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Epsilon Pi's ideas on coordinate independence

  1. Jul 26, 2004 #1
    Tensors, a reason of great schism in physics?

    Yes, this application of that aristotelian principle, you have described so well, where the third is excluded and as so uncertainty is the reason why there won`t be a quantum gravitation theory, and a reason why physical laws must not be expressed in terms of tensors. Is this not, as a matter of fact, one of the reasons of the great schism in physics?

    Regards

    EP

     
    Last edited: Jul 26, 2004
  2. jcsd
  3. Jul 26, 2004 #2

    chroot

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    Epsilon Pi,

    Ummmm... what?

    - Warren
     
  4. Jul 26, 2004 #3

    jcsd

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    Yes good point, but one would find that if you leaned mpore towards the Socratean ideal of sticking your foot up your nose, it (your foot) would not be of a tensorial nature.

    Physical laws must be expressed in terms of tensors (if a physical law cannot be expressed in terms of tensors you should expect it to be incomplete) as you cannot expect the laws of physics to be dependnt on the choice of coordinate system.
     
  5. Jul 26, 2004 #4
    Why so many paradoxes in physics?

    Hi Warren and others,

    Yes, reality is not simple but complex(not necessarely complicated), and any intent to linearize it will take us to paradoxes such as those ones Hawking is now correcting regarding black holes. How is it that at atomic level matter cannot colapse, but it can at large? How is it that a fundamental principle such that of conservation of energy is violated, and we still think everything is ok?

    Regards

    Edgar
     
  6. Jul 26, 2004 #5

    chroot

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    Epsilon Pi,

    Per physicsforums.com guidlines, you must refrain from posting non-mainstream theories to the general forums. Such posts are welcome only in the Theory Development forum.

    Black holes and the conservation of energy are simply not topics relevant to the definition of a tensor.

    - Warren
     
  7. Jul 26, 2004 #6
    Reducing geometry to algebra?

    Coordinate systems?, or as I call it, reducing geometry to algebra, must they be represented by using a tool based just in the so-called "real numbers"? Has not Roger Penrose pointed out the fact that complex numbers are fundamental in understading the physical world?

    Regards

    EP
     
  8. Jul 26, 2004 #7

    jcsd

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    Where does complex numbers come in to it??? they would onl;y bew relevant if you were sticking your foot in your ear.

    Sure geometry is just a tool, but the physics must be indepednt of the tool, just like, for example, the physics of a star must be indepednt of the telescope you use to look at it.
     
  9. Jul 26, 2004 #8
    Thank you!

    My apologies Warren, and thank you for splitting off Epsilon Pi's responses to a new thread in Theory Development. I hope we can now make some criticisms of that mathematics called Tensor Analysis from which General Relativity and as so black holes were derived

    Regards

    Ep

     
  10. Jul 26, 2004 #9
    Is reality simple or complex?

    Are you not making physics dependent on a tool such as Tensor Analysis with the generalization of the so-called coordinates systems? where they come from? Are not they an invention of the human mind? why should we make an absolute of that invention?

    Should we not ask ourselves about the fundamental structure of reality? Is it simple or complex? If it is complex as we already known by QM, should we not use a complex tool, I mean complex numbers, to represent that physical reality?

    Regards

    EP


     
  11. Jul 26, 2004 #10
    Tensor analysis is, as is mathematics a consistent theory, rather beyond reproach (ignoring any possible foundation questions). Furthermore General Relativity is not derived from tensor analysis.
     
  12. Jul 26, 2004 #11
    Another version of GTH?

    How is that? haven't you read the original paper "The foundation of the General Theory of Relativity? or do you know another version of GTR, if you do, please let me know

    Regards

    EP
     
  13. Jul 26, 2004 #12
    What does it mean?

    "The fundamental idea of this general theory of covariants is the following: - Let certain things ("tensors") be defined with respect to any system of co-ordinates by a number of functions of the co-ordinates, called the "components" of the tensor." The Principle of Relativity, pag, 121. Dover P.Inc.
    If this does not mean that tensor analysis is the main mathematical tool in which GTR is based, then what does it mean?

