# DUALITY OF TIME:

Complex-Time Geometry and Perpetual Creation of Space

# 3.2.4  Lorentz Group

The group of all Lorentz transformations of Minkowski space-time is called Lorentz group, and it 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. This group, therefore, expresses the fundamental symmetry of space and time of all known fundamental laws of nature. Lorentz transformations can also be considered as a hyperbolic rotation of Minkowski space.

For one-dimensional motion, Lorentz transformations can be expressed in terms of matrices as follows:

(3.5)

Note that a boost along the-direction does not warp the space in the- and-directions.

The Lorentz group is a six-dimensional noncompact 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. The restricted Lorentz group has often been presented through a facility of biquaternion algebra.

Lorentz transformations are, precisely, isometries that leave the origin fixed. Thus, the Lorentz group is an isotropy subgroup of the isometry group of Minkowski space-time. For this reason, the Lorentz group is sometimes called the homogeneous Lorentz group while the Poincaré group is sometimes called the inhomogeneous Lorentz group.

Lorentz transformations are examples of linear transformations; general isometries of Minkowski space-time are affine transformations. Mathematically, the Lorentz group may be described as the generalized orthogonal group, the matrix Lie group that preserves the quadratic form on:

(3.6)

This quadratic form is, when put on matrix form, interpreted in physics as the metric tensor of Minkowski space-time.

The Lorentz group is a subgroup of the Poincaré group, the group of all isometries of Minkowski space-time.

# Other Pages Related to Search Keywords:

• ... 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 ...

• ## ... Confinement To Space =>:

• ... ty of Time Theory: Complex-Time Geometry and Perpertual Creation of Space The Ultimate Symmetry: Fractal Complex-Time and Quantum Gravity The Chest of Time: Particle-Wave Duality: from Time Confinement to Space Transcendence Read this short concise exploration of the Duality of Time Postul ...

• ## ... Mohamed Haj Yousef =>:

• ... Time Postulate: DoT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics ...

• ## ... Mohamed Haj =>:

• ... Time Postulate: DoT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics ...

• ## ... Relativity And Quantum Mechanics =>:

• ... uality: from Time Confinement to 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 ...

• ## ... Concise Exploration =>:

• ... tual Creation of Space The Ultimate Symmetry: Fractal Complex-Time and Quantum Gravity The Chest of Time: Particle-Wave Duality: from Time Confinement to Space Transcendence Read this short CONCISE EXPLORATION of the Duality of Time Postulate: DoT: The Duality of Time Postulate and Its Con ...

• ## ... Short Concise =>:

• ... Perpertual Creation of Space The Ultimate Symmetry: Fractal Complex-Time and Quantum Gravity The Chest of Time: Particle-Wave Duality: from Time Confinement to Space Transcendence Read this SHORT CONCISE exploration of the Duality of Time Postulate: DoT: The Duality of Time Postulate and I ...

• ## ... Transcendence Read =>:

• ... mplex-Time Geometry and Perpertual Creation of Space The Ultimate Symmetry: Fractal Complex-Time and Quantum Gravity The Chest of Time: Particle-Wave Duality: from Time Confinement to Space Transcendence Read this short concise exploration of the Duality of Time Postulate: DoT: The Duality ...

• ## ... Perpertual Creation =>:

• ... tion has objective reality.     Read Other Books: The Single Monad Model of the Cosmos: Ibn Arabi's View of Time and Creation The Duality of Time Theory: Complex-Time Geometry and Perpertual Creation of Space The Ultimate Symmetry: Fractal Complex-Time and Quantum Gravity The Che ...

• ## ... Yousef Search =>:

• ... ate: DoT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics ...

• ## ... Perpetual Creation =>:

• ... e exploration of the Duality of Time Postulate: DoT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics ...

• ## ... Function Collapse =>:

• ... ds interpretation, proposed by Everett in 1957, a universal wave-function obeys the same deterministic and reversible laws at all times, so there is no indeterministic and irreversible wave- FUNCTION COLLAPSE associated with measurement. Rather, the phenomena associated with measurement are ...

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.
Ibn al-Arabi [The Meccan Revelations: Volume I, page 156. - Trns. Mohamed Haj Yousef]

### The Sun from the West:

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

### 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.