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.
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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
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.
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Bohr Magnetron M = he/m |
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Where: h is Planck's constant divided by 2p, e is electronic charge, and m is electron mass. |
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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.
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Equation (1) can also be expressed as: E = he2pR2f/mc (2) |
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because intrinsic B = pR2ef/c = iA, c is speed of light |
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(by definition this is the electron movement in an orbit about the nucleus) |
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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. |
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Differentiating (2) with respect to R, dE/dR = 2he2pfR/mc |
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dE/dR = e2wRl, where l = h/mc (3) |
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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:
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E = he/R2 divided by m/R2 times B where R is the radial distance of the electron to the nucleus. |
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e/R2 = e-electric field, m/R2 = G (definition), and B is magnetic vector potential |
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Equation (1) of Section 2 transforms to the energy equation, it is an isolated energy state. |
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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.
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dE/dR = dE/de de/dR + dE/dB dB/dR + dE/dG dG/dR |
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Solving
from four above: (a) dE/de = hB/G, (b) dE/dB = he/G, (c) dE/dG = -heB/G2 |
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Solving
continued: (d) de/dR = -2e/R3
(e) dB/dR = 2PRef/c, (f) dG/dR = -2m/R3 |
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Combining (a) through (f): dE/dR = h [B/G (-2e/R3) + e/G (2PRef/c) + -eB/G2 (2m/R3)] |
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B/G = pR4ef/mc, e/G = e/m, eB/G2 = pR4e2f/m2c |
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and substituting dE/dR = h[-2pRfe2/mc + 2pRfe2/mc + 2pRfe2/mc] |
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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
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
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
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.
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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:
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E = hf = mc2 |
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Where hf is particulate photon energy and mc2 is particulate energy. And: |
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hf = mc(c) |
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hf/c = mc |
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Note that the two particulate energies equated result in a wave concept, where: |
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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 (
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. n is the principal or radial quantum number (radius, defines the shell and kinetic energy)
3. l is the azimuthal quantum number (orientation of orbit defining potential energy).
4. m is the magnetic quantum number addressing the angular momentum of the electron.
5. ms is a magnetic moment due to spin of the electron and is sometimes combined with angular momentum.
9. Bohr’s Influence
Many of the concepts of the Bohr model of the atom have been preempted by a quantum approach. However, his third postulate (an electron can only be in a shell in which the distance around the nucleus is an exact fit for the wavelength of the electron; 2pR = nl) lives on as part of the wave concept of the electron and can actually be derived from it. An electron must be considered as some sort of a wave spread out through space and localized at a point. These principles lead to a wave equation (Shroedinger's equation) that must be satisfied by an electron in an atom, subject to boundary conditions determined by phase conditions for a wave.
In order that the wave may have an exact fit (no standing waves) on the circumference of the circle (or ellipse) must include some integral number of wavelengths (see Figure 3a). Think of an electron as a wave (wave function as a dependent variable of a wave equation) extending in a circle around the nucleus. The wavelength of a particle of mass m, moving with a velocity v, is given according to wave mechanics as: l = h/mv, where: h is Planck's constant and l is wavelength. Then if R is the radius and 2pR = n l, where n = 1, 2, 3, etc. By substitution it can be proven that this contains the angular momentum and the third Bohr postulate.
2pR = nh/mv or mvR = nh/2p, but mvR is angular momentum of an electron and it is observed that the wave mechanical picture leads to Bohr’s third postulate. The angular momentum equals some integral multiple of n/2p (see Figure 2).
Figure 2
10. Energy Exchange
Restrictions on the quantum numbers and states must be carefully observed. Because the Exclusion Principle also states that there can at most be one electron in each quantum state in an atom. Each principal energy state for an electron has a combination of quantum numbers and that combination also decides how the electrons of the atom are distributed. In the normal state electrons in an atom are at their lowest possible energy level.
By emitting or absorbing fixed amounts of photon energy (hf), electrons can change their energy state. When an electron changes its state, there are changes:
1. There is a radius change as a result of shell change.
2. There is orientation change (the plane with respect to the nucleus changes).
3. The magnetic properties of the atom change.
E = hf is a simple definition for the complex exchange of energy in an atom. These photons are detected as the result of an electron changing shells. According to quantum physics, hf by itself means nothing, unless there is a reference. Electron "a" exists in shell x and it changes to a new position in shell y. It has to take on a new set of quantum numbers because the radial, azimuthal, and magnetic properties change. But it is not very practical to follow the electron in this manner.
