The electromagnetic wave
Let’s look at the image below. The electromagnetic wave is illustrated. The electrical oscillation E occurs along the x plane; the magnetic oscillation B occurs along the y plane. The direction of the velocity vector is the z axis. (Figure 1)
Figure 1. A linearly polarized sinusoidal electromagnetic wave propagating in the +z direction in a homogeneous, isotropic, lossless medium (such as a vacuum). The electric field (blue arrows) oscillates in the ±x direction, while the magnetic field (red arrows), orthogonal to +z oscillates in the ±y direction, in phase with the electric field.
We note that the electromagnetic wave is composed of electric (blue arrows) and magnetic (red arrows) vectors of increasing and decreasing intensity that propagate in vacuum. The animation of the electromagnetic wave is illustrated on the Wikipedia site. In this animation you can see the formation of the vectors that generate the wave oscillation.
By observing the generation of electric and magnetic vectors we can hypothesize that the vectors are energetic pulsations.
We know that physicists use the equation of the Schroedinger wave function with its solutions as a guideline for their theorizations. Strangely, in every solution of the Schroedinger equation, complex numbers appear. For example, it may happen that at point “x” the amplitude of the wave is equal to 0.3 + 0.5i, where “i” is equal to the square root of -1. In other words, the number “i” multiplied by itself gives the result -1. A real number added to another real number multiplied by –i is called a complex number.
We too, in formulating our hypotheses on the structure of elementary particles, use the Schroedinger equation as a guide. For this reason, we hypothesize that the electromagnetic wave is generated by two vectors: one real and one imaginary. In the animation of the electromagnetic wave, the real vectors are the electric ones and the magnetic ones. The imaginary vector consists of the motion along the z axis.
We assume that energy is the “archè”, that is, the origin of the universe. We also assume that the energy is pulsating, i.e. made up of pulsations. Pulsations of energy are the constituents of everything around us. There are two types of pulsations. One type of pulsation is made up of “material energy” with “vacuum dilation”; the other type of pulsation is a simpler “vacuum dilation”. This is the “intrinsic vacuum”. This vacuum is a component of energy itself. Let’s call the first: “Energy Pulsation”; let’s call the second: “Inflationary Pulsation”.
For Einstein the vacuum is dynamic. It can expand or contract. The expansion of the vacuum is called “inflation”. For astronomers, the universe expands not because galaxies move away from each other but by inflation, that is, by dilation of the void.
This way of describing the expansion of the universe presupposes the presence of a vacuum on which an energy acts which determines its expansion. We believe that the vacuum, intrinsic to elementary particles, does not pre-exist energy, but that it is generated by the energy itself. The intrinsic vacuum is generated by pulsating energy.
Let’s imagine a pulsation that radiates linearly at a constant speed. Pulsating energy can be described by a vector in which the point of application is the source point. The direction and direction are those of motion while the module is the energized space. We call this vector: “Energy vector”. The energy vector describes the material energy that generates the “intrinsic vacuum” (figure 2)
Figure 2. Energy vector. The energy vector describes material energy. This pulsating energy generates intrinsic emptiness
Intrinsic vacuum can be generated by a pulsation in which material energy is absent. We call this pulsation: “inflationary pulsation”. The single inflationary pulsation, concerning the generation of vacuum, can be represented by a vector in which the point of application is the point of origin, the direction and direction are those of the pulsation, while the modulus is the vacuum generated by a pulsation. We call this vector: “imaginary vector”. The imaginary vector describes the inflationary pulse that generates the intrinsic vacuum. (figure 3).
Figure 3. Imaginary vector. The imaginary vector is a pulsation that generates intrinsic vacuum.
The imaginary vector allows us to interpret two paradoxical aspects of physics: the presence of complex numbers in the resolution of the Schroedinger equation and Einstein’s dynamic vacuum.
