## **Albers, Norman**:

#**From PDF Â“On_ElectronÂ”**:

**ELECTRON FIELD SOLUTION WITH CIRCULAR CURRENTS**

– **PART I: Field Solutions of the Electron**

Electromagnetic theory has been incapable of modeling the electron as a field because it represents **point charges in a vacuum**. Offered here is a reasonable and mathematically minimal construction of inhomogeneous charge and current terms, added to the usual far-field. Thus the severity of the singularity is limited and now fully integrable. The existence of a static, circular mode of solution is proposed.

It is thought by most that quantum mechanics comprises all that may be said about the fundamental quanta. A self-consistent construction assumes an inhomogeneous spherical charge, and circular current field. Working in spherical coordinates, one finds that only A. generates reasonable behaviors at the origin. For the same reason there must be no time dependence in scalar potential, U. If field strengths go as r-1 at the origin then observables have finite integrals, as they (energy, angular momentum, etc.) go as r-2. This motivated the mathematical winnowing process.

The physics is that of a static charge-current assembly with a factor of Â½ for correct accounting of energy interaction terms.

**Â“StaticÂ” means Â“unchanging in timeÂ”** and so includes momentum and current circulating steadily around the z-axis.

Â… Beyond here, and without a massive core there is no reason to be stopped at the phase changes distinguishing phases of stellar masses, one must clearly have a relativistic model 1. Density can be seen to rise to immense values as r approaches the Planck length, though there is no central spike of total energy, charge, or angular momentum.

Â… The electron is thus clearly seen as a **Â“superconductingÂ” spherical cloud** by virtue of being the sum of homogeneous and inhomogeneous fields. From his vantage point **250 years ago, Leonhard Euler** receives his due.

– **PART II: Dielectric Interpretation of Electrons**

Â… This is **another phase state of light**, just as ice is another form of water with a different physics of its constituents. There is **no further need to explain mass**. If we see how energy is “convinced” to spin in a small locale, there is no further question if it manifests the electric and magnetic fields of the electron/positron.

The physics being illuminated here is of the dipole contribution from the vacuum. Whether the picture of quantum mechanics of virtual “particles” is more accurate than one of space as a more infinitesimal sea of available inhomogeneous fluctuations, there must be the manifestation of charge and current. In a **concurrent paper on Photon Localization**, I show how such physics allows the existence of **localized wave packets**. That analysis can be applied directly to vacuum fluctuations to reveal non-quantized charge densities, such as are needed here.

Regardless, we can speculate on some fascinating possibilities. If we picture a dipole pair, and it points outward in a negative electron field, the particles will be drawn back together to annihilation. Those pointing inward, parallel to the total electric field (we defined it this way, since the inhomogeneous part is smaller than the homogeneous), will be tugged apart somewhat. We can see a natural selection in harmony with the stability of this state of energy. Furthermore, the positive end will be closer to the center and feel a slightly stronger electric field, so it is more strongly attracted than the negative end is repelled.

Thus, the dipole as a unit experiences an attraction toward the center. This is a remarkable state of affairs for a system which, viewed as a classical “assembly of charge”, should want to fly apart.

Â… Beyond that, we can say that there is a negative dipole pressure, as they are attracted inward. This is notably important especially for the relativistic solution needed at very high energy densities near the singularity. Reminiscent of **Higgs theory** which depends on negative pressure, this is presumably a manifestation different from Higgs bosons.

**References**:

1 Adler, Bazin, Schiffer, Intro. to Gen. Rel., McGraw-Hill (1965), p. 467.

2 H. London, F. London, Proc. Roy. Soc. (London), A149, 71 (1935).

3 W. Meissner, R. Ochsenfeld, Naturwiss. 21, 787 (1933).

# **From PDF Â“Photon Localization and Dark EnergyÂ”**:

**Photon Localization and Dark Energy, by Norman Albers**

1) Photon Localization

2) Photon Angular Momentum and Planck’s Constant

3) Manifesto on Quantization

4) Dark Electromagnetic Energy

– **Part I: PHOTON LOCALIZATION**

Photons are represented as **quasi-monochromatic wave packets**, where a helical, transverse magnetic-vector potential has an exponential falloff in three dimensions. The currents implied by such a limiting sheath are describable as a fundamental contribution from the virtual background, plus net charge regions responding to the potential.

The response of Â‘AlphaÂ’ derives from a **uniformly available virtual sea of dipole manifestation**, more like a plasma than bound, polarizable units. **Vacuum fluctuations** produce a mean-square dipole measure just as they do a mean-squareelectric field. This **quantum-mechanical concept** is thus shown to be necessary and sufficient to describe an understandable mechanism for localization. Either charge of a local dipole pair contributes similar current as an A-field comes and goes.

The first current term is a dipolar contribution attributable to a local polarization change or bilateral current; the second is monopolar, from net gathering of charge.

