Nature of Time and particles-caustics (1 Viewer)

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This paper is dated to the 23rd of December, and seems to be a nice idea...

http://arxiv.org/abs/hep-th/0312278

Theoretical physics has arrived to the crucial point at which it should fully reexamine the sense and the interrelations of the three fundamental entities: fields, particles and space-time geometry. String theory offers a way to derive the low-energy phenomenology from the unique physics at Plankian scale. However, it doesn’t claim to find the origin of physical laws, the Code of Universe and is in fact nothing but one more attempt to describe Nature (in a possibly the most effective way) but not at all to understand it.
In the interim, twistor structure arises quite naturally in the so called algebrodynamics of physical fields which has been developed in our works. From general viewpoint, the paradigm of algebrodynamics can be thought of as a revive of Pithagorean or Platonean ideas about “Numbers governing physical laws”. As the only (!) postulate of algebrodynamics one admits the existence of a certain unique and exeptional structure, of purely abstract (algebraic) nature, the internal properties of which completely determine both the geometry of physical space-time and the dynamics of physical fields (the latters being also algebraic in nature)
In result, physical picture of theWorld which arises as a consequence of one only algebraic structure appears as very beatiful and unexpected. As its basic elements it contains the primodial light flow – “pre-Light” – and the relativistic aether formed by the latter, multivalued physical fields and prelightborn matter (consisting of particles-caustics formed by the superposition of individual branches of the unique pre-light congruence in the points of their “focusization”)
As very natural and deep seems to be the arising in theory connection between the existence of universal velocity (velocity of “light”) and of the time flow; connection which permits to understand, in a sense, the origin of the Time itself. Time is nothing but the primodial Light; these two entities are undividible. On the other hand, there is nothing in the World except the preLight Flow which gives rise to all the “dense” Matter in the Universe.
Sort of deals with the ultimate question: where did the physical laws come from? No religious discussions here guys, let's rely on a firm fact basis :)

One question though: the author apprises that string theory is another endeavor to elucidate nature, but not to comprehend the involutions entrenched deep within it's bowels, notwithstanding exotic attemps such as LQG (Loop Quantum Gravity) that managed quite literally to infer space-time as based on a rigorious mathematical structure (spin-networks - which if spread across, form a spin-foam, if i'm not mistaken) that sort of "weaves" the space-time, and surmises it resembles whorles and loops at the Planck scale ), can it claim to take the title of "understanding nature"?

Shouldn't the author mention, while he's at it, that finding a non-perturbative regime of string theory, would go a long way towards proving it's consistency, and perhaps, in the far future, provide compelling answers to these orthic questions?
 
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Originally posted by alexsok
http://arxiv.org/abs/hep-th/0312278
Sort of deals with the ultimate question: where did the physical laws come from? No religious discussions here guys, let's rely on a firm fact basis :)
Unless physics can be derived from the principles of logic and reasoning alone, then any theory you might develop would only be begging the question as to where its fundamental axioms and postulates come from.

So far, physics has been taking a bottom up approach, advancing mathematical theories to explain observed phenomena. This is basically just curve fitting, posing equations that fit the experimental data, and offering a physical interpretation for the fundamental entities of those curve fitting equations. But this process is not capable of offering a total explanation of why physics is as it is; it can only say how elements relate to each other in a mathematical way.

What is needed is a way of describing the methods of logic in terms of mathematics. And hopefully the geometry and symmetries involved will result in the equations of physics. If physical phenomena are the propositions of logic, and we have a mathematical description of logic, then we have a mathematical description of physical phenomena, or in other words, the mathematical laws of physics. And this would be a Top down theory of everything.


We may be closer than we think. And String theory, or more likely M-Theory, or perhaps even Loop quantum gravity may serve our purposes in this. As I explain on my web-site at: http://www.sirus.com/users/mjake/StringTh.html [Broken] , The logic of propostitional calculus, Predicate logic, set theory, and probabilities (inductive logic) can all be described mathematically by imposing a coordinate system over a sample space with a probability density function to describe the density of objects at various locations. This sample space is really nothing more than the overall manifold of space-time.

