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    Thread: Spacetime Curvature Rate..

    1. #1
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      Spacetime Curvature Rate..

      ..has been gently driving me nuts for about three months on-and-off.

      Plenty of "info" about it, all over the net.. but as is so often the case, when I plough through this "info", I don't find anything concrete: nothing that answers my question(s).

      But I have a friend "on the inside" as it were, finishing a Maths Doctorate in Berlin (Algorithms of the Visual Cortex) and through Uni Professorial connections I have also managed to find.. absolutely nothing: plenty of referrals to other sources, but which turn out to be useless.

      What I would like to know is:

      1) Is the rate of curvature a constant or not?
      2) If so, how long would it take a photon to curve by one degree from its starting point?
      3) If so, how long would it (theoretically) take a photon to make a 360 degree curve (assuming it did not decay in that time, which it surely would)?

      Has any of this been calculated yet to anyone's current knowledge?

      Thanks in advance for any replies.

      [NB I'm not a mathematician].
      Last edited by Oneiro; 01-19-2012 at 04:39 PM.

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      Quote Originally Posted by Oneiro View Post

      1) Is the rate of curvature a constant or not?
      2) If so, how long would it take a photon to curve by one degree from its starting point?
      3) If so, how long would it (theoretically) take a photon to make a 360 degree curve (assuming it did not decay in that time, which it surely would)?

      Has any of this been calculated yet to anyone's current knowledge?

      Thanks in advance for any replies.

      [NB I'm not a mathematician].
      I did a uni course on GR (the actual maths, not the fluffy stuff), so I think I can try to answer these:

      1) No. Curvature is varying everywhere depending on the mass-energy distribution of any given region. In fact, it varies in both space and time. To calculate exactly how much curvature there is in a given region of spacetime, you must solve Einstein's equation, which is a nasty brute of a tensor differential equation. For the most part, people only try to solve it in special cases where they can use symmetries to eliminate some of the 16 (!) equations.

      2) See above. Photons will obviously curve a lot quicker near the event horizon of a black hole than in interstellar space. Although photons don't actually "curve" in their local frame of reference; you have to be sitting far away in relatively flat space to observe curving photons.

      3) First of all, photons don't decay. At all. Ever. As for the question, a photon within a few meters of the event horizon of a black hole will do 360 degrees (as observed from far away) in a little over one orbit, which would be a few kilometers in circumference and would take microseconds.
      PhilosopherStoned likes this.

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      Thanks for the reply cmind.

      Quote Originally Posted by cmind View Post
      3) First of all, photons don't decay. At all. Ever.
      Ouch. I just Googled "photon decay". The arguments are worse than in here!

      But I take your points about the curvature being relative to gravity sources, which can vary in intensity.

      It's brain-numbing, this stuff.

      Need beer.
      Last edited by Oneiro; 01-19-2012 at 05:10 PM.

    4. #4
      Xei
      UnitedKingdom Xei is offline
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      I have the option to study geometry this term... I'm not going to though because I'm a big fat baby. It's not directly related to my career interests so unfortunately I'm going to have to jettison it for now and basically limit my understanding of GM to fluffy stuff. I doubt I would enjoy it anyway, tensors and the like just aggravate and bore me. It's so messy in fact that nobody really got anything useful out of Einstein's theory for decades.

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      I would say that GR would expand your mind, but that's only if you get past the enormous barriers to beginners. Unfortunately, after only a single semester of learning about it, you would most likely be totally bogged down in the details of working with tensor notation.

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      Quote Originally Posted by Oneiro View Post
      Ouch. I just Googled "photon decay". The arguments are worse than in here!
      In classical physics (of which the relativities are the current(!) completion), "photon" is essentially equivalent to "null world line", i.e. they are the paths through spacetime (if such a path exists) that connect two points with zero "length" between them.

      When I say length, I mean either the t^2 - x_1^2 - x_2^2 - x_3^2 or the equivalent with the signs reversed. Note that the "spacial part" part is just the usual pythagorean metric.

      Need beer.
      QFT

      Also, Xei. Geometry is an equivelant for equations. In the same way that vector spaces can be viewed as a geometrization of linear equations, differential manifolds can be viewed as a geometrization of non-linear equations. Apparently math has something to do with what you want to do (i.e. "conciousness"). Do you expect it to all be linear?

      The more points of view the better and the one that walks the straight path never reaches to highest goals. Geometry is awesome. Just think of the symmetry groups!
      Last edited by PhilosopherStoned; 01-20-2012 at 11:57 PM.
      Previously PhilosopherStoned

    7. #7
      Xei
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      It's a very pure course, I don't believe any application exists other than general relativity. There's only a finite number of courses I can realistically do, and things like electromagnetism, waves and definitely statistics are far more important for what I want to do. I am doing some algebra too though (groups, rings, modules) because it seemed like the most likely course to be useful, and I was not too bad at it last time.

      The fundamental qualitative notions of geometry (that what had previously been considered to be the only possible one was actually one of several) have actually been very important in shaping my ideas, but I'm pretty sure that's as far as I need go.
      Last edited by Xei; 01-21-2012 at 01:29 PM.

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      Rational Spiritualist DrunkenArse's Avatar
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      Quote Originally Posted by Xei View Post
      It's a very pure course, I don't believe any application exists other than general relativity.
      Differential geometry is even being used in fincance but I totally appreciate your other points, especially regarding an upper bound on courses. Very good intuition on algebra being useful though.

      The fundamental qualitative notions of geometry (that what had previously been considered to be the only possible one was actually one of several) have actually been very important in shaping my ideas, but I'm pretty sure that's as far as I need go.

      One other important idea is that of atlases of coordinate charts. It's a very useful analogy for reality vs. models of reality. A lesson from what you cite is that whatever model we're working with is probably incomplete and will need to be replaced. The corresponding lesson from coordinate charts is that different models may be necessary to cover (still incompletely and to be refined as before) different aspects of reality (i.e. our direct experience, aside from explanations) simultaneously. The analogy is so good as to require a mechanism to smoothly translate between different overlapping patchs.

      The definition is at least worth knowing. Bundles are pretty cool too.
      Previously PhilosopherStoned

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