Quantum Phase Compactification via Spacetime Expansion

  • #1
Non-relativistic string theory was introduced by d'Alembert, in 1747,
with the first appearance of the wave equation and the d'Alembertian
operator, which eventually became the foundations of "relativistic"
field theories; for example, the theories of electromagnetism, special
relativity, and quantum mechanics.

The description of any entity inside the real universe can only be
with reference to other things in the universe. Space is then
relational, and the universe, self referential. For example, if an
object/event has a momentum, that momentum can only be explained with
respect to another object/event within the universe. Space then
becomes an aspect of the relationships between things in reality.

If the universe is a causally closed system, the "information" or
entangled quantum states cannot leak out of the closed system. So the
"event" density of entangled quantum states, continually increases, as
the entropy must always increase. While to us, it is interpreted as
entropy or lost information, it is actually recombined information, to
the universe.


The present moment is created and recreated constantly - analogous to
continually opposing/juxtaposing reflective mirror images… originating
deep in quantum phase space. The Heisenberg uncertainty relation
provides both a resolution boundary and the invariant relational
fabric for a translation between quantum[Planck scale] space and
experiential reality. It is the quantum T-dual compactification that
provides the Heisenberg resolution boudaries for
experiential[perceptual] reality. Unstable or chaotic states at a
given level are always "compactified" (stabilized and bounded by
eigenstates) into 6 higher dimensions condensing to the next level of
"event density".

Since relativity explains that there is no preferred frame of
reference, the ether becomes superfluous; consequently, the metric of
space-time must be defined by related events, such, that there is no
space-time if there are no events. Time is thus a sequence of events,
with each "event", having its own measure of location, and its own
measure of time, with reference to other events. Space becomes an
event density-probability distribution.


The organic analogues of quantum attractors are translated via
quantized fractal modes onto the classical domain via
compactification, while events on the classicaly canonical domain, of
three spatial dimensions plus time, influence the
collapse/condensation of these attractors on the quantum-level via
feedback exitation modes.


T-Duality is a symmetry that obscures the ability to differentiate
between large and small distance scales; resulting from the
compactification of the extra space dimensions in a ten dimensional
superstring/brane theory. For example, in ten spacetime dimensions,
with nine space and one time, take one of those nine space dimensions
and make it a circle of radius R, so that traveling in that direction
for a distance L=2*pi*R goes around the circle and returns back to the
starting point. A particle traveling around this circle will have a
quantized momentum around the circle, which will contribute to the
total energy of the particle. But a string is very different, because
in addition to traveling around the circle, the string can wrap around
the circle. The number of times the string winds around the circle is
called the winding number, and it is also quantized.

The momentum modes and the winding modes can be interchanged when the
radius, R, of a circle is also exchanged with the quantity L_st2/R,
where L_st is the string length. If R is very much smaller than the
string length, then the quantity L_st2/R is going to be very large.
Consequently, exchanging momentum and winding modes of the string,
exchanges a large distance scale of radius R with a small distance
scale of radius 1/R.

Theoretical physicist Richard Feynman derived the "sum over histories"
interpretation of quantum mechanics, where a system does not have a
single history, but it has every possible history, and each history
has its own probability amplitude. A probability distribution of
histories. For example, an electron travels from point A to point B by
every possible route at once. Each possible route or "path"
corresponds to a history.

The amplitude for each history defines the probability of that
particular path being followed. The number involves the "action"
associated with the history-path, which seems to determine that the
path taken, will be the history closest to the "classical" trajectory,
in accordance with the natural law: conservation of energy.

Stephen Hawking explains that when we apply the Feynman sum over
histories to particles moving in a background of spacetime, we must
also include histories[waveforms] in which the particle travels
backwards in time. This generates the space-time/event-density fractal
resonance.


The increase in mass of a body moving at relativistic speeds can also
be interpreted as a type of rotational perspective effect, and when
time is explained as a dimension, "ct", by combining one of the c's
with time to convert it to a length, E = m_0 c^2 becomes m_0 c , a
momentum, specifically, a momentum of an object's motion down its time
axis.

