1. Introduction

The concept, the Speed of Light (SOL) is a constant but it is not a universal constant as postulated by Einstein is here considered and challenged. When there is disagreement about a scientific concept, it is best to offer another concept that extends or preempts it. Standard procedure is to replace the negative with a positive and to expose it to the scientific community for the test.

If the SOL is not a universal constant; then how does it vary from medium to medium? A new energy equation is introduced and applied universally. The energy equation will be developed and derived. To understand, the reader must be versed in partial differential equations. The object of this paper is to justify a new energy equation and its use at the atomic level as well as to all energy systems. Since it is an energy equation, it can be directly related to the SOL and all radiant sources.

This paper presents the derivation of equation (1), generalizes it, and suggests that it is universal fact.

The energy equation: E = heB/G (1)

It is an energy state equation that contains eB (Poynting vector for energy at a point; this is a Maxwell connection), it is also a wave at some frequency and is singled valued like the photon. G is the gravitational force field (this is a Newton connection) and h (Planck’s constant) showing that it has a touch of Quantum physics. The new equation is developed from a single energy state (accepted in the literature) and has a quasi classical/quantum approach. Highlights of these two concepts that are pertinent to the development are set forth. A cursory review of Quantum physics will follow and the reader is encouraged to do a thorough review of the Shroedinger wave equation, the Uncertainty Principle, and the Exclusion Principle (see reference 1). This article expands on known concepts, removes mystery, and makes them more useful.

In the explanation to follow, the new concept developed extends the world, as it is known today. The author sees great potential and new developments as a result of this new energy equation.

2. Bohr Magneton

This is the starting point for the derivation of the new energy equation. The author first derived this equation in 1969 while working on a project of applied atomic physics. In the past 30 years there have been many developments and ideas that finally led to the concept that it could be applied in many other areas. It has been fun.

There are magnetic moments M associated with an electron moving in an atom that are proportional to both the orbital and spin angular momenta for an electron in a particular shell. They are expressed in terms of the Bohr Magnetron. The magnetic moment times the magnetic vector potential (B field intrinsic or extrinsic to the atom) is an energy term that relates to energy changes at the atomic level.

Bohr Magnetron M = he/m

Where: h is Planck's constant divided by 2p, e is electronic charge, and m is electron mass.

Energy E = MB = he/m B (1)

An electron wave can be thought of as an isolated energy state that is capable of moving (or positioning itself) in a shell about the atom. The following is meant as review to demonstrate electron wave movement.

Equation (1) can also be expressed as: E = he²pR²f/mc (2)

because intrinsic B = pR²ef/c = iA, c is speed of light

(by definition this is the electron movement in an orbit about the nucleus)

Where: i is current due to the electron moving around the nucleus, A is the area of the orbit, and f = w/2p, w is due to a combination of spin and angular frequency of rotation.

Differentiating (2) with respect to R, dE/dR = 2he²pfR/mc

dE/dR = e²wRl, where l = h/mc (3)

2pR = nl, where n = 1, 2, 3, etc.

3. Energy State a Derivation

Equation (1) of Section 2 is an isolated energy state. In all cases of dealing with energy properties of an electron, isolated energy states are a beginning point. Exploring this beginning and dividing the numerator and denominator of the above equation by 1/R², the following is obtained:

E = he/R² divided by m/R² times B

where R is the radial distance of the electron to the nucleus.

e/R² = e-electric field, m/R² = G (definition), and B is magnetic vector potential

Equation (1) of Section 2 transforms to the energy equation, it is an isolated energy state.

E = h eB/G new energy equation of state (4)

Does this new equation agree with previous knowledge of particulate isolated energy states of an electron?

