Clifford Algebra and Maxwell-Dirac theory.

  • Maxwell-Dirac Theory and Occam's Razor: Unified Field, Elementary Particles, and Nuclear Interactions Paperback – July 1, 2019


    by András Kovács (Author), Giorgio Vassallo (Author), Francesco Celani (Author)


    "We introduce and use the space-time Clifford algebra, showing that only one fundamental physical entity is sufficient to describe the origin of electromagnetic fields, charges and currents: the electromagnetic four-potential. This simplified electromagnetic model turns out to be an improved understanding of electromagnetism. The obtained electromagnetic Lagrangian is the simplest possible relativistic Lagrangian formulation. Quantum mechanical relations follow naturally from this model, and we derive the electromagnetic formulation of the Dirac equation. The spinor field is shown to correspond to electromagnetic energy-momentum, and the complex-valued probability density is shown to correspond to electromagnetic Lagrangian density. This initial part of the book completes the theory initiated by Maxwell and Dirac.

    The structure and dynamics of the electron are described next, showing how its mass originates from the electromagnetic field energy and showing how mass varies relativistically. Using this model, we derive the charge quantization mechanism. This part fulfills Einstein's wish for understanding the electron before attempting to understand more complex particles. Through the study of electron dynamics, a more elaborate understanding of the Heisenberg uncertainty principle is developed, which is indispensable for understanding nuclear interactions.

    The book concludes by showing how the same model can be applied to describe nuclear forces and nucleons, and a very large set of "anomalous" or unexplained experimental data suddenly make sense."


    https://www.amazon.com/Maxwell…aQ8HZjLOL883PMURR2HKs10Tk

  • In the book, in par 1.4.4, is proposed an unusual connection of a scalar field with the Feynman's concept of "unworldliness":


    1.4.4. The scalar field and the Feynman concept of unworldliness

    ...

    "Consequently in this approach the scalar field can be interpreted as a useful function, with a zero average value, that “measures” a local

    “violation” of the Lorenz gauge".

    ...



    Scalar physics has been the subject of a recent publication on Journal of Physics (Conference Series):

    Unravelling the potentials puzzle and corresponding case for the scalar longitudinal electrodynamic wave


    "However, these facts have understandably, albeit unfortunately, lulled contemporary physics into

    the false security of the perceived notion that the theoretical structure of modern classical

    electrodynamics is now written in stone and there is no compelling reason, empirical or theoretical, for

    considering the possible need for its re-evaluation or alteration."


    see also:

    Generalized Maxwell equations and charge conservation censorship (Modern Physics Letters B).

  • I really thought Wyttenbachwould rise the the bait offered above. He's a chap who knows a Clifford torus from a panama hat.


    Unluckily people doing such work only seek for a more general representation of SM physics. This usually gives marginally more insight only. If I read space/time algebra then I see that the paper does not deal with dense matter, where we don't need space-time algebra as time only occurs as a frequency relation with an orbit radius. Or simply said particles feel no time as man knows since Aristoteles...

    But we need this old style work too, latest when we want to model the interaction with a dynamic environment.


    One last thing: Clifford Algebra and Clifford torus share the creators name only ...

  • blondes know even more


    Different Clifford hair colour

    but same flawed Standard Model


    A considerable amount of the standard model's three-generation structure can be realised from just the 8C-dimensional algebra of the complex octonions. Indeed, it is a little-known fact that the complex octonions can generate on their own a 64C-dimensional space. Here we identify an su(3)⊕u(1) action which splits this 64C-dimensional space into complexified generators of SU(3), together with 48 states. These 48 states exhibit the behaviour of exactly three generations of quarks and leptons under the standard model's two unbroken gauge symmetries. This article builds on a previous one, [1], by incorporating electric charge.


    https://www.researchgate.net/p…ensional_algebra/download

  • Clifford algebra is definitely the best mathematical tool in theoretical physics


    https://arxiv.org/pdf/1611.09182.pdf


    This morning I vent through up to chapt. 5. The author explains/shows that all known SM math can be generated from C ⊗ H. This is nothing new as already ANDREW J. HANSON did show this in his book about quaternions. But the paper is much more elegant and complete.