A being's conscious awareness is what is really moving along its
world- line, which is the fourth dimensional extension of its 3
dimensional self.

m_0 c is a momentum along its time axis.

If we stopped moving through time the rest energy of objects would be
zero?

Interesting...

(mc^2)^2 = (m_0 c^2) + m^2 v^2 c^2

becomes

(mc^2)^2 - m^2 v^2 c^2 = (m_0 c^2)^2

An equation of the form:

c^2 t^2 - dx^2 = K


A quantum field unites gravity and electromagnetism.

Gravity becomes a refractive/compression effect, as light cones are
rotated near a massive object:

Topological metric spaces are defined as being diffeomorphism
invariant. Intersecting cotangent bundles[manifolds] are the set of
all possible configurations of a system, i.e. they describe the phase
space of the system. Waves are ripples in a basic medium. Einstein
explains that the ether is unecessary as a medium, so the ripples are
vibrations of space itself which are actually the overlapping of event
densities/conic sections. As the ripples overlap/intersect with each
other, it becomes a domino effect with the ripples continually
increasing in density. Very similar to taking a penny and doubling it
as a sequence.

2, 4, 8, 16, 32, 64, 128, 256, ... 2^n

Since the ripples are increasing in density they are defined by
density gradients. A compression force corresponding to the Shannon
entropy of the system.

Resonating standing waves/waveforms. The past collapses/condenses/
compactifies in 6 dimensions to the present moment, while the future
is an expanding uncertainty, in four space-time dimensions.
 
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Answers and Replies

  • #2
146
0
I like density/volume factors

Hi Russell, I agree with your following statement;

As the ripples overlap/intersect with each other, it becomes a domino effect with the ripples continually increasing in density. Very similar to taking a penny and doubling it as a sequence.

But, I don't think of it as a domino effect. I think of it as just as an increase or decrease in density based on the relative positioning factors of the systems involved.

Just my thoughts....................stay active
 
  • #3
If f(u(v)) = u(f(v)) the physics for a circle of radius R, is
equivalent to the physics for a circle of radius 1/R.


A point without another "reference" does not exist; the complement of
a
thing distinguishes it from the thing itself. What is the dynamic of
space-time? Is it a ratio? S/T = c ?

When space is taken as a measure of length, space/time is the speed of
light in vacuum for a photon of light:

space/time = c


Where, length = perception of separation between two reference points.


E = mc^2

E/momentum = E/p = c

energy/momentum = space/time

What is the EPR "superluminal?" connection? A shortcut through
configuration space? Phase space?

A point can be defined as an "infinitesimal". The Topological spaces
are defined as being diffeomorphism invariant. Intersecting cotangent
bundles[manifolds] are the set of all possible configurations of a
system, i.e. they describe the phase space of the system.

Potential infinity is defined as a limit via Newton's calculus, while
actual infinity is a Cantorian Cardinal number, which is a Platonic
form, which is also a type of potential.

[abstract representation]--->[semantic mapping]--->[represented
system]

[axiomatic]--->[Isomorphism]<---[Induction]

An abstract representation is exactly that, "abstract". It is not a
space, or time, but is instead a product of consciousness, or a
mental construct; topologically it is equivalent to a "point". The
abstract description contains the concrete topology. Likewise, the
concrete contains the abstract.

A duality?

A point/intersection/overlap contains an infinite expanse of space and
time?


Language describes the universe, because the universe is isomorphic to
a description on some level, and reality can only refer to itself,
because, there is nothing outside of ..."total existence" which
becomes equivalent to a self referential system, which must be a self
aware system. Since descriptions make distinctions, or references to
other entities, and distinctions are tautologically logical, [A or
~A], reality is logical, in that its contents can be described by a
language. The contents within reality are distinctive entities,
individually different from the others, yet consisting of the same
foundational substance. [<-[->[<-->]<-]->]

Universe, U(T) = 0 .

On one level of stratification, two photons are separate. On another
level, of stratification, the photons have zero separation.
Instantaneous communication between two objects, separated by a
distance interval, is equivalent to zero separation[zero boundary]
between the two objects.

