 # Clifford Algebra and Maxwell-Dirac theory.

• you should make geometric attempts in order to "link" them to our empty space.

It's tricky. I've drawn things like this, but they're flat 2D pictures. 3D animations is what we need. The thing on the left is trying to depict a photon. It isn't some billiard ball thing, it's a wave in space. Space waves. The thing on the right is trying to depict an electron. The electromagnetic field is a place where space is twisted. This is unfamiliar to most people, but the electromagnetic field isn't totally unlike the gravitomagnetic field. See the NASA GPB article by Tony Phillips where you can read that space is twisted. Also see the gravity probe B video:

###### Frame-dragging still image from the gravity probe B video by Bob Kahn, James Overduin, Lee Kolb, and Greg Trent
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Nice attempt to not decorrelate mathematical toughts from your geometric projections, the great Einstein knew how to do it too.

Thanks. I've read a lot of Einstein's material. I take note of what he said in his 1929 essay on the history of field theory, He said a field is a state of space. In his Nottingham lecture in 1930 he said space “remains the sole medium of reality”. It's like Clifford's space theory of matter.

• People have to start understanding the Clifford torus orbit of magnetic field lines. For a 3D torus it is simple to imagine the combined motion along two radius and inside outside. but how should this happen inside/outside ? In 3D (for a close body) its not possible without a crossing path. The Clifford torus is a single sided surface and you can move everywhere without crossing.

A classic 3D mass e.g. 2-sphere performs a complex orbit along the SO(4) Clifford torus. If it covers the full 4 rotation space, it does 8 full 360o rotations 4 front/back each. To reach the classic symmetry point (0,0,0,0) (1,1,1,1) for rotation axis! you must do 3 or 5 rotations. This also explains why we see 2,3,5 wave structure in the proton mass. (2 is an allowed short cut!) Even more interesting is that these orbits seems to follow the Fibonacci rules 1,2,3,5,8 13? The Eigenvalue of Fibonacci is the Golden ratio and its no surprise that we see the same ratio in the SO(4) physics strong force constant.

• I like Geometric Model for Fundamental Particles by Batty-Pratt and Racey“. They talked about spherical rotations, and said “our geometrical model demonstrates the difference not only between spin-up and spin-down states, but also between the particle and the antiparticle”.

###### Fair use excerpt from Geometric Model for Fundamental Particles by Batty-Pratt and Racey

The wave nature of matter and electron spin means we’re talking about waves going around and around rather than a lump spinning round bodily. Batty-Pratt and Racey said they’d “made the presumptive leap of assuming photons to be undulations of the space-time structure”. They also talked about a “theory of the continuum that purports to describe matter as a distortion of space in the manner first suggested by W K Clifford”. I like that too.

• The wave nature of matter and electron spin means we’re talking about waves going around and around rather than a lump spinning round bodily.

Good starter from SU(2). Going to SU(2) x SU(2) needs some more drawings... But you can take figure 2. and the wire as a potential. Then you immediately understand if you start to rotate the ball at equivalent rotation speed of c (in two axes) then the wire will wind up or what in reality happens it detaches from the ball as the relative speed of the incoming wire should be > c.

• The Eigenvalue of Fibonacci is the Golden ratio and its no surprise that we see the same ratio in the SO(4) physics strong force constant.

For those who are interested in basic Matrices..determinants

Fibonacci and Clifford Torus..golden ratio,3/5.. and SO(4)

• Ok I tried to motivate further for why the multiplication of the fields yields a QM correspondance. here is a new addedum of paper2.

Assume that we have a standing wave with source terms running at the speed of light. I will assume that

this is the trapped photon.

If we now ask to add a new Maxwellian field with sources free to move slower than the speed of light, with a fixed energy so that it is orthogonal

to the photon which probably mean that it minimizing the energy given that the new field has a fixed energy. Also this means that the forces on

this new fields source terms sum to zero.

• Did some more work. Found a solution to Dirac equation (matrix equation).

Also noted that this solution has infinite energy and norm. Another observation is that

we can allow a non-smooth solution at a spherical surfaces because the weighting function  has zeros

at spherical surfaces. Also I added an idea that confined fotons give rise to gravity. see paper2 link in the post above.

• Also I added an idea that confined fotons give rise to gravity. see paper2 link in the post above.

The question is how gravity is defined. I think you show how a photon adds EM mass.

The Dirac equation by definition only works with linear (energy) square (1/r2) potentials. This is halve of EM. A constant external field has been added already a long way back.

What you show looks like Mills non radiation condition with cutoffs at resonant radii in the form of x*2*π or X*r. At these radii no spherical harmonics with outgoing radial components do exist hence the product with an potential vanishes.

We should try to fit 1/r3 interaction into the model. First step - like Mills does. Calculate classic value then add magnetic correction terms.

A true full solution will connect (1/r2) potentials with (1/r3) "potentials" by the Biot-Savart Operator that is defined around a mediating virtual charge. (True "Em mass" - "Em mass" interaction with a circular solution)

• Did some more work. Found a solution to Dirac equation (matrix equation).

Also noted that this solution has infinite energy and norm. Another observation is that

we can allow a non-smooth solution at a spherical surfaces because the weighting function  has zeros

at spherical surfaces. Also I added an idea that confined fotons give rise to gravity. see paper2 link in the post above.

Unconfined photons give rise to gravity. The confinement doesn't matter.