Part 3: QUANTUM WAVE SOURCES page 4

 

3.7. Wave Sources with a Different Spin

As stated previously, an even number integer spin is a boson spin, and an odd number integer spin is a fermion spin in this article. Of course, I could divide them both by 2 and get an integer spin for bosons and a ½ odd number spin for fermions [7, 8].

The spin for the wave source in Figures 9A through 9D has a one wavelength spin, or spin 1. I give other possible spins in Figures 10A through 10F. Figures 10A, 10C, and 10E have even spin wavelengths, which are 2, 4, and 6, respectively. Figures 10B, 10D, and 10F have odd spin wavelengths, which are 3, 5, and 7, respectively. I again apply the fundamental rule for amplitude addition for the hypothetical medium of these wave sources. Amplitudes of waves with reverse direction add up in a reverse manner. (For example, two crests would cancel, if one is on a wave moving in the opposite direction to the other.) Therefore, every wave amplitude cancels out for the wave sources with even-spin wavelengths. This is true not only on the X, Z plane but three-dimensionally as well. It is only the wave sources with odd-spin wavelengths that can exist. Do these results parallel fermions’ behavior? Yes, they do. Fermions exist stably at odd-number angular momentums. Indeed, they can exist at 1⁄2 spin, 3⁄2 spin, 5⁄2 spin, etc. (The 5⁄2 spin would have a greater frequency and angular momentum than the 3⁄2 spin because of the 5⁄2 represents a greater frequency.) Furthermore, any two identical fermions can interfere in Figure 9, creating a single particle and resulting in an even spin, and they cancel each other out. According to Rule 3 in Table 1, waves that cancel will repel each other. This satisfies the Pauli exclusion principle. If I were to add any of the odd number spins in Figures 9A, 10A, 10C, and 10E, the result would give wave sources that had even-spin wavelengths. Of course, their amplitudes cancel themselves, as previously stated. I have just shown that my three-dimensional transversal wave sources exist stably only at odd number spins and that they obey Pauli’s exclusion principle.

In traditional quantum theory, waves do not interfere unless they are identical. However, I will reinterpret that concept. The only way an experimenter can know that two quantum particles interfered is by detecting the results of particles that were so near each other that they interfered. An experimenter must detect the results to determine that wave interference occurred. Instead of stating that only identical quantum particles interfere, I propose that quantum particles interfere with each other where there is no measurable difference between them. The elements of my quantum wave sources (wave pulses) cannot be measured. As a result, they can interfere with each other regardless of which direction they travel.

An interesting point to raise is that these wave sources with odd number wave spins could only exist in my hypothetical medium because of the rule for reversing the amplitudes of waves with an opposite direction. In a traditional medium, these waves with odd spins would essentially cancel themselves. Indeed, the amplitude of the entire wave source would cancel. This leads to the important question: Could a three-dimensional transversal wave source with an even spin exist in a traditional medium? The answer is still no, as the waves emitted on at least one axis would cancel. Nonetheless, three-dimensional transversal wave sources are the foundation for fermions. To eventually complete this structure, more information about fermions is required.

 

3.8. Reverse Amplitudes

In order for the idea of a quantum wave source to exist, the three-dimensional transversal wave source needed to be made viable in a medium. This was made possible when I created my rule for reversing amplitude interference for waves moving in opposing directions in reference to each other. This rule naturally leads to a question: How can this be possible? To answer this, I link the amplitude for a quantum wave to its change of radians, or degrees. For simplicity, I only refer to radians. In my hypothetical medium, a wave is waving in reverse to another wave if it is moving in a reverse direction to that other wave. I designate a reverse wave with a negative change of radians. This is not the same as taking a normal sine wave in a traditional medium and having it cycle through radians in a negative direction. A normal wave would not have its amplitude associated with the change of radians as I propose here. In this section, I am essentially giving the concept of what is waving a plus or minus direction associated with the direction of the wave. Since the direction of the wave is relative, the direction of whatever is waving is relative, too.

In Figure 11, I have three waves: P, Q, and R, with P moving in an opposite direction to the others. These waves are shown at ½ wavelengths. There are also six points (A through F) in the figure. The waves are shown separated, but in my discussion, I treat them as if they were coinciding. To be more specific, I claim that points A, C, and E coincide as well as points B, D, and F.

Next, I wish to make the amplitudes of these waves dependent on the Δθ (change of radians). Figure 11 shows that wave P is moving to the left and its Δθ is positive in that direction. Furthermore, waves Q and R are moving to the right, and each of their Δθ is positive in that direction. I examine how each wave waves as it moves with their respective Δθ. (I designate Δθ as being positive without the necessity of putting a plus sign in front of it.) Since wave P is moving from right to left, point B is waving ↑ (up) and point A is waving ↓ (down). I represent wave P’s amplitude with Δθ↑↓. This means that in the direction that the wave is propagating, the wave goes up, then down. In other words, a crest occurs. Wave Q’s amplitude is represented in the same manner with Δθ↑↓, which is also a crest. However, wave R’s amplitude is given by Δθ↓↑, which is a trough.

