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posted by martyb on Sunday July 26 2015, @07:10PM   Printer-friendly
from the BASIC:-But-Any-String-Is-Complicated! dept.

Carlos Shahbazi has presented the first two articles of a series that introduce the layman to the basics of String Theory.
link: http://mappingignorance.org/2015/05/06/the-geometry-of-string-theory-compactifications-i-the-basics/

"The sphere is also a simple example of a compact manifold, which is a particular class of manifolds of utmost importance in String Theory compactifications, as we will see in a moment. The compactness condition can be intuitively understood using Euclidean space. A manifold embedded in Euclidean space, as the sphere in figure 3, is compact if and only if it is bounded, namely it is contained in a finite size region of E and it is closed, namely it contains all its limiting points."

[The second article is "The geometry of String Theory compactifications (II): finding the Calabi-Yau manifold" -Ed.]

If that's too easy for you; the same author also has "Black hole solutions of N=2, d=4 super-gravity with a quantum correction, in the H-FGK formalism"
link: http://www.mathpubs.com/author/Carlos+S.+Shahbazi


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  • (Score: 5, Informative) by VLM on Sunday July 26 2015, @08:20PM

    by VLM (445) Subscriber Badge on Sunday July 26 2015, @08:20PM (#213963)

    This series cries out for a guest lecture/poster session with xkcd in the spirit of "up goer five"

    I can't even begin with the top 1000 word translation as per above.

    The author missed all kinds of fun analogies with mapmaping where you implode 3D earth into a 2D map and its pretty awesome on a really small scale like the size of a city, but its basically impossible to navigate the entire earth using a flat map projection. The directions and distances get all messed up on a far enough range 2d map vs 3d reality. Anyway there's a lot of math and PITA to turn 3d real world into usable 2d maps and understand whats getting distorted and do "gps navigation calculations". Likewise for reasons beyond the scope of the article series the universe seems to live in 10 or 11 dimensions (long story, trust in Great Cthulhu for now) and we're in a locally flat 4d part on a small scale but the big picture of all 11 dimensions is likely pretty funky appearing, and the math to move between 11D and 4D world is hideous although one sneaky strategy is to start with everything then cross off ridiculous solutions where the 4d world can't work as we currently know it, then with whats left (well, with what we know of thats left anyway) trying to solve it for gravity directly is an epic PITA so lets solve an indirect way which after much geometry fooling around shockingly turns out to relate to parts of the ancient and well studied group theory that we think we understand, so we're kinda not as lost as before. Also this only picks us up to the mid 80s and there's plenty of fun past then. Good luck turning this into an "up goer five" style xkcd poster.

    Now insert a bunch of "string deniers" or whatever the formal academic term is for people who aren't amused at string theory because it seems to diverge pretty far from known reality but it is a hell of an interesting math problem. So its not useless or wrong so much as its a really awesome math problem and physicists are selected for being good mathematicians so its entirely unsurprising they think its an awesome math problem. Although they're getting paid to do physics not math problems. Its a turf war!

    One big problem with finding anything to test with string theory is the basic assumption waaaaay back at the beginning that we'll simplify the math by assuming the only valid problem solutions revolve around 4D world working as we know it. Since we have no idea what doesn't work in our 4D world, its gonna be hard to make a test. Its not like the old days when no one could explain Mercury's crazy ass orbit or why clocks run at different speed based on how fast they move, this stuff is already "baked into the cake" so there's nothing weird to test. If only we had experimental evidence of reaction-mass free thrusters, or space alien warp drives or something.

    I think its fun stuff to read about. I know they're on to a good math puzzle. I feel they're probably wasting valuable physics time by playing theoretical untestable geometry games, but whatever. They can stop playing geometry games and come back to doing physics later, most likely.

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  • (Score: 2) by c0lo on Sunday July 26 2015, @09:00PM

    by c0lo (156) Subscriber Badge on Sunday July 26 2015, @09:00PM (#213973) Journal

    The author missed all kinds of fun analogies with mapmaping where you implode 3D earth into a 2D map and its pretty awesome on a really small scale like the size of a city, but its basically impossible to navigate the entire earth using a flat map projection

    Inconsequential.

