CHAPTER 24
Isotopes
While the magnetic charges involved in the phenomena that we recognize as magnetic all have the outward scalar direction, this does not mean that inward magnetic charges are non-existent. It is a result of the fact that the magnetic (two-dimensional) rotational displacement of material atoms is always inward. The principles governing the addition of motions, as set forth in Volume I, require charges to oppose the basic motions of the atoms in order to form stable combinations. The only stable magnetic charge is therefore the outward charge. However, inward charges may also be produced under appropriate conditions, and may continue to exist if their subsequent separation from the rotational combinations is forcibly prevented.
The events that take place during the beginning of the process of aggregation in the material environment were described in Volume I. As brought out there, the decay of the cosmic rays entering this environment produces a large number of massless neutrons, M ½-½-0. These are subject to disintegration into positrons, M 0-0-1, and neutrinos, M ½-½-(1). Obviously, the presence of any such large concentration of particles of a particular type can be expected to have some kind of a significant effect on the physical system. We have already examined a wide variety of phenomena resulting from the analogous excess of electrons in the material environment. The neutrino is more elusive, and there is very little direct experimental information available concerning this particle and its behavior. However, the development of the Reciprocal System of theory has given us a theoretical explanation of the role of the neutrinos in physical phenomena, and we are now able to trace the course of events even where there are no empirical observations or data available for our guidance.
We can logically conclude that in some environments the neutrinos continue to exist in the uncharged condition in which they are originally formed, just as we find that the electron normally has no charge in the terrestrial environment. In this uncharged condition, the neutrino has a net displacement of zero. Thus it is able to move freely in either space or time. Furthermore, it is not affected by gravitation or by electrical or magnetic forces, since it has neither mass nor charge. It therefore has no motion relative to the natural system of reference, which means that from the standpoint of a stationary system of reference the neutrinos produced at any given location move outward at unit speed in the same manner as radiation. Each material aggregate in the universe is therefore exposed to a continuing flux of neutrinos, which may be regarded as a special kind of radiation.
Although the neutrino as a whole is neutral, from the space-time standpoint, because the displacements of its separate motions add up to zero, it actually has effective displacements in both the electric and magnetic dimensions. It is therefore capable of taking either a magnetic or an electric charge. Probability considerations favor the primary two-dimensional motion, and the charge acquired by a neutrino is therefore magnetic. This charge opposes the magnetic rotation, and since the rotation is inward the charge is directed outward. Inasmuch as this unit outward charge neutralizes the inward magnetic rotation, the only effective (unbalanced) unit of displacement of the charged neutrino is that of the inward negative rotation in the electric dimension. This charged neutrino is thus, in effect, a rotating unit of space, similar in this respect to the uncharged electron, and, as matters now stand, indistinguishable from it.
As a unit of space, the charged neutrino is subject to the same limitations as the analogous uncharged electron. It can move freely through the time displacements of matter, but it is barred from passage through open space, since the relation of space to space is not motion. Any neutrino that acquires a charge while passing through matter is therefore trapped. Unlike the charged electron, it cannot escape from the material aggregate by acquiring a charge. It most lose its charge in order to reach the neutral condition in which it is capable of moving through space. This is difficult to accomplish, as the conditions within the aggregate are favorable to producing charges rather than destroying them. At first the proportion of neutrinos captured in passing through a newly formed material aggregate is probably small, but as the number of charged particles within the aggregate builds up, increasing what we may call the magnetic temperature, the tendency toward capture becomes greater. Being rotational in nature, the magnetic motion is not radiated away in the manner of the translational thermal motion, and the increase of the neutrino population is therefore a cumulative process. There will inevitably be some differences in the rate of build-up of this population by reason of local conditions, but in general the older a material aggregate becomes, the higher its magnetic temperature rises.
