Continuing the development of the consequences of the Fundamental Postulates, we will next consider the effect of rotation of the photons. Rotation differs from translation only in direction and this difference has no meaning from a space-time standpoint since space-time is scalar. Rotation at unit velocity is therefore indistinguishable from the normal space-time progression; that is, from the physical standpoint it is the equivalent of no rotation at all. In order to produce any physical effects there must be a rotational displacement: a deviation from unity. The magnitude of any rotational motion of the photons must therefore be greater than that of the space-time progression.

Another necessary characteristic of the rotational motion of the photons is that its direction must be opposite to that of the space-time progression, because any added displacement in the positive direction would result in a directional reversal and would produce a vibration rather than a rotation, as previously explained. This means that when the photon acquires a rotation it travels back along the line of the space-time progression, and since this retrograde motion is greater than that of the progression these rotating units are reversing the pattern of free space-time and are moving inward toward each other, either in space or in time, depending on the direction of the displacement.

We are now in a position to make some further identifications. The rotating photons, with some reservations to be discussed later, will be identified as *atoms*, collectively the atoms constitute * matter*, and the inward motion resulting from the rotational velocity will be identified as *gravitation*.

Here again we find that the Fundamental Postulates give us a very simple explanation of a hitherto mysterious phenomenon. Atoms of matter appear to exert attractive forces on each other merely because they are in constant motion toward each other. There is no action at a distance, no medium, no propagation of a force, no curved space; simply an inherent motion of the rotating units in the direction opposite to the ever-present expansion of the universe.

The next point which we will wish to explore is the nature of the atomic rotation. In approaching this subject let us for convenience visualize the photon in a vertical position. Since the photon is one-dimensional a simple rotation around this vertical line as an axis is impossible; such a rotation is indistinguishable from no rotation at all. The photon can, however, rotate around both of the horizontal axes passing through its midpoint. The basic rotation of the atom is therefore two-dimensional.

On examination of this two-dimensional rotation it will be seen that it is possible to have two coexisting rotating systems of this kind,. If there is only one unit of two-dimensional rotational displacement the original rotation may take place around either horizontal axis and this entire rotating unit then acquires a rotation around the other. Inasmuch as the displacement units are independent there is no requirement that the second unit follow the same pattern; on the contrary if the original rotation of the first displacement unit is around axis *a* the probability principles indicate that the original rotation of the second unit will be around axis *b*. The two rotations can take place simultaneously without interference and the atoms of matter therefore normally include two separate rotating systems.

Although simple rotation around the vertical axis in the same space-time direction as the two-dimensional rotation is impossible, now that the photon is rotating around the horizontal axes the entire system can be rotated around the vertical axis in the opposite space-time direction. This reverse rotation is not required for stability and is absent from certain types of atoms, which we will discuss shortly.

Since the axes may lie in any direction, the vertical orientation of the photon having been used merely for convenience in the preliminary discussion, some new terminology will be necessary for identification purposes. We will therefore call the one-dimensional rotation *electric rotation* and the corresponding axis the *electric axis*. Similarly we will refer to the two-dimensional rotation as *magnetic rotation* around the the *magnetic axes*. If the displacements in the two magnetic dimensions are unequal the rotation is distributed in the form of a spheroid and in this case the rotation which is effective in two dimensions of the spheroid will be called the *principal* magnetic rotation and the other will be the * subordinate* magnetic rotation. When it is desired to distinguish between the larger and the smaller magnetic rotations the terms *primary* and * secondary* will be used. Designation of these rotations as electric and magnetic does not indicate the presence of any electric or magnetic forces in the structures now being described. This terminology is merely being used to set the stage for the introduction of electric and magnetic phenomena in a later phase of the discussion.

Each of these three rotations may assume any one of a number of possible displacement values. This means that many different rotational combinations can exist and since the physical behavior of the atoms depends upon the magnitude of these rotational displacements the various rotational combinations can be distinguished by differences in their physical behavior, by differences in their *properties*, we may say.

