Two different types of energy
To create these models, we will seek to identify the real existence of a relationship between two diverse energies, one the energy of light and the whole range of electromagnetic waves and the other a “subquantum form of energy” that we will identify with the energy of the elementary waves in the discrete space-time aether.
Picture 7. Sources of spherical waves at rest and in motion.
The fact that an observer perceives the status of central symmetry in the system of spherical waves reflects that he is himself at rest with respect to the field of mass established by the presence of the wave source and of course also indicates that the wave source is at rest with respect to him.
On the other hand, a status of asymmetry, deduced on the basis of the existence of wave conditions similar to those created by the Doppler Effect, leads him to think that the source of spherical waves is in motion with respect to him.
To do this, we must free our minds of the complicated model of radiation that was put there by electromagnetic theory. We will then seek to develop a much simpler variational model based on the new wave concept of the field of masses as a product of elementary waves.
Let us begin by considering the sources of the elementary spherical waves as mass as producing a spherical system of waves possessing central symmetry.
The Doppler Effect, observed as a source of spherical waves in motion in space, modifies the field of spherical waves’ condition of central symmetry with respect to the observer.
For the stationary observer, the wavelengths of the wave surfaces emitted in the direction of motion become shorter whereas the wavelengths emitted in the opposite direction become longer. Thus, if the wavelengths observed are the same in every direction around the source of the spherical waves, this is a sign that the wave source is at rest with respect to the observer.
As we consider the velocity of the elementary waves to be equal to the speed of light, the wavelengths emitted in each direction can be calculated using a relativistic formula of the Doppler Effect that makes the wave number observed depend on the observer’s position with respect to the “direction” in which the source is moving.
Using this formula derived from Relativity, we can assess the distribution of waves around the wave source and can observe the variation in the geometry of space in its immediate vicinity.
It has been said that relativistic formulae of dynamics can only be applied profitably to provide greater understanding when the velocities of the bodies are comparable to the speed of light, whereas classical Newtonian formulae provide good approximations for all the mechanical phenomenons that are usually experienced.
Image 8. Relativistic Doppler effect for the wave number.
We observe, however, that it is now no longer necessary to adopt this double interpretation of dynamics based on whether or not the velocity of the object is more or less close to the speed of light.
In the context of Wave Field Theory, the relativistic formula is not only valid and appropriate at any velocity, but completely explicable as it is relativistic at low velocities as well.
The situation is altogether equivalent whether the source is in motion with respect to a stationary observer or the observer is in motion with respect to a wave source that is at rest.
Picture 9. It is easy to interpret the formula of the relativistic Doppler Effect in terms of the observer’s perspective. One must assess the angle created by the observer’s sight line with the line of the wave source’s motion. The wave length observed depends on the wave’s velocity and the relativistic time period.
We must distinguish between motion that is constant and accelerating with respect to the observer. If the motion is constant, the observer who perceives an approaching wave source will observe the wavelength as shortened, but constant in time.
When the motion is accelerating, however, the observer will perceive the wavelengths arriving from the source to be shortened progressively. The variation in the observed wavelengths will therefore be constant if the acceleration is constant and variable if it is variable.
Elementary waves, which we understand to be perturbations in space-time as described by Schild, are able to influence each other in a way peculiar to themselves.
As variations in the state of the lattice, they cause variations and create stability in the geometry of the lattice itself.
This geometry can influence the direction of motion and behavior of every other perturbation that passes through the Effected zones of the lattice.
Using Planck’s formula, let us call the elementary waves’ capacity for action subquantum energy. Let us describe this energy as a function of the frequency of the waves as the product of the capacity for action “h” of each wave surface multiplied by its frequency “ν” in the unit of time E =h ν.
We know that one of the typical characteristics of an elementary mass (an elementary particle, electron or proton) is that it possesses a spherical gravitational field, and an electromagnetic field that possesses the same spherical form.