Normally events in a "sample space" are described by hypersurfaces in this space which give the probability of events with a particular property. But since time is giving us more samples, we cannot have a completely enclose hypersurface to describe events. Instead we have "growing" events which are described as hypersurfaces which are not completely enclosed but have a boundary. These boundaries in 3D are closed loops which look like the strings of string theory. The surface from one closed string to another, then, look very much like world-sheets. It only remains to justify an Action integral to produce Lagrangian mechanics from logic alone. The theory is immature at this point. So please consider helping me in this effort.

Thanks.
 
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Since I came up with this from a sample space, then perhaps this has application in other areas where probability densities are employed, maybe even the stock market. If you can identify properties within the sample space that behave as events that grow with some parameter that conserve certain quantities, then perhaps it is possible to determine forces acting on these events that move them around. Just speculating.
 
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Re: Re: Nature of Time and particles-caustics

Originally posted by Mike2
Unless physics can be derived from the principles of logic and reasoning alone, then any theory you might develop would only be begging the question as to where its fundamental axioms and postulates come from.
Would you deem this prevailing scenario as copasetic? Plainspoken, the derivation is anything but satisfactory, and the human mind will always turn to a bottomless cavity in their never-ending search for novel ideas that drive science to the next centuries.

From this point of view, it's effortless to conclude that the toiling of the throng of individuals involved in the research is a conspicious aberrance from those idiosyncratic assessments of science reaching the end of it's cycle!

Rest assured, what you're saying is a sturdy cornerstone of science today, but it is in no way, copesettic to the veracious account science is not yet ready to provide.
 
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reply to Alex

Alex said:
Unless physics can be derived from the principles of logic and reasoning alone, then any theory you might develop would only be begging the question as to where its fundamental axioms and postulates come from.
[end of quote]

Do remember Godel's theorem. Any (at least countably infinite) system which is big enough to incude arithmetic is either incomplete or inconsistent.
Are you saying that your logical system does not include arithmetic?
If not, then What?? And if it is incomplete, how can you hope to derive all the principles of physics?

Yes this means complete GUTs are impossible, but everyone knows this, and presses on nevertheless.
 
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Re: reply to Alex

Originally posted by Ernies
Do remember Godel's theorem. Any (at least countably infinite) system which is big enough to incude arithmetic is either incomplete or inconsistent.
Are you saying that your logical system does not include arithmetic?
If not, then What?? And if it is incomplete, how can you hope to derive all the principles of physics?
I'm not trying to derive numbers with logic like Whitehead and Russel did. I'm presupposing the validity of mathematics and imposing a coordinate system on a space in which Unions and Intersections are included. This is really nothing more than what is done in manifold theory. Do you claim that point set topology or differential geometry is invalid or incomplete?

Even if mathematics is incomplete, we are only looking for physical laws using the math expression that can be derived. We are not assuming that we even need to use every valid math expression. That's not the effort here.

As far as Godel's theorem is concerned, no one has ever shown me one of these expressions that is true but not derivable from the basic axioms. No such expression has been shown to me from any system.

Yes this means complete GUTs are impossible, but everyone knows this, and presses on nevertheless.
No choice really. Questions will always continue until it can be shown that the answers are derived from the principles of reasoning itself. For you cannot question the validity of reasoning and expect a valid answer. But you can always question the reality of some physical entity used as a contingent variable in some equation.
 
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As far as Godel's theorem is concerned, no one has ever shown me one of these expressions that is true but not derivable from the basic axioms. No such expression has been shown to me from any system.
[end Quote]

Try reading group theory. The sources are no longer available to me --having long since retired--- but there were at least two. As I recall it, the first one falls in two parts: it was shown that certain properties were true of some groups, if the groups were *big enough*. It was also shown that any derivation of *big enough* would lead to inconsistency. The second was more complex, and I do not recall all the details, so won't try to describe it.
But I recall my astonishment on reading them, and thinking "The final nail in the coffin of complete theories. Now we can point to logically unanswerable questions in ordinary maths". There may well have been many more found in the last twenty years.

