The **Duality of Time Theory**, that results from the
**Single Monad Model of the Cosmos**, explains how *physical multiplicity* is emerging from absolute
(metaphysical) *Oneness*, at every instance of our normal time! This leads to the **Ultimate Symmetry** of space and its dynamic formation and breaking into the *physical* and *psychical* (supersymmetrical) creations, in orthogonal time directions. *General Relativity* and *Quantum Mechanics* are complementary **consequences** of the Duality of Time Theory, and all the fundamental interactions become properties of the new **granular complex-time geometry**, at different dimensions. - **=> Conference Talk - Another Conference [Detailed Presentation]**

Fractal Complex-Time and Quantum Gravity

In Classical Mechanics, Galilean transformations are used
to transform between the coordinates of two reference frames which differ only
by constant relative velocity . For simplicity we consider that motion
is only on the axis, so that the other two axes are
unaffected (, ),
while and are
related by the following equation: .
Together with spatial rotations and translations in space and time, these
transformations form the inhomogeneous Galilean group, which includes the set
of*non-relativistic*continuous space-time transformations, in space
with absolute time. Simple spatial rotations, translations, and
transformations, are subgroups of this Galilean group, each of them has three
parameters or dimensions: , , and , whereas temporal
translation is a subgroup of one dimension: .
Therefor, in total, the Galilean group has real
dimensions.

When we combine these transformations with the principle of the constancy and invariance of the speed of light, we get the Lorentzian transformations which led to Special Relativity. Lorentz invariance relates between two inertial coordinates systems by the following relations, again considering for simplicity that motion is only on the axis: and , where : is the ratio of the velocity over the speed of light , and is called Lorentz factor and it is given by: . Lorentz transformations can also be considered as a hyperbolic rotation of Minkowski space, as we explained in Chapter V of Volume II.

When the relative speed between the observers is very small, in relation to the speed of light, as it is the case in most classical situations, the value of will be effectively considered zero, and the value of will be equal to one. Under these conditions, Lorentzian invariance reduces back to the Galilean symmetry expressed above. Therefore, Galilean invariance is an approximation of Special Relativity that is valid for low speeds, while Special Relativity is an approximation of General Relativity that is valid for weak gravitational fields, as we shall describe in section III.1.2.

The set of all Lorentz transformations of Minkowski space-time is called Lorentz group, which describes the classical and quantum setting for all non-gravitational physical phenomena, including: the kinematical laws of Special Relativity, Maxwell s field equations in the theory of electromagnetism, the Dirac equation in the theory of the electron, and the Standard model of particle physics. All physical laws are Lorentz invariant when gravitational variances are negligible.

Lorentz violations are allowed in String Theory, super-symmetry and Horava-Lifshitz gravity, as well as some approaches to Quantum Gravity. However, there is no experimental evidence of any violation of Lorentz invariance. When gravitational variances are negligible, all physical laws are Lorentz invariant. Lorentz transformations can also be considered as a hyperbolic rotation of Minkowski space.

The Lorentz group is a six-dimensional non-compact non-Abelian real Lie group that is not connected. The four connected components are not simply connected, but rather doubly connected. The identity component (i.e., the component containing the identity element) of the Lorentz group is itself a group, and is often called the restricted Lorentz group, and is denoted . The restricted Lorentz group consists of those Lorentz transformations that preserve the orientation of space and direction of time, and it is often presented through bi-quaternion algebra. Mathematically, the Lorentz group may be described as the generalized orthogonal group , the matrix Lie group that preserves the quadratic form on : .

Lorentz group is a subgroup of the Poincar group, the group of all isometries of Minkowski space-time, because Lorentz transformations are isometries that leave the origin fixed. For this reason, the Lorentz group is sometimes called the homogeneous Lorentz group while the Poincar group is called the inhomogeneous Lorentz group. Lorentz transformations are examples of linear transformations; general isometries of Minkowski space-time are affine transformations.