The charged neutrino, as a unit of space, is an addition to the space represented by the reference system, extension space, as we have called it. Where charged neutrinos are present, some of the atoms of matter exist, for a time, in the space of the neutrinos rather than in units of extension space, or in the space of the uncharged electrons that, as we have seen previously, are also present, The charged neutrinos are rotating relative to the spatial reference system, and they are consequently rotating relative to the systems of motions that constitute the material atoms, systems that are defined relative to the reference system. The outward rotational vibration (charge) of the spatial unit, the neutrino, is therefore equivalent to, and interchangeable with, an inward rotational vibration (charge) of the time structure, the atom. When the neutrino and the atom subsequently separate, there is a finite probability that the charge will remain with the atom.
The inward scalar direction of this two-dimensional atomic charge is the same as that of the two-dimensional atomic rotation. This fact that the rotational vibration of the atom induced by a magnetically charged neutrino is compatible with the basic magnetic (two-dimensional) inward rotation of the atom has a profound effect on the participation of this motion in physical processes. The ordinary magnetic charge is a foreign element in the material system, an outward motion in a system of inward motions. Magnetism therefore plays a detached role of relatively small importance in the local environment. The neutrino-induced rotational vibration, or charge, on the other hand, adds to the net rotational displacement (the mass) of the atom, and aside from being more dependent on conditions in the environment, is fully coordinate with the basic atomic rotation. Instead of being a distinct added motion, this induced charge modifies the magnitude of the previously existing atomic rotation.
The presence of a concentration of charged neutrinos tending to produce inward rotational vibration of the atoms of an aggregate explains why an atom as a whole does not take an ordinary magnetic charge, and why these ordinary magnetic charges are confined to asymmetric atoms that have motion components which can vibrate independently of the main body. The outward motion cannot be initiated against the forces tending to produce inward motion.
In view of the very significant difference in behavior between the inward charge induced by the neutrinos and the ordinary outward magnetic charge, we will not use the term “magnetic charge” in application to the rotational vibration of the type we are now considering. Instead, we will call this a gravitational charge. Since the motion that constitutes this charge is a form of rotation, and is compatible with the atomic rotation, it adds to the net rotational displacement of the atom. However, there is only one rotating system in the neutrino, whereas the atom is a double system. The mass corresponding to the unit of gravitational charge is thus only half that of the unit of rotation (the unit of atomic number). For convenience, the smaller unit has been taken as the unit of atomic weight, or atomic mass. The primary atomic mass of a gravitationally charged atom is therefore 2Z+ G, where Z is the atomic number, and G is the number of units of gravitational charge.
In addition to the difference in the size of the units, the gravitational charge (rotational vibration) also has a relation to the atomic structure in general that is somewhat different from that of the full rotations. We will therefore distinguish between the rotational mass of the basic atomic rotation and the mass due to the gravitational charge, which we will call vibrational mass. The relation between the gravitational charge and the atomic rotation will have further consideration from the standpoint of the atomic structure in Chapters 25 and 26, and from the mass standpoint in Chapter 27.
Inasmuch as the gravitational charge is variable, the masses of the atoms of an element take different values, extending through a range that depends on the maximum size of the vibrational mass G under the prevailing conditions. The different states that each element can assume by reason of the variable gravitational charge are identified as isotopes of the elements, and the mass on the 2Z + G basis is identified as the isotopic mass. As the elements occur naturally on the earth, the various isotopes of each element are almost always in the same, or nearly the same, proportions. Each element therefore has an average isotopic mass which is recognized as the atomic weight of that element. From the points brought out in the foregoing discussion, it is evident that the atomic weight thus defined is a reflection of the local neutrino concentration, the magnetic temperature, as we have called it, and does not necessarily have the same value in a different environment.
For reasons that will be explained in Chapter 26, the transfer of magnetic ionization from neutrino to atom is irreversible under terrestrial conditions. However, there are processes, to be described later, that gradually transform the vibrational mass into rotational mass. At a low magnetic temperature (concentration of charged neutrinos) most of the single gravitational charges are removed from the system by these processes before a second charge can be added. As the magnetic temperature increases, the frequency of magnetic ionization of atoms likewise increases because of the larger number of contacts. As a result, double or multiple ionization occurs in some atoms. Each aggregate thus has a magnetic ionization level analogous to the level of electric ionization previously discussed.