According to the book "Gravitation", chapter 15, geometry of spacetime
gives instructions to matter telling matter to follow the straightest
path, which is a geodesic. Matter in turn, tells spacetime geometry
how to curve in such a way, as to guarantee the conservation of
momentum and energy. The Einstein tensor[geometric
feature-description] is also conserved in this relationship between
matter and the spacetime geometry. Eli Cartan's "boundary of a
boundary equals zero."

A quote from the book "The Expanding Universe" by Sir Arthur
Eddington:
quote:
-------------------------------------------------------------------------------
All change is relative. The universe is expanding relatively to our
common standards; our common standards are shrinking relatively to the
size of the universe. The theory of the "expanding universe" might
also be called the theory of the "shrinking atom" .
--------------------------------------------------------------------------------

Gravity exists because the information[event] density of space-time is
increasing. This creates a "pressure force" where processed space,
compresses mass-energy, and mass-energy reacts by compressing space.
The process is "time", which becomes dilated due to the increased
information density of massive objects. Stephen Hawking's excellent
book, "Universe in a Nutshell", explains holography as a phenomenon of
interference of wave patterns. Light from a laser is split into two
separate beams, one bounces off the object and gets reflected onto a
photo-sensitized plate. The other beam is reflected into a lens and
collides with the reflected light of the object. When a laser is shone
through the developed plate, a fully three dimensional image of the
original object is created. According to conventional theories, the
surface area of the horizon surrounding a black hole, measures its
entropy, where entropy is defined as a measure of the number of
internal states that the black hole can be in without looking
different to an outside observer, who can only measure mass, rotation
and charge. This leads to another theory which states that the maximum
entropy of any closed region of space can never exceed one quarter of
the area of the circumscribing surface, with the entropy being the
measure of the total information contained by the system. So the
theorists came to realize that the information associated with all
phenomena in the three dimensional world, can be stored on its two
dimensional boundary, like a holographic image.


Very interesting: http://www.space.com/scienceastronomy/time_theory_030806.html

quote:
--------------------------------------------------------------------------------
"There isn't a precise instant underlying an object's motion," he
said. "And as its position is constantly changing over time -- and as
such, never determined -- it also doesn't have a determined position
at any time."
--------------------------------------------------------------------------------
Heisenberg uncertainty: DxDp >= hbar/2
As the observed expansion of the universe continues, and, as the mean
temperature of the universe continues to approach absolute zero, could
the universe transform into a condition analogous to a "Bose Einstein
condensate"?

Is it possible to develop warp drive technology? or more correctly,
warp drive ..."trek" nology?

http://arxiv.org/abs/gr-qc/0204012

http://www.wired.com/news/technology/0,1282,20152,00.html [Broken]

Here are some more writings on the plausibility of interstellar travel
via warp drive:

http://www.astro.cf.ac.uk/groups/relativity/papers/abstracts/miguel94a.html [Broken]

http://arxiv.org/PS_cache/gr-qc/pdf/0107/0107097.pdf [Broken]

Frame Dragging:

http://msnbc.msn.com/id/3077887/

Impulse Gravity Generator Based on Charged
Y Ba2Cu3O7 Superconductor with Composite Crystal Structure:

http://superconductors.org/gravity.pdf


Back on topic:

When y(x,t) is the transverse displacement of a vibrating string,
y(x,t) can be determined by the wave equation

[@^2y/@t^2] = v^2[ @^2 y/@x^2] , where @ denotes the partial
derivative symbol.

Standing waves can be set up in an n-dimensional string, analogous to
that in a violin string. The form of the standing wave becomes y(x,t)
= psi(x) sin (wt)

Two sinusoidal travelling waves with the same amplitude and wavelength
moving in opposite directions on a string, become resonating "standing
waves":

y(x,t) = y1(x,t) + y2(x,t) = Asin(kx - wt) + Asin(kx + wt) =
[2Asin(kx)]*cos(wt).

As the entropy continues to increase in the universe, and if the
universe is a closed system, the entropy may be considered to be the
result of a "damping force". This damping force may also be one
possible solution to the dark matter enigma.

