# ULTIMATE SYMMETRY:

Fractal Complex-Time and Quantum Gravity

# III.2.1 The classical kinetic energy (in the normal time):

In normal classical mechanics, the kinetic energy is the work done in accelerating a particle during the infinitesimal time interval , and it is given by the dot product of force  and displacement :

(3.5)

thus:

(3.6)

Now if we assume mass to be constant, so that:  (and we will discuss relativistic mass further in section III.2.5 below), we will get:

(3.7)

So in the classical view of apparently continuous existence, when we consider both space and time to be real, i.e. when we consider an infinitesimally continuous and smooth change in speed from zero to , the result of this integration will give the standard equation that describes the kinetic energy of massive particles or objects moving in the normal level of time:

(3.8)

The reason why we are getting the factor of half in this equation is because the velocity increases gradually with time, which makes the integration equals the area of the triangle as demonstrated by the first arrow in Figure III.2.

Figure III.2: Gradual versus Abrupt Change of Speed - Arrow 1: gradual change of speed in the outer level of time, leading to the classical equation of kinetic energy . Arrow 2: abrupt change from zero to  in the inward levels of time, leading to the mass-energy equivalence relation , which can not happen on the normal level of time because physical objects may not move at the absolute speed of light.

# 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 ...

• ## ... Apparently Continuous =>:

• ... if we assume mass to be constant, so that:  (and we will discuss relativistic mass further in section III.2.5 below), we will get:    (3.7)   So in the classical view of APPARENTLY CONTINUOUS existence, when we consider both space and time to be real, i.e. when we consi ...

• ## ... Time Interval =>:

• ... e this Book III.2.1 The classical kinetic energy (in the normal time): In normal classical mechanics, the kinetic energy is the work done in accelerating a particle during the infinitesimal TIME INTERVAL , and it is given by the dot product of force  and displacement :    (3 ...

• ## ... Massive Particles =>:

• ... when we consider an infinitesimally continuous and smooth change in speed from zero to , the result of this integration will give the standard equation that describes the kinetic energy of MASSIVE PARTICLES or objects moving in the normal level of time:    (3.8)   The reaso ...

• ## ... Relativistic Mass =>:

• ... , and it is given by the dot product of force  and displacement :    (3.5) thus:  (3.6)   Now if we assume mass to be constant, so that:  (and we will discuss RELATIVISTIC MASS further in section III.2.5 below), we will get:    (3.7)   So in th ...

• ## ... Classical View =>:

• ... ;(3.6)   Now if we assume mass to be constant, so that:  (and we will discuss relativistic mass further in section III.2.5 below), we will get:    (3.7)   So in the CLASSICAL VIEW of apparently continuous existence, when we consider both space and time to be real, ...

• ## ... Absolute Speed =>:

• ... m zero to  in the inward levels of time, leading to the mass-energy equivalence relation , which can not happen on the normal level of time because physical objects may not move at the ABSOLUTE SPEED of light.         Read Other Books: The Single Monad Model of the ...

• ## ... Gradual Change =>:

• ... lly with time, which makes the integration equals the area of the triangle as demonstrated by the first arrow in Figure III.2. Figure III.2: Gradual versus Abrupt Change of Speed - Arrow 1: GRADUAL CHANGE of speed in the outer level of time, leading to the classical equation of kinetic ene ...

• ## ... Objects Moving =>:

• ... infinitesimally continuous and smooth change in speed from zero to , the result of this integration will give the standard equation that describes the kinetic energy of massive particles or OBJECTS MOVING in the normal level of time:    (3.8)   The reason why we are getting ...

• ## ... Classical Equation =>:

• ... riangle as demonstrated by the first arrow in Figure III.2. Figure III.2: Gradual versus Abrupt Change of Speed - Arrow 1: gradual change of speed in the outer level of time, leading to the CLASSICAL EQUATION of kinetic energy . Arrow 2: abrupt change from zero to  in the inward level ...

• ## ... Discuss Relativistic =>:

• ... interval , and it is given by the dot product of force  and displacement :    (3.5) thus:  (3.6)   Now if we assume mass to be constant, so that:  (and we will DISCUSS RELATIVISTIC mass further in section III.2.5 below), we will get:    (3.7)   ...

• ## ... Infinitesimally Continuous =>:

• ... III.2.5 below), we will get:    (3.7)   So in the classical view of apparently continuous existence, when we consider both space and time to be real, i.e. when we consider an INFINITESIMALLY CONTINUOUS and smooth change in speed from zero to , the result of this integration ...

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.