We should beware the tendency to ascribe phenomena and Â“natures of spaceÂ”.

Somehow an increasing A-field produces dipolar current which bunches up in an inhomogeneous charge field. We can understand Â“little chargesÂ” being accelerated in a B-field, but that does not mean they are there!

Mathematically I am allowing the field to be smoothly inhomogeneous..Thus a **neutral background of Lorentz transformable nature** but of local dipole availability must be the nature of what we called the vacuum, and serves to localize photons.

– **PART II: PHOTON ANGULAR MOMENTUM,**

**Calculating wave packet totals**

Â… If we integrate these totals over space, it is clear that each of the first two terms yields one-fourth the total. This total, which is **Planck’s constant**, can be figured from integration of the energy density, either by squaring the fields or by constructing pU . (The magnetic contribution should be the same.) Total energy of the packet, divided by angular frequency, is that constant. The other one-half comes from the charge-field terms.

This I offer as an inductive conclusion, though we should expect totals from source-term integrations to equal those from fields (squared).

This is where we lost our nerve in electrodynamics! Such vacuum manifestations were not considered, and without them there cannot be localization, as that depends upon transverse divergence, i.e., inhomogeneous fields.

It is not apparent that there is physical process in the field per se to render quantization, and we may hypothesize the opposite: it is only emitters and absorbers that obey quantum rules. **Only bound states are quantized**; a string uncut and unstrung has no note! Treating space as a **“ficticious oscillator”** becomes a fiction of which we can well be rid. A new accounting of vacuum fluctuations will liberate us from the extreme results offered by current interpretation.

Perhaps we can **couple the uncertainty principle with statistical mechanics** to produce a more reasonable result.

– **PART III: MANIFESTO**, by Norman Albers

**Quantization and Planck’s Constant**

The **photoelectric effect** shows interaction of the light field with a bound state, by which I refer to the electron Â“particleÂ” itself, as well as its disposition in a material. The latter is represented by the Â“work functionÂ” of the material. Beyond that we see the exchange of energy between the field and bound state being **proportional to light frequency**. It is a mistake of psychological projection to say that this quantum of energy existed in the field, per se. What is known is that an interaction scales to frequency; the root of this phenomenology may be seen as determined by the characteristics of the bound state and not of the field!

It is clear that the field energy must be localized, or interaction would not be of sufficient intensity at the atomic scale. The necessary characteristics of the exchange are set by the well-understood quantum mechanics of electrons, and it is reasonable to say, Â“A field at some frequency and sufficient energy will impart kinetic energy to the (bound state) electron, **equal to Planck’s constant times frequency**, minus the material work function.Â” We understand that correctly identified quantum oscillators have particular stable states and rules of transition between them involving absorption and emission. Here is the essence of Planck’s constant: it is the characteristic of electromagnetic energy in a bound state.

We understand atoms as bound electrons, and we must go further and admit that particles are bound light. The laws of this are accessible with **inhomogeneous electrodynamics**.

When we witnessed the exchange of photons, namely, field energy of quantized proportions, we chose to ascribe the quantization to the field.

I hypothesize that we will find it more useful to consider the field as not necessarily quantized on scales larger than the Planck length. There are surely many predictable photons but the native characteristic of the field is of arbitrary magnitude relative to frequency.

On this basis **we shall refigure our mathematics of vacuum fluctuations**, although I hesitate to say anything here, as interpretation may require a fresh attitude. I offer for consideration **the Wien blackbody law** which fundamentally combines electromagnetic energy density with thermodynamic probability in a manner appropriate for non-quantum state space. It is this sort of approach we will need if it is correct to manifest uncertainty in the local field.

Perhaps not even this is what we are coming to, but at least it may give similar results at Â“lowÂ” frequencies. Whatever the characterization, it must answer to the need for homogeneous charge and current fields.

– **PART IV: DARK ENERGY and IT’S SPECTRUM**

The field mechanism itself is not sensitive to the total angular momentum of the packet, and we may thus theorize disturbances of arbitrary fractional magnitude. Such field components will not interact with atoms except with their integer part. The fractional energy must therefore be dark with respect to spectral electromagnetic interaction with matter. Leaving quantum statistics to have fully accounted for the integer, or quantized photons, let us consider the population of fractional states between, or fractional photons, at whatever total field level. We justify this because they do not interact with mass by absorption.

Construction of a luminous energy density curve considers mode structure available, and energy likely to exist in each mode.

Rather than adding possible multiple integer energy states **weighted by the Boltzmann factor**Â…

Â… The “dark” spectrum has radically different behavior between high and low frequencies, or conversely low and high temperature. It is of compelling interest to figure this in view of cosmic expansion.

Â… Curiously the Planck high end agrees closely with **the Albers low end**, and vice versa. Further analysis will yield many secrets here.