In dealing with the path of the electrons in an atom (both Classical and Quantum Physics have gone to great lengths to define them), it is hard to keep track of all the variables. It is easy to get lost in the interaction of symbols and theories, i. e. Quantum numbers, states, classical vs quantum etc. It is known that electrons are positioned around the nucleus and that they are wave like in nature as they travel and that they follow the rules of particles when they change energy states. Quantum Physics connects state energy changes of the electron through solutions to a wave equation. The wave equation defines boxes for electrons in an atom. Each box has tags that define radial, azimuthal, and magnetic properties of the electron contained therein. In the solution of the wave equation, a certain number of these boxes are allowed in each shell. Photon energy (hf) is a fixed amount of energy that is absorbed or emitted when an electron changes from a box in one shell to a box in another shell. In fact, the total number of boxes in a shell is predictable from the relative intensities of absorption or emission of unique frequencies.
All the electrons of the atom maintain isolated energy states and are an electron defined by quantum numbers. The electrons can have co-existing definitions for their energy of state. All energy states are different but each energy state has a common characteristic expressed by a field equation. The atom is considered stable and remains stable. The emission or absorption of a photon hf accomplishes a change in energy of the electron. Stability of the atom and equality of forces is dictated by the phase conditions which are part of the energy equation (Bohr’s third postulate). Spectral frequencies are an effect and the cause is derived from the new energy equation in terms of radial change, phase, and the wavelength of the electron in a shell. Section 2.1 derives and explains how the above takes place.
The electron treated as a wave has a frequency (only a
single cycle of the sine wave is shown, see Figure 3a), which value puts demand
on the orbit {certain R-value} such that an integral number cycles exactly fit
the orbit. The electron/wave has its
definite frequency and that frequency remains a constant from shell to shell or
For the electron/wave to change energy levels or shells requires an exchange of energy hfs.
The photon energy and its frequency vary according to the exchange (distance between the shells). In most cases these photons are detectable and they define and are characteristic of the elemental atom. If the electron wave changes shells, energy must be absorbed or emitted depending on whether the level change is positive or negative. This exchange of energy is a photon.
Figure 3
Figure 3a demonstrates how the electron wave must position itself in moving around in its shell to insure proper phase conditions (no standing waves). The l shown in Figure 3a is divorced from the l derived from spectral frequency for the photon energy required for exchange of electrons between shells. The radius R must change in multiple of whole numbers in order for this condition to be maintained and 2pR = nl, where l is the same as that shown in Figure 3.
11. Gravitational Effects
The third Bohr postulate has been previously reviewed and a new concept has been developed for a universal characteristic energy state.
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The new energy equation of state E = h eB/G (4) |
When considering an energy change of state for an electron expressed in terms of the energy state equation, eB is an energy term for a single electron in a shell and is an electromagnetic wave and also energy at a point. What about G? This energy at a point in an atom can be at only one R-value according to Bohr’s third postulate and subsequently derived from Quantum Physics considerations. The position in the shell is some most probable position but the R-value is not most probable. It has to be definite because of the phase conditions of the wave. Causality plays an important role here because energy (hf) defines the R value change. And the wave of the electron can fit only one orbit exactly. The electron wave in an orbit is the same wave from orbit to orbit. Observed spectral frequencies of an atom are different and are not probable, they actually can be measured. The spectral frequencies occur during the absorption or emission of energy during atomic activity (e.g. during the voltage breakdown of a gas or laser activity at the junction of a semiconductor, etc.). They, in turn, define or cause the electron positioning according to R-values and phase.
This section looks at gravitational effects as an important aspect of the electron. In the past, gravitational effect was considered nil with respect to electrodynamics forces. This paper presents an ad hoc approach to the energy equation. It is found that the energy is inversely proportional to the gravity force field and it can be applied universally.
The following is an energy change of state:
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E = dE = hfspectral = heB/G2 - heB/G1 (5) |
It is noticed that it requires a photon hf (equation 5) to change from one energy level to the other, where G1 and G2 define the energy level or shell. It can be noticed that at the atomic level the energy state equation can only take on sets of values consistent with the energy levels of the shells. Equation 4 and 5 are completely general and can be applied universally where R is a variable without restrictions. The new energy equation was developed in conjunction with photon theory for the atom but it is not restricted to only the atom because of its relationship to all energy systems. Section 4 considered the implicit potentials and fields of the atom and the effect of the media having these same potentials and fields.
