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Complex-Time Geometry and Perpetual Creation of Space

by Mohamed Haj Yousef

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Introduction: The Secret of Time

“In reality, Time is real, yet it is only known by imagination. Like (the four elements of) Nature, whose essence is extinct in time. ... Through it all things are determined, while itself has no essence to be defined. Like vacuum, an infinite extension beyond composition, but our imagination makes everything embodied.”Ibn al-Arabi, paraphrased from the introductory poem of chapter 59 of the Meccan Revelations: I.291.1-7

“The cosmos is imaginary, yet it is in reality real. That who appreciates this fact, has truly accomplished all the secrets of the Path.”Ibn al-Arabi, The Bezels of Wisdom

It is time to reveal the secret of time: Time is real at the present instance of its being, but because it does not halt; we can only reflect upon its perpetually flowing images, and that’s why it is actually imaginary. Therefore, time itself is both “real” and “imaginary”; it is real in its own being, and imaginary in the actual outward manifestations that we usually observe in each current individual instance of its continuous flow. This “duality of time” means that it has a genuine “complex geometry”, with a real part and an imaginary part. In the real flow of time, space and matter are internally created, and they are observed in the imaginary time as they kinetically evolve. However, because observation is one single instance of time, the observed things become instantly extinct, into the past, right after their being in the indivisible present instance of time, to be perpetually re-created again in the following future instances, in ever new images that could resemble the previous with some outwardly minor changes that cause the illusion of motion and dimensions.

Therefore, although time is the essence of everything in existence, yet its own essence cannot be defined independently because it is the temporal individual instances of all discrete things that come into being only one at a time, and because the observer is one of those individual things, it is only possible to observe the instantaneous temporal images of the other things that have already vanished and are being perpetually re-created. This means that all individual entities in the Universe are continuously created anew every single instance of time, one entity at a time, so that at every real instance there is only one indivisible real entity that is the Single Monad, and all other imaginary entities are its temporal and instantaneous images.

In other words: Time is always revealing its essence when we are not watching, but when we watch; it instantly hides in our own essence, because it is all one indivisible existence that is taking the three roles of the observed thing and the observer, as well as observation itself; continuously alternating between this cosmological trinity of the subject, object and action; but not all at the same real instance of time, as it is usually conceived by normal human imagination which conveys the illusory sensation that physical objects are real because it is averaging their extremely fast and instantaneous fluctuation into the present existence, in the same manner as we are normally deceived by the seemingly continuous existence and apparent motion of characters displayed on a computer screen, when they are in fact being re-created at an extremely fast refresh rate.

Hence, for its own existence, time is real, because it is always in the state of being. For us, however, time is imaginary, because it is always becoming into the past. There is only one indivisible present moment that is continuously dividing the real flow of time into remembered past and expected future, both of them are unreal with regard to the observer, because the first has already vanished and the latter has not come yet. Therefore, our time is imaginary because its discrete instances come to us only one by one, but we imagine it in the form of continuous extension or duration, because we always expect the future and remember the past.

The “Duality of Time Theory” is the dynamic combination between this inward real and outward imaginary dimensions of time. This is expressed mathematically in the form of complex numbers, whose real and imaginary parts are dynamically connected with hyperbolic relation that produces a granular and self-contained Euclidean space-time, without invoking Riemannian geometry.

This complex time-time geometry according to the Duality of Time Theory is genuine, and not a simple mathematical trick as it is normally treated in modern physics theories. In the dynamic process of perpetual creation, the physical dimensions of space are sequentially being re-created in the inner levels of time, which is what makes the outward time genuinely imaginary with respect to the inner time, and thus easily expressed in terms of Euclidean geometry by using hyperbolic split-complex numbers.

Without postulating the Duality of Time and the resulting continuous creation of space, this concept of imaginary time does not have any genuine reality or justification outside the mathematical formulation, because both the Galilean space and Minkowski space-time consider space and time to be coexisting together, i.e. they both are real. The fact that each frame of the inner time, which constitutes space, appears as one instance on the outward time is what justifies treating time as imaginary with relation to space, thus latent or orthogonal to it.

