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Quantum Gravity

  1. Apr 28, 2004 #1
    A physical system is described by a normalized vector[state vector] in Hilbert space. All possible information can be known about the system, since, for every physical observable there corresponds a self adjoint operator in Hilbert space.

    The only allowed physical results of measurements of some observable U, are the elements of the spectrum of the operator which corresponds to U.

    So all properties of a physical system may not be completely known, but that which is known, must be necessarily true on logical or analytic grounds.

    Distance is a property between objects in space. Space is a structure, which is constructed of discrete units. The structure of space is a type of distributive lattice. A lattice is a partially ordered set, closed under least upper and greatest lower bounds. Any lattice which is isomorphic to a collection of sets, closed under complementation and intersection, is a Boolean algebra.

    Is it possible to derive Einstein's field equation strictly in terms of quantum mechanical operators? using n-dimensional cross sections of cotangent vector spaces? Near a massive object M, the *isobar* cross sections increase in density, as wave density gradients.

    Compression waves become a self embedding of surface integrals? This gives continuously increasing density gradients, as matter-energy is sequentially re-embedded from previous computations/iterations.

    If the universe is closed, the "information" or entangled quantum states cannot leak out of the closed system. So the density of entangled quantum states, continually increases, just 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. Shannon entropy.

    Spacetime Memory = Compression Waves = Interpretation of Increased Entropy?

    What is needed is a tensor equation which is a parallel to "wave" equations described in terms of a covariant d'Alembertian operator. An alternative description for the general relativistic space-time continuum that allows for "compressional" waves, rather than allowing only "transverse" waves.

    The gravitational action of matter/energy, etc. can be studied in terms of boundary value problems.


    On one level of existence two photons are separate. On another level, of existence[spacetime boundary], 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."

    Einstein's equation basically says

    Einstein Tensor [G] = Stress-Energy Tensor [T]

    [spacetime geometry] determines [matter-energy's path] = geodesic.

    [Matter-energy] determines [spacetime geometry] = non-Euclidean geometry.

    .
    Conservation of momentum energy is explained as an automatic consequence of the zero boundary of a boundary. Where conservation of energy-momentum means no creation or destruction of energy momentum in a 4D region of spacetime [4D cube] The integral of "creation events" i.e. the integral of d*T for energy momentum, over the 4D region is required to be zero, and gives the conservation of momentum energy. The mathematical machinery for identically meeting the conservation laws is the boundary of a boundary equals zero.

    [spacetime tells mass]<==[geodesic]==>[mass tells spacetime]

    An object following a geodesic has no unbalanced forces acting on it. Its energy-momentum is a constant. In order for the object to deviate from the geodesic, it must be accelerated. Energy must be expended, for example, its rocket boosters could fire, or an outside force like a meteor impact .


    Waves are ripples in a basic medium. Einstein explains that the ether is unecessary as a medium, so the ripples are vibrations of the vacuum itself.

    As the ripples 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 an iterative sequence.

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

    Since the ripples are increasing in density they are "compressed" .

    Actually, spacetime can proceed in discrete steps, yet, still be continuous[causally connected].

    [density 1]--->[density 2]--->[density 3]---> ... --->[density n]


    Quantum mechanics leads to the realization that all matter-energy can be explained in terms of "waves". In a confined region(i.e. a closed universe or a black hole) the waves exists as STANDING WAVES In a closed system, the entropy never decreases.

    The analogy with black holes is interesting with the caveat that if there is nothing outside the universe, then it cannot be radiating energy outside itself as black holes are explained to be. So the amount of information i.e. "quantum states" in the universe is increasing. It is Shannon entropy, to an information processor with huge computational capabilities.

    Quantum field theory calculations where imaginary time is periodic, with period 1/T are equivalent to statistical mechanics calculations where the temperature is T. The periodic waveforms that are opposed yet "in phase" would be at standing wave resonance, giving the action.

    Periodicity is a symmetry. Rotate into the complex plane and there are
    real numbers on the horizonal axis and imaginary numbers on the
    vertical axis.

    f(z)---->f(az+b/cz+d)

    Where the elements a,b,c,d, are arranged as a matrix, forming an
    algebraic group. An infinite number of possible variations that
    commute with each other as the function f, is invariant under group
    transformations. These functions are known as "automorphic forms".

    The continual increase of the information density of space-time is parallel to gravitational entropy. It is analogous to a "pressure force" where re-embedded iterations of space, compresses mass-energy, and mass-energy reacts by compressing space. The iterative process is "time", which becomes dilated in a gravitational field.

    Iterated space compresses matter-energy and matter-energy gives an equal and opposite reaction.

    Space-time tells matter how to move and matter tells space-time how to curve.

    [mass tells spacetime ]<==[geodesic]==>[ space-time tells mass]
     
  2. jcsd
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