Interaction between energy vector and imaginary vector
We hypothesize that an energy pulsation generates a linear energy space, whose intensity is defined by the segment “AB” in the up/down direction and in the “up” direction. At the same time, an inflationary pulsation generates a vacuum between “AA1” in a direction perpendicular to the previous one. The time of the two pulses (green arrows) is the same. A second pulse starting from “A1” generates the material vector “A1B1”. At the same time, a second inflationary pulsation generates the vacuum “A1A2”. The second energetic pulsation is double the intensity of the first, even if the time of the two pulsations (green arrows) is the same (figure 4).
Figure 4. Double upward (linear) and forward inflationary energy pulse. The two upward linear pulsations occur with a doubling of intensity; The two forward inflationary pulses occur at the speed of light. The times of the four movements (green arrows) are the same. The intensity of the second energy vector is double that of the first.
The electromagnetic wave generated by the interaction of the two vectors
Looking at figure 4 we notice that the two vectors are perpendicular. We can also observe that empty space and energetic space interact through the delimiting/delimited dichotomy. The empty space, generated by the two pulsations, delimits the energetic space and the energetic space delimits the void. The vacuum is superficial, the energy space is linear. In figure 4 the void is the white surface delimited by two lines representing the energy space. Finally, the energy pulse and the inflationary pulse are temporally synchronized. They have the same duration. The energy pulsations are parallel to each other of increasing and decreasing intensity with the same direction and the same direction.
Let’s hypothesize a series of energy pulsations that follow one another in the vacuum, generated by the inflationary pulsation, at regular intervals. They are of increasing and decreasing intensity in the up/down direction and in the “up” direction. The inflationary pulse, which is perpendicular to the energy pulse, occurs in the forward/backward direction and in the “forward” direction. Once the series of energetic pulsations is over, another one begins, completely identical to the previous one except for the direction, which is “below”.
The combination of these two pulsations generates the oscillating/pulsating energy unit, which we call “pulsar”. It is a temporal unit. The oscillation consists of two temporal moments which can be forward/forward or forward/backward. The pulsations occur in pairs. A pulse is electrical; the other is magnetic. We assume that the electrical pulsation occurs up/down and that the magnetic pulsation occurs in the left/right directions. In the time unit (pulsar), times are synchronized; the time instants of the oscillation coincide with the time instants of the pulsations. The pulsar is made up of two pairs of figures in the shape of semicircles: a crest with an upward electrical energy pulsation and a belly with a downward electrical energy pulsation; a crest with magnetic energy pulsation towards the left and a belly with magnetic energy pulsation towards the right. Crest and belly alternate front/forward or front/back. The pulsar oscillating back/forward is radiant energy, that is, energy radiating into space; the pulsar oscillating back/forward is stationary energy. All elementary particles are radiating pulsars or stationary pulsars.
Let’s look at the two images below. Two pulsars are illustrated, one radiating and one stationary. Black arrows designate electrical vectors; the red arrows indicate the magnetic vectors. Electric and magnetic vectors form a crest and a trough. The oscillation of the upward radiating pulsar (green arrows) is forward/forward. The oscillation of the stationary pulsar below (green arrows) is forward/backward (figure 5).
Figure 5. Radiating pulsar and stationary pulsar. The pulsar is an oscillating/pulsating temporal energy unit. The pulsations are electric and magnetic. They radiate in space in opposite directions: above/below (electrical pulsations and left/right (magnetic pulsations). The two pulsations generate the crest and the trough. The oscillation can occur in the forward/forward direction or in the forward/backward direction. The top image illustrates the pulsar oscillating forward/forward; the bottom image illustrates the pulsar oscillating forward/backward. The pulsar oscillating forward/forward is radiant energy, that is, energy that radiates into space; the pulsar that oscillates back/forward is stationary energy.