The degree of magnetic ionization of the individual elements depends not only on the magnetic temperature but also on the relative ability of those elements to absorb the neutrinos. This is a property of the individual units of time displacement. The effective magnetic ionization, the number of gravitational charges that are added to the atomic motion, therefore depends on the atomic mass as well as on the magnetic temperature. From the nature of the addition process we can deduce that at the unit ionization level each net unit of rotational displacement (atomic number) should be capable of acquiring one unit of gravitational charge (half the size of the atomic mass unit). But the atom exists in the time region, whereas the neutrino is not subject to the factors that apply to motion inside unit space. The relation between the charge and the atomic rotation is therefore between mv, the vibrational mass, and mr2, the second power of the rotational mass. Furthermore, the atomic rotation in the time region is subject to the inter-regional ratio, 156.444. Denoting the magnetic ionization level as I, we then have the equilibrium relation
| mv = I mr2/156.444 |
(24-1) |
|
In this equation the rotational mass, mr, is expressed in the double units (units of atomic number) and the vibrational mass, mv, in the single units (units of atomic weight).
The value of mv thus derived is the number of units of gravitational charge (mass) that will normally be acquired by an atom of rotational mass mr if raised to the magnetic ionization level I. It is quite obvious from the available empirical information that the magnetic ionization level on the surface of the earth is close to unity. A calculation for the element lead on the unit ionization basis, to illustrate the application of the equation, results in mv = 43. Adding the 164 atomic weight units of rotational mass corresponding to atomic number 82, we arrive at a theoretical atomic weight of 207. The experimental value is 207.2.
This close agreement is not quite as significant as it appears to be. Actually there are stable isotopes of lead with isotopic masses ranging from 204 to 208. The explanation is that the value obtained from equation 24-1 is not necessarily the mass corresponding to the atomic weight, nor the isotopic mass of the most stable isotope. It is the center of a zone of isotopic stability. Because of the individual characteristics of the elements, the actual median of the stable isotopes and the measured atomic weight may be offset to some extent from this theoretical center of stability, but the deviation is generally small. In more than 60 percent of the first 92 elements it is only one unit, or none at all. Furthermore, the agreement is improving as more accurate measurements become available from experimental sources. In the nearly thirty years
| Z | mv | Calc. | Obs | Diff. | Z | mv | Calc. | Obs. | Diff. |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 0.01 | 2 | 1 | -1 | 47 | 14.12 | 108 | 108 | 0 |
