# Clifford Algebra and Maxwell-Dirac theory.

• In Chapter4, using Clifford spacetime algebra Cl3,1(ℝ), is proposed an intuitive/simple fully electromagnetic interpretation of relativistic mass, De Broglie, Klein-Gordon, Dirac, Proca and Aharonov-Bohm equations together with some hypotheses on ultradense hydrogen and LENR.

A poster on the book has been presented at Assisi conference ICCF22.

• A poster on the book has been presented at Assisi conference ICCF22.

The Zitterbewegung shown is felt the 10th try of old school math and always they miss the magnetic energy because they over simplify and hope it's in the wave equation... If you move in/out of the Bohr point the forces no longer match and the sum of energies follows a non linear behavior. May be to much work for simple minds.

• with some hypotheses on ultradense hydrogen and LENR.

The poster predicts......

"

Our calculation shows the existence of a meta-stable electron state at 0.383 pm radius, requiring 35 eV and 80 eV electron energy

around a deuteron and proton, respectively?

Is there any spectra evidence for 35 ev and 80 ev yet?

• Hi Robert,

Good question about the spectral evidence. There was an ICCF22 presentation by Stankovic, where he analyzed the

spectrum of a special oxy-hydrogen plasma flame, which produces transmutations. The properties of such plasma

flame were well reported by Bob Greenyer in his "Ohmasa gas" series.

The new spectral lines showing up in the spectrum presented by Stankovic seem to match the nuclear Zeeman split

emissions upon the establishment of ZBW electron state at 0.383 pm radius. I will report more on that in the near

future.

• Title: EM vs QM

Date: 2019-09-23 23:00

Author: Stefan Israelsson Tampe

Sorry for the schematic math, I will post it in a nicer form later,

To want to understand QM you are not suppose to think what's the reson behind it is, but simply accept it and continue with the calculations. As I'm philosophically minded I don't accept this. Now there was some ideas that come to my attention. First an intresting approach to model maxwells equations for source terms that moves at the speed of light. The paper can be located at [Restricted Maxwell](https://www.researchgate.net/publication/320274378_Maxwell's_Equations_and_Occam's_Razor). Accompanioning this paper is a recent published book (discussed here) seam to claim that it can connect these EM theory with QED. I havent read this book yet but I still want to speculate how to model QED from this theory.

Let's begin. What's the simplest model of source terms that move with the speed of light? well that must be based on a plane wave e.g.

$$S = C \exp(i k \cdot x), |k| = 0.$$

If we assume the sources based on $S$ we would expect that using $A$ the potential, fields expressed as

$$\Phi = \gamma \cdot A = \Phi_0 \exp(i k \cdot x)$$, With $\Phi_0$ much slowly varying than the wave part. Therefore the value over one cycle is

$$\int \Phi_0(x_0 + dx)\exp(ik \cdot (x-x_0)\,dx = \int dx (x-x_0)\cdot \nabla \Phi_0(x+0)exp(ik \cdot (x+x_0)) = \sum \frac{2\pi i}{k_i}\partial_i \Phi_0 = \sum i \hbar \partial_i \Phi_0$$, assuming all $k_i$ is equal in magnitude.

E.g. multiplying a slowly varying field will essentially produce the derivative of it if viewed from some distance.

Now we will play a little with correctness but note that $\gamma_i = \gamma_i^-1$ and that we assume we could replace $k_i$ with $\gamma_i k_i$, then again the source terms satisfy the wave equation and also

$$\Phi(x) ~ \sum i \hbar \gamma_i \partial_i \Phi_0$$

But not only this, if we add an external field $\gamma \cdot B$ then we have exactly the same equation as the dirac equation with an external field but without mass.

$$\Phi(x) ~ \sum \gamma_i (i \hbar \partial_i \Phi_0 + B_i)$$

Note we are allowed to add a constant to the exponential function in the original source term as it will be removed taking the derivative. Now if we assume that the energy of the exponential physics is $m c$ in the small testvolume around a local and scale with the size $\Phi_0$ we get

$$0 = \Phi_0(exp(...) - mc)) = \sum \gamma_i ((i \hbar \partial_i \Phi_0) + B_i) - m c \Phi_0$$

Now this is a calculation on a napkin, take it for what it is worth.

• The paper can be located at [Restricted Maxwell](https://www.researchgate.net/publication/320274378_Maxwell's_Equations_and_Occam's_Razor). Accompanioning this paper is a recent published book (discussed here) seam to claim that it can connect these EM theory with QED. I havent read this book yet but I still want to speculate how to model QED from this theory.