    Regards

    EP


     
    Last edited: Jul 26, 2004
  14. Jul 26, 2004 #13
    As homology pointed out, GTR is not "derived" from tensor analysis. Tensor analysis is a "tool" that Einstein used (and had to learn as he was developing his theory if I remember correctly) to develop his ideas. Einstein used highschool algebra as a "tool" do develop STR. This doesn't mean the STR is derived from highschool algebra.
     
  15. Jul 26, 2004 #14
    a good mathrmatical tool must not reflect physical reality?

    If a tool is going to be useful to represent physical reality there must be a closed association between the two, and as is shown in that original paper mentioned written by Einstein, it would have been impossible for him to get GTR without it, so how can you say its main conclusions were not derived from that tool?

    Regards

    EP
     
  16. Jul 26, 2004 #15
    The mathematics of the physics doesn't have to have any particular association with reality. For example, what reality would Hilbert space have with a chemical reaction?

    I would also hesitate against saying that it would have been "impossible" for Einstein to get GR without tensors. Its an unprovable statement.

    Furthermore, again, there is nothing in tensor analysis as an area of mathematics that implies the physical theory of GR. You have to add other assumptions, not necessary to tensor analysis.

    Kevin
     
  17. Jul 27, 2004 #16
    Idealism in physical science?

    Hi Kevin,

    Your first paragraph is precisely one of the reasons why we have had such a great tendency to especulation and idealism in that field of science that should not: physics; no, I think that the mathematics of physics and its symbolism must in a certain sense reflects its profound dual structure, just as in QM, a complex expression solved the duality of the wave-particle problem.

    The main problem with Einstein is that he did not use complex numbers; it is well known that the quadratic differential element introduced by Minskownki, as another interpretation of special relativity was obtained from complex numbers, but Einstein generalized that QDE, by using tensor analysis, i.e., just the magnitud of that QDE, and here he had his great drawback. As a matter of fact I have prepared a paper where this is proved that I hope will be read by all those interested.

    Tensor analysis was the tool Einstein used to express his idea of "formulation generally covariant laws...as...all the components in the new system vanish, if they all vanish in the original system", and as so all his GRT became quite dependent on that tool...this is a fact you cannot disprove.

    Regards

    EP


     
  18. Jul 27, 2004 #17
    Why complex numbers? I don't see the need for them, where would they come up: imaginary coordinates? these wouldn't make any sense as they describe positions in space-time. Would the complex numbers show up in the metric, I think not other wise we could end up with imaginary lengths from the inner product so induced, again, doesn't make any sense. Would the complex numbers end up in the stress-energy tensor, and if so what would that mean?

    I'm not sure what you beef is with either tensors, which is just an area of mathematics, or with general relativity, which within its proper domain has shown outstanding agreement with experiment. All one can do to "improve" upon it is merge it with quantum and no one person will do that alone.

    Kevin
     
  19. Jul 27, 2004 #18
    How can you express the dual structure of reality?

    Why complex numbers? Didn't you know what I said before about Minkowski interpretation of special relativity? That quadratic differential element of space he introduced and Einstein generalized by using Riemann geometry and tensor analysis was based on complex numbers.

    The great prejudice we have had against them is precisely due to Descartes the one who first used the term imaginary numbers, an unfortunate term that has prevented his use in other ways, just as they are used in electrical engineering, where they are taken for real.

    If we want to reflect the profound dual structure of physical reality, duality of space and time, duality of wave and particle, must not we use a symbolism that permits us to reflect it?

    Regards

    EP

     
  20. Jul 27, 2004 #19

    jcsd

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    Though i've only done it with the minlowski metric (i.e. specil relativity) I assume it would work for all Lorentzian metrics.

    If you have x0 = -ict and x1 = x, etc. and treat the mertic qas Euclidean (from what I understand this what is done in Eclidean quantum gravity) you get perfectly consistent results as long as you rember you're orgianl defniitnion. You're always going to have imaginary intervals in spacetime anyway.
     
  21. Jul 27, 2004 #20
    The ict notation is no longer used in modern relativity. As far as I can see there's no need to use complex numbers.

    I have no prejudice against them. I use them in quantum mechanics all the time. However, in its modern form, I don't see their need in GR.

    Kevin
     
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