The Duality of Time Theory

This essential characteristic, that imaginary timeis negative with relation to proper time, is what makes time restricted into one direction, because it means thatcan never exceed:, because they both belong to one single existence that is flowing either in the real inward dimension which is creating the continuous space or in the outward direction which forms the imaginary discrete time, not the two together, otherwise they both would be real as we are normally deceived.

This is also equivalent to:, thus when:, we get:. Ifwe have flat infinite space without time, which is the state of vacuum:, so this imaginary time acts like a resistance against the continuous creation of space, and its interruption, i.e. going in the outward dimension of time, is what causes the inertial mass, which then effectively increases with speed according to:(as it will be also proved in sections 3.3, 3.4 and 3.6 below), and when the outward imaginary time approaches the inner time, the apparent velocityapproaches the speed of light, and.

On the other hand, the apparent velocitycan not exceedbecause it is the average of all instantaneous velocities of all individual geometrical pointsthat constitute the particle, which are always fluctuating between zero and the speed of light, as we have seen in section 3 above, so by definitionis capped by, as can be also seen from equation 5.3 above.

Furthermore, this important property, that the outward time is effectively negative with respect to the real flow of time, will be inherited by the velocity, momentum and even energy; all of which will be also negative in relation to their real counter part, as it will be discussed further in sections 3.2, 3.4, 3.6. It is this fundamental property that will enable the derivation of relativistic momentum-energy relation, the equivalence principle between the inertial and gravitational masses, in addition to allowing energy and mass to become imaginary, negative and even multidimensional.

Figure 5.2: The arrow of time is represented by the upper branch of the hyperbola, while the lower branch is the reverse arrow of time, and when these two branches are connected to form a degenerate conic, the two opposing directions of time form one dimension of space. This condition occurs whenand, thusor, which corresponds to.

This essential observation also provides the fundamental reason of the arrow of time, although the reverse arrow of time can still be conceived as the other disconnected branch of the hyperbola. When these two opposite arrows of time meet, the hyperbola (that can be described by the general equation:) turns into degenerate conic and these two opposite time directions become one dimension of space. This condition occurs whenand, hence the above equation becomes:, or:, which corresponds towhich is the state of vacuum or the ground state of matter as we mentioned in this section above.