The frequency variable
Planck’s quantum formula was incomplete, and as a result did not contain the oscillation energy constant. This in turn resulted in a quantum formula in which the units did not balance:
E (Joules) = h (Joule seconds) v(oscillations per second), but Joules Joules oscillations (16)
Scientists found they were unable to balance the quantum equations and use complete mathematical notation for frequency, namely cycles, waves or oscillations per second. As a result, mathematically incomplete notation, which omitted descriptive units for frequency’s numerator, was adopted instead. Frequency is currently described in the International System of Units ("SI") as "1/sec" or "sec1". This incomplete SI notation for frequency removes an essential mathematical element of reality in quantum mechanics. Incomplete mathematical notation for frequency is no longer required to compensate for the deficiencies of the incomplete quantum formula. With the recognition of the energy constant – energy per oscillation – frequency can once again be correctly and completely notated as oscillations per unit time. The use of complete mathematical notation in quantum mechanics restores a vital aspect of mathematical reality. Recognition of "oscillations" in the numerator of frequency measurements provides a theoretical element corresponding to each element of reality in the complete quantum formula. As Einstein argued, such a correspondence is a critical requirement of a complete quantum mechanics.
The photon
In 1926, Gilbert Lewis coined the term "photon" for Einstein’s light quantum. The energy of the photon was calculated with Planck’s (incomplete) quantum formula, "E = hv". Questions have been raised from time to time since then, as to whether the "photon" is truly an indivisible particle of light. The answer to that question is now clearly, "No". The photon as previously defined is not an indivisible elementary particle.
The fixed time variable and energy constant had been hidden in Planck’s "action" constant, and so it was not apparent to Lewis or others that what they were calling the ‘"photon" was actually a timebased quantity of light energy, which relied on a fixed and arbitrary one second measurement time interval. A timebased amount of energy which relies on an arbitrarily defined time interval cannot be a fundamental or elementary particle of light. The photon is not an elementary particle of light.
What is the elementary particle of light, then? As identified by the universal energy constant, the elementary particle of light is the single oscillation of EM energy, i.e., a single cycle or wave of light. The elementary particle of light possesses the constant energy of 6.626 X 1034 Joules. It is the smallest known quantum of energy in the universe. What was labeled a "photon" by 20th century physics is actually a collection or ensemble of these small elementary light particles. Each individual oscillation is a "complete unit" of light and can be emitted or absorbed as a complete and discreet unit.
The "photon" is not an indivisible particle of light, and is in fact a collection or ensemble of light oscillations, which can act separately and individually as complete energy units. Upon absorption by a detector or object, the energy of a collection of discreet oscillations can spread over several atoms or molecules, resulting in a multiatom, energy distribution state known as "entanglement". (Brooks, 2009, c) This entanglement of EM energy can take place in different patterns or distributions, depending on the nature of the absorbing or detecting material. Similarly, emission of light energy can occur from an "entangled" energy state shared by multiple atoms or molecules in the emitter. An ensemble of EM waves with fewer than "N" oscillations (where "v = N/ sec") results in a "subphotonic" collection of EM waves. The ultimate subphotonic particle is the elementary particle of light, the single EM oscillation.
The mass of light
De Broglie bemoaned the absence of "an isolated quantity of energy" with which he could calculate the constant rest mass of light. Using the energy constant for light, it is now possible to complete de Broglie’s calculations and determine the rest mass of a single quantum of light. Under de Broglie’s original formulation using Einstein’s energymass equivalence equation of "E = mc2", the rest mass of light is readily determined:
This value is within the same order of magnitude as the most recent and reliable estimates for the upper limits of the rest mass of light. Since the energy of a single oscillation of light is constant, regardless of its wavelength, time period or frequency, its mass is also constant regardless of its wavelength, time period or frequency. Hence, the mass of light is constant over a shift in time or space. The mass of light is thus conserved and represents another universal constant for light (Mortenson, 2011).
Just as the density of light’s constant wave energy varies with the length and volume the wave occupies, the density of its mass varies as well. The mass of long EM radio waves, spread over a distance and volume of hundreds of meters, is low in density. The identical mass, when confined to the small wavelength and volume of an Xray oscillation (on the order of 108 to 1011 meters) is trillions of times more dense. High density Xray oscillations, with their intensely concentrated mass and energy, can create interactions not typically seen with low density radio waves, and give rise to effects such as Xray scattering and particlelike properties.
The momentum of light
Momentum is classically calculated as the product of an object’s mass and its speed. Using the constant mass of an EM oscillation as calculated above, and the constant speed of light (2.99 X 108 m/ sec), De Broglie’s calculation for the momentum of light can be completed:
As with mass, the momentum of a single oscillation of light is constant, rather than being infinitely variable. The momentum of an EM wave is constant regardless of its wavelength, time period or frequency. Thus the momentum of light is constant over a shift in time or space, and is a conserved property.