Picture 10. Source of spherical waves in accelerated motion with 1 observer
Using the language of waves, we believe that what we have been calling mass, charge and particle up to now, is the expression of a wave source that exists at the center of a field that emits spherical elementary waves. We consider these waves to be responsible for all the wave, gravitational, nuclear and electromagnetic actions activity of the field.
If we were able to justify all the actions of the mass, charge or particle in terms of waves and at the same time could explain the wave-like nature of the wave source plausibly, it would be completely useless to extrapolate the presence of an entity called “corpuscle”.
This is precisely what we propose to do. We will describe the wave-like spherical organization of the elementary waves in space-time which possesses all of the characteristics which up to now we have attributed to elementary matter and to its field as mass.
Let us draw up a wave model that can explain the existence of discrete entities within the lattice of space-time described by Schild that possess specific characteristics that satisfy everything we know about elementary particles and its fields at this point.
To describe the wave-particle system’s ability to act on a co-ordinate wave-particle system, we will use a method comparing the description of elementary waves’ ability to induce a change as expressed in the energy level of the waves and the energetic description of the content of wave energy in the mass.
We feel supported in this by the numerous discussions of the equivalence of energy and mass in relativistic physics up to now. We begin with the hypothesis that the two basic formulas describing energy are equivalent.
Einstein’s formula describing the relationship of energy to mass:
E = m c2
and Planck’s formula to describe radiation:
E = h ν.
Let us equate the energies of masses and waves described in them:
m c 2 = h ν
Let us interpret this equality equation as a function of the wavelength:
λ = c / ν
expressed as the ratio of the velocity of the waves c to their frequency ν.
This equation provides the value of mass as a function of the wavelength of the spherical waves emitted by the field of the mass:
m = h / λ c.
We can now finally explain and understand fully what Einstein’s formula describing the energy of mass:
E = m c 2
Firstly, anyone with good intentions who is not blinkered by dogma can understand Planck’s simple formula defining radiation, E = hν and interpret it literally.
According to this formula, the energy of a radiation wave train is the result of each wave surface’s capacity for action “h” multiplied by the frequency of the waves “ν”, which describes the number of wave surfaces that pass a given point struck by the wave in a unit of time.
In terms of waves, Planck’s energy formula in practice describes the “density” of a wave train’s capacity for action as a function of the concentration of its wave fronts and thus of its frequency.
No one up to now, however, and not even Einstein has ever been able to understand the physical significance that can be attributed to the square of the speed of light, in the energy formula for mass, E = m c 2. This number was simply given a functional interpretation as a factor of proportionality.
Now, on the other hand, by equating the two energies and interpreting the equivalence in terms of waves, it becomes easy and very significant to understand this number. The square of the speed of light assumes a precise and physical significance “only” when it becomes necessary to equate the two formulas.
It becomes clear that the value of the mass of an at rest body, where the mass at rest:
m o = h / λo c,
is equal to the product of the capacity action “h” of each of the wave surfaces of its wave field of mass multiplied by the wave number 1 / λ o .
Where: the wave number of the waves that constitute the field of mass, is the number of waves that fit in one meter, divided by the velocity “c” of the waves and multiplied by the action “h” of each of the wave surfaces.
This is not a simple, repeated tautology.
It is a very real interpretation of mass as attribute of the waves.
An interpretation in which all the parameters are at the same time both meaningful and explanatory. The resulting physical model includes all the terms necessary to describe the wave nature of mass and its field.
It will permit us to identify mass precisely as an expression of these waves so that all the relevant properties are ascribed to the field of mass that permit it to deform the geometry of the space in which the mass exists and acts as the source of all the fields attributed at the mass-particle.
The primary element to understand this formula is the wavelength
“lambda zero λ o”:
the wavelength λ o = h / m o c
has been known for some time as the “Compton wavelength”.
It provides us with a precise wavelength to associate with electrons’ at rest mass in estimating the data required to explain the most elementary possible interaction between radiation and matter that takes place between a single photon and a single free electron in the Compton Effect.
