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DUALITY OF TIME:

Complex-Time Geometry and Perpetual Creation of Space

by Mohamed Haj Yousef



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3.5.1  Classical and Quantum Fields


A field in physics is a region or space in which a given effect exists, such as magnetism, static electricity, gravity, or even temperature. In classical physics, a field is a quantity, represented by a number or tensor, that has a value for each point in space and time. In the modern framework of the quantum theory of fields, a field occupies space, contains energy, and its presence precludes a classical “true vacuum”.

This led physicists to consider electromagnetic fields to be a physical entity, making the field concept a supporting paradigm of the edifice of modern physics. As Feynman said:

The fact that the electromagnetic field can possess momentum and energy makes it very real ... a particle makes a field, and a field acts on another particle, and the field has such familiar properties as energy content and momentum, just as particles can have. Feynman et al. (1963)

In general, a field can be classified as a scalar field, a vector field, a spinor field or a tensor field, according to the represented physical quantity. A field has a unique tensorial character in every point where it is defined, so a field cannot be a scalar field somewhere and a vector field in other regions. However, for all these categories, a field can be classical or a quantum field, depending on whether it is characterized by numbers or by quantum operators.

A classical field is a function defined over some region of space and time, such as gravitation and classical electromagnetism. Because such fields can in principle take on distinct values at each point in space, they are said to have infinite degrees of freedom, called classical oscillators. However, classical field theory does not account for the quantum-mechanical aspects of such physical phenomena. Quantum Field Theory, therefore, define the field as a function over space and time, but in a way that accommodates the observations of Quantum Mechanics.

To achieve this task, the infinity of classical oscillators representing the modes of the classical fields are promoted to quantum harmonic oscillators. This means that they are functions whose values are abstract operators acting on an abstract state space. In such space, which is called Hilbert space, the observables represent physically observable quantities, and the state space represents the possible states of the system under study.

There are two common ways of handling a quantum field: canonical quantization and the path integral formalism.



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  • ... r his derivation, and in the following forty years, he produced more than half dozen proofs that all suffer from unjustified assumptions or approximations. He never succeeded in producing a VALID GENERAL proof. In 1955 he wrote in a letter to Carl Seelig: “I had already previously fo ...


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  • ... Original Derivation =>:

  • ... without ever being able to prove it in any theoretical way, neither did anyone else. Based on Doppler effect and Maxwell’s theory of radiation, the reasoning that he gave in his 1905 ORIGINAL DERIVATION was questioned by Planck and shown to be faulty. In 1907, Einstein acknowledged ...


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  • ... Normal Behavior =>:

  • ... ecome inapplicable since they prohibit massive particles from moving at the speed of light, in which case the mass would be infinite. In the inner levels of time, however, this would be the NORMAL BEHAVIOR because the geometrical points are still massless, and their continuous coupling and ...


  • ... Prohibit Massive =>:

  • ... levels of time, because it must involve motion at the speed of light that appears on the normal level of time as instantaneous, hence the same Relativity laws become inapplicable since they PROHIBIT MASSIVE particles from moving at the speed of light, in which case the mass would be infini ...


  • ... Involve Motion =>:

  • ... exact derivation of this famous formula. It can be readily seen from Figure 5.4 that the transmutability between mass and energy can only occur in the inner levels of time, because it must INVOLVE MOTION at the speed of light that appears on the normal level of time as instantaneous, henc ...


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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.

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Mohamed Haj Yousef


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The time of anything is its presence; but I am not in time, and You are not in time; so I am Your time, and You are my time!
Ibn al-Arabi [The Meccan Revelations: III.546.16 - tans. Mohamed Haj Yousef]
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