ULTIMATE SYMMETRY:
Fractal Complex-Time and Quantum Gravity
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I.4.5 The Genuinely-Complex Time-Time
Frame
Mathematically, the nested levels of time can be
represented by imaginary or complex numbers where space is treated as a plane
or spherical wave, and time is the orthogonal imaginary axis. However, in
addition to the normal complex number plane: , that
can describe Euclidean space, split-complex, or hyperbolic, numbers: , are
required to express the relation between space-like and time-like dimensions,
which are the inner and outer levels of time, respectively. Normal complex
numbers can describe homogeneous or isomorphic space, without (the outer) time,
where each number defines a circle, or sphere, because its
modulus is given by ,
while in split-complex numbers the modulus is given by , so ,
which defines a hyperbola. This negative sign in calculating the modulus of
complex time reflects
the essential fact that the perpetual re-creation of space and matter particles
in the inner levels of time is
interrupted and re-newed every instance of the outward time , which
produces kinetic motions on the physical level, as dynamic local deformations
of the otherwise flat and homogeneous Euclidean space.
Therefore the non-Euclidean Minkowski space-time
coordinates are an
approximation of the complex space-time coordinates , or
complex time-time coordinates: where
or represent
the innerreal part of time: , and represents
the outerimaginary time, so the totalcomplex timeis , where
is the
split-imaginary unit which defines hyperbolic numbers, thus: , and
its modulus is .
These hyperbolic numbers have been also called: tessarines, motors, bireal,
perplex, semi-complex, or split-complex, but in this article, unless otherwise
stated,imaginaryandcomplexrefer to these hyperbolic numbers
.
In this abstract complex frame, space and time are
absolute, or mathematical, just as they had been originally treated in the
classical Newtonian Mechanics, but now empty space isvoid, which is a
pure mathematical space, because it does not have any material reality, to
differentiate it from the physicalvacuum, which is the dynamic aether,
or the ground state of matter. So, for void both the real and imaginary parts
are null: , while
for vacuum only the imaginary part is null: , which
indicates infinite and inert space that is the ground state of matter
particles, that are then described by , or: , which
means that they are internally being re-created at the speed of , that is the real part,
and moving outwardly at the apparent velocity , that is the imaginary
part; given by equation 3.1. We shall see in sections 2.1.5 and 3.3.3 that the
complex-time space provides simple alternative mass generation mechanism that
could alter or replace the Higgs.
... 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 ...
... quences on General Relativity and Quantum Mechanics ...
... y instance of the outward time , which produces kinetic motions on the physical level, as dynamic local deformations of the otherwise flat and homogeneous Euclidean space. Therefore the non-Euclidean Minkowski space-time coordinates are an approximation of the complex space-time coor ...
... peed of , that is the real part, and moving outwardly at the apparent velocity , that is the imaginary part; given by equation 3.1. We shall see in sections 2.1.5 and 3.3.3 that the complex- TIME SPACE provides simple alternative mass generation mechanism that could alter or replace the Hig ...
... ated, imaginary and complex refer to these hyperbolic numbers . In this abstract complex frame, space and time are absolute, or mathematical, just as they had been originally treated in the classical Newtonian Mechanics, but now empty space is void , which is a pure mathematical space, bec ...
... inary and complex refer to these hyperbolic numbers . In this abstract complex frame, space and time are absolute, or mathematical, just as they had been originally treated in the classical Newtonian Mechanics, but now empty space is void , which is a pure mathematical space, because it do ...
... ;are an approximation of the complex space-time coordinates , or complex time-time coordinates: where or represent the inner real part of time : , and represents the OUTER IMAGINARY time , so the total complex time is , where is the split-imaginary unit which ...
... y treated in the classical Newtonian Mechanics, but now empty space is void , which is a pure mathematical space, because it does not have any material reality, to differentiate it from the PHYSICAL VACUUM , which is the dynamic aether, or the ground state of matter. So, for void both the ...
... ated, imaginary and complex refer to these hyperbolic numbers . In this abstract complex frame, space and time are absolute, or mathematical, just as they had been originally treated in the classical Newtonian Mechanics, but now empty space is void , which is a pure mathematical space, bec ...
... r) time, where each number defines a circle, or sphere, because its modulus is given by , while in split-complex numbers the modulus is given by , so , which defines a hyperbola. This NEGATIVE SIGN in calculating the modulus of complex time reflects the essential fact that the ...
... onian Mechanics, but now empty space is void , which is a pure mathematical space, because it does not have any material reality, to differentiate it from the physical vacuum , which is the DYNAMIC AETHER , or the ground state of matter. So, for void both the real and imaginary parts are nu ...
... act complex frame, space and time are absolute, or mathematical, just as they had been originally treated in the classical Newtonian Mechanics, but now empty space is void , which is a pure MATHEMATICAL SPACE , because it does not have any material reality, to differentiate it from the phys ...
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.
