While the series of elements contains no combinations of motions with net positive displacement less than that of hydrogen, 2-1-(1), this does not mean that such combinations are non-existent. It merely means that they do not have sufficient speed displacement to form two complete rotating systems, and consequently do not have the properties, which distinguish the rotational combinations that we call atoms. These less complex combinations of motion can be identified as the sub-atomic particles. As is evident from the foregoing, these particles are not constituents of atoms, as seen in current scientific thought. They are structures of the same general nature as the atoms of the elements, but their net total displacement is below the minimum necessary to form the complete atomic structure. They may be characterized as incomplete atoms.
The term “sub-atomic” is currently applied to these particles with the implication that the particles are, or can be, building blocks from which atoms are constructed. Our new findings make this sense of the term obsolete, but the name is still appropriate in the sense of a system of motions of a lower degree of complexity than atoms. It will therefore be retained in this work, and applied in this modified sense. The term “elementary particle” must be discarded. There are no “elementary” particles in the sense of basic units from which other structures can be formed. A particle is smaller and less complex than an atom, but it is by no means elementary. The elementary unit is the unit of motion.
The theoretical characteristics of the sub-atomic particles, as derived from the postulates of the Reciprocal System, have been given considerable additional study since the date of the last previous publication in which they were discussed, and there has been a significant increase in the amount of information that is available with respect to these objects, including the theoretical discovery of some particles that are more complex than those described in the first edition. Furthermore, we are now in a position to examine the structure and behavior of the cosmic sub-atomic particles in greater depth (in the later chapters). In order to facilitate the presentation of this increased volume of information, a new system of representing the dimensional distribution of the rotation has been adopted.
This means, of course, that we are now using one system of notation for the rotation of the elements, and a different system to represent the rotations of the same nature when we are dealing with the particles. At first glance, this may seem to be introducing an unnecessary complication, but the truth is that as long as we want to take advantage of the convenience of using the double displacement unit in dealing with the elements, while we must use the single unit in dealing with the particles, we are necessarily employing two different systems, whether they look alike or not. In fact, lack of recognition of this difference has led to some of the confusion that we now wish to avoid. It appears, therefore, that as long as two different systems of notation are necessary for convenient handling of the data, we might as well set up a system for the particles in a manner that will best serve our purposes, including being distinctive enough to avoid confusion.
The new notation used in this edition will indicate the displacements in the different dimensions, as in the first edition, and will express them in single units, as before, but it will show only effective displacements, and will include a letter symbol that will specifically designate the rotational base of the particle. It is necessary to take the initial non-effective rotational unit into consideration in dealing with the elements because of the characteristics of the mathematical processes that we will utilize. This is not true in the case of the sub-atomic particles, and as long as the atomic (double) notation cannot be used in any event, we will show only the effective displacements, and will precede them with either M or C to indicate whether the rotational base of the combination is material or cosmic. This will have the added advantage of clearly indicating that the rotational values in any particular case are being expressed in the new notation.
This change in the symbolic representation of the rotations, and the other modifications of terminology that we are making in this edition, may introduce some difficulties for those who have already become accustomed to the manner of presentation in the earlier works. It seems advisable, however, to take advantage of any opportunities for improvement in this respect that may be recognized in the present early stage of the theoretical development, as improvements of this nature will become progressively less feasible as time goes on and existing practices become resistant to change.
On the new basis, the material rotational base is M 0-0-0. To this base may be added a unit of positive electric displacement, producing the positron, M 0-0-1, or a unit of negative electric displacement, in which case the result is the electron, M 0-0-(1). The electron is a unique particle. It is the only structure constructed on a material base, and therefore stable in the local environment, that has an effective negative displacement. This is possible because the total rotational displacement of the electron is the sum of the initial positive magnetic unit required to neutralize the negative photon displacement (not shown in the structural notation) and the negative electric unit. As a two-dimensional motion, the magnetic unit is the major component of the total rotation, even though its numerical magnitude is no greater than that of the one-dimensional electric rotation. The electron thus complies with the requirement that the net total rotation of a material particle must be positive.