| 2 | 0.03 | 4 | 4 | 0 | 48 | 14.73 | 111 | 112 .5 | +1.5 |
| 3 | 0.06 | 6 | 7 | +1 | 49 | 15.35 | 113 | 115 | +2 |
| 4 | 0.10 | 8 | 9 | +1 | 50 | 15.98 | 116 | 119 | +3 |
| 5 | 0.16 | 10 | 11 | +1 | 51 | 16.63 | 119 | 122 | +3 |
| 6 | 0.23 | 12 | 12 | 0 | 52 | 17.28 | 121 | 128 | +7 |
| 7 | 0.31 | 14 | 14 | 0 | 53 | 17.96 | 124 | 127 | +3 |
| 8 | 0.41 | 16 | 16 | 0 | 54 | 18.64 | 127 | 131 | +4 |
| 9 | 0.52 | 19 | 19 | 0 | 55 | 19.34 | 129 | 133 | +4 |
| 10 | 0.64 | 21 | 20 | -1 | 56 | 20.05 | 132 | 137 | +5 |
| 11 | 0.77 | 23 | 23 | 0 | 57 | 20.77 | 135 | 139 | +4 |
| 12 | 0.92 | 25 | 24 | -1 | 58 | 21.50 | 138 | 140 | +2 |
| 13 | 1.08 | 27 | 27 | 0 | 59 | 22.25 | 140 | 141 | +1 |
| 14 | 1.25 | 29 | 28 | -1 | 60 | 23.01 | 143 | 144 | +1 |
| 15 | 1.44 | 31 | 31 | 0 | 61 | 23.78 | 146 | 145 | -1 |
| 16 | 1.64 | 34 | 32 | -2 | 62 | 24.57 | 149 | 150 | +1 |
| 17 | 1.85 | 36 | 35.5 | -0.5 | 63 | 25.37 | 151 | 152 | +1 |
| 18 | 2.07 | 38 | 40 | +2 | 64 | 26.18 | 154 | 157 | +3 |
| 19 | 2.31 | 40 | 39 | -1 | 65 | 27.01 | 157 | 159 | +2 |
| 20 | 2.56 | 43 | 40 | -3 | 66 | 27.84 | 160 | 162.5 | +2.5 |
| 21 | 2.82 | 45 | 45 | 0 | 67 | 28.69 | 163 | 165 | +2 |
| 22 | 3.09 | 47 | 48 | +1 | 68 | 29.56 | 166 | 167 | +1 |
| 23 | 3.38 | 49 | 51 | +2 | 69 | 30.43 | 168 | 169 | +1 |
| 24 | 3.68 | 52 | 52 | 0 | 70 | 31.32 | 171 | 173 | +2 |
| 25 | 4.00 | 54 | 55 | +1 | 71 | 32.22 | 174 | 175 | +1 |
| 26 | 4.32 | 56 | 56 | 0 | 72 | 33.14 | 177 | 178.5 | +1.5 |
| 27 | 4.66 | 59 | 59 | 0 | 73 | 34.06 | 180 | 181 | +1 |
| 28 | 5.01 | 61 | 59 | -2 | 74 | 35.00 | 183 | 184 | +1 |
| 29 | 5.38 | 63 | 63.5 | +0.5 | 75 | 35.96 | 186 | 186 | 0 |
| 30 | 5.75 | 66 | 65 | -1 | 76 | 36.92 | 189 | 190 | +1 |
| 31 | 6,14 | 68 | 70 | +2 | 77 | 37.90 | 192 | 192 | 0 |
| 32 | 6.55 | 71 | 73 | +2 | 78 | 38.89 | 195 | 195 | 0 |
| 33 | 6.96 | 73 | 75 | +2 | 79 | 39.89 | 198 | 197 | -1 |
| 34 | 7.39 | 75 | 79 | +4 | 80 | 40.91 | 201 | 200.5 | -0.5 |
| 35 | 7.83 | 78 | 80 | +2 | 81 | 41.94 | 204 | 204 | 0 |
| 36 | 8.28 | 80 | 84 | +4 | 82 | 42.98 | 207 | 207 | 0 |
| 37 | 8.75 | 83 | 85.5 | +2.5 | 83 | 44.03 | 210 | 209 | -1 |
| 38 | 9.23 | 85 | 88 | +3 | 84 | 45.10 | 213 | 209 | -4 |
| 39 | 9.72 | 88 | 89 | +1 | 85 | 46.18 | 216 | 210 | -6 |
| 40 | 10.23 | 90 | 91 | +1 | 86 | 47.28 | 219 | 222 | +3 |
| 41 | 10.74 | 93 | 93 | 0 | 87 | 48.38 | 222 | 223 | +1 |
| 42 | 11.28 | 95 | 95.5 | +0.5 | 88 | 49.50 | 226 | 226 | 0 |
| 43 | 11.82 | 98 | 98 | 0 | 89 | 50.63 | 229 | 227 | -2 |
| 44 | 12.37 | 100 | 101 | +1 | 90 | 51.78 | 232 | 232 | 0 |
| 45 | 12.94 | 103 | 103 | 0 | 91 | 52.93 | 235 | 231 | -4 |
| 46 | 13.53 | 106 | 106.5 | +0.5 | 92 | 54.10 | 238 | 238 | 0 |
since the publication of the first edition of this work, in which the comparative values were tabulated, the accepted atomic weight of six elements has been changed by a significant amount, and in all of these cases the change has been in the direction of closer agreement with the theoretical values.
