows no electric asymmetry. This is well understandable if we assume that the two planes of fux interaction between adjacent p-n(e-) orbits stays in the (E+-, E-+.) dimensions and cancel. From measured nuclear data it is clear that in 4D physics charge is not the dominant factor for the 4D volume, that a nucleus flls. Contrary to 3D(3, 1) where the magnetic feld can be explained as a relativistic efect of charge, in 4D charge seems to be an efect of the basic magnetic-equivalent fux. Any point, that not exactly lives on the above Fig. 13 shown – projective - 4D torus, will exhibit an additional radial movement, what leads to eccentricity. At the same moment – leaving the torus – only three free rotations axis will survive (In physical 4D space! In 6D no problem). We believe that the torus - surface represents the generation area of all physical phenomenas and internally is charge & mass neutral.
11.1.1
Energy
In our common “3D(3, 1) conform fat space time” energy is a scalar of single dimension nature. Energy can move in any of the three space dimensions, but not in time only. In 4D space the bulk energy can only rotate. Any radial oscillation introduces a potential coupling to the common 3D x time dimension, what may lead to decay (alpha beta gamma, p,n,v etc..) See [6] and [2] about the non radiation conditions. In 4D space any fux is fowing at the speed of light, thus the energy/mass is just given by the area the fux passes through. But in 4D, contrary to 3D(3, 1) the 4D fux can choose 3 planes it likes to fow through simultaneously. This gives also a perfect analogy to 3D mass, because there, three disjoint planedimensions are the border of a 3D cube (of mass).
11.1.2
Classical quantization of energy
From the 3D(3, 1) quantum model we know, that the energy in a central feld is proportional to 1/r 2. And the quantization thereof is x2: 1,4,9,16 … overlaid by radial perturbations! In general form, energy occurs in multiples of h, as known from the photon equation.
36
11.1.3
Energy structure of 4D space
The only method we had, to analyze the energy structure, was looking at gamma-ray resonances. We had to invent everything from scratch. We had to carefully evaluate alternate paths and to acquire knowledge, about how the structures of diferent nuclei answer. One thing was obvious: Overall all, most gamma spectra are similar to an extent, which must be frustrating for somebody doing similar work, without having the key to the solution. We do not say that our method is perfect, but it allowed us to draw some fnal conclusion. For a very long time it was not clear whether 4D quanta are just released and the bulk matter just remains in a 3D/4D state. Now we are convinced, that the bulk matter is fowing in a 4D orbit with 4 rotations. Nevertheless, there are two main fux-release processes and we in the following classify the matter by the type of energy-hole (3D/4D or 4D) it leaves behind. Nuclear 4D orbits, for stable nuclei, have the quantum numbers of 1,2,4. (one times 1,2,4,8 in U238 – the long-time stable nucleus). These number sum up and 7 is the highest single resonance factor we see in our analyses up to Pb207. (15 for U238) Seen from a fux-compression view-point, Ni64 is the must dense nucleus. It has an 4D orbit/quanta structure of (7,7);(7,7);(1,0). (Classically people think Iron Fe56 is the most stable/dense nucleus. It has the (7,7);(7,1);(1,1) 4D orbits structure.) Lead is the last stable nucleus in the periodic system. It has 6 complete 2 x ( 1,2,4) fux fow attached waves, with the following structure of (7,7);(7,7);(7,7);(7,7);(7,7);(7,7);(= 84 4D quanta). Other possible ways to structure the orbits are: 4 groups (7,7,7);(7,7,7);(7,7,7);(7,7,7); or three groups: (7,7,7,7);(7,7,7,7);(7,7,7,7). To answer, which one of the three structure is the true (better ftted) one, needs some more hundred spectra being analyzed. An other efect that can directly be seen in the gamma spectra of larger isotopes is the distribution of lineenergies and the number of lines. The more 4D quanta an isotope releases, the more possibilities to split the energies exist. Also do high 4D quanta pairs lead to smaller resonant line energies, because the allowed fractions are smaller. For every Z/2 up to Z=82 (Pb) there is 1 to 41 default 4D quantum released together with 8 full 3D/4D quanta. Releasing a 4D quantum without making 4 rotation is difcult to believe. Thus we assume that the red circle below Fig.14 represents true 4D fux energy. Any excess of about 5 full 3D/4D quanta is converted into a 4D quanta. In the spectra we can notice, that, after adding one more 4D quanta, the base 8 full 3D/4D bond structure (the 3D/4D energy-holes) increases it coupling force by a factor of 2 or n for the number of 4D quanta in the orbit. For orbit numbers greater than 2 we also see n2 coupling.