As brought out earlier, adding motion with negative displacement has the effect of adding more space to the existing physical situation, whatever it may be, and the electron is therefore, in effect, a rotating unit of space. We will see later that this fact plays an important part in many physical phenomena. One immediate, and very noticeable, result is that electrons are plentiful in the material environment, whereas positrons are extremely rare. On the basis of the same considerations that apply to the electron, we can regard the positron as essentially a rotating unit of time. As such, it is readily absorbed into the material system of combinations, the constituents of which are predominantly time structures; that is, rotational motions with net positive displacement (speed = 1/t). The opportunities for utilizing the negative displacement of the electrons in these structures, on the contrary, are very limited.
If the addition to the rotational base is a magnetic unit rather than an electric unit, the result could be expressed as M 1-0-0. It now appears, however, that the notation M ½-½-0 is preferable. Of course, half units do not exist, but a unit of two-dimensional rotation obviously occupies both dimensions. To recognize this fact we will have to credit one half to each. The ½-½ notation also ties in better with the way in which this system of motions enters into further combinations. We will call this M ½-½-0 particle the massless neutron, for reasons, which will appear shortly.
At the unit level in a single rotating system, the magnetic and electric units are numerically equal; that is, 12 = 1, Addition of a unit of negative electric displacement to the M ½-½-0 combination of motions, the massless neutron, therefore produces a combination with a net total displacement of zero. This combination, M ½-½-(1), Can be identified as the neutrino.
In the preceding chapter, the property of the atoms of matter known as atomic weight, or mass, was identified with the net positive three-dimensional rotational displacement (speed) of the atoms. This property will be discussed in more detail in the next chapter, but at this time we will note that the same relationship also applies to the sub-atomic particles; that is, these particles have mass to the extent that they have net positive rotational displacement in three dimensions. None of the particles thus far considered meets this requirement. The electron and the positron have effective rotation in one dimension; the massless neutron in two. The neutrino has no net displacement at all. The sub-atomic rotational combinations thus far identified are therefore massless particles.
By combination with other motions, however, the displacement in one or two dimensions can attain the status of a component of a three-dimensional displacement. For instance, a particle may acquire a charge, which is a motion of a kind that will be examined later in the development, and when this happens, the entire displacement, both of the charge and of the original particle, will then manifest itself as mass. Or a particle may combine with other motions in such a way that the displacement of the massless particle becomes a component of the three-dimensional displacement of the combination structure.
Addition of a unit of positive, instead of negative, electric displacement to the massless neutron would produce M ½-½-1, but the net total displacement of this combination is 2, which is sufficient to form a complete double rotating system, an atom, and the greater probability of the double structure precludes the existence of the M ½-½-1 combination, other than momentarily.
The same probability considerations likewise exclude the two-unit magnetic structure M 1-1-0, and its positive derivative M 1-1-1, which have net displacements of 2 and 3 respectively. However, the negative derivative, M 1-1-(1), formed in practice by the addition of a neutrino, M ½-½-(1), to a massless neutron, M ½-½-0. can exist as a particle, as its net total displacement is only one unit; not enough to make the double structure mandatory. This particle can be identified as the proton.
Here we have an illustration of the way in which particles that are individually massless, because they have no three-dimensional rotation, combine to produce a particle with an effective mass. The massless neutron rotates only two-dimensionally, while the neutrino has no net rotation. But by adding the two, a combination with effective rotation in all three dimensions is produced. The resulting particle, the proton, M 1-1-(1), has one unit of mass.