This is the first time in the history of mathematics that imaginary numbers have any intrinsic genuine reality. In fact, the real numbers’ line is now a special abstract or extreme “unrealistic” approximation of those genuine complex numbers which describe the real flow of existence. This extreme approximation is realized only when the normal level of time is zero or infinite, and in this latter case it is also equivalent to zero but on a higher level of the inner time that is creating the dimensions of space.

Therefore, this will also have deep implications on the various fields of mathematics, such as geometry and number theory, because complex numbers are now genuinely natural while the reals are one of their special approximation. In the physical sense, space-time has become naturally quantized although it may look continuous, depending on the relative dimension in which the observer is situated. For example: theplane is itself continuous with relation to its inner dimensions but it forms one discrete instance with relation to the flow of time in the encompassing, which then appears internally continuous but discrete with regard to the encompassing outward time.

One of the striking conclusions of this process of sequential re-creation in the inner levels of time is the fact that it conceives of only two primordial states: vacuum and void, whose spatial and temporal superposition is producing the multiplicity of all intermediary states that appear in the cosmos as matter particles. Vacuum, or empty space, is the continuous existence in the inner level of time, and void is the discrete existence in the outer level.

For normal observers who are habitually living, as discrete instances in the outer time, the continuous existence of vacuum appears moving at the terminal cosmological speed (of light) since it does not suffer the inertia that is experienced by massive particles and objects as they advance in the outer time. This inertia is the resistance that results from interrupting the continuous creation in the inner time in order to appear as discrete instances in the outer time. That is why the outer time is genuinely imaginary with relation to the inner time that is the real flow of creation.

Therefore, this dynamic and complex nature of time is the fundamental fact that underlines the emergence of dimensions. In other words: vacuum is the continuous and infinite existence which forms the inner real part of time, and whenever this existence is interrupted it makes a new dimension that appears as a discrete instance on the outer imaginary level which is then described as void because it does not last for more than one discrete instance, before it is re-created again in a new state that may resemble the previous perished states.

All the geometrical points of space and matter are sequentially fluctuating between these two existence and nonexistence states, or vacuum and void, which means that the actual instantaneous speed of each point in space can only change fromto, and vice versa.

This instantaneous abrupt change of speed does not contradict the laws of physics, because it is occurring sequentially in the inner levels of time before the physical objects are formed, while “space” and “mass”, and all other physical properties, are actually generated from the temporal coupling and decoupling, or entanglement, of these geometrical points, which is exhibited only on the outward time level. The normal limited velocities of massive physical particles and objects are a result of the spatial and temporal superposition of the various dual-states velocities of their individual points.

This single postulate explains the three principles of Relativity all at once, since the speed of light is the only real speed in nature, and all frames are effectively at rest in the normal (imaginary) level of time, so there is no difference between inertial and non-inertial frames, thus there is even no need to introduce the second principle of Special Relativity, which says that the laws of physics are invariant between inertial frames, neither the equivalence principle that leads to General Relativity. These two principles, which are necessary to derive Lorentz factor and Einstein’s field equations, will follow directly from the complex-time geometry as it will be explained and derived in the book.

Furthermore, it will be shown that this essential fact that results from the genuinely complex nature of time is the only way that allows exact mathematical derivation of the mass-energy equivalence relation () directly from the fundamental classical principles. Einstein gave various heuristic arguments for this relation without ever being able to prove it in any theoretical way, as he repeatedly acknowledged.

Accordingly, the Duality of Time will lead to full quantum field theory of gravity because it is now based on discrete instances of dynamic space, without any background. Additionally, the other fundamental forces can now be interpreted in terms of this new complex-time geometry, but in lower dimensions:,, and, while gravity is in.

As a result of this unification, most, if not all, of the major fundamental problems of physics and cosmology are easily solved in this model. The homogeneity problem, for example, will instantly cease, since the universe, no matter how large it could be, is re-created sequentially in the inner time, so all the states are updated and synchronized before they appear in the outer level of time.