Ernies
 
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I'm not sure I have added anything more than what has already been advanced by others. I simply have a justification for a world-sheet which seems to be only postulated in theories so far. So I ask questions such as how to justify the math given the geometry.

I'm not totally convinced that Godel's incompleteness theory is valid. He seems to be using an argument outside the forms given by propositional calculus. There is no way that I know of to present a self-referencing proposition in propositional calculus and so his argument must be outside that fundamental system of argumentation. Thus, if his argument is valid, then he is suggesting that even the most fundamental system of argumentation (propositional calculus) is incomplete. And this seems to undermind the validity of any argument whatsoever.

Also, his argument relies on the ability to assign numbers to operators of that system. But if you are dealing with a continuum, where the variable can take on an infinity of different values, how can you say that the operators have a unique number. I think his argument only applys to discrete systems and not continuous systems such as ordinary calculus.
 
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Thus, if his argument is valid, then he is suggesting that even the most fundamental system of argumentation (propositional calculus) is incomplete.[end of quote]

Yes, of course, if it is able to deal with multiplication and division in arithmetic as part of its consequences.

And this seems to undermind the validity of any argument whatsoever.[end of quote]

Not at all. you just have to be careful.

I see that you did not comment on the group theory, but you can hardly have had time to investigate.
May I remind you of the words of Richard Feynmann in his final illness:
"I suppose there are things we just can't know" (or words very close to this}. Having talked to the man, and read his works I feel quite sure that he meant 'can't' in an absolute sense.

As regards continuity opposed to granularity, this still seems to be a moot point. I do not see what you are going to do with the roots of quantum theory in a real continuum. They have been trying to quantise gravity for some decades now (without a lot of success, despite Hawking's claims). However, you will no doubt be here when the answer is found.
Cheers, and a happy new year.

Ernies
 
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Originally posted by Ernies
Thus, if his argument is valid, then he is suggesting that even the most fundamental system of argumentation (propositional calculus) is incomplete.[end of quote]

Yes, of course, if it is able to deal with multiplication and division in arithmetic as part of its consequences.

And this seems to undermind the validity of any argument whatsoever.[end of quote]

Not at all. you just have to be careful.
You seem to have missed my point. That Godel's argument is outside the scope of deductive logic. So you are starting with the premise of acknowledging the truth of statements without the use of proof.

For example, when we say 2+2=4. The truth of it is not derived from logic. It is acknowledge through experience. But as you can see, here we have a truth not derived from logic.
 
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You seem to have missed my point. That Godel's argument is outside the scope of deductive logic. So you are starting with the premise of acknowledging the truth of statements without the use of proof.[End of quote]

I did not wish to state the fact so brutally, as I assumed you would take it into account. Godel's theorem is not about the content of argument, but about the process. Any theory consists of a set of propositions/axioms, (not neccessarily numerical, but considered as unarguable for this purpose) --- call them what you will-- and results derived from them. These are discrete, and denumerable. Provided the set is big enough to include all arithmetic, Godel shows that it is either incomplete, in the sense that one can always state something in terms of the set, which is not provable by the processes included in the set. or the theory is inconsistent.
It does *not* repeat *not* say that this last theorem may not be true, simply that it is not provable. Indeed the statement may be true even 'obvious' to a human intelligence, but it is not provanble in terms of the set. That was the point of introducing the unprovability of what is 'big enough' in the group theory example, since the fist part *is* provable, and it is obvious that there must be a 'big enough'.

You quote 2+2 =4, and it has been shown that systems containing only addition and subtraction are complete (I forget the formal name for this type of arithmetic-- Peano???): but I specifically said in my last post that this was not so if multiplication or division are included.

I simply do not understand what you mean by saying Godel's Theorem is outside the scope of deductive logic.
To me it seems itself a piece of deductive logic, so we must mean different things.

