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PFanalog57
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Quantum entities are described as probability distributions, which are attributes of an underlying phase space, where the properties-attributes such as "spin" and "charge" are not the attributes of individual particles, but they are universally distributive entities, being the attributes of a "coherent wave function". It is this wave-distribution property that then "decoheres" into the ostensible "wave function collapse", as waves become localized particles that are "in phase" creating standing-spherical-wave resonances, which are condensations of space itself. The continual collapse-condensation of space into matter-energy is the continual "change", i.e. the property called "time". The spherical waves, or probability distributions are represented by the Schrödinger wave function, "psi".
The continual intersection and collapse of probability distributions, also known as quantum phase entanglement, is a continual increasing of the "total" combined information of the universal wavefunction itself. Information density. With more information, more complex structures can be created.
Quantum mechanics leads us to the realization that all matter-energy can be explained in terms of "waves" or probability distributions containing information. In a confined region(i.e. a closed universe or a black hole) the waves exist as STANDING WAVES In a closed system, the entropy never decreases.
The analogy with black holes is an interesting one but 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. We see it as entropy, but to an information processor with huge computational capabilities, it is compressible information.
The information density of the universal system must be increasing. The increase of information density is analogous to a pressure gradient.
[density 1]--->[density 2]--->[density 3]---> ... --->[density n]
[<-[->[<-[-><-]->]<-]->]
Intersecting wavefronts = increasing density of spacelike slices
As the wavefronts intersect, it becomes a mathematical computation:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...2^n
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 must measure only mass, rotation, and charge. Another theory 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.
S' = S_m + A/4
So the "black hole" theorists came to realize that the information associated with all phenomena in the three dimensional world, can be stored on a two dimensional boundary, analogous to the storing of a holographic image.
Since entropy can also be defined as the number of states, that particles can be in within 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.
Of course, thermodynamic entropy is popularly described as the disorder or "randomness" in a physical system. In 1877, the physicist Ludwig Boltzmann defined entropy more precisely. He defined it in terms of the number of distinct microscopic states that the particles in a system can be configured, while still looking like the same macroscopic system. For example, a system such as a gas cloud, one would count the ways that the individual gas molecules could be distributed, and moving.
In1948, mathematician Claude E. Shannon, introduced today's most widely used measure of information content: entropy. The Shannon entropy of a message is the number of binary digits, i.e. "bits" needed to encode it. While the structure, quality, or value, of the information in Shannon entropy may be an unknown, the quantity of information can be known. Shannon entropy and thermodynamic entropy are equivalent.
The universal laws of nature are explained in terms of symmetry. The completed infinities, mathematician Georg Cantor's infinite sets, could be explained as cardinal identities, akin to "qualia" [Universally distributed attributes] from which finite subsets, and elements of subsets [quantum decoherence-wave function collapse] can be derived.
Completed infinities, called "alephs" are distributive in nature, similar to the way that a set of "red" objects has the distributive property of redness[qualia]. Properties, or "attributes" like red are numbers in the sense that they interact algebraically according to the laws of Boolean algebra. Take one object away from the set of red objects and the distributive number "red" still describes the set. The distributive identity[attribute] "natural number" or "real number" describes an entire collection of individual objects.
The alephs can be set into a one to one correspondence with a proper subset of of themselves. The "infinite" Cantorian alephs are really distributive[qualia].
Yet, if we have a finite set of 7 objects, the cardinal number 7 does not really distribute over its individual subsets. Take anything away from the set and the number 7 ceases to describe it[wave function collapse-condensation into specific localization?].
Symmetry is analogous to a generalized form of self evident truth, and it is a distributive attribute via the laws of nature, being distributed over the entire system called universe. A stratification of Cantorian alephs with varying degrees of complexity. Less complexity = greater symmetry = higher infinity-alephs. So the highest aleph, the "absolute-infinity" distributes over the entire set called Universe and gives it "identity".
The highest symmetry is a distributive mathematical identity[also a total unknown but possibly analogous to a state of "nothingness"]. This fact is reflected in part, by the conservation laws.
So an unbound-infinite-potentia and a constrained-finite-bound-actuality, are somehow different yet the same. The difference and sameness relation is a duality. Freedom(higher symmetry) and constraint-complexity-organizational structure(lesser symmetry) form a relation that can be described by an invariance principle.
On a flat Euclidean surface, the three angles of a triangle sum to 180 degrees. On the curved surface of a sphere, the three angles add up to more than 180 degrees. On the hyperbolic surface of a saddle they sum to less than 180 degrees. The three types of surface are not equivalent.
There is a rotational invariance for a triangle, that seems to hold for the three types of surface though.
ABC = BCA = CAB
CBA = BAC = ACB
According to Einstein, and the CTMU of Langan, www.ctmu.org , "space and time are modes by which we think, and not conditions in which we live". Space becomes abstract, a relation that is perceptual and "mental", where distance interval between two points becomes a mental perception.