Many physicists felt vaguely that there had to be some fundamental significance to the Compton wavelength that would one day play an important role in microphysics. Quantum mechanics however attributed no precise physical significance to it.
The Compton wavelength appeared as an isolated rock in a sea of uncertainty and did not provoke any in depth investigation of its significance.
And yet its physical significance is now clear and explicit:
“it describes the constant distance between the wave surfaces of the spherical perturbations that constitute the system of elementary waves that, taken together, we identify with the wave field of stationary mass.”
For larger masses, the wavelength of the system of spherical waves is smaller, the wave field contains more energy and its ability to curve the geometry of space around itself is greater.
The dynamics of the wave structure of wave sources of masses in motion can be described fully by the relativistic Doppler formula, which expresses all the variations in wavelengths surrounding wave sources in motion.
The variations between wave states that are stationary and ones in which the source of spherical waves is in a state of uniform motion explain the reasons for the accumulation of kinetic energy in masses that are in motion clearly and explicitly.
These variations allow us to verify that the accumulation of kinetic energy is in fact equivalent to an accumulation of mass as the wave source produces a wavelength in front of itself that is shorter and a shorter wavelength is equivalent to the energy of a larger mass.
The relativistic Doppler Effect in fact states that the wavelength of wave sources diminishes in the direction of motion, and, as mass depends on the value of the wavelength, this makes the mass increase relativistically.
This fact has been interpreted in two different ways up to now: for low velocities, as an accumulation of kinetic energy whereas for velocities approaching the speed of light, it was interpreted as a relativistic increase in mass.
It may have seemed legitimate to distinguish between the two cases when mass appeared to possess a mysterious nature. But now that we have the wave interpretation of mass, it is no longer necessary to make this distinction. In the wave model, the relativistic increase in mass as a cause of motion and an increase in kinetic energy are perfectly equivalent.
2 “Photons as variations”
The wave model of mass allows us finally a new (second) tipe to explain the profound nature of that strange entity we have called “energy”.
The accelerated motion imposed on the wave source to alter its motion at rest with respect to the observer produces “for the observer” and in the moment that it occurs a variation in the observed subquantum energy of the waves emitted by the source.
The Doppler variation in the wavelength of elementary waves received by the observer is equivalent to a “variation in the energy” of the subquantum waves observed.
This analysis of the conditions governing the observation of the wave source in accelerated motion shows us that what physics up to now has been calling “energy”, are in fact variations in the subquantum energy of elementary waves.
We have called this wave train, of which the wavelength of the waves emitted by the source varies and which propagates in space at velocity “c”, a “photon”.
Einstein sensed that photons existed and was not joking when he called these elementary waves “phantom” or “empty waves” by which he meant “devoid of energy”, devoid of the energy we know and normally detect with our sensors and instruments. He even concluded that these empty waves were able to support light quanta that possess energy and he was almost right.
If we now analyze the characteristics of these “variations in the other energy”, we will see that they possess many of the characteristics of photons, the same characteristics that Einstein wished to explain with the wave packets he called “light quanta”.
Let us begin with the principal problem area: the localization of photons as bearers of energy.
The localization of energy transfers from photons striking single atoms made many people believe it might be possible and even useful to reintroduce the concept of corpuscle into the physics of radiation. We should now be able to demonstrate, however, that we can also identify among the wave systems’ properties the ones which up to now have been attributed exclusively to corpuscles.
How can we find characteristics in the wave model of the variations of energy in waves originating in a wave source that would make photons’ energy transfers almost punctual?
This can be done. Examine the spherical waves that originate in an electron as an accelerating wave source.
If we place numerous ideal observers in a spherical pattern around the source, the Doppler Effect will make them observe different wavelengths. Two observers occupy privileged positions, however. The conditions under which they observe are different from those of the others. One is the observer toward whom the electron is moving who thus sees the electron coming closer, whereas the other finds himself on the path the electron has already traversed and thus sees it becoming more distant.
Image 11. Source of spherical waves in accelerated motion with two observers.