In terms of de Broglie’s earlier calculations for the masses and momenta of photons, the mass and momentum constants for EM waves are not contradictory or confounding. It should be remembered that the photon of 20th century concepts was actually a collection of elementary light particles, i.e., EM oscillations. Collections of masses and momenta can be additive. Summation of the constant mass and momentum of single oscillations (based on the number of oscillations "N" in a one second "photon") yields the same collective mass and momentum that de Broglie obtained with his photonbased calculations. Although de Broglie’s mass and momentum calculations provided infinitely variable results, it is now recognized that his variable results were an artifact of the missing energy, mass and momentum constants. A previously unrecognized symmetry for conservation becomes apparent. Energy, mass and momentum are all conserved for both light and matter, completing the triad of conservation relationships outlined earlier by Helmholtz, Einstein and de Broglie.
The force of light
Energy, mass and momentum are all constant and conserved for light. Using classical mechanics, however, it is easily discerned that the force exerted by light is not constant. According to Lagrange, force is the product of mass and the change in velocity "during the instant dt" when the velocity changes:
For changes in velocity occurring in an interval of time equal to or greater then the velocity unit time, the same time variable for both velocity and acceleration can be used. If, on the other hand, the acceleration (or deceleration) occurs in a time interval much smaller than the velocity unit time (i.e., an "instantaneous" event), a second time variable, "ta", must be used for the acceleration time interval. When an EM oscillation is emitted by an object, a small bit of mass of 7.372 X 1051 kg is instantaneously accelerated to the speed of light, "c". Likewise, when a light wave is absorbed by an object, its mass is instantaneously decelerated. The acceleration or deceleration occurs "during the instant dt" which is the time period "t" of the EM wave. The force that accelerates an EM oscillation at its emission (or that is exerted by an oscillation when it is absorbed) is thus:
The time periods of EM waves are infinitely variable, as are their frequencies (t = 1/v). Thus, although the mass and velocity of EM waves are constant, the forces which they exert are not. The forces associated with light oscillations vary inversely with their time periods, and directly with their frequencies ("F = m c v").
The energy and mass of a radio wave, distributed over a comparatively long period of time, exert relatively little force on an absorbing detector. The energy and mass of an Xray or gamma ray oscillation, on the other hand, are concentrated in a minute period of time and exert tremendously large forces on an absorbing object.
These EM light forces are additive, and given sufficient accumulation the forces can be quite large and result in the physical acceleration of absorbing matter. (Liu et al, 2010) The force of light is the operative mechanism behind "space sails" which are now being employed on space craft. The sails of the ancient mariners were pushed by the forces of the wind which filled them. The sails of modern space explorers are now filled by the forces of light which impinge on them. Likewise, an object emitting light experiences a recoil force proportional to the emission force of the EM waves. (She et al, 2008)
Classical limit
The quantum pioneers anticipated that classical mechanics would be used to provide a description of physical processes at very small length and energy scales. Numerous roadblocks were encountered, however, due to the hidden quantum variables and constants. The quantum mechanics developed by Heisenberg and Schrodinger provided a mathematical framework for low energy kinetics, however they were unable to obtain the certainty and definitiveness provided by classical mechanics. Without the mass constant for EM waves, it was impossible to use classical properties of position, time, and mass in any meaningful way. Heisenberg and Bohr found that they were limited to finding just probabilities, and that they could apply classical mechanics only at very high electron energy levels. The region where the classical and quantum mechanics formed a boundary zone, was deemed the "classical limit" by Bohr. (Bohr, 1920) Above the limit, classical mechanics could be applied with reality and certainty, while below the limit all was uncertain and only quantum mechanics could be applied.
Using the new quantum variables and constants, the classical limit/boundary zone between quantum and classical mechanics is disappearing. (Mortenson, 2010,a) It is now possible to use classical mechanics at the smallest possible energy levels for light, equivalent to fractions of a percentage of the lowest known electron energy levels. The kinetics of energy absorption for a single EM oscillation, namely 6.626 X 1034 Joules, are now fully describable using classical mechanics. In this regard, the classical limit previously theorized by Bohr, is being recognized as an artifact of the missing quantum variables and constants. The application of classical physics at the smallest known energy levels, is made possible with the use of the second hidden time variable, Lagrange’s acceleration time variable, "ta". The absorption or emission of an EM oscillation in the visible light region takes place in 1010 seconds. This results in a near instantaneous deceleration or acceleration of light’s mass. The energy required to accelerate a body is a function of the distance over which the force acts, "F 8s". In the case of an individual EM oscillation, the distance over which the force acts is the wavelength, "A" of the oscillation. Multiplying the variable force for light by its wavelength, i.e., "F 8s = (m c v) A", results in constant energy of "mc2", or in other words 6.626 X 1034 Joules/osc. The energy constant for light is thus quickly derived from first principles of position, time and mass.