We may now identify these rotational combinations as the *chemical elements*, each rotating unit of a particular kind constituting an atom of that element. For convenience in referring to the various combinations of rotational displacement a notation in the form 2-2-3 will be used, the three figures representing the displacements in the principal magnetic, the subordinate magnetic, and the electric rotational dimensions respectively.

Because of the scalar nature of space-time the rotation cannot have the same space-time direction as the primary oscillation. The net rotational displacement must therefore oppose the space or time displacement of the oscillation. The rotating units may be linear space displacements rotating with net displacement in time, or linear time displacements rotating with net displacement in space. The latter combinations, however, do not constitute matter and consideration of this type of rotating unit will be deferred until later. For the present the discussion will be confined to those combinations in which the net rotational displacement is in time and unless otherwise specified the displacement figures will refer to time displacement. If space displacement is present the applicable figure will be enclosed in parentheses.

Looking first at those combinations which have zero electric displacement, a single unit of magnetic time displacement results in the combination 1-0-0. This single displacement unit merely serves to neutralize the oscillating displacement in the opposite space-time direction and the resultant is the rotational base, a unit with a net displacement of zero; that is, the physical equivalent of nothing. One additional unit of magnetic time displacement results in the combination 1-1-0. In order to avoid interference it is necessary that the two rotating systems of the atom have the same velocities. Each added unit of displacement therefore increases the rotation of both systems in one dimension rather than one system in both dimensions. For reasons which will be developed later, the effect of a displacement less than 2 is negative in direction and the combination 1-1-0 still does not have the properties which we I will recognize as those of matter. We cannot go directly to 2-0-0 because the probability principles operate to keep the eccentricity at a minimum and the successive increments of displacement therefore go alternately to the principal and subordinate rotations. The first magnetic rotational combination which qualifies as matter requires one more unit of magnetic displacement, bringing the system up to 2-1-0. This combination we identify as the element helium. Additional units of magnetic displacement result in a series of elements which we identify as the inert gases. The complete series is as follows:

Displacement | Element |
---|---|

2-1-0 | Helium |

2-2-0 | Neon |

3-2-0 | Argon |

3-3-0 | Krypton |

4-3-0 | Xenon |

4-4-0 | Radon |

The number of possible combinations of rotations is greatly increased when electric displacement is added to these magnetic combinations, but the combinations which can actually exist as elements are limited by the probability principles. Where the two-dimensional magnetic displacement is *n* the equivalent number of one-dimensional electric displacement units is *n*^{2} in each dimension. The magnetic displacement is therefore numerically less than the equivalent electric displacement and is correspondingly more probable. Any increment of displacement consequently adds to the magnetic rotation if possible rather than to the electric rotation. This means that the role of the electric displacement is confined to filling in the intervals between successive additions of magnetic displacement.

At this point it is necessary to develop some further facts concerning the characteristics of the space-time progression. In the undisplaced condition all progression is by units. We have first one unit, then another similar unit, yet another, and so on, the total up to any specific point being *n* units. There is no term with the value * n*; this value appears only as the total.

The progression of displacements follows a different mathematical pattern because in this case only one of the space-time components progresses, the other remaining fixed at the unit value. The progression of 1/*n*, for instance, is 1/1, 1/2, 1/3, and so on. The progression of the reciprocals of 1/*n* is 1, 2, 3… *n*. Here the quantity n is the final term, not the total. Similarly when we find that the electric equivalent of a magnetic displacement* *is 2*n*^{2}, this does not refer to the total from zero to n; it is the equivalent of the nth term alone. To obtain the total electric equivalent of the magnetic displacement we must sum up the individual 2*n*^{2} terms.

From the foregoing explanation it can be seen that if all rotational displacement were in time the series of elements would start at the lowest possible magnetic combination, helium, and the electric displacement would increase step by step until it reached a total of 2*n*^{2} units, at which point the relative probabilities would result in a conversion of these 2*n*^{2} units of electric displacement into one additional unit of magnetic displacement, whereupon the building up of the electric displacement would be resumed. This behavior is modified, however, by the fact that electric displacement in matter, unlike magnetic displacement, may be in space rather than in time.