The problem with all these QM like claims is that they only work if you neglect the inner magnetic energy, what is kindergarden physics. Already Mills did show that the reduced mass term in the coulomb gauge is the magnetic force contribution. Unluckily the magnetic force is not a central force as it works on the boundary of a rotation and induces a further rotation. This has severe consequences!

The whole approach of QM for deep potentials simply is wrong as it has no physical basis that works. Only at elevated levels (higher n states) the contribution of the magnetic force can be "neglected".

The lucky thing for classic QM modeling is that the two resulting coupled energy states are orthogonal and thus the contribution of the missing state to the classic wave energy is small -much smaller than than the missing energy.

The paper claims as many before the existence of a so called Zitterbewegungs -orbit. But the author does not explain the magnetic energy of such a state.

• Having a link between EM and QM will mean that we have a better argument. We can say yes QM is proper physics in some regards. But using QM for the particles

themselves is wrong, QM works for an electrons in hydrogen because the electron is small compared to the size of an atom, because QM is an approximation. Hence don't

use it for particle physics. I also think that your SO(4) physics is hidden in a correct formulation of particles using EM. So QM is EM but you remove details and get something

that is close to EM sometimes but very wrong to EM sometimes. Then they make a kludge: the standard model, to try churn the properties that was lost back in again.

• Zitterbewegung is scalar motion, it should have no magnetism attributed.

Not exactly. In the proposed Zitterbewegung model the elementary charge e is always associated with a magnetic flux ΦM:

ΦM=h/e

• Hi Stefan,

The relationship between EM and QM equations is a good question, and very non-trivial. Certainly, a person truly

interested in understanding Nature cannot accept the "shut up and calculate" mentality.

Several people tried to establish the link between Maxwell and Dirac equations. You can search the literature for

"optical Dirac equation" for instance. It's not easy to show how Maxwell equation leads to the Dirac equation,

otherwise it would be in textbooks already. But it's one of the most important basic questions, in my view.

In chapter 2, we show that the Dirac equation is the same as the Klein-Gordon equation. In chapter 4, we show that

the Klein-Gordon equation is the same as the Proca equation. These are three faces of the same equation, yet most

physicists consider them to apply to different kinds of particles. The problem is not with the equations, but with

understanding their meaning and correct application to elementary particles.

For instance, "i" is just treated as imaginary complex number in QM, without ever explaining what the imaginary values

physically mean. We show that "i" of QM is the Clifford pseudo-scalar which we get by multiplying unit vectors:

e_t*e_x*e_y*e_z. Understanding the correct geometry is the first step towards understanding what the equations mean.

We make the first steps to derive the Dirac equation from Maxwell equation, but some points remain open. In the 2nd

edition of the book, we plan to present the complete derivation of QM equations from EM equations.

Regarding Wyttenbach's and Zephir's comments: obviously neither of you looked into the book.

A wise person would not make dogmatic statements without first reading and understanding the authors' work.

Especially not in a thread which is catering to those who are interested to understand this topic.

Even more so when you have never yet written down a physical equation which is predictive, and not just numerology.

The reason I am mentioning this is not for being mean to you, but to point out that your activity reduces my

motivation to participate in this forum.

Best regards,

Andras

• Several people tried to establish the link between Maxwell and Dirac equations. You can search the literature for

"optical Dirac equation" for instance. It's not easy to show how Maxwell equation leads to the Dirac equation,

otherwise it would be in textbooks already. But it's one of the most important basic questions, in my view.

In chapter 2, we show that the Dirac equation is the same as the Klein-Gordon equation.

If you are interested in the mathematical relation between al known dense matter models including Clifford Algebra please study the dissertation of "C. Furey"

"Standard model physics from an algebra?" arXiv 1611.09182.

In octoxnion space you can transform all models and show the basic homomorphisms ==>

From a logic point of view we can say if, with the current models physics knows nothing could be found then this was it!

Regarding Wyttenbach's and Zephir's comments: obviously neither of you looked into the book.

How should we ?? paywall.... As said Fury is open and complete.

A wise person would not make dogmatic statements without first reading and understanding the authors' work.

Especially not in a thread which is catering to those who are interested to understand this topic.

Before loosing ground I suggest that you study the transportation of the Maxwell equations to S3 first (Parsley).

Even more so when you have never yet written down a physical equation which is predictive, and not just numerology.

We predicted the quantization of the proton magnetic moment, that can be measured in LENR spectra.. What did you predict so far? We also predict SO(4) spin currents and dense Hydrogen being a weak nuclear bond.

What is wrong about a model that is able to calculate the correct experimental data?