4D Energy hole
4D Energy hole
4D Energy Fig. 14 a) Core energy structure
4D Energy 14.b) Free 3D/4D fux light green
The red core stands for Energy that is associated with at least one released 4D fux quantum. The green shell is 3D/4D rotation energy, which couples to 4D. The green energy is associated with released 3D/4D fux. The blue/dashed outer ring is the residual (+-) efect of the acting felds or eccentricity. We call it charge efect because for lower Z it is bound to the charge. In Fig.13 b) you may see that in reality the 3D/4D rotation energy is split into at least two diferent structures. The inner core of 3D/4D rotation energy is directly attached to the 4D fux. The light green (Fig. 14b) 3D/4D
37
rotation energy is called free fux, because it is able to interact with external quanta and it also connects, only with one dimension of the 4D attached fux. There is one open question: Does, in Fig. 14, the dark green area of 3D/4D-fux also represent true 4D fux energy or is it just a 3D/4D-wave at a higher wave-number? This is very difcult to decide because the relation of 1 4D quantum to 5 3D/4D quanta is close to the number Z, we defned in chpt. 4.3.1 (25). Further on 5 3D/4D quanta closely correspond to one 3D/4D quanta released in each of the 5 rotation dimension in 6D.
11.1.4 6-Li 7-Li 9-Be 10-B 11-B 12-C 13-C 14-N 15-N 16-O 17-O 18-O 19-F
4D orbits 1 1 1 1 3 2 3 3 3 3 3 5 5
Remarks about orbit flling 1 1 1 1 1 1 2 2 2 1 2
20-Ne 21-Ne 22-Ne 23-Na 24-Mg 25-Mg 26-Mg 27-Al 28-Si 29-Si 30-Si 31-P 32-S
4D orbits 5 5 7 7 7 7 7 7 7 7 7 7 7
1 2 2 2 1 2 3 4 3 4 5 5 5
These two tables (32,33) have been compiled using gamma-spectrum analysis. Up to 32S we see only one orbit pair that is active. Ca43 seems to be the frst nucleus that is able to fll the frst (7,7,x,y) pair of the 4D coupled orbits. Thus, Ca43 in the gamma-ray analysis, the frst time, shows the characteristic of a strong denominator of 49. 40-Ca 42-Ca 43-Ca 44-Ca
Table 32 shows 4D orbit numbers of low Z isotopes
7 7 7 7
5 5 7 7
2 4 3 4
1 1 1 1
Table 33 shows how the diferent calcium isotopes fll the 4D orbits.
Two orbits with the same 4D quantum number usually show a n 2 behavior in the gamma line splitting.
11.1.5
Simple physical/logic conclusions of 4D space
In dense 4D (6D) space there is no time, at least no time that can be separated from any dimension! It is obvious that below the radius of equivalence of E/H energy (de Broglie) the horizon of classical 3D+t physics ends, because you can no longer associate time/location with a concrete value of E/H. In 4D (6D) space everything the standard model invented about symmetries is lost. Also 3D+t pseudo particles like quarks seem to ft very well into the 4D model. They correspond 1:1 to the three hidden (3D/4D) spheres of the classic 4D model – which are based on the 4 th “a” dimension. (This is also the implicit assumption Mills [2]chpt. 38 makes in his quark calculations!) Sample: The proton charge radius: The classic de Broglie radius of the proton is 1.317 fm. or in the light-like frame (see Mills [2]) it changes from 1.317 fm. to 1.317/ 2π. From this sample calculation it should be clear, that the charge radius of the proton should be 0.2095 fm. and not the actually measured one of 0.84087 fm. But if you look at 4D space you will immediately notice that the surface of the charge fow is 4 time larger, the same holds for a radial movement along all 4 3/4D sub-spheres. Now, we are already very close to the measured radius. A good example to explain the 4D radius is He-4. It looks like 4-He does not need to make all 4D rotations. Further its mass seems to be to low for a full wave, that covers the whole 4D subspace. Additionally He-4 has no free 3D/4D fux. Thus it's charge-radius can be modeled with simple fux logic. The helium charge is fowing on a toroidal 2D/4D surface and not on a 3D spheric one. If you use a torus for modeling the 4-He and the proton charge radius, then the proton and He4 charge radii do very well agree.