In classical physics, the Galilean group is a comparable ten-parameter group that acts on absolute time and space. Instead of boosts, it features shear mappings to relate co-moving frames of reference, whereas Poincar symmetry is the full symmetry of Special Relativity. Objects which are invariant under this group are then said to possess Poincar invariance or relativistic invariance.

Similarly, a physical quantity is said to be Lorentz**covariant**
if it transforms under a given representation of the Lorentz group. As we
explained in the Introduction, according to the representation theory of the
Lorentz group, these quantities can be built out of scalars, four-vectors,
four-tensors, and spinors. In particular, a Lorentz covariant scalar, such as
space-time interval, remains the same under Lorentz transformations and is said
to be a Lorentz invariant, which means that they transform under the trivial
representation. This can also be generalized to equations, which can be Lorentz
covariant if they can be written in terms of such quantities, which hold in all
inertial frames.

## ... Monadology =>:

## ... Full Symmetry =>:

## ... Reference Frames =>:

## ... Galilean Transformation =>:

## ... Real Dimensions =>:

## ... Lorentzian Transformation =>:

## ... Gravitational Field =>:

## ... Identity Element =>:

## ... Lorentz Factor =>:

## ... Classical Physics =>:

## ... Lorentzian Transformations =>:

## ... Experimental Evidence =>:

... 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 ...

... a comparable ten-parameter group that acts on absolute time and space. Instead of boosts, it features shear mappings to relate co-moving frames of reference, whereas Poincar symmetry is the FULL SYMMETRY of Special Relativity. Objects which are invariant under this group are then said to p ...

... ty by Mohamed Haj Yousef Search Inside this Book III.1.1 Symmetry in Special Relativity In Classical Mechanics, Galilean transformations are used to transform between the coordinates of two REFERENCE FRAMES which differ only by constant relative velocity . For simplicity we consider that m ...

... and Quantum Mechanics ...

... is Galilean group, each of them has three parameters or dimensions: , , and , whereas temporal translation is a subgroup of one dimension: . Therefor, in total, the Galilean group has REAL DIMENSIONS . When we combine these transformations with the principle of the constancy and invar ...

... Therefor, in total, the Galilean group has real dimensions. When we combine these transformations with the principle of the constancy and invariance of the speed of light, we get the Lorentzian transformations which led to Special Relativity. Lorentz invariance relates between two i ...

... refore, Galilean invariance is an approximation of Special Relativity that is valid for low speeds, while Special Relativity is an approximation of General Relativity that is valid for weak GRAVITATIONAL FIELD s, as we shall describe in section III.1.2. The set of all Lorentz transformation ...

... Abelian real Lie group that is not connected. The four connected components are not simply connected, but rather doubly connected. The identity component (i.e., the component containing the IDENTITY ELEMENT ) of the Lorentz group is itself a group, and is often called the restricted Lorentz ...

... relations, again considering for simplicity that motion is only on the axis: and , where : is the ratio of the velocity over the speed of light , and is called Lorentz factor and it is given by: . Lorentz transformations can also be considered as a hyperbolic ...

... ar group is called the inhomogeneous Lorentz group. Lorentz transformations are examples of linear transformations; general isometries of Minkowski space-time are affine transformations. In CLASSICAL PHYSICS , the Galilean group is a comparable ten-parameter group that acts on absolute time ...

... Therefor, in total, the Galilean group has real dimensions. When we combine these transformations with the principle of the constancy and invariance of the speed of light, we get the Lorentzian transformations which led to Special Relativity. Lorentz invariance relates between two i ...

... al variances are negligible. Lorentz violations are allowed in String Theory, super-symmetry and Horava-Lifshitz gravity, as well as some approaches to Quantum Gravity. However, there is no EXPERIMENTAL EVIDENCE of any violation of Lorentz invariance. When gravitational variances are negli ...

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.

Welcome to the Single Monad Model of the Cosmos and Duality of Time Theory

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".

Download the Book "DOT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics" or: READ ONLINE .....>>>>

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