Lack of appreciation, for the caveats of Lagrange and Coriolis regarding acceleration time intervals and instantaneous events, contributed to the perception that a barrier or limit existed between classical and quantum mechanics. The new fundamental physics of EM waves reveals that particle mechanics can be described at both the macroscale and microscale levels using the certainty, realism and determinism of classical mechanics.
The uncertainty principle
Heisenberg suggested the uncertainty principle as a response to the inability of early quantum pioneers to determine quantum properties related to time or energy with any certainty. He proposed that changes in energy and time are uncertain to the extent that their product must always be greater than or equal to Planck’s constant (AE At > h). That principle included, of course, the incomplete quantum constant "h", which hid an energy constant and a fixed time variable. Heisenberg’s uncertainty principle cured a multitude of quantum paradoxes, and as David Bohm wrote a generation later, "the physical interpretation of the quantum theory centers around the uncertainty principle". When "h" is properly replaced with the energy constant and measurement time however, the physical interpretation of quantum theory is changed dramatically and centers around certainty and constancy, where the change in energy is the energy of a single EM wave, and the change in time "At" and measurement time "tm" are equal to the time period "t" for the oscillation.:
The smallest possible change in energy is the energy of a single wave of light. This concept was obscured in the past due to the absence of a separate energy constant and time variable in Planck’s quantum formula. Under the circumstances, it was inevitable that calculations of quantities involving time and energy, would yield uncertain results. The uncertainty is now gone, replaced by a quantum mechanics that accommodates a more certain and realistic physical interpretation.
The fine structure constant
The finestructure constant "has been a mystery every since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it….It’s one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man…" (Feinman, 1988)
Using the newly discovered quantum constants and variables, the fine structure constant "a" is far less of a mystery. Examination of the fine structure constant in relation to light’s action "S" and Planck’s constant "h" (i.e., "a h = S"), and substitution of "h" with the energy constant " h " one finds:
The fine structure constant is not dimensionless. It represents a scaling constant between time and a single oscillation of EM energy, i.e., "osc t". As such, a theoretical element corresponding to an element of reality is now provided for the fine structure constant. This is a critical requirement for a complete quantum mechanics.
Wave – Particle duality
Two opposing models of light – particles and waves – have been debated for centuries. Some investigations suggest light is composed of waves, while others suggest particles. This conundrum led Einstein to object, ""But what is light really? Is it a wave or a shower of photons? There seems no likelihood for forming a consistent description of the phenomena of light.we must use sometimes the one theory and sometimes the other…". (Einstein, 1938) Bohr responded to these two contradictory pictures of reality with his complementarity principle, asserting that certain aspects of light could be viewed one way or another, but never both at the same time. We are now presented with a picture of reality which demands that we view light simultaneously as a wave and a particle. The elementary "particle" of light is the single EM oscillation or "wave". Although the time and space the wave occupies may vary, that variance is according to the constant ratio "c", and the elementary particle’s energy, mass and momentum remain constant as well.
The divergent pictures of the past resulted from relative size differences between the EM waves and the matter with which they interacted. For example, scattering studies were first performed using soft Xrays with wavelengths larger than atoms, and no clearcut particle properties were detected. When Arthur Compton used ultrashort hard Xrays and gamma rays, however (up to two orders of magnitude smaller than an atom) he observed particlelike properties. (Compton, 1923) The concentrated energy and mass of the Xray and gamma ray waves appeared as small points relative to the size of the atoms in the irradiated materials. On the other hand, one and twoslit experiments demonstrate wavelike properties for light via interference bands. These wavelike properties are also relative, however, to the sizes of the light oscillations and the matter with which they interact. For a slit whose width is equal to the wavelength of the light, no interference bands are observed and particlelike behavior is seen. It is only when the width of the slit is increased relative to the wavelength of the light that interference bands and wavelike properties begin to appear.
Recent experiments with light slits and "single photons" reveal as much about the detecting material as they do about the light itself. A "photon" is merely a collection of individual EM quanta. When visible light waves (which are much larger in size (400 – 800 nm) relative to the individual atoms in the detector (0.1 – 0.5 nm)), strike a detector the energy of the light wave ensemble impinges on multiple detector atoms simultaneously. This produces an energy entanglement state in several of the detector atoms. (Brooks, 2009, c) Distribution of the light energy over several atoms excites a small pointlike portion of the detector material resulting in a photonic reaction, and produces a particlelike pattern in the detector. (Roychouhuri, 2009) Although the resulting detector imaging appears to show the buildup over time of "photon" collisions, they actually show the buildup of energy entanglement states in the detector itself, which are subject to positive and negative interference within and between groups of entangled atoms.
