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Nature of Time and particles-caustics

  1. Dec 30, 2003 #1
    This paper is dated to the 23rd of December, and seems to be a nice idea...


    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?
    Last edited: Dec 30, 2003
  2. jcsd
  3. Dec 30, 2003 #2
    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 , 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.

  4. Dec 31, 2003 #3
    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.
  5. Jan 1, 2004 #4
    Re: Re: Nature of Time and particles-caustics

    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.
  6. Jan 2, 2004 #5
    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.
  7. Jan 2, 2004 #6
    Re: reply to Alex

    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.

    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.
    Last edited: Jan 2, 2004
  8. Jan 3, 2004 #7
  9. Jan 3, 2004 #8
    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.
  10. Jan 3, 2004 #9
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  15. Jan 10, 2004 #14
    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?
  16. Jan 10, 2004 #15
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