At the present, rather early, stage of the theoretical development it is not possible to make a precise evaluation of the probability factors and other influences that determine whether or not a theoretically feasible rotational combination will actually be able to exist under a given set of circumstances. The information now available indicates, however, that any material type combination with a net displacement less than 2 should be capable of existing as a particle in the local environment. In actual practice none of the single system combinations identified in the preceding paragraphs has been observed, and there is considerable doubt as to whether there is any way whereby they can be observed, other than through indirect processes which enable us to infer their existence The neutrino, for example, is “observed” only by means of the products of certain events in which this particle is presumed to participate. The electron, the positron, and the proton have been observed only in the charged state, not in the uncharged condition, which constitutes the basic state of all of the rotational combinations thus far discussed. Nevertheless, there is sufficient evidence to indicate that all of these uncharged structures do, in fact, exist, and play significant roles in physical processes. This evidence will be forthcoming as we continue the theoretical development.
In the previous publications, the M ½-½-0 combination (1-1-0 in the notation utilized in those works) was identified as the neutron, but it was noted that in some physical processes, such as cosmic ray decay, the magnetic displacement that could be expected to be ejected in the form of neutrons is actually transferred in massless form. Since the observed neutron is a particle of unit atomic weight, it was at that time concluded that in these particular instances the neutrons act as combinations of neutrinos and positrons, both massless particles. On this basis, the neutron plays a dual role, massless under some conditions, but possessing unit mass under other circumstances.
Further investigation, centering mainly on the secondary mass of the sub-atomic particles, which will be discussed in Chapter 13, has now disclosed that the observed neutron is not the single effective magnetic rotation with net displacements M ½-½-0. but a more complex particle of the same net displacement, and that the single magnetic displacement is massless. It is no longer necessary to conclude that the same particle acts in two different ways. Instead, there are two different particles.
The explanation is that the new findings have revealed the existence of a type of structure intermediate between the single rotating systems of the massless particles and the complete double systems of the atoms. In these intermediate structures there are two rotating systems, as in the atoms of the elements, but only one of these systems has a net effective displacement. The rotation in this system is that of the proton, M 1-1-(1). In the second system there is a neutrino type rotation.
The massless rotations of the second system can be either those of the material neutrino, M ½-½-(1), or those of the cosmic neutrino, C ½-½-1. With the material neutrino rotation the combined displacements are M ½-½-(2) This combination is the mass one isotope of hydrogen, a structure identical with that of the normal mass two atom (deuterium), M 2-2-(2), or M 2-1-(1) in the atomic notation, except that it has one less unit of magnetic rotation, and therefore one less unit of mass. When the cosmic neutrino rotation is added to the proton, the combined displacements are M 2-2-0. the same net total as that of the single magnetic rotation. This theoretical particle, the compound neutron, as we will call it, can be identified as the observed neutron.
The identification of the separate rotations of these intermediate type structures with the rotations of the neutrinos and protons should not be interpreted as meaning that neutrinos and protons actually exist as such in the combination structures. What is meant is that one of the component rotations that constitutes the compound neutron, for instance, is the same kind of a rotation as that which constitutes a proton when it exists separately.
Inasmuch as the net total displacement of the compound neutron is identical with that of the massless neutron, those aspects of the behavior of the particles—properties, as they are called—which are dependent on the net total displacement are the same for both. Likewise, those properties that are dependent on total magnetic displacement, or total electric displacement, are identical. But there are other properties that are related to those features of the particle structure in which the two neutrons differ. The compound neutron has an effective unit of three-dimensional displacement in the rotating system with the proton type rotation, and it therefore has one unit of mass. The massless neutron, on the other hand, has no effective three-dimensional displacement, and therefore no mass.
The two neutrons also differ in that, although it is (or at least, as we will see in Chapter 17, may be) a still unobserved particle, the massless neutron is theoretically stable in the material environment, whereas the life of the compound neutron is short because of the “foreign” nature of the rotation in the second system. After about 15 minutes, on the average, the compound neutron ejects the second rotating system in the form of a cosmic neutrino, and the particle reverts to the proton status.
The structures of the sub-atomic particles of the material system may now be summarized as follows:
|M 0-0-0||rotational base|
|M ½-½-0||massless neutron|
|Particles with mass|
|M+ 0-0-1||charged positron|
|M- 0-0-(1)||charged electron|
|M+ 1-1-(1)||charged proton|
|M 1-1-(1)||compound neutron|