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More than 3 dimensions?

  1. Mar 21, 2004 #1

    phy

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    i understand the concept of dimensions untill we get to 3 but having more than 3 dimensions is beyond me. anyone care to explain? thanks.
     
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  3. Mar 22, 2004 #2
    i thought our world have 4 dimensions, and that light is understood to be a possible rippling effect of a 5th dimension, but from there on I don't know
     
  4. Mar 22, 2004 #3

    selfAdjoint

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    The math of string theory has the number of dimensions as a variable, and when you work out the theory you find that the variable takes on the value 26 (for bosonic strings) or 10 (for superstrings. M-theory adds one dimension to superstring theory, making 11.

    Nobody can visualize these dimensions, and physicsts understand that the extra dimensions over 4 are not seen. The major way they deal with this is compaction. They say the six extra dimensions (treating only the superstring case) are rolled up into tiny blobs. The analogy is a long thin tube. If you look at it from a distance it seems one dimensional. It's only if you look close that you see it has another dimension, "compacted" into a circle.

    So the physicsts say that the tiny blobs are really tiny, smaller than protons by far, and that we can't see them even with our most powerful atom smashers. But you have to understand that the blobs are everywhere in our space; each point has its blob, just as each point along the tube lies on a little circle.
     
  5. Mar 22, 2004 #4
    yeah...the very fabric of space-time is made of the tiny 6 dimensional blobs, and when M-theorists talk about vibrations in the 5th dimension, they are talking about strings that reside on the fifth dimension vibrating.
     
  6. Mar 25, 2004 #5
    I may be slow and i still dont understand these higher dimensions however i would still like to know the point of these higher dimensions. So far I haven't found out their names or what they actually are. Could someone please enlighten me?
     
  7. Mar 25, 2004 #6

    phy

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    wow, you took the words from straight out of my mouth. someone enlighten me too.
     
  8. Mar 26, 2004 #7
    As far as I understand it, these extra higher dimensions are, according to string theory, occupied by strings. Picking up the example of a long, thin tube - for you it may seem one-dimensional, but what if you were really really tiny, so tiny, that you could also move around the tube's perimeter? Strings are really that tiny (a lot tinier than a single particle), so they can move and vibrate in these extra dimensions which are too small for you to see. I don't think they actually have names though, but then neither do the known 4 dimensions of spacetime (commonly the 3 visible spatial dimensions are refered to as height, length and width, but can you really say which one is which?).
     
  9. Mar 26, 2004 #8
    Extra Dimensions


    http://www.geocities.com/shanisonnagel/10dimensions.bmp

    Its a quick picture, along with time.

    But certainly one would have to understand the difference between euclidean and non-euclidean?

    What extra dimensions, you probably think, having just read the title. We know very well that the world around us is three-dimensional. We know East from West, North from South, up from down – what extra dimensions could there possibly be if we never see them?

    Well, it turns out that we do not really know yet how many dimensions our world has. All that our current observations tell us is that the world around us is at least 3+1-dimensional. (The fourth dimension is time. While time is very different from the familiar spatial dimensions, Lorentz and Einstein showed at the beginning of the 20th century that space and time are intrinsically related.) The idea of additional spatial dimensions comes from string theory, the only self-consistent quantum theory of gravity so far. It turns out that for a consistent description of gravity, one needs more than 3+1 dimensions, and the world around us could have up to 11 spatial dimensions!


    http://wc0.worldcrossing.com/WebX?14@31.30JtbJJEMqB.0@.1dde9178/3

    Again without filling this forum full of the information I have gathered such links are important to help illustrate the question here on dimension. These links help to further elucidate, and I hope to further concretize this information here in this forum.

    http://www.tech.port.ac.uk/staffweb/seahras/images/Kaluza.jpeg

    In 1919, Kaluza sent Albert Einstein a preprint --- later published in 1921 --- that considered the extension of general relativity to five dimensions. He assumed that the 5-dimensional field equations were simply the higher-dimensional version of the vacuum Einstein equation, and that all the metric components were independent of the fifth coordinate. The later assumption came to be known as the cylinder condition...

