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Quantum Phase Compactification via Spacetime Expansion

  1. Jul 23, 2004 #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.
     
    Last edited: Jul 23, 2004
  2. jcsd
  3. Jul 23, 2004 #2
    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
     
  4. Jul 24, 2004 #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

    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

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

    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
     
  5. Jul 24, 2004 #4
    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.
     
    Last edited: Jul 24, 2004
  6. Jul 24, 2004 #5
    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.
     
  7. Jul 25, 2004 #6
    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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