38
mamu He4 He4 from particles compression ratio (CR) torus area r*r → r * CR(1/2) measured He4 chg radius half of He4 radius Measured proton radius compressed proton radius relative error
4'002'603.25 4'032'979.91 0.992468 0.996227 1.6753 0.83765 0.8408739 0.8377011567 0.000061
Table 34 shows the derivation (frst try.., better in table 22) of the Helium charge radius according basic fux laws. The compression factor of matter from particles to He4 is 0.992468. It works on the area of fux, which for a torus is proportional to r2. Thus the radial compression is 0.992468 (-1/2). This approximation (compression of proton radius by 4-He compression factor) is very exact, if we assume that in each dimension the fux needs double the path length.
Table 34 He4 and proton charge radius.
11.1.6
How to refne the model ?
3FC He4 4D particle mass *(1-FC) alpha/2phi (2FC) One 3D/4D quanta 5 3D/4D quanta 4D to 4D/5D surface 4 quark splin-flip units 1/3 of flux difference 4*alpha^2/pi()^2 (1FC) one charge quantum Excess flux of electron in neutron ¼ of electron excess flux
0.9971130759 11642.907 0.0011614097 2341.971 11709.855 -66.949 67.384 -22.316 0.0000215820 21.769 87.309 21.827
If we apply our building rule, with freeing one 4D quanta together with 8 3D/4D quanta for each Z/2 and afterwards divide the rest by 4D quanta amount to get the added 4D quanta, then we get the correct orbit numbers, we see in the gamma-ray analysis. But if we look at the fux evolution, we must notice, that for 5 (not 8) added 3D/4D quanta one new 4D quanta will be substituted.
Table 35 possible quantum fractions (mamu) What is the reason behind this behavior? One released 4D quanta of energy is a little bit (-66.95 mamu) smaller that 5 3D/4D quanta. Despite this reduction ( 5 3D/4D → 1 4D quanta) needs energy it happens. Why? There are many possible explanations for this process. The 4D surface is fve times smaller than the inner 4D/5D surface. This would nicely ft with the amount of 5 bonds needed for one added quanta. We could also think, that the 3D/4D-fux just migrates to a bigger (5D) surface. But this process needs fux and we do not know from where it will be delivered. The best explanation for the diference between the sum of 5 3D/4D quanta compared to 1 4D quanta is the change of 4 quark like (= 4D fux node weight), spinequivalents, which would be adequate, if the added quantum increases, by one base unit. To insert one new 2D/4D wave (4D quanta) 4 additional nodes must be created.