    The main reason to comment about this is the fact that mathematics/algebra is just a framework of complex logic that allows to elegantly express relations between physical phenomena. But already on page 4 the authors shows a graph that is based on the most fundamental theory of mathematics (only a few people know) called category theory. It's basic for people that do graph theory one of my favorites.

    Real meaning of math tied to facts must be expressible as a graph and actions of changing a graph position. One method to reason about complex facts are PRT nets, we e.g. used to model the tcp/IP protocol.


    As the paper shows, all effects covered by SM can be mutually transformed using the above groups. As a direct conclusion we can say if nobody could find an exact match between physics (measurable reality) = theory and the so far usingd (SM) math, then nobody ever will find it using classic known math, what ever you call it. Dirac spinors Weyl spinors, bending Lorenz group ...


    The reason for the current SM failure state, from the math point of view, is the missing correct mapping of physical facts to the basic logic of connecting the math. Nevertheless SM can produce a kind of directory for measured energies, but fails to explain the source/reason of the energies. To be fair in the 3D,t = kinetic case it can do a bit more down to the medium precision you get with a radial potential.


    SO(4) uses the "x" connection what leads to amore complex symmetry, than just the ⊗ connection. It's a small change that allows to deal with the r x r potential of internal magnetic fields.


    Why the field was doomed with blindness, now for 80 years, is a mystery for somebody like me that did strong logic work for quite a long time. But my guess is that the initial success of QM given the 1950 data did lead to a complete false judgment of the physical/modeling reality.

  • Wyttenbach

    "The reason for the current SM failure state, from the math point of view, is the missing correct mapping of physical facts to the basic logic of connecting the math. "

    Can you illustrate, using intuitive concepts, the main points of your electron model ? Is it in agreement with Mills theory ?

  • Can you illustrate, using intuitive concepts, the main points of your electron model ? Is it in agreement with Mills theory ?


    Mills models the electron as a disk what is unphysical but if you use proper math and due to symmetry you will always find a working result.


    In my "universe" the mass is all EM mass an ideally flows on SO(4) orbits (along Clifford detours surface). Mills ideas of two generating source currents (needs for two magnetic moments) staying on a simple connect surface is not possible as there is no medium that supports crossing currents. On a torus you can define an orthogonal two current that in the projected plane runs along the diagonal and looks like a single current.

    The new feature of NPP2.0 is the splitting of mass into 4D relativistic mass 3D/4D rotating mass and perturbative mass. The electron contains no 3D/4D mass and its mass distribution is highly asymmetric its looks, in a projection, like a flat torus.


    The strength of the model is that we can exactly show that e.g. fussing D-D to 4-He exactly removes known amounts of 3D/4D mass and perturbative mass.


    In the next update I will show the mass/charge/force relation for the proton that also works for the electron.

  • Clifford algebra is neat and as geometric algebra really the appropriate way to formulate space-time equations in maths.


    It is a cleaner better motivated way to express known QM (and also GR).


    It does not itself provide new physics. But, it does exactly replicate SM physics as experimentally tested with a more intuitive framework.


    So: the question for those wanting more, is does there theory quantitatively reproduce SM physics. There is an also lot of this proven from experiment. My first test for a new claimed UFF, passed with flying colors by Clifford algebra reformulation, is can you derive existing equations and qualitative phenomena (e.g. SM particles) from it?


    The next UFF test (failed by Clifford algebra) is does the theory make some definite quantifiable testable prediction different from SM?


    Those proposing alt theories would do well to consider these two tests: you get new physics only if both are passed. If just the first one is passed you may have a reformulation that hints at something new, without actually being new. If only the second is passed you have a theoretical construction not grounded in reality - not physics.

  • Wyttenbach

    It's possible to compare your SO(4) theory to the Cl3,1 approach proposed in the book "Maxwell-Dirac Theory and Occam's Razor"?

    Mass and spin in the book are a direct consequence of the Zitterbewegung current generated by an elementary charge that rotates at light speed, coupled to a magnetic flux phi=h/e. Inertia and relativistic mass are strictly related to the charge momentum p=eA.

    THHuxleynew

    Before trying to understand SM, are we sure that we have well understood some very basic elementary concepts as mass, charge, spin, inertia? Have we a realistic, intuitive electron model ?