Table 35 is an updated version of the original tabulation. The first column of the table gives the atomic number, The second column shows the value of mv calculated from equation 24-1. Column 3 is the theoretical equilibrium mass, 2Z + G, taken to the nearest unit, since the gravitational charge does not exist in fractional units. Column 4 is the observed atomic weight, also expressed in terms of the nearest integer, except where the excess is almost exactly one half unit. Column 5 is the difference between the observed and calculated values. The trans-uranium elements are omitted, as these elements cannot have (terrestrial) atomic weights in the same sense in which that term is used in application to the stable elements.
The width of the zone of stability is quite variable, ranging from zero for technetium and promethium to a little over ten percent of the rotational mass. The reasons for the individual differences in this respect are not yet clear. One of the interesting, and probably significant, points in this connection is that the odd-numbered elements generally have narrower stability limits than the even-numbered elements. This and other factors affecting atomic stability will be discussed in Chapter 26. Isotopes that are outside the zone of stability undergo spontaneous modifications that have the result of moving the atom into the stable zone. The nature of these processes will be examined in the next chapter.
In addition to the limitation on its width, the zone of isotopic stability also has an upper limit due to the restrictions on the total rotation of the atom. It was established in Volume I that the maximum effective magnetic rotational displacement is four units. The elements of rotational group 4B have magnetic rotational displacements 4-4. By adding rotation in the electric dimension it is possible to build the total rotation up to 4-4-31, or the equivalent 5-4-(1), corresponding to atomic number 117, without exceeding the overall displacement maximum. But the next step brings the electric rotation up to the equivalent of the next unit of magnetic rotation. The effective magnetic rotation (that is, the total less the initial unit) is then four units in each magnetic dimension. As explained earlier, a displacement of four full magnetic units is equivalent to no displacement at all. Arrival at this point therefore terminates the rotation. The speed displacement reverts to the translational status. Element 118 is thus unstable, and will disintegrate promptly if it is formed. All rotational combinations above element 118 (rotational mass 236) are similarly unstable, whereas all elements below 118 are stable at a zero ionization level.
At a finite ionization level the corresponding vibrational mass is added to the rotational mass, and the 236 limit is reached at a lower atomic number. As indicated by Table 35, the equilibrium mass of uranium, atomic number 92, is 238 at the unit ionization level. This exceeds the 236 limit. Uranium and all elements above it in the atomic series are therefore unstable in an environment that is subject to this degree of ionization. The converse is not necessarily true; that is, it does not necessarily follow that all isotopes below the 236 limit are stable if they are within the zone of stability defined by the ratio of vibrational to rotational mass. At the magnetic temperature corresponding to the unit ionization level most atoms of an aggregate have one gravitational charge. But some have none, whereas others may possess two charges. The existence of a doubly charged atom has no observable physical consequences, other than the added mass, unless the second charge puts the total mass over the 236 limit. In that event, the atom will eventually disintegrate.
All of the factors that determine the extent of instability in the elements just below uranium in the atomic series have not yet been identified, but, as would be expected, there is a general decrease in the tendency toward instability as the atomic number decreases. The lowest element that could theoretically become unstable by reason of acquisition of two gravitational charges is gold, element 79, for which the total mass with two units of charge is 238. However, the probability of the second ionization drops rapidly as we move down the atomic series, and while the first few elements below uranium are very unstable, the instability is negligible below bismuth, element 83.
As the magnetic ionization level rises, the stability limit decreases still further in terms of atomic number. It should be noted, however, that the rate of decrease slows down quickly. The first stage of ionization reduces the stability limit from 118 to 92, a difference of 26 in atomic number. The second unit of ionization causes a decrease of 13 atomic number units, the third only 8, and so on.