The pulsar, as already written, is a pulsating/oscillating energy unit. What pulsates is electrical energy and magnetic energy. This is “material energy”. It is made up of energy packets. Each packet corresponds to the Planck energy “h”. The pulsating energy, therefore, can be “h” or multiples of “h”. The simplest and most intuitive way to show the energetic interaction between pulsation and oscillation is to consider the forward/forward and forward/backward oscillation as a space/time container of the material energy “h” and its multiples. We call this space/time container: “bubble”.
The “bubble” is the intrinsic vacuum generated by the two vectors, material and imaginary. It has a wave shape and contains the material energy of the vectors. The wave motions of quantum particles are the motions of the dynamic vacuum that contains material energy.
The Schroedinger wave function
Schroedinger, in formulating a law that explained the wave motions of quantum particles, introduced a new fundamental quantity, the wave function, indicated by Ψ, which represents its solution. The wave equation is a type of differential equation that, if solved, gives us the “wave function” Ψ (x,t). From a formal point of view, a quantum particle was described by the wave function Ψ (x,t). By solving the Schroedingher equation one could, in principle, calculate the wave function of every particle then known. As a consequence of the introduction of Ψ, it can no longer be stated that “at time t the particle is at x”; we must instead say that “the motion of the particle is represented by the function Ψ (x,t), which provides the amplitude Ψ at time t at point x”. The precise location is no longer known. If we see that Ψ is particularly large at a point x and almost nothing elsewhere, we can say that the particle is “about at position x”. The wave functions of elementary particles are considered by physicists to be “abstract spaces”, better defined as “Hilbert spaces”. They are obtained through the solution of the “Schroedinger” equation. The square of the Schroedinger wave function is considered the volumetric space in which it is highly probable to find the particle.
In our hypothesis based on energy and energy vectors, the wave function describes the perturbation of the intrinsic vacuum of the particle. Hilbert spaces are real spaces proper to quantum particles. The square of the Schroedinger wave function describes the intrinsic space of material energy. Material energy is distributed in Hilbert spaces. In other words, the particle, understood as a material point, does not exist. The particle is the material energy distributed in the bubble. The bubble is described by the Schroedinger wave function.
The electromagnetic wave of the photon is a succession of bubbles, which can vary in size but contain the same energy “h”. The electromagnetic wave of the electron is a succession of bubbles which can vary in size by varying in a directly proportional way in energy “h”.
The photon bubble increases/decreases spatially/temporally. The electron bubble increases/decreases spatially, with invariance of time.
Let’s represent the space/time bubble in the simplest way possible. On the x-axis we indicate time, that is, the duration of a forward/forward or forward/backward oscillation of radiant or stationary energy. This duration coincides with the duration of the generation of the material carriers. On the ordinate axis we indicate the space, that is, the void generated by the two real and imaginary vectors.
Space and time are bubbles that contain the material energy “h”. The photon bubbles are shown above. They vary in size but are invariant for the material energy contained, which is always “h”. Below are the electron bubbles. They vary in size; concomitantly with the change in size, the energy “h” contained also varies, in a directly proportional manner. Photon and electron bubbles are different in shape. Photon bubbles enlarge spatially/temporally and are shaped like squares. The electron bubbles enlarge spatially, with invariance of time, and have the shape of rectangles (figure 6).
Figure 6. Space/time bubbles containing material energy “h”. In the top row three space/time bubbles of three photons with decreasing energy are depicted. The smaller the space/time bubble, the greater the energy. In the bottom row three space/time bubbles of three electrons with increasing energy are depicted. The larger the space/time bubble, the greater the energy. Photon space/time bubbles zoom in/out both spatially and temporally. The space/time bubbles of the electron enlarge/shrink spatially and remain invariant temporally.
Growth time and growth duration of the intrinsic vacuum
The simplest way to explain what happens is to consider the forward/forward and forward/backward oscillation as the “growth” of the bubble (this time is the same as the material carriers). Of growth we can consider the “growth time” and the “growth duration”. Growth time tells me how long it took to grow. The growth duration tells me how long the energy takes to generate the single bubble.