    ----

    this extract from D. Reed paper well illustrate one of the conceptual foundations of the book:


    "Consequently, we propose the second directive –confluent with the first – to make the potentials

    completely independent of one another, resulting in a unique purely “gauge-free” electrodynamics. This

    novel prescription also closely follows the principle of Occam’s razor, which dictates that a system of

    scientific knowledge should not introduce concepts or entities that are not strictly necessary,

    emphasizing the simplicity and conciseness of the model. Consequently, a wholesale reinterpretation

    of Maxwell’s equations is proposed without gauged potentials. Also, according to Occam’s razor, this

    reformulation must also of necessity, invoke the constraint that the electromagnetic 4-potential, as per

    the Minkowski space-time prescription, should be considered as an inseparable single unit entity. "

  • Here below some of the key points presented in the book:


    1) Does exist a a scalar field that is the four divergence of the four electromagnetic potential

    2) Charge density is the partial time derivative of the scalar field

    3) Current density vector components are the partial space derivatives of the scalar field

    4) D’Alembert equation can be applied to both scalar field and charge density

    5) Electron mass is the angular frequency of a rotating elementary charge along a circumference which length is equal to Compton wavelength

    6) Electron charge follows an elicoidal motion that can be encoded with a single spinor of Cl(3,1).

    7)The concept of relativistic mass is easily derived from the electron charge elicoidal motion.

    8 ) The electron charge is distributed on the surface of a sphere that follows a circular or elicoidal motion.

    9)The value of the elementary charge is equal (in natural units) to the square root of the radius of this sphere with the radius of the charge orbit

    10) The electron spin 1/2 is the quantized component along an external magnetic field of electron angular momentum (=hbar)

    11) The elementary charge e is always associate to a quantized magnetic flux phi=h/e

    12) The electron charge has a pure electromagnetic momentum eA equal to its mass in natural units

    13) Newton law F=ma can be easily explained inside the theory framework

    14) The charge moves at speed of light

    15) Heisenberg uncertainty principle has a simple geometric interpretation

    16) Ultradense hydrogen (and consequently AHE and LENR experiments) may be explained with the formations of pseudo-neutrons where the proton is at center of electron Zitterbewegung charge orbit

    17) The electron model suggests a pure electromagnetic-geometric interpretationof Proca, Klein-Gordon, Dirac and Aharonov-Bohm equations

  • 8 ) The electron charge is distributed on the surface of a sphere that follows a circular or elicoidal motion.


    As I don't have the book (I can only read pdf's currently) I cannot comment about the proposed model. But anything that proposes a sphere as a base projection has not enough freedom to support a 2D x 2D current needed for the (then old Bohr!!) mass equation of the electron.

    Only a torus can do it.

    If they talk of light speed for charge.. I would like to see how they treat this relativistically without using Mills metric factors... In a real world there are no mass free quantities...

  • Quote

    Celani, as a physicist, should know that magnets do not store or make appreciable amounts of energy and in any case, no usable energy at all


    Francesco Celani looks like quite Renaissance character for me - he is consistently around most of breakthrough findings of recent era: cold fusion, magnetic motors and now unitary theory.


    For example Celani started to study Superconducting Tunnel Junctions (Ni-Pb; T=4.2K) and he found intriguing results using thick junctions in 1985 already. One of these were contaminated (by chance) from several other elements and showed behavior similar to superconductivity even at temperature as large as 77K (Ln2). It was stated a multi-disciplinary commission in order to clarify the origin of this effect. Unfortunately the results were rejected, because in disagreement with the BCS model/theory (for which the max. temperature of superconductivity stated at 32K). One year later Bednorz and Muller (from IBM, Zurich), independently (and starting from different points of view), found similar results in Cuprate oxides mixed with rare-hearts and got Nobel Prize for it.


    So that once Celani gets interested about magnetic motors, you can be sure, there is something about it. Unfortunately for cold fusion supporters the overunity is getting to be the same economical competition for LENR research, like LENR already is for mainstream nuclear researchers. We can even experience the same evasions on this very forum: the fear of losing reputation, adherence to only scientifically published reports, etc.


    Now the bullied became the bulliers itself. Why people cannot learn even from their very fresh personal history?