You're neglecting the fact that there is destructive as well as constructive interference; intersecting waves sometimes complement and sometimes cancel. You also have no additional sources of energy; the total energy in a closed universe is constant, there cannot be a constant increase of the total, thus no compression.
I will respond to the above Raithere
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. 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.
http://www.maths.usyd.edu.au:8000/u/hughl/PI.html
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 law of conservation of energy.
So, waves that constructively interfere, are "re-enforced".
The waves that are out of phase destructively interfere with each other and form cancel, forming a basis of stochastic noise and quantum fluctuations.
Since general relativity is a background independent theory, spacetime must also have its own probability density wavefunctions and sum over histories. Distributed identity. A stratification of probability density functions for relational space-time.
According to the mathematician "John Nash" these waves are analogous to "compression waves", which agrees with the CTMU?
John Nash gives a most excellent equation for spacetime:
http://www.math.princeton.edu/jfnj/texts_and_graphics/Equation_an_Interesting/note2
http://www.math.princeton.edu/jfnj/texts_and_graphics/
QUOTE:
Remarks added 22 May 2002: The remarks below are given as they were in a (memo) note that wasn't generally accessible. Now I am not really updating it, but since the equation (vacuum) itself is now included on my "web page" it is time also to include these remarks. At the present time I think the "input" of the gravitational action of matter, etc. might be studied in terms of boundary value problems. Then on one side of a boundary there could be the vacuum equation to be satisfied. And there are some ideas that relate to this. But these are ideas that call for further study.
3 memo of May 31, 2001: The equation is tensor equation which has a parallel or similarity to "wave" equations and can be described in terms of a d'Alembertian operator. It is thought of as of interest as an alternative description of the general relativistic space-time continuum that allows for "compressional" waves rather than allowing only for "transverse" waves. At the present time I am still seeking to find a good "input relation" for matter as the source of gravitation (analogous to the relation found by Einstein and Hilbert for the 2nd order tensor equation of standard GR). The vacuum equation can be described as having (on a LHS side that is equated to zero) a fourth order term formed by the covariant d'Alembertian operating on the G-tensor of Einstein plus an additive portion of second order (as to the differentiation) formed by quadratic combinations of curvature tensor elements. The precise additive portion or set of terms is defined by the condition that the total LHS is so structured so as to be formally divergence free (like the G-tensor is intrinsically divergence free). The plan is to put into this directory, ultimately, files of graphic type including the tensor equations in handwritten form.
---END QUOTE---
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, 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.
Spacetime Memory = Compression Waves = Interpretation of Increased Entropy.
If our universe is a self projecting computer simulation within a simulation within... within a simulation, which is a process, it would need to be an accelerated process.
locally, as the distance between two objects approaches zero, and velocity is low, space-time is a Euclidean geometry.
As the distance between two objects increases, space-time is a "non-Euclidean" geometry.
This non-Euclidean geometry uses a Euclidean tangent vector space to approximate its curvature properties. "tangent vectors".
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 wavefunction density gradients, a possible solution? to Hartle and Hawking's "wavefunction of the universe"?
There is the Schrodinger equation:
H(psi) = E(psi),
where H is the Hamiltonian operator, the sum of potential and kinetic energies, and "psi" is the wavefunction. E is the energy of the system. The square of the wavefunction, is the probability of the position and momentum for the system.
The Wheeler DeWitt equation is the Schrodinger equation applied to the whole universe. Since the total energy of the universe is postulated to be zero(even though the Hamiltonian for the universe isn't quite defined) the Wheeler DeWitt equation is:
H(psi) = 0
There is a complementary path integral approach for this equation. Stephen Hawking derived the wavefunction of the universe as a path integral, for a complex function of the classical configuration space:
psi(q) = integral exp(-S(g)/hbar) dg
The problem is that "dg" is not well defined either
exp is the base of the natural logarithm "e" raised to a power. The power in this case, is the quantity -S(g)/hbar, where S(g)
is the Einstein Hilbert action.
The Einstein Hilbert Action:
The Lagrangian, which is the difference of kinetic and potential
energies, has a formulation in general relativity:
Lagrangian = R vol
R is the Ricci scalar curvature of the metric g, derived by contracting the Ricci tensor and "vol" is the volume form associated to g. The Einstein Hilbert action then becomes:
S(g) = integral R vol
Spacelike hypersurfaces are endomorphically projected Compression waves. A self embedding of surface integrals. This gives continuously increasing density gradients, as matter-energy is quantum mechanically re-scaled. What appears as universal expansion with radius R, is actually matter-energy contraction with radius 1/R. Total spacetime is constant.
According to string theory, from the principle called "T-Duality", the physics for a circle of radius R is the same as the physics for a circle of radius 1/R. So if total spacetime is a constant, and matter-energy would be shrinking at a uniform accelerated rate, it would appear to the shrinking beings in the universe, that their universe's spacetime was expanding and matter energy is the constant.
Hawking's entropy equation:
Entropy = [Area of event horizon]*[Boltzmann's constant]*[speed of light^3]/4*[Planck's constant/2pi]*[Newton's universal gravitational constant]
S = [A*k*c^3]/[4*hbar*G]
Quantum gravity and thermodynamics are related.
The R - 1/R duality of string theory, gives two ways of looking at the world. Which way is correct? R with spacetime expansion? Or 1/R with matter-energy requantization?
Both could be correct, depending on the perspective of the observer.