The growth time is invariable in all forms of energy. It flows uniformly and always in the same way. We can consider it as a temporal background, against which the space/time bubbles containing the “h” energy stand out.
Let’s focus on the photon. It, as energy radiating in space, is a succession of space/time bubbles in the temporal background. Let’s look at the image below. Two photons with different energies are depicted. In the more energetic photon the space/time bubbles, containing the energy “h”, are smaller. The red arrows designate the invariable temporal background (Figure 7).
Figure 7. Photons with different energies. The photon, represented above, has double the energy of the photon represented below. The more energetic photon is a succession of smaller bubbles than those of the less energetic photon.
Let’s focus on the durations of the bubbles, leaving aside the spatial size of the container. Let’s look at the figure below. The red arrow designates the temporal background (growth time). Each segment indicates the growth duration. These are temporal instants “t” (temporal figures) that follow one another on the temporal background. Each instant contains the energy “h”. In the more energetic photon the time instants containing the energy “h” are smaller. The relationship between the temporal instants and the temporal background is the “frequency”, that is, how many instants are contained in time understood as the background. The more energetic photon has a higher frequency than the less energetic photon (figure 8).
Figure 8. Photons with different energy and different frequency. The photon, represented at the top, has double the energy of the photon represented at the bottom. In the same temporal background (red arrow), the most energetic photon oscillates six times; the least energetic photon oscillates three times.
Photon time is Einstein’s “relative time”. The moments that follow one another in the background have different durations. In the more energetic photon, time “flows faster” compared to the less energetic photon.
Let’s focus on the electron. It too, like radiant energy, is a succession in space of space/time bubbles in the temporal background. Let’s look at the image below. Two electrons with different energies are depicted. In the more energetic electron the space/time bubbles, containing the energy “h”, are larger. The red arrows designate the invariable temporal background. The size of the bubbles of the two electrons varies as space varies with time remaining unchanged. The bubbles of both electrons, in fact, have the same “duration”, represented on the x-axis. The bubbles of the more energetic electron are twice as large and contain twice as much energy as the less energetic electron (figure 9).
Figure 9. Electrons with different energy and same frequency. The electron, depicted at the bottom, has double the energy of the electron depicted at the top, despite the fact that they oscillate at the same frequency. Each oscillation of the more energetic photon contains twice as much material energy as the oscillation of the less energetic electron.
In the electron the frequency with which temporal instants follow one another on the temporal background is constant. What varies is the size (only spatial) of the bubble and the amount of energy that each bubble contains.
Electron time is Newton’s “absolute time”. Instants of equal duration follow one another on the temporal background, whatever the energy of the electron. Newton’s time is invariable.
Let us now try to clarify what “mass” is. The concept of “mass”, intuitively, is the quantity of matter contained in a space. The same space can contain more or less matter. If the same space contains more matter, we will say that the matter is more concentrated; if the same space contains less matter, we will say that the matter is more diluted. At the level of elementary particles, the simplest and most intuitive explanation is to assume that it is time that contains matter. Time, in elementary particles, is made up of a temporal figure on a temporal background. The time figure is the duration of the space/time bubble.
Mass of the photon
The Einstein time of the photon is a succession of “t” moments on the temporal background. Every instant contains the same energy “h”. We wrote that Einstein’s time is relative, that is, variable. It varies as the energy of the photon varies. The instant “t” of the less energetic photon is longer lasting than the instant “t1” of the more energetic electron. The longer-lasting instants follow one another at a lower frequency than the shorter-lasting instants of the more energetic photon.
In all photons the temporal background is invariant. This background, in the more energetic photon, contains a greater number of smaller instants, compared to the number of instants of the less energetic photon. The more instants, the more concentrated the energy in the temporal background. The number of moments in the time background is the frequency. The higher the frequency, the higher the energy. Frequency, therefore, is a measure of the concentration/dilution of material energy, i.e. mass.