12
Initial summary
For simple nuclei (like Li6, Li7, Be9) it is easy to derive their basic properties. The presented model also explains, why He-4 has no (low energy) gamma levels at all, because there is no free 3D/4D fux (holes!) that could couple. Beryllium 8 is well known to be unstable, what also corresponds with the result of our calculation (8 digits exact, if we relativistically (by γ*2 ) compensate 2 unbound 4D dimensions), because the measured mass is below the needed one for 2 full 4D orbit structures. Our investigations did show that in general two adjacent He-4 4D fux orbits generate a repulsive 2D/4D fux term. (Can be explained by the structure of 4D space) In this case the produced negative (=missing) 2D/4D fux caused by charge correction is -87.003 mamu's for all four protons together. Like He4, Be8 has no free 3D/4D fux too. With this knowledge it should be possible to calculate the total repulsive force and also the general infuence of charge on the radius of a the 4D orbit. Carbon with an odd number of 4D fux quanta (like He4) has no 2D/4D fux term. But keep in mind that this term works at the 7&8th digit and there might be a second order correction! If we go to C13 we encounter the same problems as for Li7. The excess energy (2/3) is easy to predict, if we assume one more 4D quanta, but otherwise, we have to do painful work by mapping bonds into the 4D
39
space. There are three possible stable confgurations. To predict, which one is the true one, nature prefers, is currently not possible without looking at the gamma lines. Using our model, together with the known gamma lines, will give strong support for further mathematical modeling. If one follows the rule that 3D/4D fux can only occur in quanta of 780.657 mamu (possibly divided by the orbit splitting number (2,4) induced by 2/4 combined He-4 orbits), then it is easy to derive the possible states. But the fner the splitting is, one applies, the more potential isomer structures will result. The frst C13 gamma line is easy to fnd it occurs at 7/10 of the coupling between a double P-N bond and a double strength He4 attached fux. The error is far below 1/1000. An other consequence of these fnding is that there is nothing left from the standard model. There is no Yukawa potential no electro weak force. The so called strong nuclear force equivalent has two components, which can be measured by the 3D/4D = 2FC Flux Compression constant and the 4D =3FC compression constant. The electric force is just degraded to balance the 4D(6D) fux of matter = compressed magnetic fux-lines. Everything is now expressed by diferent compression/expansion constants for the various forms of fux energy. And last, for energy calculations, there are only three base nature constants remaining gravitation and alpha and h and particle masses. This does not imply that there are no potential energy terms in the 4D model. But 4D(6D) space has no classical center of mass and no classical symmetry and these terms (representing stored potential energy) possible are just oscillating. Because this model is based on the diferences of masses, we did not fnd any efect based on the amount of energy stored in the external coulomb feld. But for larger nuclei the total “chemical” potentials may sum up to an electron mass, which should be visible. Indeed experiments do show that e.g. Gold has no discrete electron ionization levels on the k-shell level. But Gold has low energy gamma states. Thus it is easy to predict that in heavy nuclei the lower electrons are a part of the nucleus structure!
13
Final summary and outlook
Nuclei are a special state of matter. Particles (n-p-e), that join to form a nucleus, release two diferent quanta of energy. The 4D(6D) structure (+ fux holes) based on SO(4)-equivalent curved space has been verifed by the successful matching of hundreds of nuclear gamma lines. A simple model can be used to derive the nuclear orbit (4D quanta) numbers, that nicely fts with many unexplained features of nuclear behavior like: Missing gamma line of He4 instability of Be8, last stable nuclei Pb. Long metastable U238. The 4D fux-compression constants can also be used to calculate the magnetic moments and the massrelations between charge/neutral kaons/pions. The energies and relations between gamma-lines can be consistently explained by the laws of 4D physics. We did show a method to exactly model the proton energy as a magnetic fux equivalent. The known rules work fne for symmetric systems. It is obvious from our model and Mills[2] modeling, that the standard model is outdated because it uses the classic space/time metric, that cannot be applied to dense matter/space.
13.1
Outlook
We did just uncover a new version of nuclear &particle physics. Most formulas used are simple and reliable, but do not allow the modeling of dynamic behavior. The world of physics needs a new generation of people that is willing to explore the true space of physics to model the basic parts of our world. We need people that are fexible enough to construct their own opinion based on facts not on 100 years of followers believe. First a 4(6)D equivalent model (static time free and dynamic) for Maxwell physics must be constructed. Further we must explore all connections of SO(4) to the current models (SU(2), SO(3) x...) that can be successful projections of certain 4D physics aspects. Other model(s) for gamma-line matching must be investigated. Old experiments must be reevaluated to refect the correct relativistic metric. Also hidden 4D resonances must be counted in.
40
There are enough facts on the table to say, that the presented 4(6)D model is sound. If the world waits and wants to spoil an other 10, 20 years, and two more generations of physicists, in developing nonsense models or crazy technologies like hot fusion, then let them do it. The author will switch back to the LENR feld and will try to use the presented model to calculate some needed quantities to enable “low energy fusion”.
