# ULTIMATE SYMMETRY:

Fractal Complex-Time and Quantum Gravity

# III.2.8 Method III (the total relativistic energy):

The total relativistic energy in equation 3.11 can also be obtained by integrating the starting equation 3.6 over the inner and outer time together, since in the inner time the rest energy , or mass , is generated at the speed of creation  as a result of the instantaneous coupling between the geometrical points which constitute the particle of mass  (thus  and  in the inner time), and in the outer time the kinetic energy  is generated as this mass  moves gradually so its apparent velocity changes by , which corresponds to increasing the effective mass from  to , thus we can integrate:

(3.13)

Thus we get the same equation 3.11:

(3.14)

This equation can also be given in the general form that relates the relativistic energy and momentum:

(3.15)

This last equation, that is equivalent to equation 3.14, will be also derived in section III.2.9 starting from the definition of momentum as , but because it is genuinely complex, and hyperbolic, the imaginary part of momentum will have negative contribution just as we have seen for the outer time when we discussed the arrow of time in section II.4.2 above.

Again, however, this fundamental derivation of equation 3.15, which gives the relativistic energy-momentum relation, is not possible without the Duality of Time postulate. All the current derivations in the literature rely on the effective mass relation: , which is equivalent to the same relation we are trying to derive (see above), while finding this equation from the four-momentum expression, or space-time symmetry, relies on induction rather than rigorous mathematical formulation.

# Other Pages Related to Search Keywords:

• ... Space Transcendence Read this short concise exploration of the Duality of Time Postulate: DoT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics ...

• ## ... Instantaneous Coupling =>:

• ... egrating the starting equation 3.6 over the inner and outer time together, since in the inner time the rest energy , or mass , is generated at the speed of creation  as a result of the INSTANTANEOUS COUPLING between the geometrical points which constitute the particle of mass  (t ...

• ## ... Imaginary Part =>:

• ... equation, that is equivalent to equation 3.14, will be also derived in section III.2.9 starting from the definition of momentum as , but because it is genuinely complex, and hyperbolic, the IMAGINARY PART of momentum will have negative contribution just as we have seen for the outer time w ...

• ## ... Kinetic Energy =>:

• ... nbsp;as a result of the instantaneous coupling between the geometrical points which constitute the particle of mass  (thus  and  in the inner time), and in the outer time the KINETIC ENERGY  is generated as this mass  moves gradually so its apparent velocity change ...

• ## ... Apparent Velocity =>:

• ... s which constitute the particle of mass  (thus  and  in the inner time), and in the outer time the kinetic energy  is generated as this mass  moves gradually so its APPARENT VELOCITY changes by , which corresponds to increasing the effective mass from  to , th ...

• ## ... Mathematical Formulation =>:

• ... ent to the same relation we are trying to derive (see above), while finding this equation from the four-momentum expression, or space-time symmetry, relies on induction rather than rigorous MATHEMATICAL FORMULATION .       Read Other Books: The Single Monad Model of the Cosmo ...

• ## ... Geometrical Points =>:

• ... over the inner and outer time together, since in the inner time the rest energy , or mass , is generated at the speed of creation  as a result of the instantaneous coupling between the GEOMETRICAL POINTS which constitute the particle of mass  (thus  and  in the inner ti ...

• ## ... Genuinely Complex =>:

• ... :    (3.15)   This last equation, that is equivalent to equation 3.14, will be also derived in section III.2.9 starting from the definition of momentum as , but because it is GENUINELY COMPLEX , and hyperbolic, the imaginary part of momentum will have negative contribution ju ...

• ## ... Momentum Relation =>:

• ... e have seen for the outer time when we discussed the arrow of time in section II.4.2 above. Again, however, this fundamental derivation of equation 3.15, which gives the relativistic energy- MOMENTUM RELATION , is not possible without the Duality of Time postulate. All the current derivation ...

• ## ... Time Symmetry =>:

• ... rely on the effective mass relation: , which is equivalent to the same relation we are trying to derive (see above), while finding this equation from the four-momentum expression, or space- TIME SYMMETRY , relies on induction rather than rigorous mathematical formulation.     &nbs ...

• ## ... Current Derivations =>:

• ... .2 above. Again, however, this fundamental derivation of equation 3.15, which gives the relativistic energy-momentum relation, is not possible without the Duality of Time postulate. All the CURRENT DERIVATIONS in the literature rely on the effective mass relation: , which is equivalent to ...

• ## ... Negative Contribution =>:

• ... ion 3.14, will be also derived in section III.2.9 starting from the definition of momentum as , but because it is genuinely complex, and hyperbolic, the imaginary part of momentum will have NEGATIVE CONTRIBUTION just as we have seen for the outer time when we discussed the arrow of time in ...

The science of Time is a noble science, that reveals the secret of Eternity. Only the Elites of Sages may ever come to know this secret. It is called the First Age, or the Age of ages, from which time is emerging.
Ibn al-Arabi [The Meccan Revelations: Volume I, page 156. - Trns. Mohamed Haj Yousef]

### The Sun from the West:

Welcome to the Single Monad Model of the Cosmos and Duality of Time Theory

### Message from the Author:

I have no doubt that this is the most significant discovery in the history of mathematics, physics and philosophy, ever!

By revealing the mystery of the connection between discreteness and contintuity, this novel understanding of the complex (time-time) geometry, will cause a paradigm shift in our knowledge of the fundamental nature of the cosmos and its corporeal and incorporeal structures.