As previously brought out, the net rotational displacement of any rotational combination must be in time in order to give rise to those properties which are characteristic of matter. It necessarily follows that the magnetic displacement, which is the major component of the total, must also be in time. But as long as the larger component is in time the system as a whole can meet the requirement of a net time displacement even if the smaller component, the electric displacement, is in space. It is possible, therefore, to increase net time displacement a given amount either by direct addition of the required number of units of electric displacement in time or by adding magnetic displacement in time and then adjusting to the desired intermediate level by adding the appropriate number of units of the oppositely directed electric displacement in space.

Which of these alternatives will actually prevail is again a matter of probability and from probability considerations we deduce that the net displacement will be increased by successive additions of electric displacement in time until *n*^{2} units have been added. At this point the probabilities are nearly equal and as the net displacement increases still further the alternate arrangement becomes more probable. In the latter half of each group, therefore, the increase in net displacement is normally attained by adding one unit of magnetic displacement and then reducing to the required net total by adding electric displacement in space (negative displacement), eliminating successive units of the latter to move up the atomic series.

By reason of this availability of electric displacement in space as a component of the atomic rotation, an element with a net displacement less than that of helium becomes possible. This element, 2-1-(1), which we identify as hydrogen, is produced by adding one unit of electric displacement in space to helium and thereby in effect subtracting one electric time displacement unit from the equivalent of four units (above the 1-0-0 datum) which helium possesses. Hydrogen is the first in the ascending series of elements and we may therefore give it the *atomic number* 1. The atomic number of any other element is equal to its net equivalent electric time displacement less two units.

One electric time displacement unit added to hydrogen eliminates the electric displacement in space and brings us back to helium, atomic number 2, with displacement 2-1-0. This displacement is one unit above the initial level of 1-0-0 in each magnetic dimension and any further increase in the magnetic displacement requires the addition of a second unit in one of the dimensions. With *n* = 2 the electric equivalent of a magnetic unit is 8, and we therefore have eight elements in the next group. In accordance with the probability principles the first four elements of the group are built on a helium type magnetic rotation with successive additions of electric displacement in time. The fourth element, carbon, can also exist with a neon type magnetic rotation and four units of electric displacement in space. Beyond carbon the higher magnetic displacement is normal and the successive steps involve reduction of the electric space displacement, the final result being neon, 2-2-0, when all space displacement has been eliminated. The following elements are included in this group:

Displacement | Element | Atomic No. |
---|---|---|

2-1-1 | Lithium | 3 |

2-1-2 | Beryllium | 4 |

2-1-3 | Boron | 5 |

2-1-4 2-2-(4) | Carbon | 6 |

2-2-(3) | Nitrogen | 7 |

2-2-(2) | Oxygen | 8 |

2-2-(1) | Fluorine | 9 |

Another similar group with one additional unit of magnetic displacement follows.

Displacement | Element | Atomic No. |
---|---|---|

2-2-1 | Sodium | 11 |

2-2-2 | Magnesium | 12 |

2-2-3 | Aluminum | 13 |

2-2-4 3-2-(4) | Silicon | 14 |

3-2-(3) | Phosphorus | 15 |

3-2-(2) | Sulfur | 16 |

3-2-(I) | Chlorine | 17 |

On completion of the 3-2 magnetic combination at element 18, Argon, the magnetic rotational displacement has reached a level of two units above the rotational datum in both magnetic dimensions. In order to increase the rotation in either dimension by an additional unit, a total of 2 × 3^{2} or 18 units of electric displacement are required. This results in a group of 18 elements, which as before is followed by a similar group differing only in that the magnetic displacement is one unit greater.

