Quantum Phase Relativity

From: analog57 (analog57_at_yahoo-dot-com.no-spam.invalid)
Date: 07/25/04 

Date: 25 Jul 2004 05:28:12 -0500

Quantum Phase Relativity :D :D :D

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.

Question:

Let T be a metric space with distance function r(x,y) expressing the
definitive predication that involves T with the real numbers, R.
Therefore the juxtaposition of left and right hemispheres resonates
in perfect accordance with the proposition that T and R are embedded
simultaneously in the full structure of manifold M. Ergo we pass on
to an enlargement *M of M, whereby the non-standard metric space is
diffeomorphism invariant.

So if f(x) is a homeomorphism from T onto S, then for every point p in
T, does f(u(p) = u(f(p)) ?

The metric space has distance function r(x,y), definitively
characterized by involvement with the real numbers, R, such that the
metric space and R are embedded simultaneously in the full structure
of manifold M. A topological space consists of sets of points which
are defined to be the intersections of cotangent
bundles.

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 model]->[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?

Universe, U(T) = 0 .

[<-[->[U]<-]->]

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.

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.

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.

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. 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 at 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.

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