1. Introduction

Electromagnetic waves are a form of radiant energy, which were first studied and characterized by Maxwell. Light is a very common form of radiant energy that everyone knows. The waves move at a finite speed and their energy is proportional to frequency. This paper addresses the cause of the wavelength variation as a measurement tool.

Based on Einstein's postulate, "the speed of light is a universal constant", the theories of relativity were born. These theories questioned established facts of Newton's work by taking time and distance from the objective real world and placing them in a subjective world based on movement of the observer or the observed.

The development and derivation of a new energy concept containing new roots for the speed of light is presented. The new roots establish that the speed of light is a variable dependent on wavelength and Gravitational Force Field (GFF). It is an attempt to preempt the postulate, "the speed of light is a universal constant". This article investigates some practical applications of a new energy equation related to source brightness and frequency variations.

2. Electromagnetic Radiation

All around us is radiation. A common source of radiation is space (night sky) and there are many other sources artificially produced (radio, radar, television etc.). The amount of energy from any source equals the power of the wave times it duration. A source of radiation and of paramount interest to the scientific community is the night sky. Fixed point sources (stars) of continuous electromagnetic waves can be observed. Telescopes provide the best means to capture the energy of these sources (galaxies, planets, quasars, pulsars, solar systems etc) for evaluation.

The science of Astronomy studies and makes measurements of received radiation from the heavens. The explicit purpose of the measurements is to study velocities, distances, and light (radiation) intensities of heavenly bodies. The radial velocity of a heavenly body is the speed with which it approaches or recedes from a set position (e.g. a fixed point on earth).

It is observed that the frequency of the wave shifts proportional to its movement in the heavens. Advanced photography technology allows science to measure frequency shifts. The frequency shifts are named Doppler shifts; named after their founder who first explained them. This paper investigates spectral frequencies and their associated Doppler shifts. It also derives and presents a new energy equation that contains Doppler shifts and introduces gravity shifts. Scientists are undecided about frequency shifts in the heavens. Are they Doppler shifts or gravity shifts? The new equation will show that the shifts are a combination of the two.

3. Cosmology

There are multiple cosmological models and all in some way answer or fill in part of the pie. The Cosmological Principle states that the part of the universe that we are able to observe is characteristic of the entire universe. There is a model based on the Big Bang Theory (expanding universe) and is considered evolutionary in nature. The General Relativity Theory (GRT) in Cosmology treats light as traveling on curved lines in a gravitational field which have world points that are considered in an invariant space time interval. The Steady State Theory says that matter is being created continuously in empty space at a rate just sufficient to replace what is leaving due to recessions of heavenly bodies. With all these models, explorations of space look at many uncertainties.

4. Astronomy

A good starting point asks the question; what do we see when we look into the heavens? We are observing radiation sources in the visible spectrum that have brightness and frequency associated with them. There are other sources that might be too distant to be seen or they are in the non-visible part of the spectrum. Other means of observing can be used (e.g. telescopes or radio frequency receivers). At night much of the radiation observed is in the visible spectrum. Further investigation indicates that the sources of radiation are characteristic spectral frequencies of gaseous elements found in space. Every elemental atom can be identified by its characteristic frequency. By measuring variations (frequency shifts of radiation from stars, galaxies etc), a determination of radial velocities and distances of these sources can be found.

It turns out that at the root of most of the discoveries in Astronomy as well as in communications (satellites) are the variation of these frequency measurements. The radial velocity of a star, galaxy, etc. or a satellite is the speed with which it approaches or recedes from a set position. It is measured by Doppler shift of lines of some absorption spectrum (boundary lines separating frequencies) and can be observed for any entity in the heavens that can be photographed. The radial motion along the line of sight is a complicated problem in geometry and must be worked out (see ref 2, pp. 253-4).

4.1 Star Brightness and Frequency

The amount of light energy (luminous flux) received from stars is among the most important and fundamental observational data of astronomy. It is used to estimate both distance and energy of stars. The light gathering power of a telescope is proportional to the area of its aperture (lens or mirror). By varying the size of the aperture, a means for calibrating a telescope to detect classified light magnitudes (1 to 6) by photoelectric photometry has been devised. The lowest number represents the brightest star or object and the larger number represents the faintest detection.

The classification of this light magnitude (1 to 6) dates back to the Greeks in the second century BC. It has led to the development of a measuring technique used today (developed in the18th century). It was noticed that a first magnitude star received 100 times as much light as the sixth magnitude star. Thus a difference of five magnitudes corresponds to a ratio in luminous flux of 100:1. The literature publishes differences in magnitude and light ratios as well as magnitude data for different objects (sun, moon, planets, stars etc., see reference 2).