12. Commonality of Energy States
Expansion of knowledge obtained from the Bohr model and the Quantum approach lead to practical aspects of the atom. It is a cause and effect approach that fulfills all necessary stability requirements at the atomic level. There are no restrictions or uncertainty about the shell (thus the radius) where the electron can be found. This approach uses a convolution technique proving the causes from the effect (spectra measured) and introduces gravitational effects (necessary R definition). There are two considerations about R for an electron during energy exchange; one is the change due the shell change and the other is the change in R that results in no standing waves in the random planes. The two R's are related and can be solved for in terms of each other. An intrinsic gravitational force on the electron remains negligible but the radius of the electron position plays an important roll in the stability concept of the atom. The field concept for the atom dictates the dependence on e, B, and G internal and external to the atom. This opens the door for the interpretation of observed frequencies (through a telescope, on the moon, in water, whatever media of electromagnetic wave travel) as a function of environment.
An atom can be a radiating source. Since the isolated energy states are in terms of fields, all internal and external fields that add or subtract like vectors with each other effect them. Frequency exchanges at the atomic level encounter shifts as a function of the media in which they are being observed because of field variations. Radiated photons are not restricted to quantum jumps. All electromagnetic radiation can be explored using this new energy equation that has been developed at the atomic level in terms of fields. Field energy interacts with all fields of the universe.
13. New Energy Equation of State
This energy equation ties all fields intrinsic and extrinsic to the atom and to all electromagnetic waves. It has far reaching consequences when dealing with Doppler shifts and Gravity shifts, which are addressed in reference 8.
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The energy equation of state E = h eB/G (4) |
Time varying electric fields give rise to time varying magnetic fields and vice versa and in the dynamic case it is impossible to distinguish between electric and magnetic energy (cause and effect). This proves to be the case at the atomic level and the energy equation demonstrates that fact. These characteristics and G (not probable states) are not dictated by quantum numbers and probability. They are independent. The Poynting vector, eB defines energy (flow) of a wave at a point and it is in perfect agreement with the quantum treatment of an electron (eB’s source). It also extends the new equation to include all electromagnetic waves. The new energy equation for an electron in terms of fields has a personality of its own with unrestricted degrees of freedom.
It can be stated that the energy state equation can be treated as a separate entity and can be considered as a wave itself just like hf. Each energy box contains a wave as depicted in Figure 2 that can move in space. The wave can be investigated and defined under various external field conditions. Separate energy states and their fields and force field characteristics are general and universal and follow the mathematical developments of this paper. Since they are universal, it applies independent of the atomic level, from which, it was developed. This energy concept has the capability of presenting energy diagrams for any type of radiation in terms of the Poynting vector, gravitational field intensity and radial distance. This is extremely helpful in studying the heavens and the determination of Doppler and Gravitational shifts.
14. Conclusions
There are electric fields, magnetic vector potential and gravitational force fields implicit at the atomic level. A new energy equation E = h eB/G demonstrates these facts. The force fields are linked to energy states of the atom. Environments with like force fields affect these energy states. This allows the energy equation to be applied universally.
The equation has the unique form of radiation energy (eB) divided by gravity (force field). In reference 7 it was used to demonstrate that the speed of light is inversely proportional to the gravitational force field, in which it is measured. In reference 8, the energy equation is used to investigate Doppler shifts, Gravity shifts, and time varying gravity force fields.
The energy equation was developed from the intrinsic properties of the atom extending Quantum Physics. At the atomic level the energy equation is considered as an energy equation of state that coexists with the wave equation and quantum numbers.
In dealing with radiation effects of the atom in the macroscopic world the external fields add or subtract like vectors with those intrinsic fields produced in the atom and override them. This new energy equation has other applications but this paper was written to justify the use of the energy equation, universally. When considering energy states and characteristics of energy states, the energy equation can be applied universally to radiations and their frequencies. For a full treatment of radiation frequency change, the reader is referred to a sequel to this paper entitled: Doppler and Gravity Shifts by Thomas J. Besmer, Sr. (see reference 8)
This new concept of energy state needs a name. It seems appropriate to call it a Newton/Maxwell photon because of the fields and waves involved and its similarity to a photon. We could call it, a New-Maxton.