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DUALITY OF TIME:

Complex-Time Geometry and Perpetual Creation of Space

by Mohamed Haj Yousef



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3.5.10  Symmetry


In the beginning of the 1950s, QED become a reliable theory, but it took more time until Quantum Field Theory could be applied successfully to important physical problems in a systematic way. The theories explored relied on a rich variety of symmetries pioneered and articulated by Murray Gell-Mann (b. 1929). This made it possible to apply Quantum Field Theory to new particles and new interactions and fully explain their structure.

In the following decades, Quantum Field Theory was extended to describe the electromagnetic force and also weak and strong interaction, so that new Lagrangians were found which contain new classes of particles or quantum fields. The search still continues for a unified theory of all interactions that more comprehensively explain all matter and energy, including gravity.

The new focus on symmetry led to the triumph of non-Abelian gauge theories, pioneered by the work of Chen-Ning Yang (b. 1922) and Robert Mills (1927-1999), and spontaneous symmetry breaking, by Yoichiro Nambu (1921-2015).

A combined re-normalizable theory associated with the gauge groupis dubbed the standard model of elementary particle physics, that was assembled by Sheldon Glashow (b. 1932), Steven Weinberg (b. 1933) and Abdus Salam (1926-1996), between 1959 and 1967, in addition to many other scientists, including: Peter Higgs, Francois Englert, Robert Brout, Martin Veltman, Gerard ’t Hooft, Frank Wilczek, David Gross and David Politzer.

According to the standard model, described further in section 5.18, there are six types of leptons and six types of quarks, where the members of both groups are all fermions with spin-half. On the other hand, there are four spin-one particles, or bosons, that mediate the interaction between elementary particles and the fundamental forces. The linchpin of the symmetry breaking mechanism of the theory is the spin-zero Higgs boson which was discovered in 2012, after 40 years of its prediction.



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  • ... Time Concept =>:

  • ... eads to equation 5.15, as it is derived in section 3.3.8. This derivation of the relativistic energy-momentum relation from the fundamental definition of momentum is based on the Duality of Time concept, by taking into account the complex nature of time, as hyperbolic numbers, which is why ...


  • ... Potential Energy =>:

  • ... and do not realize its complex dimensions (see also section 3.6). Practically, in any mass-energy interaction or conversion, the negative term will be converted to positive because when the POTENTIAL ENERGY is released, in nuclear interactions for example, this means that it has been conve ...


  • ... Hyperbolic Number =>:

  • ... ation of the relativistic energy-momentum relation from the fundamental definition of momentum is based on the Duality of Time concept, by taking into account the complex nature of time, as HYPERBOLIC NUMBER s, which is why the contribution of the imaginary term appears here as negative in ...


  • ... Negative Sign =>:

  • ... to the real momentum , just like the case of and as we have seen in sections 2.2 and 3.2, and as it will be also the case for energy as we shall see further below. These equations, with the NEGATIVE SIGN , do not contradict the current equations, such as: which treat energy as scalar and do ...


  • ... Essential Modification =>:

  • ... , when we take into account the complex nature of time as we described in sections 2.2 and 3.2 above (Figures: 5.1 and 5.3), energy and momentum will be also complex. This will introduce an ESSENTIAL MODIFICATION on the relativistic energy-momentum equation which will lead to the derivatio ...


  • ... Average Velocity =>:

  • ... he speed of light in the inner time , before it appears as an instance in the imaginary outer time where its instantaneous velocity is but the re-creation makes it appear to be moving at an AVERAGE VELOCITY . So in the inner time it behaves as a wave with instantaneous velocity , and in th ...


  • ... Simple Form =>:

  • ... etry and Perpetual Creation of Space by Mohamed Haj Yousef Search Inside this Book 5.3.4  Relativistic Energy-Momentum Relation In addition to the previous two methods that derived the SIMPLE FORM of the mass-energy equivalence: in equations 5.9 and 5.10 above, the relativistic energy ...


  • ... Hyperbolic Numbers =>:

  • ... ation of the relativistic energy-momentum relation from the fundamental definition of momentum is based on the Duality of Time concept, by taking into account the complex nature of time, as HYPERBOLIC NUMBERS , which is why the contribution of the imaginary term appears here as negative in ...


  • ... Normal Kinetic =>:

  • ... obtained by averaging these two instantaneous velocities over all its metaphysical points , as we described in section 3 above. Therefore, the real momentum in the inner time is , while the NORMAL KINETIC momentum, which is the imaginary part, is . Thus the total complex momentum is: , who ...


  • ... Current Equations =>:

  • ... case of and as we have seen in sections 2.2 and 3.2, and as it will be also the case for energy as we shall see further below. These equations, with the negative sign, do not contradict the CURRENT EQUATIONS , such as: which treat energy as scalar and do not realize its complex dimensions ( ...


  • ... Imaginary Momentum =>:

  • ... us its effective mass increases from to , and this term makes the imaginary part of the complex momentum : (5.24) The first term gives us the real momentum , while the second term gives the IMAGINARY MOMENTUM . Thus: (5.25) Hence the modulus of this total complex momentum is: (5.26) Again ...


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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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