# DUALITY OF TIME:

Complex-Time Geometry and Perpetual Creation of Space

# 3.2.5  Poincaré Group

The Poincaré group was first defined by Minkowski (1908) as the group of Minkowski space-time isometries. It is a ten-generator non-Abelian Lie group of fundamental importance in physics.

A Minkowski space-time isometry has the property that the interval between events is left invariant. In Minkowski space (i.e. ignoring the effects of gravity), there are ten degrees of freedom of the isometries, which may be thought of as translation through time or space (four degrees, one per dimension); reflection through a plane (three degrees, the freedom in orientation of this plane); or a “boost” in any of the three spatial directions (three degrees). Composition of transformations is the operator of the Poincaré group, with proper rotations being produced as the composition of an even number of reflections.

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.

Poincaré symmetry is the full symmetry of Special Relativity. It includes: translations, or displacements, in time and space (P), forming the abelian Lie group of translations on space-time; rotations in space, forming the non-Abelian Lie group of three-dimensional rotations (J); boosts, transformations connecting two uniformly moving bodies (K).

The last two symmetries, J and K, together make the Lorentz group; the semi-direct product of the translations group and the Lorentz group then produce the Poincaré group. Objects which are invariant under this group are then said to possess Poincaré invariance or relativistic invariance.

The Poincaré group is the group of Minkowski space-time isometries. It is a ten-dimensional noncompact Lie group. The abelian group of translations is a normal subgroup, while the Lorentz group is also a subgroup, the stabilizer of the origin. The Poincaré group itself is the minimal subgroup of the affine group which includes all translations and Lorentz transformations. More precisely, it is a semidirect product of the translations and the Lorentz group.

# 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 ...

• ## ... 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 =>:

• ... Self-Aware Universeâ€.     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 ...

• ## ... Quantum Theory =>:

• ... the point of intersection between Quantum Mechanics and the mind/body problem; and some researchers are working to detect conscious events correlated with physical events that, according to QUANTUM THEORY , should involve a wave-function collapse, but there are no conclusive results so far. ...

• ## ... Dinger Equation =>:

• ... umann deeply analyzed the measurement problem, or the effect of the observer as discussed in section 4.4.5. He concluded that the entire physical Universe could be made subject to the Schroe DINGER EQUATION , which is called: the universal wave-function. He then described how measurement cou ...

• ## ... Function Collapse =>:

• ... tum Mechanics and the mind/body problem; and some researchers are working to detect conscious events correlated with physical events that, according to quantum theory, should involve a wave- FUNCTION COLLAPSE , but there are no conclusive results so far. John Archibald Wheelerâ€™s parti ...

• ## ... Schroedinger Equation =>:

• ... von Neumann deeply analyzed the measurement problem, or the effect of the observer as discussed in section 4.4.5. He concluded that the entire physical Universe could be made subject to the Schroedinger equation, which is called: the universal wave-function. He then described how measureme ...

• ## ... Physical Universe =>:

• ... Mathematical Foundations of Quantum Mechanics, von Neumann deeply analyzed the measurement problem, or the effect of the observer as discussed in section 4.4.5. He concluded that the entire physical Universe could be made subject to the Schroedinger equation, which is called: the universal ...

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.