Could you please explain?

Ernies
 
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Originally posted by Ernies
I simply do not understand what you mean by saying Godel's Theorem is outside the scope of deductive logic.
To me it seems itself a piece of deductive logic, so we must mean different things.

Could you please explain?

Ernies
Yes, this all sounds familiar. Though, I am far from being an expert in this area.

As I recall, Godel's argument rests in part on the ability to construct self referencing statements (in the system under consideration). But no such self referencing is possible in deductive logic (propositional calculus). You cannot construct a proposition which can only be either true or false that also refers to itself. Thus, whatever argument Godel is using does not rely on the forms of valid argumentation which come from deductive logic.

We are asked to acknowledge the "validity" or the "truth" of the propostion proposed by Godel. But he uses methods outside the methods of proving truth or validity, which is precisely what deductive logic is.

Godel states that there are statements in advanced systems that are true but not provable. But this fact is seen in the set of axioms itself. In such systems, whatever set of axioms you choose, those axioms are accepted as true without proof. And in fact if they are considered axioms, then no one tries to prove them. So Godel proved what we already know, that axioms are accepted as true beyond the ability of proving them. If you could prove them with something more basic, then they would not be axiom.

Even in deductive logic we accept that a proposition can be only either true or false, but no one tries to derive these two states from something more basic. Nothing more basic exists in that system and they are accepted without proof. So what Godel proved is that yes, indeed, there are axioms.
 
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Yes, this all sounds familiar. Though, I am far from being an expert in this area. [End of quote].

What you said after this sounded familiar to me too, though I do not think you are being logical.Rather the contrary.

Clearly one, or both of us, suffers from what the R.C. Church calls 'invincible ignorance': equally clearly, each thinks it is the other, so that further debate is not useful.

I can only console myself that five out of six world-class physicists (e.g. Penrose, Barrow, etc.) when asked to consider what they thought the greatest intellectual achievement of the last century came up with the answer "Godel's Theorem". They probably , like my- (admittedly much lesser) -self, had spent several years of spare time trying, and failing, to find the fallacy.

( The odd one out, if you are interested, said he couldn't decide between Relativity and Quantum Theory.
Several biologists were asked the same question, and were unanimous in saying
'Discovery of the DNA Spiral').

Goodbye.

Ernies
 
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Well, let's suppose that you are perfectly correct about mathematical systems which may have true statements expressible in those systems though not provable from the axioms of those systems. My question is how does that change any of our efforts? We are simply stuck trying to understand things by explaining them in terms of simpler axioms. Isn't that the very definition of understanding? So does Godel's theorem require us to stop learning and striving to understand the world? What?
 
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Well, let's suppose that you are perfectly correct about mathematical systems which may have true statements expressible in those systems though not provable from the axioms of those systems.[end of quote]

No 'suppose' about it;it is true. The propositional calculus you mentioned is not 'the most basic' but only the simplest. True, it is 'complete' but is simply cannot handle maths. For that we need 'predicate calculus', which can handle relationships, such as 'less than' or greater than'. It is not, repeat not, 'complete'.( In fact there are many orders of such calculus, depending on the degree of abstraction)

My question is how does that change any of our efforts? We are simply stuck trying to understand things by explaining them in terms of simpler axioms. Isn't that the very definition of understanding? [end of quote].

NO! As I showed in my theory of groups example, one can understand, without proof. This is certainly true of new work, as I can testify from from my own experience. One 'sees', and understands the new pattern, but the proof comes later--- if one can. If one cannot prove it, this does not mean the result is untrue.For that one needs a proof of its falsity.
.
So does Godel's theorem require us to stop learning and striving to understand the world? [end of quote]

NO!!! This answer follows from my previous paragraph. All it means is that any theory which includes arithmetic will always be incomplete. No end to Physics or Maths! But one can always learn new things, if one is interested. I still am at 77.

I will add the I do not intend to carry this discussion further. I will not reply to any further posts from you on this thread.

Ernies
 

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