6.4.  Complex Energy

 

Since it is intimately related to time, energy has to have complex, and even multiple intersecting dimensions in accordance with the dimensions of space and matter which are generated in the inner levels of time before they evolve throughout the outer level. We must notice straightforward, however, that not all these levels of energy are equivalent to mass which is only a property of  space. In lower dimensions, energy should rather be associated with the corresponding coupling property, such as the electric and color charges. Therefore, it is expected that negative mass is only possible in  spatial dimensions, as it has been already anticipated before (Bonnor, 1989; Petit and D’Agostini, 2014).

It is clear initially that, just like time, velocity and momentum that were discussed above, when we take the complex nature of time into account, the kinetic energy  in equation 13, or  in the relativistic energy-momentum equation 17, becomes negative with relation to the potential energy  stored in mass . Therefore the energy  in equation 15 becomes complex  with real  and imaginary  parts. The real part  represents re-creation through the change in mass , and the imaginary part  represents the kinetic evolution of this mass in the outer time through the change in the apparent velocity :

                                             (22)

The real part is  and the imaginary part is , thus we get:

                                (23)

This negative contribution of the kinetic energy, however, does not falsify the current equations 13 and 17, but it means that the potential energy and the kinetic energy are in different orthogonal levels of time and the conversion of potential energy into kinetic energy is like the conversion from the inner time into the outer time, so when they are in the outer time they are added together as in the previous equations because they become both in the same level of time.

Again, just as it is the case with the absolute conservation of momentum that we have seen in section 6.3 above, energy is also always conserved, even when the apparent velocity  changes, since the instantaneous velocity  in the outer level of time is always zero, as we have seen in section 5 and Figure 5 above. As it is the case for momentum, this absolute conservation of energy is conceivable because it means that as the velocity changes, the change in kinetic energy  (that is the imaginary part) is compensated by the change in the effective mass:  due to motion, which causes the real part of energy  also to change accordingly, but since  is hyperbolic, thus its modulus  remains invariant between all inertial or non-inertial frames.

This means that:

                                                                              (24)

This equation provides even an additional method to derive the mass-energy equivalence, because the left side in this equation can be reduced to :

                   (25)

So when we combine the two equations: 14 and 15, we get the effective mass relation:  that is equivalent to  as we have seen above and in 9.