A star’s brightness is also a function of its distance from us (most of the literature addresses stars and can be extended to include all heavenly objects). The light that is observed from a star or heavenly body is inversely proportional to the square of its distance. The apparent brightness (1 to 6 magnitudes) of stars that has just been discussed does not provide a basis for comparing the amounts of light that they actually emit into space. In astronomy another scale is devised for comparing how much light is received from an object if all objects were at the same distance from the measuring device. A common distance of 10 parsecs (PC) is arbitrarily chosen for all objects and the inverse square law is used to calculate magnitudes and to derive a distance modulus (1pc = 200,000 AU, and 1 AU » 92,960,000 mi.).

Besides brightness differences, all objects emitting radiation have a frequency spectra that varies for each object or star. These frequencies indicate the makeup of the object and also indicate the movement of the object and its speed. Today, seven principal spectral classes (sequences) are recognized and classified (published in the literature see ref. 2, p. 271). Many of the spectra observed in the stars were first observed in known terrestrial elements.

Newton showed that white sun light is really a composite of all the colors (visible spectra, rainbow) and that passing light through a glass prism can separate the various colors (frequencies). It was also observed that dark lines characterized the transitions between frequencies. These dark lines can be tracked and easily measured because photoelectric photometry measures the degree of blackness of these lines. The spectra of a star is photographed and compared to a photographed laboratory reference source. The lines of the star’s spectrum are compared and the frequency determined.

This has been a cursory treatment of luminous flux density and frequency spectrum for stellar objects as measured by a telescope. For more details the reader is asked to review these aspects in more detail if reference 2. The object of this paper is to present a new concept for extending astronomical measurement techniques and knowledge of those observations.

5. Spectral Frequency

Niels Bohr presented an atom model with defined orbits for the electrons that were separated by discrete energy levels called quantum transitions. Bohr first defined the spectral frequencies and identifying earmarks of material. His presentation was an ad hoc approach that predated DeBroglie’s wave-particle works by about ten years.

One transition of an electron is a quantum of energy and is measured as one photon; E = hf, where E is energy, h is Planck’s constant, and f is spectral frequency of the photon and characteristic of the element. The transitions are a constant and highly predictable and are used as a defining concept for distances and speeds of heavenly bodies. This is possible because it is found that materials spectrally studied here on earth are some of the same materials found in space. Spectral absorption lines from radiating sources are observed and related to movement and distance.

6. Atom Characteristics

This paper uses some of the concepts of atoms without offering proof (for proof and justification, see reference 7, pages 2-4). It is assumed that the reader is familiar with the classical as well as the modern day concept of the atom. It is suggested that the atom concepts be studied because an ad hoc approach is presented using the atom to find the influence of gravity on spectral frequency.

Each electron in an atom has a defined energy state. It is known that proportional to both the spin and angular momentum of an electron in an atom are magnetic moments, which are expressed in terms of the Bohr magneton and are considered isolated energy states.

Bohr Magneton M = h/2p(e/m) 4.1

Energy of Bohr Magneton E = MB 4.2

Where h = Planck’s constant, e = electric charge, m = electron mass,

and B = Magnetic Field Intensity.

7. A New Concept and Energy Equation

The Bohr Magneton is effected by externally applied magnetic fields. Is the atom also effected by the external gravity gradients that exist? Presently, the spectral frequencies studied in outer space are shifted either due to Doppler shift (as a result of radial velocity) or Gravity (red) shifts. The scientific community has encountered repeatability problems in defining luminosity, distances, velocities, and a relationship between Doppler and gravity shifts or their combination. To investigate this aspect, substitute equation (4.1) above into equation (4.2).

E = h/2p (e/m)B 4.3

Next divide numerator and denominator of equation (4.3) by 1/R² where R is electron distance from the nucleus of the atom.

E = h/2p [{e/R²}/{m/ R²}]B

Where {e/R²} is e the electric field intensity, {m/ R²} is G the gravitational field intensity and B is the magnetic vector potential. The energy equation is derived for atoms and it depends on the intrinsic properties of e, B, or G.

E = h/2p [{e}/{G }]B = h/2p eB/G 4.4

It makes sense that if this energy equation is proper (see reference 7 for full treatment of derivation and justification), then the like vector fields of the environment for e, B, or G add. In many cases, fields of the environment are the dominating fields and profoundly determine the atom's frequency (especially true when observing frequencies from space).