41
Appendix A tables 10
Flux loss in o/oo
9 8 7 6 5 4 3 2 1 0 2-H
10-B 22-Ne 34-S 44-Ca 54-Cr 64-Ni 73-Ge 82-Kr 92-Zr 100-Ru 109-Ag 117-Sn 126-Te 130-Ba 143-Nd 155-Gd 164-Dy 173-Yb 183-W 192-Pt 204-Hg 16-O 28-Si 40-Ar 49-Ti 59-Fe 68-Zn 78-Se 86-Sr 96-Mo 104-Pd 114-Cd 121-Sb 130-Xe 138-Ba 150-Sm 156-Dy 168-Er 178-Hf 188-Os 196-Hg 208-Pb
Table 36 Total 3FC/2FC/1FC flux-loss by the stable nuclei
10
Flux loss in o/oo
9 8 7 6 5
4D flux
4 3 2 1 0 2-H
10-B 22-Ne 34-S 44-Ca 54-Cr 64-Ni 73-Ge 82-Kr 92-Zr 100-Ru 109-Ag 117-Sn 126-Te 130-Ba 143-Nd 155-Gd 164-Dy 173-Yb 183-W 192-Pt 204-Hg 16-O 28-Si 40-Ar 49-Ti 59-Fe 68-Zn 78-Se 86-Sr 96-Mo 104-Pd 114-Cd 121-Sb 130-Xe 138-Ba 150-Sm 156-Dy 168-Er 178-Hf 188-Os 196-Hg 208-Pb
Table 37 Total 3FC/2FC/1FC flux-loss by the stable nuclei in relation to 4D flux-loss
10
Flux loss in o/oo
9 8 7 6 5
4D flux
4 3 2 1
3D flux
0 2-H
10-B 22-Ne 34-S 44-Ca 54-Cr 64-Ni 73-Ge 82-Kr 92-Zr 100-Ru 109-Ag 117-Sn 126-Te 130-Ba 143-Nd 155-Gd 164-Dy 173-Yb 183-W 192-Pt 204-Hg 16-O 28-Si 40-Ar 49-Ti 59-Fe 68-Zn 78-Se 86-Sr 96-Mo 104-Pd 114-Cd 121-Sb 130-Xe 138-Ba 150-Sm 156-Dy 168-Er 178-Hf 188-Os 196-Hg 208-Pb
Table 38 Total 3FC/2FC/1FC flux-loss by the stable nuclei in relation to 4D flux-loss and 3D/4D flux loss.
42
Appendix B “New” constants used throughout this paper: (Second value =.) Energy conversion constants: 3D/4D - 4D Flux capture 3D-3D/4D Flux capture 2D-3D/4D Flux capture
3FC 2FC = 1 - (α/2π) 1FC = 1 -16*(α/2π)2
1D/2D-/3D relativistic fux capture γ* = 1/(1+πα2) [ 1D/2D-/3D relativistic fux capture γ* = (1– πα2)
For mass reduction = 0.9971130759339820 = 0.99883859026758 = 0.99997841803894
for fraction/amount 0.00288692406602; 0.00116140973242; 0.00002158196106;
= 0.9998327339..
4D → 2D reduction of 3FC = 3FC/γ*2
= 0.9998327059.. ] = 0.99744672603801
Conversion constant (1 mamu → eV) CME Ex4D Eccentricity of 4D space
= 931.494095 eV = (1.6180339887 – 1.6)/2π = 0.00287019845321
3FC converts 3D/4D energy into 4D energy. 3FC = (1 - Ex4D/2FC5 ) This new constant converts 3D/4D mass/fux into its 4D equivalent mass/fux. It defnes the amount of energy that will be released by this process in 3D equivalent mass. 2FC converts 2D/3D energy into 3D/4D energy. This constant converts 3D measured mass/fux into its 3D/4D equivalent mass/fux. It defnes the amount of energy that will be released by this process in 3D equivalent mass. 1FC converts 2D/3D energy into “+,-” 2D/4D potential energy. This new constant converts 2D/3D measured charge-coupled mass/fux into its 4D equivalent chargecoupled mass/fux. It defnes the residual amount of energy, that will be released/accepted by the frst two processes in 3D equivalent mass. 1 mamu = 931.494095 eV = CME (converts mamu in eV) γ* = 1/(1+ πα2); see [2]36.15 relativistic mass/energy correction for 1D/2D -3D Conversion constant for photon energy. We here use the term 3D for any quantity that lives in classical physical space with 3 space dimensions and time as the fourth dimension. The term 3D(3, 1) space is meant to cover 3 Euclidean space dimension plus 1 time dimension. The term 4D(3, 1) space is meant to cover 3 curved space dimension plus 1 radial dimension. The term 4D space is used as a simplifcation for all possible 4D space (sub-) structures, that include 4 rotations. Mathematically spoken this needs 6 space dimensions. N-P is used for better readability instead of n-p (e.g.: neutron – proton bond).
