# Dark Matter as Variations in the Electromagnetic Zero-Point Field Induced by Baryonic Matter

## Abstract

**:**

## 1. Introduction

- Freely moving charges in a lab trace parabolas rather than straight lines. CED needed Newton’s gravity by its side, with its distinct (Galilei rather than Lorentz) symmetry group, making it impossible to merge the two into a consistent theory.
- CED was mathematically ill-defined due to the so-called classical self-force problem: Both the Lorentz force equation of a point charge and the total energy of a group of interacting point charges are ill-defined [1].
- CED was not generally covariant. The coordinates appearing in CED’s Minkowskian form as well as the dynamical fields are merely abstractions of physical entities—rods, clocks, magnetometers, etc.; spacetime is not “marked” with coordinates, nor are there “little vectors” scattered in it. A fundamental theory, in turn, should be able to represent any such physical entity, and if the required mathematical representation resorts to coordinates, an infinite regression (or circularity) is created. The only way to avoid it is for coordinates to enter a description of nature as “scaffolding”, used in calculating the “real thing”: a measurement, which is just some coordinate-independent number (e.g., the number of clock ticks). A particularly simple way of guaranteeing the scaffolding independence of the real thing is to make CED’s equations look the same in any coordinate system, identifying the results of measurements with certain (coordinate-independent) scalars. The principle of general covariance, which crept into physics as a mathematical corollary of Einstein’s field equations, could have therefore been proclaimed much earlier.
- CED began showing some discrepancies with observations, such as the photoelectric effect and black-body radiation, with no apparent resolution in sight.

## 2. Extended Charge Dynamics (ECD) in Brief

#### 2.1. Advanced Solutions of Maxwell’S Equations

#### 2.2. Scale Covariance

#### 2.3. The Zero-Point Field and Broken Scale Covariance

## 3. ECD and Particle Physics

#### 3.1. A Tentative Ontology Based Solely On ECD

#### 3.1.1. Charged Leptons

#### 3.1.2. Hadrons

#### 3.1.3. Nuclei

#### 3.1.4. (The Illusion of) Photons and Neutrinos

## 4. ECD and Astrophysics

#### 4.1. ECD and Dark Matter

#### 4.1.1. Outline of a ZPF-Based Model of Dark-Matter

#### 4.1.2. Spiral Galaxies

#### 4.1.3. Clusters of Galaxies

#### 4.1.4. Gravitaional Lensing

## 5. Conclusions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Nonclassical scenarios for extended charge dynamics (ECD) particles: (

**a**) creation and annihilation of a pair and (

**b**) scale transition (the varying gray-level represents charge density)

**Figure 2.**The thick vertical line represents the spatially extended world line of dense nebula $\mathcal{N}$ (existing for a finite time for illustrative purpose only), and the dashed horizontal line represents the constant-time three-surface to which our analysis of the outer halo applies (Equations (30) through (34)).

**Figure 3.**Mutual absorption between two particles in equilibrium with the zero-point field (ZPF): the dashed ray represents the locus of destructive interference. Note that, in $3+1$ spacetime, radiation fields decay with distance (26), implying that the degree of interference is minimal near each dipole, transversely extending beyond the ray, and its overall effect decreases with increasing interparticle separation.

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**MDPI and ACS Style**

Knoll, Y. Dark Matter as Variations in the Electromagnetic Zero-Point Field Induced by Baryonic Matter. *Symmetry* **2020**, *12*, 1534.
https://doi.org/10.3390/sym12091534

**AMA Style**

Knoll Y. Dark Matter as Variations in the Electromagnetic Zero-Point Field Induced by Baryonic Matter. *Symmetry*. 2020; 12(9):1534.
https://doi.org/10.3390/sym12091534

**Chicago/Turabian Style**

Knoll, Yehonatan. 2020. "Dark Matter as Variations in the Electromagnetic Zero-Point Field Induced by Baryonic Matter" *Symmetry* 12, no. 9: 1534.
https://doi.org/10.3390/sym12091534