Please show us what exactly = a measurable quantity you predict. May be we can find a way how to measure it. I respect all models and can exactly say where e.g (for a given precision ) the barrier/limit for QM is.

• +

Wyttenbach

I did another try today in formulating a EM - QED connection, it was great fun not sure if it works though but Wyttenbachs SO(4) seam to pop up as well.

In order to have some nice markup I placed it at PhysStackExchange

• In order to have some nice markup I placed it at PhysStackExchange

I had a first look at it: The structure that pops up is similar (equivalent!) to the equations used for the force corrections.

The derivation is may be high over the heads of many as you do not give some explanations like the range for indexes or how you get ikk. May be going for right to left is easier. If it works out that we can include γ3 that easily then it's a major achievement.

We know that Dirac was unhappy that he could not find a way to include magnetism into his formula and only a constant external field did match with conservative potentials, what left his work as being inconclusive at all.

Later on people did forget about this fact and simply thought that just mapping potentials only to Maxwell would satisfy the requirements of being compliant with EM theory...

The history of error made in physics theory is well understood. But most physicists are no longer able to rationally analyze the facts as it would invalidate their skills...

• New version added, cleanup, more straightforward deduction more details added to enable people to follow

• New version added, cleanup, more straightforward deduction more details added to enable people to follow

New version, better explanation of what I'm doing I think. Also I put it on google docs download the pdf from there

and read it on your home computer. The reason for this is that the page in physExchange is on hold, it's a bad question

simply.

• The reason for this is that the page in physExchange is on hold, it's a bad question

simply.

I predicted it yesterday : The physics mafia is getting more nervous...

• Not exactly. In the proposed Zitterbewegung model the elementary charge e is always associated with a magnetic flux ΦM:

ΦM=h/e

That's because electron spin is real. The evidence for that is the circular motion of the electron in a uniform magnetic field. The positron goes the other way because it has the opposite chirality. See Hans Ohanian's 1984 paper what is spin? He said “the means for filling the gap have been at hand since 1939, when Belinfante established that the spin could be regarded as due to a circulating flow of energy”. Also see what Schrödinger said on page 26 of quantization as a problem of proper values, part II: "let us think of a wave group of the nature described above, which in some way gets into a small closed ‘path’, whose dimensions are of the order of the wave length”. I think of it as something like this: You wrap a sinusoidal wave into a closed chiral spin ½ path, and the result is a phase-invariant standing-wave Möbius-like spinor configuration. The photon isn't a flat sinusoidal strip of course, and nor is the electron a Möbius strip. But note how the Möbius strip is the same width all round. I think the analogy is pretty good. What was a sinusoidal field variation is now an all-round standing field.

Check out to Dirac’s belt and William Kingdon Clifford's space theory of matter. IMHO Maxwell was ahead of his time with his theory of molecular vortices.

PS: I couldn't see inside the book, but IMHO what this says is right: https://www.researchgate.net/p…uations_and_Occam's_Razor. It says "only one fundamental physical entity is sufficient to describe the origin of electromagnetic fields, charges and currents: the electromagnetic four-potential". The spatial derivative is E, the time derivative is B.

## Images

• "only one fundamental physical entity is sufficient to describe the origin of electromagnetic fields, charges and currents: the electromagnetic four-potential".

The four potential is a time dependent potential as Maxwell equations contain time derivatives. Further if you use the vector potential instead of real fields then you imply some symmetry. This is no proble if you do e.g. a

proof for one body only that body produces a field .. but that's the old problem of SM. What happens if you have more than one source? And even worse, the forces are not equal in structure?

The free electron partially lives in the time domain but a proton completely avoids it as it does not follow time. What happens if you combine both? SM obviously fails.

Now the more deep problem: The electron is equal charge = electron. If you now use Maxwell to describe an electron you induce a self recursion. Thus from a simple point of view - logic is simple - such an approach must fail as otherwise you should be able to derive the Maxwell equations from the electron properties. The workaround was to declare the electron point particle...and charge being invariant. Now if you imply a microscopic structure = Zitterbewegungs-radius then the Maxwell equations no longer hold because the source is no longer uniform & of point nature...

A classic Hen eats the egg situation!

• From "The Electron and Occam's Razor":

"By using the electromagnetic four-potential as a “Materia Prima” a natural connection between electromagnetic

concepts and Newtonian and relativistic mechanics seems to be possible. The vector potential should not be viewed

only as a pure mathematical tool to evaluate spatial electromagnetic field distributions but as a real physical entity, as

suggested by the Aharonov–Bohm effect, a quantum mechanical phenomenon in which a charged particle is affected

by the vector potential in regions in which the electromagnetic fields are null"
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