http://home.jam.rr.com/dicksfiles/reality/CHAP_I.htm
Doctordick:
Suppose, just for the sake of argument, that we already know the algorithm which yields these observations. To begin with, that algorithm must be independent of time as, if it is not, the solution of our problem depends on when we begin the examination and different observers will obtain different solutions (remember, the solution is the complete explanation of the universe). (As an aside, I am not being loose here, "when" refers to the time as defined above.) Secondly, as the algorithm is independent of time, it must be that knowing the algorithm is insufficient to predict any particular observation unless the time of the observation is contained in some implicit manner. If there is information implicitly embedded in the data, it must be presumed that there are patterns of data which are possible and patterns of data which are not possible.
By quantizing spacetime geometry, it seems that the
wavefunctions 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.
[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.
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. It 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.
Langauge 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.
A quote from the book "The Expanding Universe" by Sir Arthur Eddington:
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" .
Quantum mechanics leads us 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 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 categorical representation of a propositional conundrum, in which deductive invalidity depends on the modality of the truth conditionals concerning the prerequisite of the contingent assumption and consequent conclusion. The totally relevant content of the assumption and conclusion, definitely contains no modal terms. But, the modality attaches to the fact that the conditional assumption is quite possibly true, while the conditional conclusion is necessarily false.
Which leads us to an argumentational representation of a completely non-bogus modal formulation of the paradox of existence itself, and, the oh so elusive "ultimate truth" that Dr.D earnestly seeks. Deductive invalidity is most excellently predicated on the categorical truth of the modal-term-laden assumption and the definitive categorical falsehood of the modal-term-laden conclusion. Hence, the assumption is, such, that if the antecedent of a contingently true conditional is false, then, the consequent of the conclusion can be true is itself quite simply and most elegantly ...true. Therefore, the conclusion that if it is not the case that the consequent of a contingently true conditional can be true, then it is not the case that the antecedent of the true conditional is false, is itself quite simply, false.
Meta-philosophical scruples notwithstanding, existence is, a paradox.
Alpha = Omega
It is the categorical formulation of the simultaneous, situational, instantiated contradiction, where deductive invalidity is the product of the utmost categorical truth of the assumption that if the antecedent of a true conditional is false, then the consequent of the conditional is true or false indifferently, and of the categorical falsehood of the conclusion consequently predicates that if it be not the case that the consequent of a true conditional is true or false indifferently, then, it is not the case that the antecedent of the conditional is false. To pronounce the consequent of a true conditional as being true or false indifferently is tantamount to saying modally that where the antecedent of a true conditional is notoriously false, then the consequent can, or could be, or is, possibly true or false. But it may be worthwhile to see that the definitive, simultaneous equality of both true, and false, can be formulated without explicitly including modal terms, which become the predicating operators, which, for the sake of showing that the consequent paradoxical conundrum is not straightforwardly resolvable by appealing to concrete philosophical scruples concerning the intensionality of predicated modal contexts.
But then again, Einstein said it best:
Einstein:
For pure logic all axioms are arbitrary , including
the axioms of ethics. But they are by no means
arbitrary from a psychological and genetic point of
view. They are derived from our inborn tendencies
to avoid pain and annihilation, and from the
accumulated emotional reaction of individuals to the
behavior of their neighbors.
It is the privilege of man's moral genius,
impersonated by inspired individuals, to advance
ethical axioms which are so comprehensive and so
well founded that men will accept them as grounded
in the vast mass of their individual emotional
experiences. Ethical axioms are found and tested not
very differently from the axioms of science.
Truth is what stands the test of experience.