Consider equation (4) and differentiate it with respect to R. If it has truly not changed anything, the result will be the same as equation (3) of Section 2.

dE/dR = dE/de de/dR + dE/dB dB/dR + dE/dG dG/dR

Solving from four above: (a) dE/de = hB/G, (b) dE/dB = he/G, (c) dE/dG = -heB/G²

Solving continued: (d) de/dR = -2e/R³ (e) dB/dR = 2PRef/c, (f) dG/dR = -2m/R³

Combining (a) through (f): dE/dR = h [B/G (-2e/R³) + e/G (2PRef/c) + -eB/G² (2m/R³)]

B/G = pR⁴ef/mc, e/G = e/m, eB/G² = pR⁴e²f/m²c

and substituting dE/dR = h[-2pRfe²/mc + 2pRfe²/mc + 2pRfe²/mc]

dE/dR = h/mc times e²Rw = le²Rw

Note that the result of this differentiation is identical to the previously derived dE/dR (equation 3 of Section 2). The first approach was straightforward and simple. The second approach although complex using partial derivatives was necessary to stress the validity of the energy equation expressed as a combination of fields and a force field. An atomic quantum concept for an isolated energy state has been converted and has incorporated the field equations of Maxwell and Newton’s law of gravity.

Finally, it can be stated that at the atomic level, an energy equation can represent an isolated energy state of the electron. The e and B fields are considered as two aspects of a single phenomenon, an electromagnetic wave whose source is a moving charge (the electron is in a stable atom). Equation 4 is a new energy concept, as well as, it expresses an energy state of an electron. The new force field equations in conjunction with quantum concepts are used to complement energy level changes. Its development and validation have just been considered.

4. Energy State Justification

It is hoped that the reader is becoming aware of the thought process that there are electric fields, magnetic vector potentials and gravitational force fields implicit at the atomic level. The same force fields can be linked to energy states in the atom. A full treatment of the energy equation applied as energy states follows in subsequent sections. The potentials and fields of an atom add as vectors with like potentials and fields of the medium in which they are positioned. Media that have these same force fields affect the energy states of the atom. This allows the energy equation to be applied universally. Why is this important? The following are a few concepts that science may want to reinvestigate:

1. The speed of light is directly related to energy and therefore varies. The energy equation can be equated to E=hf, the speed of light is dependent on electric field, magnetic field, and Gravity force field.

2. The speed of light is zero for infinite gravity (black holes).

3. The energy observed through the telescopes that we use for studying the heavens is affected because the frequencies observed is the direct result of the atom of the materials being observed moving toward us or away from us.

There are other applications treated in reference 8. Number one above has the most impact because it questions the constancy of the speed of light regardless of environment.

The energy equation advances and extends Quantum Mechanics and has the potential of reaching out into space. It is an extension of concepts already known and adds the dimension of a force field and its affect on spectral frequencies of the atom as well as the speed of electromagnetic radiation (light). Equation (4) is the direct result of an algebraic manipulation of an atomic level concept derived from a Bohr magneton energy state. In the process, it presents itself as a stepping-stone from that energy state to a universal concept as an energy transporting entity similar to a photon.

5. Review

The remaining sections of this paper are to give the reader an appreciation of Atomic Physics and energy systems. It is hoped that the presentation shows that energy states at the atomic level have opened up a New World and a new way of looking at radiant energy. Total energy is made up of Potential Energy (PE), Kinetic Energy (KE), and Radiant Energy (RE). Everyone understands PE and KE because they are dealt with everyday where RE is negligible. When RE is large, PE and KE are negligible. The energy equation applies in this latter case and opens the door to many new developments.

This is not a course in Atomic Physics but it is necessary to review many aspects in order to declare justification for some of the author's conclusions. Quantum Physics uses a statistical approach to the energy of the electron in an atom. The new energy equation suggests causality be also involved. In order to study causality, it is necessary to look at some of the highlights of atomic physics.