    http://www.tech.port.ac.uk/staffweb/seahras/neat_physics/extra_dimensions/gravity_and_EM.htm

    Kaluza-Klein theory has been enjoying a revival thanks to
    string/M-theory, where adding more spatial dimensions to the metric
    promises to yield all the known interactions. This is in direct
    analogy with the original K-K theory, where the addition of a fifth
    dimension was shown to yield both gravitation and EM. Also in line
    with the original theory is the notion that the extra dimensions must
    be "compactified" (very small) because we do not "see" them.


    http://www.lns.cornell.edu/spr/2001-11/msg0036758.html
     
    Last edited: Mar 26, 2004
  10. Mar 26, 2004 #9
    http://www.geocities.com/shanisonnagel/10dimensions.bmp

    Now just take one of these directions, and you realize that the one dimension as a string, moves our thinking to hyperdimensional thinking?

    That direction as a cylinder, is expansive, but at the same time recognizes....


    http://physicsweb.org/objects/world/13/11/9/pw1311091.gif

    Inspired by this idea, Kaluza and Klein proposed including the U(1) symmetry of electromagnetism into this geometric scheme by adding a fourth spatial dimension, giving a total of five. The 5-D space-time begins with the full 5-D Lorentz symmetry. However, if the extra dimension is curled up on itself, or "compactified", part of the symmetry is lost. What remains is precisely the 4-D Lorentz symmetry of general relativity and the U(1) gauge symmetry of electromagnetism. In this picture, the "internal space" of electromagnetism is actually a real extra dimension that is curled up, and the photon is really a component of the higher-dimensional graviton (see figure 1).

    http://physicsweb.org/article/world/13/11/9#pw1311091

    You have to understand that U(1)is a photon?

    I am open to corrections
     
  11. Mar 26, 2004 #10

    selfAdjoint

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    Sol,
    You have to understand that U(1)is a photon

    U(1) is a group. It's actually the group you get be rotating a circle through angles. The angles of rotation represent the phases of the EM radiation (or photon, if you prefer).

    Think of a sine wave along the x-axis, and somewhere you mark a zero and put in the y-axis. Now the sine curve repeats itself every length of [tex]2\pi [/tex] along the x-axis, because it's the stretched out equivalent of going around a circle where the circumference is [tex]2\pi [/tex] times the radius. So where the y-axis cuts in corresponds to some angle or other, which equals some group operation from U(1) or other. This is the phase angle.

    Now it's important that we can't detect this phase angle! Or what's the same thing, Nature doesn't give us a fixed zero to measure the sine curve of EM from, it's just an arbitrary convention. So the theory of EM is the same whatever phase angle you pick, or in other words, the operations from the group U(1) don't affect the physics. This is GAUGE INVARIANCE, the big noise in physical principles of the last 50 years. And U(1) is the gauge group of electromagnetism.
     
  12. Mar 26, 2004 #11
    I saw this as I was reading your post:

    http://wikibooks.org/upload/e/e2/Emwave.png

    If you were to look at the end of this wave, and imagine a circle then we would see what you were saying?

    Can you help bring clarity to this.

    http://physicsweb.org/objects/world/13/11/9/pw1311091.gif

    (a) Compactifying a 3-D universe with two space dimensions and one time dimension. This is a simplification of the 5-D space*time considered by Theodor Kaluza and Oskar Klein. (b) The Lorentz symmetry of the large dimension is broken by the compactification and all that remains is 2-D space plus the U(1) symmetry represented by the arrow. (c) On large scales we see only a 2-D universe (one space plus one time dimension) with the "internal" U(1) symmetry of electromagnetism.

    http://physicsweb.org/box/world/13/11/9/pw1311091


    Since the theory was considered to be a wild speculation, it was never taught in graduate school; so young physicists are left to discover it quite by accident in their casual readings. This alternative theory gave the simplest explanation of light; that it was really a vibration of the fifth dimension, or what used to be called the fourth dimension by the mystics. If light could travel through a vacuum, it was because the vacuum itself was vibrating, because the “vacuum” really existed in four dimensions of space and one of time...