Another definition is in order; eB º S is the Poynting vector or an electromagnetic energy wave (at some frequency) at a point and named after its discoverer. Note that the energy equation is a function of two fields (electric and magnetic) and an inverse function of gravity force field (Gravity). Examining its structure it can be addressed as electromagnetic radiation (at some frequency) divided by the gravity force field vector. The combination of these concepts points to the measurement and study of observed frequency shifts of the heavenly bodies.

8. Wave Characteristics

The dependence of a uniform plane wave depends only on the characteristics of the medium in which it propagates (treated in Section 9). In free space it travels at a constant speed determined for space and for the case of heavenly bodies (star, galaxy, etc.), they travel at a relative speed to or from the earth or planet from which they are observed. This latter velocity is known as the radial velocity of the body and is an important part of determining positions in the heavens.

If a light (or radiation) source is approaching or receding from earth, there is a shift in frequency of that energy source. This principle is known as the Doppler principle of the Doppler effect named after its discoverer. It effectively says that the radiation waves are crowded closer together (toward the observer, a blue shift) or spread out (away from the observer, a red shift), respectively. These wave fronts are traveling in a radial direction with respect to the observer and are characterized by some radial velocity. The simplest of the Doppler shift can be expressed as (delta l)/l = v/c where v is radial velocity, c is the constant speed of light from the medium of measurement, and l is wavelength. In the scientific community there are uncertainties about the frequency shifts leading to velocity, distance, and luminosity problems (see Figure 1).

Figure 1

9. Frequency Shifts

In developing the energy equation at the atomic level, definite values for R, f, l, etc. were dictated. In dealing with radiation effects of the atom in the macroscopic world, the intrinsic properties remain unchanged. The external fields add or subtract like vectors from those intrinsic fields produced in the atom and override them.

This new energy concept has the capability of presenting energy diagrams for any type of radiation in terms of the Poynting vector, GFF and radial distance. This is extremely helpful in studying the heavens and the determination of Doppler and Gravitational (red) shifts.

Equation 4.4 above is used as the starting point to reach into outer space and to look at frequency shifts (see derivation in Section 7). The R value in the following equations is the distance to the radiation source and the radial velocity of the source is the speed with which it approaches or recedes from a set position (e.g. a fixed point on earth).

E = h/2p [{e}/{G }]B = (h/2p) eB/G 4.4

eB º S the Poynting Vector 4.5

and E = hf 4.6

Substituting: f = (1/2p) S/G 4.7

For frequency shift in the radial direction; differentiate equation 4.7 with respect to R.

df/dR = 1/2p [ df/dS (dS/dR) + df/dG (dG/dR) ] 4.8

Each term in equation 4.8 will be treated separately and then substituted and solved. For the first partial term df/dS, differentiate 4.7 with respect to S.

df/dS = 1/2pG 4.9

It is a change in frequency with respect to S and indicates that it is inversely proportional to gravity force field.

NOTE

The second term dS/dR = 0 (see ref. 7) at the atomic level because e and B change in such a way that their product remains constant and thus S is a constant.

However, frequency change with respect to radial distance requires the following considerations of the atomic source being observed. S is a radiation energy wave and its energy is proportional to frequency.

S = eB = kw, where w = 2pf, f = v_radial/R, and k is a constant

The positive crests of e and B (orthogonal to each other) occur every 2p radians.

Therefore: S = kw = k2pf = k2p v_radial/R 4.10

The second term for equation 4.8 is equation 4.10 differentiated with respect to R; it becomes:

dS/dR = -4kp v_radial/R² 4.11

Combining equations 4.9 and 4.11:

df/dS (dS/dR) = -2kv_radial/GR² 4.12

Assuming radial direction, equation 4.8 is Doppler shift by definition. The third term is frequency shift due to the gravitational force field. Differentiating the third term of 4.7 with respect to G gives the following results, equation 4.13.

df/dG = -S/pG² 4.13

For the fourth term of equation 4.8, differentiate G with respect to R, G = m/R² because the gravity force field varies according to the inverse square of the distance from the earth (observer is assumed on earth).

dG/dR = -3m/R³. 4.14

The following is a review of common definitions for field intensities in their simplest form at the atomic level because their effects produce the radiation source. Remember the sources of radiation are characteristic spectral frequencies of gaseous elements found in space. Every elemental atom can be identified by its characteristic frequency. By measuring variations (frequency shifts of radiation from stars, galaxies etc), a determination of radial velocities and distances of these sources can be found.

e = e/R², B = pR²ef/c (see page 76, reference 4), G = m/R², S = eB (Atomic level)

And substituting S/G² = e²fR⁴/m²c 4.15

Combining equations 4.13, 4.14, and 4.15

df/dG (dG/dR) = 3e²/pm (v_radial/c) 4.16

Collecting and combining terms and substituting equations 4.12 and 4.16 into equation 4.8, it becomes:

df/dR = 1/2p [-2kv_radial/GR² +3e²/pm (v_radial/c)] 4.8

(Change in l)/l = v_radial/c º Doppler shift and the v_radial/G term indicates a shift due to GFF

According to the literature frequencies are sometimes attributed to gravity and sometimes Doppler, this equation indicates a combination of the two.