Solve the Schwarzschild solution for the entire universe. Since the
universe can be postulated to be a closed system with "nothing"
outside the universe. The condition of "nothingness" leads one to ask
"What are the properties of nothingness?" Of course there are no
measurable properties, but nothingness in itself must be a type of
massless solid. A condition that has no distance - metric scales. In
other words, there is no outside to the universe, no measurable border
between something and nothing.

Nothing then becomes analogous to a perfectly symmetrical pressure
force on the surface of existence.

---->|U|<----

U stands for universe. So it becomes reasonable to assume that the
entire universe is analogous to that which is inside the event horizon
of a black hole. The universe becomes a quantum superposition of
states, collapsing under the crushing force of "nothingness".

Analytically continue the Schwarzschild solution to the imaginary
values of the time variable. The Schwarzschild solution becomes
periodic in the imaginary time direction.

All waves would then be standing waves in the closed universe. A
Schrodinger wave equation in one dimension is of the form:

d^2 psi/dx^2 + 2m/hbar^2 [E - U(x)] psi(x)

U(x) is the potential energy and E is the total energy.

psi(x) is the wave function for a state in which the energy E is
constant in time. Such states are called stationary states. Certain
definite vibration frequencies are allowed multiples of fundamental
wavelengths

lambda = h/p

|psi(x)|^2 dx, is the probability of finding a particle(universe) in a
certain state between the region x and x+dx

psi^2 = psi psi* . When psi is complex, psi* is the complex conjugate
of psi. psi^2 (x) is the probability density.


So the goal must be to derive a nonlinear Schrodinger equation that
gives local the invariances that we currently observe! A global
nonlinear, locally invariant system ...?

http://lsec.cc.ac.cn/~ttang/MMref/references/budd99.pdf
 
Last edited by a moderator:
  • #4
146
0
Russell E. Rierson said:
As the entropy continues to increase in the universe, and if the
universe is a closed system, the entropy may be considered to be the
result of a "damping force". This damping force may also be one
possible solution to the dark matter enigma.

Solve the Schwarzschild solution for the entire universe. Since the
universe can be postulated to be a closed system with "nothing"
outside the universe. The condition of "nothingness" leads one to ask
"What are the properties of nothingness?" Of course there are no
measurable properties, but nothingness in itself must be a type of
massless solid. A condition that has no distance - metric scales. In
other words, there is no outside to the universe, no measurable border
between something and nothing.

Nothing then becomes analogous to a perfectly symmetrical pressure
force on the surface of existence.

---->|U|<----

U stands for universe. So it becomes reasonable to assume that the
entire universe is analogous to that which is inside the event horizon
of a black hole. The universe becomes a quantum superposition of
states, collapsing under the crushing force of "nothingness".

Analytically continue the Schwarzschild solution to the imaginary
values of the time variable. The Schwarzschild solution becomes
periodic in the imaginary time direction.

[/url]

Hi Russell;
My model indicates just the opposite in the relation to 'nothing' or non-existence. I think of the 'nothing' as a 'pure' vacuum that exerts a 'pull' force on the system(cosmos).

<----|U|---->

I'm sorry but you present to much information for my poor simple mind to absorb all at one time. So, I just pick out something simple that I can deal with.

just my thoughts.
 
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  • #5
force5 said:
Hi Russell;
My model indicates just the opposite in the relation to 'nothing' or non-existence. I think of the 'nothing' as a 'pure' vacuum that exerts a 'pull' force on the system(cosmos).


<----|U|---->

Thanks for your interesting perspective force 5.


It is, in essence, a complementary duality.

---->|U|<----

is the same as:

<----|U|---->



T-duality proposes that the winding particles for a circle of radius R are the same as the "vibration" particles for a circle of radius 1/R, and vice versa. The two two sets of particles are in a sense, indistinguishable: theoretically speaking, a large compact dimension appears to give the same particles as a thin one.