    Hyperspace, by Michio Kaku Pg 9
     
    Last edited: Mar 26, 2004
  13. Mar 26, 2004 #12
    yahhhhh.....abstract algebra and non-euclidian geometry all roled into one!!!

    my head is hurting :-p
     
  14. Mar 26, 2004 #13

    selfAdjoint

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    Yes. In that diagram focus on the red arrows. Or the blue ones, but the red ones are easier to see. The length of each red arrow is actually the sine of an angle (this is a sine curve,after all). To see this imagine that you have a circle drawn, with a horizontal diameter. Take each red arrow and fit it into the circle perpendicular to the x-axis so its tail sits on the diameter and its point touches the circle. Now if you measure the arc of the circle from where the diameter hits it to where the point of the arrow is, that arc length, divided by the radius of the circle, is an angle whose measure is the same as the x value on the sine curve where you took the arrow from in the first place. And the length of the arrow, divided by that radius, is (by definition) the sine of that angle.

    Now I did that assuming the zero was where they have the curves starting, and they cross the x-axis there. But the point of U(1) is that you could start measuring at any point along the x-axis.

    I'm going to leave the discussion of the Kalusza Klein geometry and compactification till another time, if you don't mind.
     
  15. Mar 27, 2004 #14
    The Standard Model and Superstringtheory(U(1)*SU(2)*SU(3)

    That's fine. I appreciate the time given.

    There is no doubt that the geometrical basis must arise from this discussion at some point.

    Is there a generalized version, you can give of the standard model arising from the brane?


    http://www.geocities.com/shanisonnagel/The_Standard_Model_and_Superstring_Theory.html.pdf

    This is exchange between Paul and myself under the title of Tipping Light Cones.

    His interest in Warp Drives with brane scenarios is really interesting. Not many are engaging from what I have understood in his group.

    I needed to focus in on the departure point so iIwill show this post in part. here.



    Some theorists propose that our Universe exists as a slice through multidimensional space. Could this 'brane-world' concept unify gravity with nature's other fundamental forces?
    Brane New World, by Roland Pease

    http://wc0.worldcrossing.com/WebX?14@33.HtOpblQDN1e.14@.1dde934e/114


    and in Pauls response:

    Since the second principle of general relativity tells us that particles move along geodesics, we should interpret the gravitational potential as somehow effecting the geodesics. But the most fundamental determinant of geodesics is the underlying metric g. Thus we will generalize this potential to g. In other words, Einstein replaced a mysterious "force" by a purely geometric quantity. Put another way, gravity is nothing but a distortion of the local geometry in space-time.

    Brane World models only carry this unique topology solution a bit further returning in part, though often modified in present format, to Klien's solution to the unification of gravity to electromagnetism through an additional dimensional set. The beauty of this path as we should rightly call it is that it is a natural progression of Einstein's dream of a pure geometric explination for everything we see around us in nature.


    http://wc0.worldcrossing.com/WebX?14@33.HtOpblQDN1e.15@.1dde934e/117

    The Starting Point

    GAB=M-3*TAB

    This is a very significant explaination for me to understand how we might move into the departure of what has been understood on the brane, and where we see the beginning of the Bulk.

    Of course we are relating the perspective of gravitational production, with a fifth dimensionl perspective that many do not understand. The graviton is free to roam here, and is a defintion of a force carrier?

    That beginning point is extremely important to grasp and why I bring it up, as I too need help here to define Einsteins equations,* in the fifth dimension.

    Would you not agree that the time spent here might be quite fruitful, to moving deeper into the understanding of what is happening in the bulk, and what that graviton represents?



    Reference: http://home.fnal.gov/~rocky/academic_4.pdf
     
    Last edited: Mar 27, 2004
  16. Mar 27, 2004 #15

    selfAdjoint

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    Is there a generalized version, you can give of the standard model arising from the brane?