Energy dynamics
The experimental data Planck used to derive the blackbody equation and thermodynamic formula did not include any measurements arising from orderly work energy. Hence, Planck did not include work energy in his thermodynamic formula, "E = kB T". Instead, Planck’s formulation was limited exclusively to the energy of a small system element (e.g., an atom, molecule or ion) based only on its temperature and random chaotic motion. When orderly work energy is present in a system, more inclusive formulae must be used to represent the total energy of a system or its elements. (Brooks, 2009b and Mortenson, 2010b) Helmholtz’s energy equation, "E = A + TS", embodies once such inclusive formula on the macroscale, and represents the total energy of a system as the sum of its work and thermal energies. This more complete formula encompasses significantly more than simple thermodynamics, and is more appropriately referred to as an energy dynamics formula.
Energy dynamics formula
A complete energy dynamic formula for an entire system is given by Helmholtz’s energy equation, "E = A + TS", (Equation 4., above). While calculation of the thermal energy of a system is relatively simple and straightforward, determination of the total work energy can be considerably more involved. Work energies come in many forms, including mechanical, chemical, gravitational and resonant energies. Resonance work energy is a broad category encompassing timevarying forces and fields such as sound waves, electric or magnetic fields, and light waves. These resonant energies couple to matter via "sympathetic resonance" and are denoted in the fundamental energy dynamics formula as, "Ar":
The fundamental principle described by Galileo in his pendulum studies holds true for resonant work energies, i.e., "by [providing a timevarying energy one may] confer a Motion, and a Motion considerably great by reiterating.but only under the Time properly belonging to its Vibrations". Anyone who has pushed a child on a swing has applied a resonant mechanical energy to the child/swing system. Pushing the child at just the right time (i.e., the resonant frequency for the child/swing ensemble) increases the speed, height and excitement of the child’s ride. Pushing at the wrong time, when the child is a few meters away, produces no effect on the system and may detract from the excitement of the child’s ride. In the same way, electromagnetic waves impinging on a material transfer resonant EM energy to the absorbing matter via their momentum, force, speed and mass. An acceleration of the oscillating element within the system results from the applied EM force, and an increase in the oscillation amplitude of that element results (see Fig. 1, above). Thus, "pushing" the system elements with EM waves at just the right time increases the amplitude (height) of the system’s oscillations and excites them to higher energy levels. The amount the system’s oscillation amplitude increases is a function of how close the resonant EM wave frequency is to the oscillation frequency inside the system (Eq. 2., and Fig. 2, above). The increased oscillation amplitudes and energy levels in the system can perform work in a variety of ways, depending on which element or oscillation amplitude is increased. For example, changes in motion, chemical, material, organizational, or behavioral states may all result from a resonant energy excitement in the system.
Expressed at the microscale level, a complete energy dynamics formula for the total energy of an individual element in a system is formulated parallel to Helmholtz’s system formula:
where "We", is the total microscale work variable representing the total work performed on an individual element. In the case of resonance work energy, a resonance work variable, "rA" can be used. This microscale resonance work variable represents the energy gained by an individual element in a system, as a result of resonance work energy, "Ar ", applied to the system as a whole:
Determination of system resonance work energy "Ar"
The resonance work energy (system/ macroscale) and variable (element/microscale) may be determined experimentally. An aqueous solvent system under resonant conditions was compared to an identical system under thermal conditions (see Table 1., below): 1
^{}
Resonant system 
Thermal system 

Weight Dissolved (g/100ml NaCl) 
26.0 
23.8 
Moles Dissolved (NaCl) 
4.65 
4.25 
Heat of solution (kJ) 
17.4 
16.0 
Table 1. Resonant vs. Thermal aqueous solvent system
The heat of solution is a measurement of the work performed by the solvent on the dissolving solute. The work performed by the resonant system was 17.4 kJ, while the thermal system performed only 16.0 kJ of work on the NaCl solute. The energy dynamics formulae for both systems are:
Subtracting, one finds that the resonance work energy, "Ar ", in the resonant system is 1.4 kJ of energy:
The resonance factor
The ratio of the total energy in the resonant system to the total energy in the thermal system:
is the resonance factor, "rf ". In the aqueous solvent system described above, the resonance factor is 1.09. There was 9% more energy available in the resonant system to perform work on the solute and to dissolve it. This resonance work energy was in addition to the thermal energy already inherent in the system as a result of its temperature.
Determination of element resonance work energy "rA"
The amount of resonance work energy at the microscale is the resonance work variable, "rA". In the solvent system example, individual elements in the system irradiated with resonant EM waves possessed greater energy than the elements in the thermal system. The value of the microscale resonance work energy can be calculated using Equation 25., above:
Subtraction shows that each water molecule in the resonant system performed an additional 35 X 1023 J of work on the solute, as a result of absorption of the resonant EM waves.