A wave always propagates in the direction of its Δθ, and not its −Δθ. Since wave P is waving to the left, it interferes with wave Q in a reverse direction. Therefore, wave Q is a reverse amplitude relative to wave P, with a negative Δθ↑↓, i.e., −(Δθ↑↓). This means that relative to wave P, wave Q’s point C is still waving ↑, and point D is still waving ↓. As wave P propagates in the direction from point B to A, it propagates in the direction from point D to C and interferes with all the points from D to C. Hence, wave P moves in its direction of Δθ while going from point D waving ↓ to point C waving ↑. Wave P interferes with wave Q so that −(Δθ↑↓) = Δθ↓↑, which is a trough. Consequently, when waves P and Q interfere in Figure 11, they cancel. On the other hand, wave R’s amplitude is Δθ↓↑, and −(Δθ↓↑) = Δθ↑↓, which is a crest. Waves R and P interfere constructively. The equation −(Δθ↓↑) = Δθ↑↓ does not mean that wave R has changed the direction of its propagation. Instead, it only represents how wave P’s amplitude interferes with wave R’s amplitude.

In this section, I have discussed how whatever is waving is affected by the direction of the propagation of that wave. This is not the case for waves in traditional mediums. In traditional mediums, the amplitude is not influenced by the direction of propagation of one wave relative to another.

 

3.9. Single-Directional Wave Sources and Translational Motion of All-Directional Wave Sources

In Figure 1, I delineated two types of point-wave sources found in traditional mediums. However, Figure 1 was only an analogy in two dimensions. I leaped beyond this analogy by creating a three-dimensional hypothetical medium which I claimed to be the cosmic quantum medium. I have up to now constructed for my cosmic quantum medium the type of point-wave source that is spreading out in all directions (a central wave source). This was the three-dimensional transversal wave source. Now I wish to construct the other wave source discussed in Figure 1. This is the single-directional wave source which constitutes a wave front moving in one direction across a medium.

Referring to Figure 12, there are three images (12A, 12B, and 12C), and each represents a wave with a different spin around an axis represented by its respective gray arrows. Figure 12A has spin 0; Figure 12B has spin 1; and Figure 12C has spin 2. The gray arrows in all three images represent the center or axis of rotations for the wave and gives the direction of the wave’s propagation. In Table 1, the rules for wave behavior in my three-dimensional quantum medium are given. Rule 4 in this table is as follows: Waves vibrate so that there are opposite points of amplitude at ½ a wavelength apart, and these two opposing points of a wave happen at opposing sides of the center of the wave within any space. Figure 12A satisfies this rule because the crest and troughs are on the opposite sides of the wave center given by the gray arrow. Of course, Figure 12A wave has spin 0 so that the wave is not spinning around the gray arrow. Hence, the wave vibrates so that the crest and trough will always be on the opposite side of the arrow. Figure 12B has a wave with spin 1. This means that for one full wavelength of the wave, the wave will spin once around. Therefore, at ½ a wavelength, the wave will spin halfway around and the trough will be on the same side of the gray arrow as the crest. This contradicts Rule 4. Consequently, the spin for the wave in Figure 12B cannot exist. Figure 12C has spin 2. This means the wave will spin twice around the gray arrow per one wavelength. At ½ a wavelength, the trough will be below the gray arrow because at this time the wave should have one complete spin around the gray arrow. This result agrees with Rule 4. In Figure 12C, at one full wavelength, the crest will occur above the gray line. All these images show that a one-directional wave in my quantum medium can have an even spin but not an odd spin, as an even spin—not an odd spin—results in a permissible vibration according to Rule 4. Hence, one-directional waves have a boson spin. Consequently, wave fronts made out of one-directional point-wave sources should be bosons.

Fermions always move (translational motion) as wave fronts. Therefore, their spin in the wave front (i.e., spin associated with translational motion) should be even. Of course, an even number plus an odd number always gives another odd number. (The translational motion even number spin can be 0.) Consequently, an odd number spin is still the result when the wave front spin and the rest spin (i.e., spin of the particle when it is at rest) are added up for a fermion. Furthermore, photons never come to rest as photons. They always travel as wave fronts. Hence, photons can only have an even spin, which is a boson spin. Like particles of matter, there is a correspondence between the spin of a photon and its frequency, which for spin 2 is the following: one complete cycle of the frequency equals two complete rotations of the particle. Of course, for spin 0 there is no such correspondence because there is no spin. Looking at this equation between a photon’s spin and frequency, we see that it is a linear equation. According to this linear equation, as the frequency speeds up, so will the spin, or as the frequency slows down, so will the spin. Furthermore, in my theory, photons necessarily have an axis of spin that is parallel to the direction of the photon’s velocity. This means their spins are perpendicular to their velocities. These results are the case in the standard model, too [10]. If two photons are identical, they can interfere constructively. This constructive interference should cause an attractive force between them according to Rule 3 of Table 1.

