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Gudrun Kalmbach HE*

- Department of Mathematics, Mathematics Professor, Inventor of MINT, Germany

**Received:** July 11, 2018; **Published:** July 19, 2018

***Corresponding author: **Gudrun Kalmbach HE, PF 1533, D-86818 Bad Woerishofen, Germany

**DOI:** 10.26717/BJSTR.2018.07.001448

In Physics today it is accepted that the findings on the particles properties require that the old 4-dimensional vector spacetime description is not adequate. In contrary to the known string theory I work with octonians and double up the spacetime dimensions as also done for the physics phase space. I describe in [1] deuteron states through the known properties for three of the three basic four basic interactions or forces in physics. Field quantum’s for this are the weak bosons of the weak interaction, gluons of the strong interaction, rgb-graviton whirls (newly added) for a gravitational action, phonos for heat transfer. Stochastically can a six-fold energy exchange between a deuterons inner space and its environment occur. This is more complicated as in biology or chemistry. Using only one main factor: biology is based on DNAs and evolution of systems in time. Chemistry is based on the electron number in atoms shells which is also the proton number of atomic kernels AK. The neutron content of AKs may also have a chemical influence. Now physics treats its systems P as a portion of the universe under investigation. This means for a mathematician that they accept what experiments tell them.

This is the first mistake: quantum measurements mean that a measured system P has to be prepared before the measurement like a patient before a medical operation. Then the measuring apparatus A is applied to P. It is known that P can then change its state by being measured. The best-known example is the spin measurement in the Stern-Gerlach experiment. My octonian view is that quantum measurements are also done without such an external A. The new measures are Gleason frame GF triples like the three spin coordinates in S = (sx,sy,sz) in the Euclidean xyz-space. In octonian coordinates, named 0,1,...,7 these are 123 and 4 is for the time coordinate. As listed in [1,2] beside the space measuring apparatus everyone experience seven octonian GF: 145 is for the electrical induction. This is also my model for new measuring systems A: an electrical charged loop is rotating in a transversal crossing magnetic field and as measured output the induction vector is generated, orthogonal to the magnetic momentum and a loop.

For the observed neutrino oscillation, I suggested a mass triple GF 247: instead of the spin vector length as scalar, the three possible
masses for the e, mu, tau neutrinos are used with a common weight which for every GF can be measured like the spin length |S|. Such mass triples may also be useful for quark systems. All fermion series are provided with 6 possible masses. Mathematically I treat this with the unused symmetry S4 in physics, the permutations of four elements. My second claim is that not only the use of quantum measurements has to be extended by octonian GF’s, but also the range of symmetries of the standard model: it can be extended for gravity. Added are in [1,3] the symmetry of Moebius transformations MT on a 2-dimensional Riemannian sphere S_{2}. Concerning the symmetry S4, one needs three reference points, called 0,1,∞. In a central projection, a harmonic middle point can be constructed which is taken as a variable complex number z. Then use a multivalued function for measuring fermionic masses, the complex cross ratio. The S4 gives six MTs which can be listed as complex fractions z, 1/z, 1-z, 1/(1-z), z/(1-z), (1-z)/z. In octonians I use a MT of order 6 related to the general relativistic factor of Einstein’s Schwarzschild metric in the form (r-1)/r, r radius.

This acts for a Higgs field as decay operator. I call it a Higgs compass with a needle which can only change in discrete steps using the sixth roots of unity. Its six-fold numerical values appear not only for fermion masses but for the six color charges of QCD, for the six electrical charges and in my model also for six energies. Reducing physics to one main factor: these six energies have to be studied in experiments. Biological version: use the Feigenbaum equation for generating them in a bifurcation from the octonian e0 vector, set them on six energy coordinates: 1 (123 triple) is for electrical charge and potential, 2 (246) is for heat and entropy in a volume, 3 (347) is for rotational energy with the GF tirple L = rxp, L angular momentum, p = mv momentum; 4 (145) is for time and magnetic (momentum), 5 for barycentrical mass, 6 for frequencies. The 7th octonian coordinate (167) is rolled as a U (1) circle for light and exponential or periodic functions.

