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Thread: Is it plausible that a new mathematical relationship will change our view on the geom

  1. #31
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    Quote Originally Posted by steveupson View Post
    We make choices all the time when it comes to using math to describe nature. ...
    The choice of coordinate systems does not change the laws of physic or their predictions. It is not even really a choice of math - it is a choice of convenience. If you have a system with spherical symmetry then it is easier to do the math in spherical coordinates. A "new mathematic relationship" in that context is just another coordinate system.

  2. #32
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    Quote Originally Posted by steveupson View Post
    The question is whether or not an error could exist in the math. Is it possible, or even plausible, that the model overlooks some mathematical relationship that no one knew existed?
    GR has been studied for over a century now. There is basically no chance of an error in the math of GR. A "mathematical relationship" that no one knows about making any math wrong is not plausible.

  3. #33
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    Quote Originally Posted by steveupson View Post
    I think we're both saying that the model is being implemented incorrectly. The question is whether or not an error could exist in the math. Is it possible, or even plausible, that the model overlooks some mathematical relationship that no one knew existed?
    As in the example I gave it is perfectly plausible that more modelled systems can be linked or related by new theorems or techniques. There being new theorems or techniques is not an error though, what these new components do is either increase the scope of a model or create links between previously disparate models.

  4. #34
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    Quote Originally Posted by Shaula View Post
    As in the example I gave it is perfectly plausible that more modelled systems can be linked or related by new theorems or techniques. There being new theorems or techniques is not an error though, what these new components do is either increase the scope of a model or create links between previously disparate models.
    Do you think that you would be able to recognize a new geometric identity that fits your description if someone were to show it to you?

  5. #35
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    Quote Originally Posted by steveupson View Post
    Do you think that you would be able to recognize a new geometric identity that fits your description if someone were to show it to you?
    Um, you do know that not every physicist is an expert on every area of physics, right? It is something of a large subject. I've probably read hundred of pure maths papers and only in a few cases has something jumped out at me as relevant to a problem I have been working on. More commonly I've had an inkling, then gone on to spend some time applying, testing and developing the relationship. Science is not generally about making snap judgements or having sudden revelations - it is about putting in the work to build a strong case that what you have found/developed is useful and worth other people working on.

    Again, as I said before, the key is that someone (ideally the person proposing that the relationship is relevant) can show that the relationship has at least some relevance by developing at minimum back of envelope proofs that the relationship produces novel and useful results or links previously disparate models or theories. And by back of envelope I mean actual physics examples (even if simplified), not hand waving descriptions of vague intuitive leaps.

    In the AdS/CFT case the holographic principle had been around for some time and thought to be relevant ('t Hooft was working it in the 70s, Susskind developed String theory relationships with it in the 80s, Hawking/Beckstein used it in the 70s/80s) but it was only when Maldacena wrote his seminal paper in '97 explicitly developing a relationship between conformal field theory and the boundary of an anti-de Sitter space that it really started to give results. After that Hawking's work on Black holes was made more rigorous in the early 2000s and ... well, thousands of papers later it is pretty obvious how useful this relationship is.

    So, sorry, but your question can be answered (No) but it is a question that somewhat fails to capture the important bits of how pure maths and physics interact. It is somewhat like asking an engineer "If I show you a lump of a new metal alloy can you tell me if it is going to be useful?" The answer is no, you have to test, evaluate and work with it.

  6. #36
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    This particular area of mathematics hasn't seen anything new for a couple of centuries.


    https://en.wikipedia.org/wiki/Spherical_trigonometry
    "The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics are discussed fully in History of trigonometry and Mathematics in medieval Islam. The subject came to fruition in Early Modern times with important developments by John Napier, Delambre and others, and attained an essentially complete form by the end of the nineteenth century with the publication of Todhunter's textbook Spherical trigonometry for the use of colleges and Schools. This book is now readily available on the web.[1] The only significant developments since then have been the application of vector methods for the derivation of the theorems and the use of computers to carry through lengthy calculations."


    Everyone is positive that this is all there is to it, even in the face of incontrovertible mathematical proofs to the contrary. And yes, it's been proven twice, by separate methods. First using Mathematica to build a model and then by a collaboration here at this forum.

    Every piece of physics that has anything at all to do with spacetime is affected by this identity.

    That's about as much work as I'm capable of without more help.

  7. #37
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    Quote Originally Posted by steveupson View Post
    Everyone is positive that this is all there is to it, even in the face of incontrovertible mathematical proofs to the contrary. And yes, it's been proven twice, by separate methods. First using Mathematica to build a model and then by a collaboration here at this forum.

    Every piece of physics that has anything at all to do with spacetime is affected by this identity.

    That's about as much work as I'm capable of without more help.
    Even if I accepted the 'incontrovertible proofs' (I don't believe you have shown what I would term a mathematical proof of a new theorem in your other thread - you have simply shown that you can construct a complex relationship between geometric shapes - but this thread is not the place to delve into this) it would still just be a piece of pure maths. It would need to be shown to be relevant and applicable to physics problems. If people are not interested in working on it then perhaps you need to take a crash course in the area of physics you think it is relevant to? There are plenty of places online where you can find guides, book recommendations and so on. There are threads on here about that, and people willing to help you learn by answering questions.

  8. #38
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    And there we have it. As a reminder, here is Swift's warning at the beginning of this thread.

    Quote Originally Posted by Swift View Post
    Lastly, if you use this thread to even hint at any of your ATM ideas, you will likely be banned from this forum.
    Now we have:

    Quote Originally Posted by steveupson View Post
    This particular area of mathematics [...]
    Spherical_trigonometry [...]
    a collaboration here at this forum. [...]
    [...] this identity.
    That's about as much work as I'm capable of without more help.
    So much for just a general conversation about a theoretical new mathematical relationship. I hope your attempts to fool moderators on other forums will be less transparant. On this forum, it ends here.
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  9. #39
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    And with that, this thread is closed.

    Frankly, it is hard to imagine anyone here wanting to reopen this thread, but if you do, you know the drill; you'll need a very convincing argument to do so.
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