More precise observation allows the first observer to perceive that the area of the sections of wave surfaces that appear parallel becomes increasingly restricted around the trajectory traversed by the wave source. This characteristic of the “parallelism” of the wave surfaces in the wave train emitted by the wave source proves that the wave-like energy quantum follows a trajectory and thus can legitimately be considered “localized”.The first observer confirms that the waves originating in the electron are parallel to one another and along with the observer on the opposite side is the only one to be able to verify this as all other observers around the electron cannot confirm that the wave surfaces they receive are parallel.
We will demonstrate the rational proofs below by which we show that the parallelism of the wave surfaces conditions the localized energy transfer to matter and justifies the conclusion that the wave surfaces’ point of impact on a screen can be considered “localized”.
The aforementioned parallelism is a fundamental property of the wave surfaces, but it is not a property of the waves that has been constructed “ad hoc”. It is not born and does not die with the need to justify the localization of the light quantum.
And, as we shall see below, the parallelism of the wave surfaces will play a determining role in wave interactions in the macro- and microscopic worlds and have a new and extraordinary Effect in the fields of astrophysics and cosmology.
This obviates the need to recuperate the corpuscle as the only representative object that can be localized, as we can also define the impact of a series of wave fronts to be localizable.
Another of the photon’s characteristics that the accelerated wave source model can explain easily, is one typical of the current electromagnetic wave model.
According to this model, a photon consists of a wave train containing different energies that moves through space as a whole. In the current electromagnetic model, a photon must consist of a wave train of different energies that can be localized precisely.
A monochromatic photon made up of a single energy should be of infinite length. It would thus be impossible to localize in space and thus would not exist as an independent entity as it would possess neither an end nor a beginning.
The wave source model can explain very simply how an electron in motion with a constant velocity can construct a monochromatic wave train in front of itself. It is similarly clear that when the electron is accelerating, it can construct a wave train that contains different wavelengths and thus different energies.
As we can see intuitively, the accelerated wave source produces a wave packet made up of waves of differing wavelengths during the acceleration phase followed by a period of uniform motion whose linear dimension is a function of the duration of the acceleration.
- Such packets contain different wavelengths and thus different energies.
- These wavelengths have the characteristic of decreasing in size as the acceleration increases.
- The wave packet’s energy thus increases constantly toward the end.
- When the acceleration phase is complete, the cause of the variation in wavelength ceases.
- The increment in Doppler Effect disappears and the photon’s length finishes there.
Picture 12. Source of spherical waves with alternating phases in the direction of accelerate motion.
We will demonstrate below how the simple wave source model of the field of mass can explain the identical experimental results for radiation with an accelerated charge which up to now could only be explained by electromagnetic theory.
Here we will verify whether our model of the photon can express another of its fundamental properties in terms of the elementary phenomenon of the pressure of radiation.
This phenomenon demonstrates the simplest interaction between radiation and matter. A photon strikes a screen and transfers energy to it and the screen uses as kinetic energy of the photon to set itself in motion.
Picture 13. Radiation can exert pressure on the Solar sail of a spaceship as a function of the sum of the individual quanta of motion transmitted by each of the photons that strike the sail.
One of the most imaginative potential uses of this phenomenon involves the possible exploitation of pressure of photons from the Sun to propel a spaceship using extremely light “solar sails” in the space between planets.
Pressure from radiation is one of the key phenomenons in the nature of micro-physical interactions, and a new interpretation of it will allow us to establish a new and different dynamic in quantum physics.
We can use the new wave model to justify the pressure from radiation in a new and extremely productive way and demonstrate that this new interpretation of the pressure from radiation constitutes the basis for a new dynamic that is valid at all levels in physics.
It will reveal to us a new principle of basic physics and a new model of the electron that will guide our interpretation of the four fundamental interactions in terms of waves.
It will provide us with a strictly deterministic key to the code that will lead us toward a unified vision of all physical phenomenons from the most elementary to the most complex.