For including gravity in an extension of the standard model also the geometry has to be extended. Einstein added in his special relativity SR the affine Minkowski metric. This must be projective extended. The QCD geometry is a toroidal product S_{3}xS_{5} fo a 3- with a 5-dimensional sphere. S_{5} can be normed to the complex 2-dimensional space CP_{2} with boundary S_{2}. It is taken as inner
space for nucleons and deuteron. Mathematically I describe then
the exchange of field quantums inside between the observed
three or six quarks in the prism Figure 1. It is possible to make a
switchboard where young researchers can list which action or
superposition of actions shall take place. This changes the state of
deuteron. The CP_{2} projection is gravity GR bound. My rgb-gravitons
whirls are inside CP_{2} as neutral color charge red, green, blue whirls
(superposition). They fix three observable points for quarks. For
the switchboard is important that the MT symmetry of the quark
triangle generates a strong interaction SI rotor. There are three
driving rotors (acting like motors): the SI rotor which is also for
the energy exchange of deuteron with its environment, carrying the
six color charge caps in the hedgehog figure; the weak interaction
WI rotor is generating Euclidean spin co-ordinates while the SI
rotor (GF triple 356) generates barycentrical coordinates for mass
barycenter’s (GF triple 257) (Figures 1-4).

**Figure 3: **rgb-graviton whirls at left, at right deuteron contraction/expansion of radius, middle part fixing the three quark
barycenters, below this: WI exchange of isospin, next figures below: the hedgehog, the six roll mill, the switchboard, Higgs
compass, wheel.

The GR action acts in addition as a deuteron radius S_{2}
contraction together with a heat expansion. This has in addition to
the rgb-graviton whirls an GR/EM potential motor as third driving
force (EM: electromagnetism). I mention that a unification of GR
and EM fields was published by E Schmutzer [4]. His common field
can come from the former S_{5} sphere of the QCD geometry. GR and SI
are not independent but overlap in the nuclear range geometrically.
The field quantums act on deuteron states which means that the
three driving motors GR/EM, SI, WI generate in the model of [1] a
finite number of possible states; SI uses gluon exchanges and the
SI rotor, WI uses for deuteron kernels the inner u-quark decay by a
W+ boson into a d-quark where the W+ is absorbed (in pairing the
six quarks) by an oppositely (on the x-, y- or z-axis) located d-quark
which generates an isospin exchange between the deuterons
proton and neutron, and GR/EM uses a GR rgb-graviton whirl or
heat energy exchange between deuterons inner CP_{2} space and its
environment, and changes the deutron Bohr-radius in three values
small-middle-large (Figures 5-8).

**Figure 6: **1-6 energies, 12, 16, 26, 34, 35, 45 gluons. 15, 23, 46 W+ bosons, then GF octonian measures.

For biology or medical considerations, the model has the
energy bifurcation as biological Feigenbaum equation (Pascal
ellipse below), the hedgehog for vectorial source/sink polar
caps energy exchange between an inner part of a system with
its environment, for chemistry a tool chest with a switchboard
macroscopical constructible prism model like those for molecules.
Parts of the model are constructed for a three motors driven flow
called six roll mills [4], for the WI motor as wheel, for the SI rotor
and the potential generated GR/EM contraction/expansion can be
demonstrated by a possible S_{2} projection in a plane E where an MT
changes the distance between S_{2} and E [5]. From [6] is taken that
the WI motor runs with a different speed than the SI+POT motors.
For getting a common group speed for the nucleons inner dynmaics
it is assumed that the Euclidean WI coordinates are in special
relativistic SR motion against the SI/GR coordinates’. The SR speed
can come from the observed mass rescaling of the u-quarks when
measured as GF weight in WI coordinates. There are 5 videos for
the model’s inner dynamics available.

- G Kalmbach E (2017) MINT-WIGRIS, MINT Verlag, Bad Woerishofen, Scholars’ Press, Beau Bassin.
- G Kalmbach HE (1997-2017) (Chef-Hrsg.) MINT (Mathematik, Informatik, Naturwissenschaften, Technik), MINT Verlag, Bad Woerishofen, p. 1-36.
- G Kalmbach HE (2017) Deuteron States. Nessa Journal of Physics 1(2): 1-17.
- Internet video under YouTube: Moebius Transformations Revealed (2014) MINT, PF 1533, D-86818 Bad Woerishofen, Germany.
- T Poston, I Stewart (1978) Catastrophe theory and its applications, Pitman, (see the 6-roll mill for deuteron integrations)London, Uk, p.3.
- E Schmutzer, Projektive einheitliche Feldtheorie, Harry Deutsch, Frankfurt (2004) (the unified electrical and gravity fields is here 5-dimensional with three 4-dimensional projections similar to the above octonians in [1] into spacetime (e1, e2, e3, e4), the deuteron space (e2, e3, e5, e6) and a scalar field (e1, e4, e5, e6).

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