T-duality, if true, has interesting consequences. There has been a long conceptual struggle, by theorists, to understand reality at the extremely small scales near the Planck length at 10^35 meters. The supposition has always been that the laws of nature break down at the extreme micro scales. T-duality basically suggests that that at the Planck scales, the universe looks just the same as it does at large scales. One may even imagine that if the universe were to shrink to less than the Planck length, it would simultaneously transform as an expanding space-time of macroscopic dimensions.


When four of the 10 dimensions compactify, or "curl up" and the five-brane wraps around them, the latter ends up as a one-dimensional object described as a solotonic string in six-dimensional space-time. In addition, a fundamental string in 10 dimensions remains fundamental even in six dimensions. So the concept of duality between strings and five-branes gives another interesting conjecture, which is a duality between a solitonic string and a fundamental string.


When the six-dimensional space-time is reduced to four dimensions, via the compactification of two dimensions: the fundamental string and the solitonic string each inherit a T-duality. Consequently, the T-duality of the solitonic string is just the S-duality of the fundamental string, and vice versa; an S-duality transformation maps states with coupling constant g in one theory to states with coupling constant 1/g in the dual theory. It exchanges the electric and magnetic fields, and the electrically charged particles with magnetic monopoles. :eek: :eek: :eek:


Where the interchange of charges in one picture is just the inversion of length in the dual picture, is named the Duality of Dualities by string theory. :eek: :eek: :eek: It is puts the previously shaky S-duality on as firm a footing as the well-established T-duality. In addition, it predicts that the strength with which objects interact, i.e. their charges, corresponds to the size of the invisible dimensions. What is charge in one universe of radius 1/R may be size in its dual universe of radius R.
 
  • #6
146
0
Russell E. Rierson said:
Thanks for your interesting perspective force 5.

It is, in essence, a complementary duality.

---->|U|<----

is the same as:

<----|U|---->

T-duality proposes that the winding particles for a circle of radius R are the same as the "vibration" particles for a circle of radius 1/R, and vice versa. The two two sets of particles are in a sense, indistinguishable: theoretically speaking, a large compact dimension appears to give the same particles as a thin one.

T-duality, if true, has interesting consequences. There has been a long conceptual struggle, by theorists, to understand reality at the extremely small scales near the Planck length at 10^35 meters. The supposition has always been that the laws of nature break down at the extreme micro scales. T-duality basically suggests that that at the Planck scales, the universe looks just the same as it does at large scales. One may even imagine that if the universe were to shrink to less than the Planck length, it would simultaneously transform as an expanding space-time of macroscopic dimensions.


When four of the 10 dimensions compactify, or "curl up" and the five-brane wraps around them, the latter ends up as a one-dimensional object described as a solotonic string in six-dimensional space-time. In addition, a fundamental string in 10 dimensions remains fundamental even in six dimensions. So the concept of duality between strings and five-branes gives another interesting conjecture, which is a duality between a solitonic string and a fundamental string.


When the six-dimensional space-time is reduced to four dimensions, via the compactification of two dimensions: the fundamental string and the solitonic string each inherit a T-duality. Consequently, the T-duality of the solitonic string is just the S-duality of the fundamental string, and vice versa; an S-duality transformation maps states with coupling constant g in one theory to states with coupling constant 1/g in the dual theory. It exchanges the electric and magnetic fields, and the electrically charged particles with magnetic monopoles. :eek: :eek: :eek:


Where the interchange of charges in one picture is just the inversion of length in the dual picture, is named the Duality of Dualities by string theory. :eek: :eek: :eek: It is puts the previously shaky S-duality on as firm a footing as the well-established T-duality. In addition, it predicts that the strength with which objects interact, i.e. their charges, corresponds to the size of the invisible dimensions. What is charge in one universe of radius 1/R may be size in its dual universe of radius R.

Hi Russell;

I agree that they are fundamentally the same, but, have a very different effect on things. Kind of like mirror twins, where one deals with space/time and the other deals with nuclear effects.

<----(U)----> deals with the macro world.

(U---->(M)<----U) M = the micro world.

Maybe we aren't talking about the same thing? If not, I still like your logic.

Just my thoughts.
 

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