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DUALITY OF TIME:

Complex-Time Geometry and Perpetual Creation of Space

by Mohamed Haj Yousef



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3.5  Quantum Field Theory


Quantum Field Theory combines classical fields, Special Relativity, and Quantum Mechanics in one theoretical framework for constructing quantum mechanical models of subatomic particles, as well as quasi-particles in condensed matter physics. The theory allows infinite numbers of particles, but it predicts how many and with which probabilities or numbers they should exist. When developed further, the theory often contradicts observation, but its creation and annihilation operators can be empirically tied down or renormalized.

Since it was able to combine Special Relativity with Quantum Mechanics, Quantum Field Theory was first believed to be fundamental, but due to its continued failures in quantizing General Relativity, as we shall discuss further in section 5.15, it is only a very good low-energy approximation, or an effective field theory, to some yet undiscovered fundamental theory. The essence of the problem is because it is impossible to quantize space-time itself without supposing some background space in which it is quantized. The Duality of Time seems to be the only way out of this riddle, because it produces a dynamic and self-contained space-time, which will be even extremely easier than the current approaches, such as Strings Theory and Loop Quantum Gravity, because the resulting genuinely-complex time-time geometry is Euclidean and it is intrinsically granular, as we shall discuss this further in chapter V.

Quantum Field Theory treats particles as excited states, or field quanta, of the underlying field, and the interactions among these particles are described by interaction terms among the corresponding underlying quantum fields. These interactions are conveniently visualized by Feynman diagrams, described further in section 5.8.

As Richard Hammond described the conceptual difference between Quantum Mechanics and Quantum Field Theory: “Sometimes we distinguish between Quantum Mechanics (QM) and Quantum Field Theory (QFT). QM refers to a system in which the number of particles is fixed, and the fields (such as the electromechanical field) are continuous classical entities. Quantum Field Theory ... goes a step further and allows for the creation and annihilation of particles.” Hammond (2008)



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  • ... Apparent Motion =>:

  • ... pace at the speed of light, so that in the end the actual velocity is: , which means that everything in space is intrinsically moving at the speed of light in the real flow of time, and its APPARENT MOTION in the outward time is causing an apparent (or imaginary) slow down from this real s ...


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  • ... variant speed of light, or in general: . See also Figure 5.1, and also Figure 5.3. Using the concept of split-complex time, we can easily derive Lorentz boost for example by calculating the PROPER TIME as it can be readily seen from Figure 5.1, which is replicated in Figure 5.3 that repres ...


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  • ... -Time Geometry and Perpetual Creation of Space by Mohamed Haj Yousef Search Inside this Book 5.3.2  Deriving Lorentz Factor It was originally shown by Poincaré that by using the MATHEMATICAL TRICK of imaginary time, Lorentz transformation becomes a rotation between inertial fra ...


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  • ... l moving at this same real speed. Figure 5.3: The actual velocity is the modulus of split-complex velocity that combines the real speed with the imaginary velocity , calculated according to HYPERBOLIC NUMBERS , thus: , from which we can easily calculate Lorentz boost as . Lorentz boost is t ...


  • ... Invariant Speed =>:

  • ... then the speed of light will be the ground state, or the rest speed, so when the apparent imaginary velocity on the outer time is zero there is still the real speed that is the constant and INVARIANT SPEED of light, or in general: . See also Figure 5.1, and also Figure 5.3. Using the conce ...


  • ... Easily Calculate =>:

  • ... The actual velocity is the modulus of split-complex velocity that combines the real speed with the imaginary velocity , calculated according to hyperbolic numbers, thus: , from which we can EASILY CALCULATE Lorentz boost as . Lorentz boost is therefore the ratio of the real velocity over t ...


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  • ... e are , then its (primed) coordinates with respect to another frame, that is moving with uniform velocity with respect to the first frame, are: , where , and since: , then: . In the complex- TIME FRAME of the Duality of Time Postulate, however, the outer time is the (genuinely) imaginary pa ...


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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.

Enjoy reading...

Mohamed Haj Yousef


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