When additional pulsons enter a mass chain and cannot add to its structural stability, an inertial chain is formed. An inertial chain remains broken (open) as it winds through space and consists of a mass component and a velocity component. The number of nodes in an inertial chain (ni) is the sum of the mass number (nm) and the velocity number (nv). The inertial chain length is equal to the pulson wavelength λp which results in an inertial chain wavelength λi of:
Equation 8
Figure 5A
In figure 5A, a single pulson center (nv=1) joined an 8 node mass chain (nm=8) and formed a 9 node inertial chain (ni=9). The original 8 node planer octagon structure of the mass chain is drawn to scale behind the newly formed helical structure of the open inertial chain. In each node to node step of an inertial chain, there is a mass component (drawn in the plane of the octagon which is called the mass plane) and a velocity component (normal to the mass plane called the velocity plane). The inertial chain traces the mass chain path while adding a translation component with each step. Since the last node in the inertial chain is always ahead of the first node, they can never join together and the chain remains open. Because the number of inertial chain nodes is greater than the number of mass chain nodes, an inertial chain forms more than one mass structure at any given time. This is principle behind relativistic mass, or apparent mass, which is the rest mass multiplied by the quantized velocity factor (γq):
Equation 9
This quantized velocity factor has the same value as the Lorentz factor in the classical relativistic mass energy equation. According to (9), when nv=nm, two elongated mass structures are formed by an inertial chain (relativistic mass is twice the value of the rest mass). In figure 6, the mass chain was drawn as a planer structure resulting in a helical inertial chain. In complex three dimensional mass structures, the resulting inertial chain path would be much more complex. The energy equation for an inertial chain is directly proportional to the number of nodes (pulson centers) in the chain:
Equation 10
If the velocity number equals zero (nv=0), the inertial chain reverts back to a mass chain at rest and (10) simplifies to (3). It is assumed the mass number nm remains constant as an inertial chain increases in velocity, however, it is possible enough energy would be available to form a new, more stable particle with a higher mass number.
Figure 5B
In figure 5B, four pulson centers (nv=4) joined an 8 node mass chain (nm=8) and formed a 12 node inertial chain (ni=12). As the velocity number increases, a mass structure shrinks in size and elongates towards the pulson wavelength λp.
Figure 5C
The total inertial chain energy is proportional to nm+nv as shown in figure 5C. This total energy can be broken into a mass component and velocity component by using Pythagorean’s theorem since the two components are normal to each other. Since the inertial chain travels at the speed of light, the velocity component of this speed (v) is:
Equation 11
The inertial chain speed projected onto the mass plane is the relativistic mass chain speed (vrm) and is also a fraction of light speed.
Equation 12
This slower relativistic mass chain speed has the effect of slowing time down relative to the particle. The relativistic mass time dilation (trm) factor can be calculated as:
Equation 13
By substituting (9) into (13), the effective mass time dilation can also be calculated as:
Equation 14
The mass wavelength projected onto the mass plane is called the relativistic mass wavelength λem and it also decreases with increasing speed. A mass structure shrinks and elongates with increasing speed as shown in figures 6 and 7.
Equation 15
By substituting (8) into (15), the relativistic mass wavelength is also equal to:
Equation 16
The length of the inertial chain (di) as measured in the velocity plane is equal to:
Equation 17
Though different in form, the quantized equations for energy, velocity, and time dilation provide the same results as Einstein’s classical relativistic mass energy equation [2]:
Equation 18
(18) can be written in a form using the Lorentz factor [2]:
Equation 19
Where the Lorentz factor (γ) is equal to:
Equation 20
To prove equivalency between Einstein’s classical relativistic mass energy equation and the quantized relativistic mass energy equation, the values for the Lorentz factor (20) versus the quantized velocity factor (9) must be equal over all values of energy and velocity. The two factors do prove to be equivalent and the results are shown in table 1.