In the photon, the energy varies by concentration/dilution. The maximum dilution occurs when the temporal background contains only one instant, that is, an oscillation. The maximum concentration occurs when the temporal background contains a number of instants (oscillations) of the order of hundreds of billions (gamma rays). The variable Einsteinian instant is the temporal magnitude of space/time bubbles. The temporal size of each bubble is a measure of the concentration/dilution of material energy
Mass of the electron
Let’s focus on the electron. Electron time is Newton time. It is invariant, being made up of instants that follow one another at the same duration on the temporal background. In the electron, the oscillation frequency is constant and very high. Hundreds of billions of moments follow one another in the temporal background of one second. This number does not vary as the energy of the electron varies. The level of energy concentration, which depends on the frequency, is constant. This means that in all electrons, the energy is concentrated at the same level. This energy is the rest mass of the electron. The rest mass, therefore, is the level of concentration of energy which is constant in the electron and which depends on the invariable frequency. Every instant, that is, every bubble duration contains material energy at the same degree of concentration/dilution.
Since the frequency is invariable, all the electrons, even of different energy, contain the same number of instants of equal duration in the temporal background. What makes one electron different from another is the energy “h” contained in each Newtonian instant. In the more energetic electron the same instant in time contains greater energy “h” at the same degree of concentration/dilution.
Material energy is “mass”. The photon is mass energy varying by concentration/dilution. The formula E = fh describes, in the photon, the variation of mass. The higher “f” i.e. the frequency, the higher concentration of mass is present in the container. In the electron, the formula E = fh describes the highly concentrated mass of the electron. This is the “rest mass”. Indicating the rest mass with mr, we will have: E = mr = fh
Change in energy of the photon and electron
To make the two variations in energy of the photon and the electron intuitive, let’s give two examples. The first concerns stationary energy that oscillates forward/backward; the other example concerns radiant energy oscillating back/forward. Suppose we have two lamps (two stationary pulsars) that turn on/off, giving off flashes of light. Each glow represents the material energy “h”. The first lamp always emits flashes of the same intensity, i.e. “h”. When it acquires energy, it increases the frequency of the flashes. If it loses energy, the frequency of the flashes decreases. This lamp describes the behavior of the photon.
The second lamp behaves in a complementary way. It always emits flashes at the same frequency. When the energy increases it emits more intense flashes; the material energy that was “h” increases and becomes “2h”, “3h”, etc.. When it loses energy, it emits less intense flashes. The material energy that was “3h” decreases and becomes “2h”, “h”. This lamp describes the behavior of the electron.
Let us now analyze radiant energy. We have three rows of lamps (each row is a radiating pulsar) arranged over a 100 m wide field. In the first row there are 10 lamps, in the second row there are 8 and in the third row there are 6. The lamps light up in succession, that is, one after the other. The lamps of the three rows complete the lighting in the same time of 10 seconds. Each lamp is invariant to the intensity of the glow. The energy of each row depends on the frequency. The first row has a frequency of 10 flashes every 10 seconds; the second row has a frequency of 8 flashes every 10 seconds; the third row has a frequency of 6 flashes every 10 seconds. The apparent motion (which corresponds to the speed of light) of each row, generated by turning on the lamps, is invariant. Each row represents photons of different energy in decreasing order (figure 10).
Figure 10. Representation of the energy of three photons in decreasing order. Each row of lamps represents the energy of a single photon. All lamps emit flashes at a frequency of 6 flashes every 10 seconds. The apparent motion generated by the succession in space has the same intensity. The lamps of the first have a frequency of 10 flashes every 10 seconds; the second row lamps have a frequency of 8 flashes every ten seconds; the third row lamps flash at the same speed, row by row.
