Mathematically speaking, the existence of a "dual" vector(adsbygoogle = window.adsbygoogle || []).push({});

space, abstractly reflects the relationship between row

vectors (1×n) and column vectors (n×1). The construction

can also take place for infinite-dimensional spaces and

gives rise to important ways of looking at different

distributions and Hilbert space. The use of the dual space can be a characteristic of functional analysis. It is also built into the Fourier transform.

Because the tangent space and the cotangent space at a

given point are both real vector spaces of the same

dimension, they are isomorphic to each other. But they are

not "naturally isomorphic", since, for an arbitrary tangent

covector, there is no canonical tangent vector

associated with it. With the introduction of a symplectic

form, the additional structure gives a "natural

isomorphism". Longitudinal compression waves agree with

thermodynamic, and Shannon, entropies.

In the general relativistic curved spacetime, there is no

preferred definition for the concept of particles, it

seems. Representations of canonical commutation relations

will be unitarily inequivalent, correspondingly, in both

the asymptotic past and the asymptotic future, for a

"natural notion of particles", analogously to the

"infrared catastrophie" of quantum electrodynamics.

The solution?

Derive quantum theory in terms of general relativity

tensors, using cotangent bundles.

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.

Shannon entropy.

What is needed is a tensor equation which is 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 parallel "compressional" waves, rather than allowing

only "transverse" waves.

Interesting...

By quantizing spacetime geometry, it seems that the

wavefunctions/waveforms aren't based on a background space.

The wavefunction space, can be thought of as the space of

square-integrable wavefunctions over classical

configuration space.

In ordinary quantum mechanics, configuration space is space

itself {i.e.,to describe the configuration of a particle,

location in space is specified}. In general relativity,

there is a more general kind of

configuration space: taken to be the space of 3-metrics

{"superspace", not to be confused with supersymmetric

space} in the geometrodynamics formulation,{or the space of

connections of an appropriate gauge group)in the

Ashtekar/loop formulation. So the wavefunctions will be

functions over these abstract spaces, not space itself--

the wavefunction/algorithm defines "space itself".

The resultant metric spaces are thus 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. When the "wave-functions/forms"

intersect/entangle, and are "in phase", they are at

"resonance", giving what is called the "wave-function

collapse" of the Schrodinger equation. the action principle

is a necessary consequence of the

resonance principle.

Here is mathematician John Nash's "Einstein field equation"

where he talks about gravity "compression" waves:

http://www.stat.psu.edu/~babu/nash/intereq.pdf

A phonon is a quantized mode of vibration occurring in a rigid crystal

Wave-Like Form of the Scalar Equation

It was discovered only recently by me that the scalar

equation naturally derived from the tensor equation for

vacuum, particularly in the case of 4 space-time

dimensions, has a form extremely suggestive

of waves. The scalar derived equation can be obtained by

formally contracting the general vacuum equation with the

metric tensor. This results at first in an equation

involving G (the scalar derived from the Einstein tensor)

and the Ricci tensor and the scalar curvature R.

And G, being the scalar trace of the Einstein tensor, can

be expressed in term of R but this expression involves the

number of dimensions, n.

[...]

And now two things are notable about the form of this

resulting scalar equation: (1): If n = 2 there is a

singularity and this simply corresponds to the fact that

the Einstein G-tensor is identically vanishing if n = 2, so

there isnt any derived scalar equation of this

type for two dimensions. (2): For n = 4 we find the nice

surprise that the scalar equation entirely simplifies and

then asserts simply that the scalar curvature satisfies the

wave operator [], (which is a d'Alembertian if we think in

terms of 3 + 1 dimensions). So the scalar equation is

[]R = 0 PROVIDED that n = 4

lattice, e.g. as in an atomic lattice of a solid.

Could it be that reality surfs on the universal standing wave of

spacetime, emerging out of a "solid block" of nothingness? Standing

wave resonance i.e. "spacetime phonons". The present moment is thus

created and recreated constantly - like a continuous image…

originating deep in twistor space. The Heisenberg Uncertainty Relation

provides both a boundary and the fabric for a translation between

twistor[Planck scale] space and experiential reality, and it is

quantum phase compactification that provides the color electric

superconductive "bricks" for the boundary. Unstable or chaotic states

at a given level are always "compactified" (stabilized and bounded by

a finite number of eigenstates) into higher dimensions at the next

level. The organic analogues of quantum attractors are translated into

quantized fractal exitation modes onto the classical domain via

compactification, while events on the classical domain influence the

collapse or transition of these attractors on the quantum-nano level

via feedback oscillations. The state vector becomes an interactive

participant.

Background independence!

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 has a momentum, that momentum can only be explained with

respect to another object within the universe. Space then becomes an

aspect of the relationships between things in reality.

Physicist Lee Smolin says that space becomes analogous to a sentence,

and it is absurd to say that a sentence has no words in it. So the

grammatical structure of each sentence[space] is defined by the

relationships that hold between the words in it.

For example, relationships like object-subject or adjective-noun. So

there are many different grammatical structures composed of different

arrangements of words, and the varied relationships between them.

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.

Since entropy can also be defined as the number of states within a

region of space, and the entropy of the universe must always

increase, the next logical step is to realize that the spacetime

density, i.e. the information encoded within a circumscribed region

of space, must be increasing in the thermodynamic direction of time.

The entropy of thermodynamics and entropy of Shannon, are equivalent

concepts, because the number of arrangements that are counted by

Boltzmann entropy reflects the amount of Shannon information needed

to implement any particular combination, or arrangement. The two

entropies also appear to have superficial differences.

Thermodynamic entropy is interpreted in units of energy divided by

temperature, while, the Shannon entropy is interpreted in terms of

dimensionless bits. This seems to point towards a computational/language or "cognitive-mind" structure for reality.

[1.] Mathematics is a meta language.

[2.] Language is descriptive.

[3.] Language must be free of contradiction. Mathematics is also

defined as a descriptive system that has "freedom from contradiction".

[4.] Mathematics describes physical existence/processes/events.

[5.] Observation is a physical process.

[6.] Mathematics describes observations.

[7.]A description of an observation must be free of

contradiction-following from [3.]

[8.] Observation must be free of contradiction.

[8.] A description is an abstract representation of a physical system.

The description must be as exact as possible.

[9.] An exact description[as an algorithmic limit] implies equivalence between abstract structures and physical[natural] systems.

[10.] If the exact description exists, then physical existence is a computational-algorithmic meta-language. A self descriptive entity, free of contradiction. The universe is equivalent to its[exact] abstract representation.

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# Unification of Quantum Theory and General Relativity

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