|Jun18-04, 01:48 PM||#52|
The Universal Geometric Set
|Jun18-04, 02:37 PM||#53|
First of all, you have not presented anything that could be called an interpretation of any physical theory. And second, the Wheeler-Feynman Absorber theory is not a secret.
You keep throwing technical terms around, but you don't seem to have the foggiest idea of what any of them mean.
Has it occured to you to go into the Math and Physics Forums and ask people for help? This place is loaded with people who can do just that.
|Jun19-04, 01:02 AM||#54|
Mathematics is a meta-language. Yes, mathematics "describes" the physical universe and it also "explains" :
Here is an interesting paper by Max Tegmark that you have probably read before?
Here is a quote about the equivalence of mathematical existence with physical existence:
Faraday recognized that action at a distance was absurd, and he solved the problem with the "field" concept.
You are saying that fields are not mathematical structures? I disagree. You are saying that Faraday didn't think mathematically? I disagree.
If the physical universe includes all that is real and excludes all that is not real, then the physical universe is the universal set.
References for the first axiom:
"Three Roads to Quantum Gravity"
Refute the first axiom. You are a mentor.
|Jun19-04, 03:28 AM||#55|
2. I am not saying that Faraday didn't think mathematically. I am saying that there is no reason to think that your assertion, "Physics would not exist without mathematics", is correct.
|Jun19-04, 12:09 PM||#56|
From the quote of Tegmark and Hilbert: Hilbert defines mathematical existence as "freedom from contradiction"
If mathematical existence equals physical existence:
Physical theories must be free of contradiction.
Physical theories would not exist without mathematics.
Physics must be free of contradiction
|Jun19-04, 01:37 PM||#57|
"Mathematical existence equals physical existence,"
was true in the first place.
I feel compelled to echo Matt's earlier thought: When you have figured out what it is you want to prove, let us know.
|Jun19-04, 10:09 PM||#58|
Mathematics is THE LANGUAGE that express human thoughts in the most logical way. Physics is the study of what exists. You can consider an observation made in an experiment to be part of the mathematical terminology, but in our mathematical system they aren't always included.
Also if you meant to say that "existence" is due to mathematics it isn't true since language isn't by definition the root of existence.
|Jun20-04, 01:57 AM||#59|
Since mathematical existence is defined by David Hilbert as "freedom from contradiction" It holds that, if, mathematical existence is equal to physical existence, then physical existence is also freedom from contradiction. That is to say, physical phenomena[events] are constrained by an intrinsic, logical self-consistency.
Ergo, it follows that your statement: "observation is not a mathematical process" is false.
[1.] Physics would not exist without an ability to describe phenomena.
[2.] The description of phenomena must be logically consistent[free of contradiction].
[3.] Mathematical existence is defined as freedom from contradiction.
[4.] Mathematics describes phenomena.
Physics would not exist without mathematics.
If the universe includes all that is real and excludes that which is not real, then the universe is the "universal set".
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 structure for reality.
The Heisenberg uncertainty principle follows directly from the Cauchy-Schwartz inequality for scalar products. 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. Geometric quantization can be constructed, via fiber bundles.
|Jun20-04, 05:18 AM||#60|
|Jun20-04, 05:43 AM||#61|
You agree that physical observations must be non-contradictory.
You must also agree that descriptions of physical existence must be
non-contradictory since observations must be non-contradictory.
We can drop the label "mathematical existence"
if it puts a burr in your saddle.
In other words, you appear to be arguing semantics, not physics.
|Jun20-04, 01:17 PM||#62|
It has occured to me that, just because you use terms such as "modus ponens", it just might not be the case that you understand them. So, I am going to go into more detail on these arguments.
The fundamental statements of the argument are these:
p: Mathematical existence is equivalent to physical existence.
q: Physical existence is free from contradiction.
r: Observation is free from contradiction.
s: Observation is not a mathematical process.
Your argument proceeds as follows:
1.) p-->q (Premise)
2.) q-->r (Premise)
3.) Therefore, ~s (Conlcusion)
That this is a non-sequitir is obvious to anyone with any familiarity with logic. The basic statements of the premises do not even appear in the conclusion, which makes the conclusion totally unconnected to the statements cited to support it. Furthermore, it is a simple fact that conclusions of valid arguments cannot contain statements that do not appear in the premises, but this argument does. You can test it for validity yourself by determining the truth table for the compound statement:
You will see that the statement is not tautological, and so the argument cannot be valid.
But perhaps you didn't mean to include a new term in the conclusion, and that it only looks like you did due to a poor choice of words?
If physics exists, then it has the ability to describe phenomena.
I'll contract it to:
p: Physics exists.
q: Physics has the ability to describe phenomena.
So we have:
If physics exists, then mathematics exists.
The antecedent was already denoted as "p". Let the consequent be "u". So we have:
And your argument proceeds as follows:
1.) p-->q (Premise)
2.) r (Premise)
3.) s (Premise)
4.) t (Premise)
5.) Therefore, p-->u (Conclusion)
This argument has the same malady as the first one, though to a lesser extent (one logical variable from the premises actually occurs in the conclusion!). But this argument is not valid either, which you can verify using a truth table.
On to your next post:
|Jun20-04, 04:11 PM||#63|
Thanks for the help
[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 implies equivalence between abstract structures and physical systems.
[10.] If the exact description exists, then physical existence is a meta-language. A self descriptive entity, free of contradiction. The universe is equivalent to its[exact] description.
|Jun21-04, 04:36 AM||#64|
of course there's then the problem that you cannot prove that any model *exactly* fits the system, so it's all vacuous.
then there's the fact that language needn't be free or contradiction. cleave means to split apart or to stick together...
|Jun22-04, 11:36 PM||#65|
The only certainty is uncertainty
X = certainty
The only X is not-X ?
A contradiction. But what we understand about reality, must make sense.
We must assume? that a non-contradictory description [stratified variables]of reality exists.
X = certainty, exists, even if it is an incompletely constructed map by self aware systems within the universe...?
|Jun23-04, 03:51 AM||#66|
I was thinking in terms of nested "hyper-realities" , where the algorithim arises spontaneously, analogously to a quantum fluctuation description.
These nested hyper curves are level-surfaces, analogous to resonating phase spaces:
The laws and constants of physics become the laws of geometry. Any measured piece of reality is observed to be constructed of discrete units. The resonating wave functions are the infinite number of possible combinations of position Dx, and momentum Dp.
A quantum computer "algorithm".
Overlapping waves become phase entangled. There are two types of wave "motion", which becomes a mixed wave form. Both transverse and longitudinal wave propagation occurs.
Hypothetically speaking, of course
|Similar Threads for: The Universal Geometric Set|
|universal gravitation||Introductory Physics Homework||2|
|universal law of gravitation||Introductory Physics Homework||1|
|geometric series/geometric progression||Precalculus Mathematics Homework||2|
|Universal Sequence||Brain Teasers||3|