    The mathematicians (and physics theoreticians) don't deal with the trivial matter of map navigation, for them the existence of an isomorphism* between the two maps is more than enough (remember? a topologist is a mathematician who can't tell the difference between a coffee mug and a donut).
    And you know what? They are usually demonstrable right quite a long time before somebody find a domain of applicability for their distorted view of the mundane reality.

    ---

    * supplementary, to be useful, the isomorphism need to preserve intact some properties of the model, all the other properties be damn'd (as inconsequential).
    You know? Pretty much like car analogies, except that they need to be rigorous analogues in the... ummm... matters that matter.

    --
    https://www.youtube.com/watch?v=aoFiw2jMy-0 https://soylentnews.org/~MichaelDavidCrawford
    • (Score: 2) by hendrikboom on Monday July 27 2015, @06:13PM

      by hendrikboom (1125) Subscriber Badge on Monday July 27 2015, @06:13PM (#214445) Homepage Journal

      The isomorphisms are topological; in particular, stretching and shrinking is allowed. But even with stretching and shrinking, you can only map local pieces of the surface of a sphere 1-1 onto a Euclidean plane. Mapping a whole sphere 1-1 onto a plane is not possible. You have to leave out at least one point.

      That's why the mathematicians invented this whole local patches thing. They stitch complicated manifolds together out of patches, much as a seamstress might sew a pair of pants out of many ordinary pieces of cloth.

  • (Score: 3, Informative) by c0lo on Sunday July 26 2015, @09:08PM

    by c0lo (156) Subscriber Badge on Sunday July 26 2015, @09:08PM (#213978) Journal

    If only we had experimental evidence of reaction-mass free thrusters

    You mean something like EM drive [wikipedia.org]? 'Cause even NASA seems to have experimentally detected something.

    --
    https://www.youtube.com/watch?v=aoFiw2jMy-0 https://soylentnews.org/~MichaelDavidCrawford
  • (Score: 3, Interesting) by opinionated_science on Sunday July 26 2015, @09:27PM

    by opinionated_science (4031) on Sunday July 26 2015, @09:27PM (#213983)

    the problem is at school everyone only learns about Euclidean geometry, as it is useful in building "stuff" (look around your residence).

    The natural world (e.g. Trees, animals etc.. ) is non-Euclidean. and therefore it should not be surprise that the fundamental components off the universe are non-Euclidean.

    The mathematical concept of ordinality is one of the reasons Euclid wrote "Elements" in the first place, and mathematics is needed to "visualise" that which is impossible to make.

    One of the consequences of the "untestable" theoretic geometries, is that in the real world they map to energetic states of a system. And these *can* be measure as they are represented by the entropy.

    It might take another 50 years, but eventually we will have a theory that can be tested. For now, lets just try and understand the basics...

    • (Score: 2) by Geezer on Monday July 27 2015, @11:24AM

      by Geezer (511) on Monday July 27 2015, @11:24AM (#214231)

      "The natural world (e.g. Trees, animals etc.. ) is non-Euclidean."

      Physical structures and shapes in the natural world, narrowly defined as stuff on this planet, can be quite complex and irregular taken as a whole. However, they can all have their component structures' shapes described perfectly well by simple solid geometry. It takes a lot of polygons and spheres to build an elephant.

      • (Score: 2) by opinionated_science on Monday July 27 2015, @11:30AM

        by opinionated_science (4031) on Monday July 27 2015, @11:30AM (#214235)

        I suggest reading about fractal geometry and the mathematics of non-Euclidean space - it is truly surprising how little of the natural world is compactly described by Euclidean geometry.

        I suppose the contrast might be illiustrated as that between a vector drawing and a raster image... one is an arbitrary precision representation and the other is an approximation.

  • (Score: 5, Interesting) by Non Sequor on Sunday July 26 2015, @10:47PM

    by Non Sequor (1005) on Sunday July 26 2015, @10:47PM (#214005) Journal

    I'll give it a shot.

    Okay, so classical physics takes place in Euclidean space. It has up/down, left/right, and forward/backwards.