    I am afraid I am not up on this branch of string theory. I'll see what I can find out. Meanwhile, maybe someone else can explain this?
     
  17. Mar 27, 2004 #16

    selfAdjoint

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    Sol, while I was looking for good papers on branes and the Standard Model (I found one!), I also found this wonderful Visual QCD site . I don't know if you've seen it before, but it might be a candidate for a link from your website.
     
  18. Mar 28, 2004 #17
    Did Picasso Know About Einstein

    This is a fine exchange and I appreciate it. The Visualizations are extremely important for teaching and comprehension. Why I named my site M Theory Visionists. By accumulating all this information the views of our imagination become extremely important. I should say here that the imagination should be grounded in math, and as the math changes so does the vision. It's accumulative

    I have a link for you that you might be interested in.

    http://physicsweb.org/objects/world/thumb/15/11/8/pwa&s2_11-02.jpg

    Miller has since moved away from conventional history of science, having become interested in visual imagery through reading the German-language papers of Einstein, Heisenberg and Schrödinger - "people who were concerned with visualization and visualizability". Philosophy was an integral part of the German school system in the early 1900s, Miller explains, and German school pupils were thoroughly trained in the philosophy of Immanuel Kant.

    http://physicsweb.org/article/world/15/11/8
     
    Last edited: Mar 28, 2004
  19. Mar 28, 2004 #18

    selfAdjoint

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    Boy is that link ever interesting to me! I have long been interested in the history of ideas, and the many breakthroughs right after 1900 are indeed startling. Going beyond relativity and cubism we have also Schoenberg's atonalism and Lenin's Bolshevism as breakthroughs into "not your father's future".

    But the idea of a common source for Picasso and Einstein had never ocurred to me. And Poincare, of all people! Who says Mathematicians can't influence history!

    Another thought. Historians of the future are going to have a hard time doing what Miller has done: demonstrating a source connection by identifying a common individual (the Poincare fan in Picasso's circle). With the web, the range of influence is incalculable. Any individual in the world today could bear an idea to any other individual through the web, and leave no detectable source.
     
  20. Mar 28, 2004 #19
    Susskind

    Self Adjoint,


    Understanding the history is important.

    Seeing Brian Greene's show on Nova was a good summation for the lay person, and being involve with you guys in the string forum was a good opportunity for me. One of the things that I took from Brian Greene's show was the visualization value I found in Susskinds work.

    How many mathemticians can actually see what it is they are doing with their equations? I took it for granted, that they all do? What is your thought here?


    At that time I was a very young professor in New York, and I was not an elementary particle physicist. I tended to work on things like quantum optics and other things, just whatever I happened to be interested in. A fellow by the name of Hector Rubinstein came to visit me and my friend, Yakir Aharonov, and he was wildly excited. He said, "The whole thing is done! We've figured out everything!"

    I said, "What are you talking about, Hector?"

    And jumping up and down like a maniac, he finally wrote this formula on the blackboard.

    I looked at the formula and I said, "Gee, this thing is not so complicated. If that's all there is to it I can figure out what this is. I don't have to worry about all the particle physics that everybody had ever done in the past. I can just say what this formula is in nice, little, simple mathematics."

    I worked on it for a long time, fiddled around with it, and began to realize that it was describing what happens when two little loops of string come together, join, oscillate a little bit, and then go flying off. That's a physics problem that you can solve. You can solve exactly for the probabilities for different things to happen, and they exactly match what Veneziano had written down. This was incredibly exciting.

    I felt, here I was, unique in the world, the only person to know this in the whole wide world! Of course, that lasted for two days. I then found that Yoichiro Nambu, a physicist at Chicago, had exactly the same idea, and that we had more or less by accident come on exactly the same idea on practically the same day. There was no string theory at that time. In fact, I didn't call them strings—I called them rubber bands.


    http://www.edge.org/3rd_culture/susskind03/susskind_index.html
     
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