6. Atom

Figure 1 shows the traditional structure for the atom found in most of the literature. Atoms are characterized by energy levels, which correspond to various distances of their electrons from their nuclei. By absorbing or emitting energy (photon), an electron can move from one to another of those levels (synonymous with raising or lowering its energy). There are only certain discrete energy levels for each kind of atom and define the distances for electrons with relation to the nucleus. The absorbed or emitted radiation only occurs at certain energies or wave frequencies (an electron changing its radial position). These are known as spectral identifying frequencies for a particular atom. Electrons in the atom of Figure 1 are at different energy level.

Figure 1.

Our modern atom is the result of Bohr’s postulates followed by the fact that an electron can be treated as a wave (see the work of DeBroglie). Quantum Physics/Modern Physics, to distinguish it from Classical Physics, treats electrons as waves. It defines the boundaries (an isolated energy state) for treating an electron as a wave. Statistically, a most probable configuration is assumed for the electron/wave. Ironically, it is a photon (particle of fixed energy) that is necessary to alter the boundaries of the electron wave.

7. Quantum Mechanics/Physics

Quantum Physics is an extension of Classical Physics, the Bohr model, and its accompanying postulates. Atomic particles, including electrons, interact with electromagnetic waves and the results of these interactions could not be explained in terms of the Bohr model and Classical Physics. DeBroglie suggested that matter (atoms) may act in many ways like light, which is dualistic in nature. Light sometimes behaves as waves and other times as particles. One way to deal with it was to tie the electrons and particles to wave concepts. DeBroglie's went that extra step and equated photon energy to atomic energy (both considered particles) in the following manner:

E = hf = mc²

Where hf is particulate photon energy and mc² is particulate energy. And:

hf = mc(c)

hf/c = mc

Note that the two particulate energies equated result in a wave concept, where:

Wavelength l = h/mc, mc is momentum of the electron (particle).

Wave (Quantum) Mechanics was born and it introduced partial solutions for atomic phenomena that could not be explained by the Bohr model. It redefined the nature of the electron in an atom in terms of a wave and as a particle and accounted for its probable position in the atom.

At the heart of Quantum Physics is the Shroedinger wave equation, which can account for atomic particles interacting with electromagnetic waves and also replaces F = ma (Newton's second law) for motion of a particle on the atomic scale sizes. In the light of DeBroglie's work (he showed that particle energy is synonymous with wave energy for an electron), a wave equation was necessary to show how electrons move from place to place and interact with electromagnetic waves. The Quantum theory specifies certain regions in which an electron is more or less likely to be found. The electron occupies a position somewhere in a shell (Energy State) with other electrons around the nucleus. There are concentric shells (the number of shells is determined by the particular element) and each shell represents a different energy level separated from each other by fixed quantum (E = hf). For an electron to move from shell to shell, it is necessary to absorb (for a lower level to a higher) or to give up (higher level to a lower level) a fixed quantum of energy hf.

8. Electron Identification

Quantum Mechanics answers questions about atoms containing multiple electrons and their wave/particle duality. It is also a synthesis of two approaches of when to treat the electron as a particle and when to treat it as a wave. For a better explanation of this statement, the reader is referred to a quantum physics book and all the experiments of wave/particle duality that ultimately led to the Shroedinger wave equation.

The modern atom is treated in terms of a wave function as a dependent variable of a wave equation. Each electron surrounding the nucleus is described in terms of what are called quantum numbers for its energy state. There are sets of quantum numbers that specify the way the wave function varies from point to point in space. Each set of quantum numbers corresponds to a physically distinct wave function of a particle (electron/wave) in a box. The quantum numbers are considered Eigen values in the solution of the wave equation and are an approximation. The Shroedinger wave equation can be solved for the hydrogen atom only but it is able to predict solutions for atoms with more than one electron.

The Exclusion Principle insists on the uniqueness of each electron in an atom and states that the interaction between electrons is more than a force between electrons. It describes electron interaction is in terms of isolated energy states, where each state has a set of quantum numbers, and even this procedure is not simple or complete.

The following definitions (result of solutions to the wave equation) assign isolated energy states:

1. Quantum numbers associated with electrons are represented by the symbols n, l, and m.

2. &nb