    Special relativity takes place in Minkovsky space. It has up/down, left/right, and forwards/backwards plus earlier/later. The notion of distance in Minkovsky space is finagled so that moving in the normal dimensions is positive distance and moving in time is negative distance. If you go from point a to point b at the speed of light, the "distance" traveled is 0. Going faster than the speed of light means traveling a negative "distance".

    General relativity takes place on some manifold. Not any particular manifold mind you, just some manifold. Manifolds are like Euclidean space, except you just say, "up, down, whatever... we'll just sort it out later". You can define your dimensions anyway you want, as long as at any point you have some way of talking about n different directions you can go from that point. You can even use completely different ways of talking about directions in different parts of the manifold as long as you can explain how to switch between them at the fringes.

    So remember, that for special relativity, we basically took the notion of distance from Euclidean space, and then screwed around with it to make things traveling at the speed of light move distance 0. General relativity goes deeper and says that the notion of distance and how to measure angles in our manifold is tied to the energy content of space.

    You solve problems in general relativity by working out a combination of energy content and notion of distance and angles that fit together. This is pretty hard. I think that generally you only ever solve problems in them by studying an incredibly abstract problem, or doing some heavily approximated numerical stuff.

    So, we apparently live in a world with up/down, left/right, forward/backward and earlier/later. We use the models above to finagle them sometimes to explain how these things when we're in one place relate to the same things when we're in some other place.

    So mathematically, what kinds of different ways are there of having a notion of up/down, left/right, forward/backward and earlier/later, that corresponds with our finagles, plus also quantum stuff, which involves a completely different kind of finagle? Well it seems that a lot of the answers involve making up a lot of different kinds of crazy directions, mapping out our universe and all of our lives on those crazy directions, and then translating that back into our own up/down, left/right, forward/backward and earlier/later, somehow.

    It makes a lot of sense for the extra crazy directions we're adding to not involve putting information related to stuff in a small space in the part of the universe we see all over the dang place in that crazy made up thing. That's called compactness. The up/down, left/right, forward/backward and earlier/later in our place doesn't need to be compact, in fact, to some extent, we expect stuff here to be all over the dang place, but if this extra stuff is all over the place, how does it know to stick together in our place to make small things?

    So what makes something compact? Well it's a quarter of a mile to the gas station from my house. The space between me and the gas station is compact. Spaces with end points that you can travel between are compact. If the end points are unattainable, then its not compact. The space between me and Valinor is an example of a space that isn't compact.

    We can also make spaces that aren't compact compact, by changing their end points from imaginary unreachable places to real places. If you say that if you go infinitely far in any direction in the Euclidean plane, that you reach a real place called the Point at Infinity, then basically you've reinvented the sphere, since you can start at the origin, walk to the Point at Infinity, then come back to the origin from a different direction, just like walking through the north pole and heading south again. We're treating the notion of distance as being entirely negotiable here.

    --
    Write your congressman. Tell him he sucks.
    • (Score: 2, Touché) by wirelessduck on Monday July 27 2015, @07:41AM

      by wirelessduck (3407) on Monday July 27 2015, @07:41AM (#214165)

      And this is why I come to lurk on SoylentNews. Thanks for the enlightenment!

    • (Score: 2) by BananaPhone on Monday July 27 2015, @02:59PM

      by BananaPhone (2488) on Monday July 27 2015, @02:59PM (#214339)

      This is the type of explanation I was expecting for a "layman".

      The linked articles read like Coles notes for the post-grad math-major.

  • (Score: 0) by Anonymous Coward on Monday July 27 2015, @03:50AM

    by Anonymous Coward on Monday July 27 2015, @03:50AM (#214061)

    It also damage science. You got Jenny McCarthy's of the world screaming vaccine causes autism. And then you have eco-nazies hollering "earth is warming, we have sinned, we all gonna die". And then we have physicists, and not just some eccentric cranks but of the establishment big-shot top academic brand names, in physics - the hardest of hard sciences - spewing hocus-pocus new-agey multiverse "anthropic" bullshit, writing pop science books, making PBS "educational" shows, acting like cheap whore/hustler aiming for Opera Winfrey audiences.

    Why wouldn't average joes dismiss science? Why wouldn't they think scientists are no better than used salesmen?