Implicit in equation 4.8 are the speed of light and the radial velocity because the original equation 4.7 contains the Poynting vector which is derived from Maxwell’s equations. Equation 4.8 has information that says that frequency change (shift) is the result of Doppler Effect and GFF as well as its intensity. Equation 8 has information that says that frequency change (shift) is the result of Doppler Effect and GFF of the object observed as well as its intensity. This Gravity shift is different from the so called “Red Shift” talked about in the literature. “Red Shift” used in that context refers to whether the object is moving away from the observer. In the development of equation 4.8, the Gravity term refers to the value for the gravity of the object being observed. It has a personality and glamour all of its own with a novel completeness. This has been an ad hoc approach and presents a challenge to obtain data to verify or discredit the results.

10. Speed Of Light In Materials

It is not a secret that the frequencies we observe, whether in a vacuum or a material, are functions of velocity and wavelength and are related. It is quite obvious that it is not a simple function of E = hf. All media that allow the flow of light or electromagnetic radiation are dispersive in nature. The velocity of light in a material substance depends on wavelength and all media offer some resistance to flow or transmittal of radiation. All substances have a dielectric constant and a magnetic permeability, which cause the speed of light to change. These properties (dielectric constant) and (magnetic permeability) have a value in space but cannot be divorced from frequency shifts because of the resistance they offer to flow. They are intrinsic to electric fields and magnetic fields, respectively. They are an integral part of the wave equation derived from Maxwell’s equations. Relations among the wavelength, momentum, and energy at a point in materials are approximately the same as for free particles traveling or moving in a region of constant potential.

E = h/2p [{e}/{G }]B = (h/2p) eB/G 5.1

The following relationships are presented and are very much part of electromagnetic radiation. Equation 5.1 is the same initial equation used to investigate space medium variances. In various materials, the wavelength, frequency, and radiation speed will differ according to the variations presented in equations 5.2 and the added variations presented in equations 5.3, 5.4, and 5.5. These considerations show that the speed of light varies and mathematically it can be converted for all medias of travel.

f = (1/2p) S/G = c/l 5.2

and c = (1/2p) Sl/G

c (vacuum) = 1/square root ofÎ₀m_0,Î₀is the dielectric constant 5.3

m₀is the magnetic permeability

Z_intrinsic = square root of m/Î, 377 ohms for free space 5.4

c/v = square root of Îm/Î₀m₀, Where v represents the speed 5.5

of radiation in different medias

11. Gravitational Force Field at a Point

Newton’s works questions the certitude and limits of velocity and rest and affirms the certitude of acceleration and gravity. It is found that the above statement is the direct result of Galileo's work for an object in free fall; Y = 16T² where Y is distance and T is time. Using Newton’s calculus and differentiating the equation twice with respect to time results in a constant that is described for each planet as universal. It presents the concept of gravity as a natural phenomenon and unchangeable.

The concepts of gravity fields and gravity waves are still being questioned and investigated. The scientific community is looking to discover gravity waves, gravitons, field's etc. The new energy equation introduced in this paper assumes that gravity is a force field and is related to electromagnetic waves according to that equation. This new equation opens the door to a vast new field of knowledge for exploration. Is it possible that the natural phenomena of gravity can be manipulated as function of electromagnetic waves? Is it possible that this new equation is the key to discovering more about illusive gravity?

To investigate this possibility, it is necessary to solve the new energy equation for G. The new energy equation is restated here.

E = h/2p [{e}/{G }]B = (h/2p) eB/G

Solving: G = (h/2p)S/E, S º eB 6.1

Equation 6.1 for G offers an interesting suggestion. It states that as energy E of S (possibly a beam of radiation) becomes greater and greater, then G will decrease. Does this indicate that it is possible to decrease GFF at a point to zero? This is quite a concept stating that G can be varied with energy beams. Since G = S/E, is it a wave?

Continuing the investigation, differentiate G (equation 6.1) with respect to time.

dG/dt = h/2p [dG/dS (d