We have three rows of lamps spread across a 100 meter wide field (each row represents a radiating pulsar). In all three rows there are 10 lamps. In the first row, the lamps are grouped in 25 meters, in the second row, the lamps are grouped in 50 meters; in the third row, the lamps are grouped in 100 meters. They turn on/off in succession. All three rows complete the succession of flashes in 10 seconds. The frequency of the flashes is the same: 10 flashes every 10 seconds. The lamps in a single row emit flashes of the same intensity. However, the intensity of the flashes varies from row to row. The glow intensity of the first row is half that of the second, and the glow intensity of the second is half that of the third. Even the apparent motion (which corresponds to the speed of the electron), generated by the switching on of the lamps, varies row by row. The third row has double the speed of the second and the second has double the speed of the first. Each row represents electrons of different energy in ascending order. The set of flashes is the rest mass of the electron. It doubles row by row (figure 11).
Figure 11. Representation of the energy of three electrons in ascending order. Each row of lamps represents the energy of a single electron. The lamps emit flashes with increasing intensity row by row. Each row consists of 10 lamps. The frequency of the flashes is the same row by row. The apparent motion, generated by the succession of flashes in space, occurs at different speeds. The speed of the second row is double the speed of the second row and the latter is double the speed of the third row.
Intensity and number of lobes of the electron
The electrons bound to the nucleus are “stationary pulsars” that oscillate back and forth at the same fundamental frequency. The electrons differ in intensity and number of lobes. Single-lobed electrons are single-oscillating pulsating units. Bilobed electrons are two-oscillating pulsating units. Tetra-lobed electrons are four-oscillating pulsating units. Eight-lobed electrons are eight-oscillating pulsating units. This means that the time it takes for the single-lobed electron to make one oscillation is the same time that the bi-lobed electron makes two oscillations, the tetra-lobed electron makes four oscillations and the eight-lobed electron makes eight oscillations .
Mono-lobed, bi-lobed and tetra-lobed electrons can be at different energy levels. The first-level mono-lobed electron has half the energy of the second-level mono-lobed electron. The second level two-lobed electron has half the energy of the third level two-lobed electron. The third-level tetra-lobed electron has half the energy of the fourth-level tetra-lobed electron.
Energy variation in the macroscopic world and in the microscopic world
As regards energy, what happens at the level of elementary particles is analogous to what happens at a macroscopic level. At a macroscopic level, kinetic energy is the energy possessed by a body as a consequence of its own motion. The formula for kinetic energy is: K = 1/2mv2. Mass and velocity are two energetic components of kinetic energy, which can vary as the mass varies or as the velocity varies.
Let’s imagine that in the macroscopic world there are two objects that behave in a complementary way. The first enlarges/shrinks, increasing/decreasing mass and keeping speed constant; the second remains with the same mass but increases/decreases in speed. The first “object” is energy invariant for velocity and mass variation; the second “object” is mass invariant energy and velocity variant.
At the level of elementary particles, something similar happens. The photon resembles the macroscopic object that varies in mass but is invariant in velocity; the electron resembles the macroscopic object that varies in speed but is invariant in mass.
To illustrate the variance/invariance of energy due to velocity in elementary particles we must focus on the speed of the forward/forward or forward/backward oscillation. The photon always oscillates at the same speed and is distributed in space, as radiant energy, at the speed of light which is invariable. (Remember that in the photon the duration of each bubble varies). The electron can increase the speed of oscillation, for example, doubling it. In this circumstance the spatial size of the space/time container doubles while the temporal duration remains invariant. The electron, as radiant energy, is distributed in space at a double speed.
The minimum velocity of the electron is a measure of its energy, similar to rest mass and frequency. If we indicate with vm the minimum speed of the electron, we will have: E = vm = ms = fh. Speed, mass and frequency are three forms of energy. The energy of the electron varies as the minimum speed varies. If the minimum velocity doubles, the rest mass doubles: vm = ms, 2 vm = 2ms, 4vm = 4ms