In this section, I describe a one-directional wave with a single pulse, and I use it to describe the photon. This means these one-directional wave pulses are essentially bosons. They can have even spin, which includes zero spin. Yet previously, I define matter (fermions) as having one-directional wave pulses pointed in all directions. Hence, fermions are constructed out of bosons. Within the construct for fermions, the one-directional wave pulses have zero spin themselves. However, they interfere together in a manner that produces 1/2 spin. The series of events that led to this fermion structure would have to obey the conservation of angular momentum. Therefore, photons would be destroyed and fermions created such that the total angular momentum of all the photons destroyed would equal the total angular momentum of all the fermions created. Also, this parallels the relationship between the two different waves sources discussed in Figure 1. The wave sources that parallel photons are in the wave front that propagates in one direction. The central wave source in Figure 1 propagates in all directions and it parallels fermions. In Figure 1, the wave sources that parallel photons (bosons) can add up to make the central wave source, which parallels fermions. This relationship shows the fundamental similarities and differences between light and matter. It is probable that the constructs for light and matter are more complex than I present here in my work. I intentionally keep all structures to their simplest forms. Figure 1 is only an analogy of the relationship between light and matter. This means that there are differences between Figure 1 and the relationship between light and matter. The one-directional wave pulses are emitted by the central wave source in Figure 1. In Figure 8, the one-directional wave sources are not being emitted with speed c but are trapped within the central wave source, which is the three-dimensional transversal wave source. The forces, discussed in section 5, trap the waves pulses represented in Figure 8. To emit or release these wave pulses, matter needs to be destroyed and light emitted or released. To summarize, the wave pulses in Figure 8 are bosons. Individually, these wave pulses have a zero spin, which makes them bosons. As bosons, these individual wave pulses attract each other, creating a three-dimensional transversal wave source. Also, these individual wave pulses are trapped, making them standing waves.

 

3.10. Conclusion to Part 3

Instead of the Copenhagen interpretation, I used Huygens’ principle to interpret the double-slit experiment for quantum theory and named it the wave source interpretation. Since Huygens’ principle describes the behaviors of waves in small regions as wave sources, I concluded that the best way to understand elementary quanta is to understand wave sources. I then gave a definition of a wave source as being the central originating wave to other waves. I also developed Huygens’ principle so that characteristics of a central wave source could be conserved in the wave front emitted from it. Furthermore, I discussed the concept of a compound wave source which starts to exist when two identical wave sources overlap. I briefly discussed how this relates to hadrons. I created a three-dimensional transversal wave source structure. Without relying on the standard model and only using this structure, I predicted a quantified odd number spin and the Pauli exclusion principle for these wave sources, both of which parallel fermions’ behavior. Furthermore, I discussed the concept of a wave moving in the opposite direction to another wave and how this reverses amplitude interference between them. At the end, I discussed the spin of wave fronts and photons.

In quantum theory all particles are essentially treated as wave packets [1–5]. Here, on the other hand, I create a foundational new structure—the three-dimensional transversal wave source. This structure for the quantum gives us a greater ability to understand and predict fermion behavior than traditional quantum theory does. Hence, the result is a deeper quantum theory.

When I discussed compound wave sources, I brought up the nuclear strong force. (The nuclear strong force is the force that holds quarks together in a hadron.) The idea that compound wave sources correspond to compound particles is a clue to understanding the nuclear strong force and other forces. In section 5, I do discuss forces caused by constructive interference, and these forces are similar to the nuclear strong force and the nuclear weak force. However, I only discuss them briefly.

It is best to think of the spin in these particles as being intrinsic to their structures. It is not the medium that is spinning. A string could spin in such a manner that the wave on it would spin as well. Here I have presented a three-dimensional medium (the cosmos) that is not spinning. Therefore, the spin derives from the intrinsic structure of the particle. I did not put spin in my theory; rather it popped up on its own.  A three-dimensional transversal wave source has to spin. Without a spin, the three-dimensional transversal wave source would not work. The spin allows for wave pulses to exist in all directions and mesh in a smooth continuous fashion. There are two aspects of the three-dimensional wave source. There are the wave pulses, which I define as one directional and which exist at ½ a wavelength. These are the most basic components to the holistic wave, which is the other aspect of the wave. The wave pulses themselves are not spinning, but they mesh together or interfere to create the holistic wave, which is spinning. It is how these wave pulses interfere with each other that causes the spin of the holistic or total wave, which is intrinsic to the three-dimensional transversal wave source. Also, all things would have to be considered in designing possible permissible wave constructs beyond what I have discussed so far. In other words, what goes into an interaction, or a colliding of particles, must come out. What comes out, however, may look different in some manner than what went into the mix.