Displacement | Element | Atomic No. | Displacement | Element | Atomic No. |
---|---|---|---|---|---|

3-2-1 | Potassium | 19 | 3-3-1 | Rubidium | 37 |

3-2-2 | Calcium | 20 | 3-3-2 | Strontium | 38 |

3-2-3 | Scandium | 21 | 3-3-3 | Yttrium | 39 |

3-2-4 | Titanium | 22 | 3-3-4 | Zirconium | 40 |

3-2-5 | Vanadium | 23 | 3-3-5 | Niobium | 41 |

3-2-6 | Chromium | 24 | 3-3-6 | Molybdenum | 42 |

3-2-7 | Manganese | 25 | 3-3-7 | Technetium | 43 |

3-2-8 | Iron | 26 | 3-3-8 | Ruthenium | 44 |

3-2-9 3-3-(9) | Cobalt | 27 | 3-3-9 4-3-(9) | Rhodium | 45 |

3-3-(8) | Nickel | 28 | 4-3-(8) | Palladium | 46 |

3-3-(7) | Copper | 29 | 4-3-(7) | Silver | 47 |

3-3-(6) | Zinc | 30 | 4-3-(6) | Cadmium | 48 |

3-3-(5) | Gallium | 31 | 4-3-(5) | Indium | 49 |

3-3-(4) | Germanium | 32 | 4-3-(4) | Tin | 50 |

3-3-(3) | Arsenic | 33 | 4-3-(3) | Antimony | 51 |

3-3-(2) | Selenium | 34 | 4-3-(2) | Tellurium | 52 |

3-3-(1) | Bromine | 35 | 4-3-(1) | Iodine | 53 |

The effective magnetic displacement now steps up to 4 in one dimension and consequently there are 2 × 4^{2} or 32 members in each of the next two groups. Only half of the elements in the second of these groups have actually been identified thus far, but theoretical considerations indicate that this group can be completed under favorable conditions. The general situation with respect to atomic stability and the limitations to which the rotational displacement is subject will be discussed in a subsequent section. The known members of the 32 element groups are as follows:

Displacement | Element | Atomic No. | Displacement | Element | Atomic No. |
---|---|---|---|---|---|

4-3-1 | Cesium | 55 | 4-4-1 | Francium | 87 |

4-3-2 | Barium | 56 | 4-4-2 | Radium | 98 |

4-3-3 | Lanthanum | 57 | 4-4-3 | Actinium | 89 |

4-3-4 | Cerium | 58 | 4-4-4 | Thorium | 90 |

4-3-5 | Praseodymium | 59 | 4-4-5 | Protactinium | 91 |

4-3-6 | Neodymium | 60 | 4-4-6 | Uranium | 92 |

4-3-7 | Promethium | 61 | 4-4-7 | Neptunium | 93 |

4-3-8 | Samarium | 62 | 4-4-8 | Plutonium | 94 |

4-3-9 | Europium | 63 | 4-4-9 | Americium | 95 |

4-3-10 | Gadolinium | 64 | 4-4-10 | Curium | 96 |

4-3-11 | Terbium | 65 | 4-4-11 | Berkelium | 97 |

4-3-12 | Dysprosium | 66 | 4-4-12 | Californium | 98 |

4-3-13 | Holmium | 67 | 4-4-13 | Einsteinium | 99 |

4-3-14 | Erbium | 68 | 4-4-14 | Fermium | 100 |

4-3-15 | Thulium | 69 | 4-4-15 | Mendelevium | 101 |

4-3-16 4-4-(16) | Ytterbium | 70 | 4-4-16 5-4-(16) | Nobelium | 102 |

4-4-(15) | Lutetium | 71 | |||

4-4-(14) | Hafnium | 72 | |||

4-4-(13) | Tantalum | 73 | |||

4-4-(12) | Tungsten | 74 | |||

4-4-(11) | Rhenium | 75 | |||

4-4-(10) | Osmium | 76 | |||

4-4-(9) | Iridium | 77 | |||

4-4-(8) | Platinum | 78 | |||

4-4-(7) | Gold | 79 | |||

4-4-(6) | Mercury | 80 | |||

4-4-(5) | Thallium | 81 | |||

4-4-(4) | Lead | 82 | |||

4-4-(3) | Bismuth | 83 | |||

4-4-(2) | Polonium | 84 | |||

4-4-(1) | Astatine | 95 |

For convenience in the subsequent discussion these groups of elements will be identified by the magnetic *n* value with the first and second groups in each pair being designated A and B respectively. Thus the sodium group, which is the second of the 8-element groups (*n* = 2) will be called Group 2B.