Actually, the Duality of Time postulate is capable of taking the fundamental philosophical observations to profound new levels, because the most basic principle of causality becomes a consequence of the sequential re-creation. Therefore, without breaking the speed of light limit, this sequential re-creation can explain non-locality, the uncertainty principle, and various other critical quantum mechanical issues.

Furthermore, in addition to solving the major problems of physics and cosmology, the Duality of Time does not only unify all the fundamental interactions in terms of its genuinely-complex time-time geometry, but it unifies this whole physical world with the two other even more fundamental domains of the psychical and spiritual worlds. All these three conclusive and complementary realms are constructed on the same concept of complex time-time geometry that together form one single absolute and perfectly symmetrical spherical space.

Among many other astonishing consequences, this astounding conclusion means that the psychical world is composed of atoms and molecules that are exactly identical with the physical world, except that they are evolving in a conjugate time direction, which is why we feel them but describe them as incorporeal. It may initially appear impossible to believe how spiritual worlds may have the same atomic structure as the physical world, but it is more appropriate to say that physical structures are eventually incorporeal, because they become pure wave phenomena and energy interactions as soon as we dive into their microscopic levels, as it is now confirmed by Quantum Field Theories. In the Duality of Time Theory, since rigid space is created sequentially in the inner time, energy may become negative, imaginary and even multidimensional, which simply means that all things in creation are various kinds of energy moments that are spreading on different intersecting dimensions of time, and contributing in physical and non-physical interactions depending on their plane of existence, although they all have the same fundamental space-time structure. Therefore, not only mass and energy are equivalent and convertible according to, but also charge and all other physical and metaphysical entities are geometrical space-time structures with interconvertible types of energy, including consciousness and abstract information.

Therefore, speaking, writing, painting, and all kinds of interfering colors, shapes and inscriptions; all these otherwise abstract meanings are essentially made of particles covered by the same symmetry of the Standard Model, and this is indeed the missing super-symmetry which solves many fundamental problems, such as the hierarchy problem and baryonic asymmetry.

Finally, what is even more amazing is that this extraordinary unification between the various apparently incompatible physical and spiritual sciences is based on the same classical conceptions found in most ancient philosophies and contemporary religions, that describe different layers of creation beyond the physical world, such as the incorporeal creations of angels and jinn, in addition to describing the various unseen fundamental structures beyond stars and galaxies, such as the seven heavens and the four classical elements of earth, water, air and fire; all these creations and realms are now equally described in terms of the same complex-time geometry. This will open many doorways to whole new kinds of sciences and give the possibility of extending existing technologies onto the other spiritual domains, and vice versa. Many overwhelming historical records and manuscripts show that sciences and applications such as Alchemy and other occult practices have been widely used in ancient traditions, although most have been actually interpreted in various wrong manners and were eventually greatly misused by swindlers and magicians. This, however, does not falsify other sciences, such as energy meditation, dowsing, and many other mysterious applications.

The Duality of Time Theory is the result of more than two decades of ceaseless investigation and searching through the forgotten remarkable heritage that includes many ancient manuscripts of discounted philosophies and mystical Sufi traditions, and comparing all that with the conclusive results of modern physics theories, until I was able to put together all the contradicting puzzles into this brilliant portrait. Without the strong indications and overwhelming proofs that gradually accumulated over time, it would have been impossible to pursue this long research path, as it is extremely challenging to appreciate this unfathomable secret of time and ongoing perpetual creation. Ultimately, this theory does not only explain how the Universe appears ex-nihilo, but that it is always in this ontological state of potential existence, only perpetually and discreetly coming into being for some series of consecutive discrete instances of time, the duration of each is absolutely zero, but as a result of our manipulative past memory and future expectation we imagine time extensions in which we are no more than passing shadows making some monotonous noise for this short period of imaginary time, before we leave this world to a relatively higher level of existence. Often when I retire, for a few days, and then come back again to think about this mysterious nature of time and perpetual creation, I need to study everything thoroughly from the beginning again, in order to retain the logical image of this impermeable reality beyond ordinary human imagination.

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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

Check this detailed video presentation on "Deriving the Principles of Special, General and Quantum Relativity Based on the Single Monad Model Cosmos and Duality of Time Theory".

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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]