43
[1] 1995: Mills, Randell L., The GRAND UNIFIED THEORY of CLASSICAL QUANTUM MECHANICS, Technomics Publishing Company, Lancaster, PA, (1995). [2] 2016: Mills, Randell L., The GRAND UNIFIED THEORY of CLASSICAL QUANTUM MECHANICS;ISBN 9780-9635171-5-9 (2016) online. [3] Mills, Randell L., PHYSICS ESSAYS 21, 2 Exact classical quantum mechanical solution for atomic helium, which predicts conjugate parameters from a unique solution for the first time ( 2008 ) [4] Peter H. Richter: Die Theorie des Kreisels in Bildern, Fachbereich Physik und Institut für Dynamische Systeme Universität Bremen (1990) [5] F. Klein, A. Sommerfeld: Über die Theorie des Kreisels in vier Heften, Teubner, Leipzig (1910) [6] H. A.Haus, “On the radiation from point charges,” American Journal of Physics, 54, (1986), pp. 1126-1129. [7] R. Hasty et al., “Strange magnetism and the anapole structure of the proton,” Science, Vol. 290, (2000), pp. 21172119. [8] Andrey E. Miroshnichenko1 et al., Nonradiating anapole modes in dielectric nanoparticles, DOI: 10.1038/ncomms9069 (2015) [9] Chiu Man Ho and Robert J. Scherrer, Anapole Dark Matter, Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, arXiv: 1211.0503v3 (2013) [10] Gertrud E. Konrad Measurement of the Proton Recoil Spectrum in Neutron Beta Decay with the Spectrometer aSPECT: Study of Systematic Effects ; Phd Thesis. Johannes Gutenberg-Universität in Mainz (2011) (page 18) [11] IAEA Livechart page: https://www-nds.iaea.org/relnsd/vcharthtml/VChartHTML.html (online) [12] Klee Irwina, , Marcelo M. Amaralab†, Raymond Aschheima‡, Fang Fanga§, Quantum Walk on a Spin Network and the Golden Ratio as the Fundamental Constant of Nature aQuantum Gravity Research Los Angeles, CA bInstitute for Gravitation and the Cosmos, Pennsylvania State University, University Park, PA (year ????
[email protected]) [13] Bernard Schaeffer, 7, rue de l’Ambroisie, 75012 Paris, France E-mail:
[email protected] Electromagnetic Nuclear Physics. ADVANCED ELECTROMAGNETICS AES proceedings 2016 (pp. 204) [14] Jack Nachamkin, FORCE-FREE TIME-HARMONIC PLASMOIDS, PILLIPS LABORATORY Propulsion Directorate DTIC O LC2T8199 ELECTE SOCT2 81992 N 0 AIR FORCE MATERIEL COMMAND EDWARDS AIR FORCE BASE CA 93524-7001 [15] B.I. Ivlev Conversion of zero point energy into high-energy photons Instituto de F ́ısica, Universidad Auto ́noma de San Luis Potos ́ı, San Luis Potos ́ı, 78000 Mexico, Revista Mexicana de F sica 62 (2016) 83–88 [16]Boris I. Ivlev , X-ray and neutron emissions by shock waves , Instituto de F ́ısica, Universidad Auto ́noma de San Luis Potos ́ı, San Luis Potos ́ı, 78000 Mexico , https://arxiv.org/abs/1704.01837v2
44