[ abstract representation]--->[semantic mapping]--->[represented system]
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 contains an infinite expanse of space and time?
Could it be, that the "absolute" infinity, is actually a dimensionless point? Or more correctly, an "infinitesimal"?
Universe? = Zero?
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 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.
Waves are then abstract distributions and particles are convergent "concrete" localizations.
The continual intersection and collapse of probability distributions, also known as quantum phase entanglement, is a continual increasing of the "total" combined information of the universal wavefunction itself. Information density. With more information, more complex structures can be created.
Quantum mechanics leads us to the realization that all matter-energy can be explained in terms of "waves" or probability distributions containing information. In a confined region(i.e. a closed universe or a black hole) the waves exist as STANDING WAVES In a closed system, the entropy never decreases.
The analogy with black holes is an interesting one but 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. We see it as entropy, but to an information processor with huge computational capabilities, it is compressible information.
The information density of the universal system must be increasing. The increase of information density is analogous to a pressure gradient.
[density 1]--->[density 2]--->[density 3]---> ... --->[density n]
[<-[->[<-[-><-]->]<-]->]
Intersecting wavefronts = increasing density of spacelike slices
As the wavefronts intersect, it becomes a mathematical computation:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...2^n
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 must measure only mass, rotation, and charge. Another theory 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.
S' = S_m + A/4
So the "black hole" theorists came to realize that the information associated with all phenomena in the three dimensional world, can be stored on a two dimensional boundary, analogous to the storing of a holographic image.
Since entropy can also be defined as the number of states, that particles can be in within 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.
Of course, thermodynamic entropy is popularly described as the disorder or "randomness" in a physical system. In 1877, the physicist Ludwig Boltzmann defined entropy more precisely. He defined it in terms of the number of distinct microscopic states that the particles in a system can be configured, while still looking like the same macroscopic system. For example, a system such as a gas cloud, one would count the ways that the individual gas molecules could be distributed, and moving.
In1948, mathematician Claude E. Shannon, introduced today's most widely used measure of information content: entropy. The Shannon entropy of a message is the number of binary digits, i.e. "bits" needed to encode it. While the structure, quality, or value, of the information in Shannon entropy may be an unknown, the quantity of information can be known. Shannon entropy and thermodynamic entropy are equivalent.
The universal laws of nature are explained in terms of symmetry. The completed infinities, mathematician Georg Cantor's infinite sets, could be explained as cardinal identities, akin to "qualia" [Universally distributed attributes] from which finite subsets, and elements of subsets [quantum decoherence-wave function collapse] can be derived.
Completed infinities, called "alephs" are distributive in nature, similar to the way that a set of "red" objects has the distributive property of redness[qualia]. Properties, or "attributes" like red are numbers in the sense that they interact algebraically according to the laws of Boolean algebra. Take one object away from the set of red objects and the distributive number "red" still describes the set. The distributive identity[attribute] "natural number" or "real number" describes an entire collection of individual objects.
The alephs can be set into a one to one correspondence with a proper subset of of themselves. The "infinite" Cantorian alephs are really distributive[qualia].
Yet, if we have a finite set of 7 objects, the cardinal number 7 does not really distribute over its individual subsets. Take anything away from the set and the number 7 ceases to describe it[wave function collapse-condensation into specific localization?].
Symmetry is analogous to a generalized form of self evident truth, and it is a distributive attribute via the laws of nature, being distributed over the entire system called universe. A stratification of Cantorian alephs with varying degrees of complexity. Less complexity = greater symmetry = higher infinity-alephs. So the highest aleph, the "absolute-infinity" distributes over the entire set called Universe and gives it "identity".
The highest symmetry is a distributive mathematical identity[also a total unknown but possibly analogous to a state of "nothingness"]. This fact is reflected in part, by the conservation laws.
So an unbound-infinite-potentia and a constrained-finite-bound-actuality, are somehow different yet the same. The difference and sameness relation is a duality. Freedom(higher symmetry) and constraint-complexity-organizational structure(lesser symmetry) form a relation that can be described by an invariance principle.
On a flat Euclidean surface, the three angles of a triangle sum to 180 degrees. On the curved surface of a sphere, the three angles add up to more than 180 degrees. On the hyperbolic surface of a saddle they sum to less than 180 degrees. The three types of surface are not equivalent.
There is a rotational invariance for a triangle, that seems to hold for the three types of surface though.
ABC = BCA = CAB
CBA = BAC = ACB
According to Einstein, and the CTMU of Langan, www.ctmu.org , "space and time are modes by which we think, and not conditions in which we live". Space becomes abstract, a relation that is perceptual and "mental", where distance interval between two points becomes a mental perception.
[ abstract representation]--->[semantic mapping]--->[represented system]
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 contains an infinite expanse of space and time?
Could it be, that the "absolute" infinity, is actually a dimensionless point? Or more correctly, an "infinitesimal"?
Universe? = Zero?
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 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.
Waves are then abstract distributions and particles are convergent "concrete" localizations.