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What would be the fifth dimensional property of a Tesseract?

  1. Mar 18, 2003 #1
    I understand the Tesseract, but What would be the fifth dimensional property? Does it have to do with tunneling properties of particles? And how would time act in the fourth dimension?

    I do understand a little about physics, but in consideration that I know very little, please IN LAMENS TERMS!
  2. jcsd
  3. Mar 18, 2003 #2
    I don't quite understand the question. Are you asking about the properties of the 4th spacial dimension? Or are you talking about the T dimension (which is commonly believed to be the "fourth" dimension).
  4. Mar 18, 2003 #3
    I mean to ask what the physical properties of the 5th spacial dimension.
    Like I said I understand the tesseract. Which is the 4th dimensonal base shape.

    The other question I am asking is if time would act differently in the 4th spacial dimmension or would it have the same one directional properties?
  5. Mar 18, 2003 #4
    1) I'm not really sure what the properties of the 5th spacial dimension would be like. I know that the existence of such higher dimensions helps physicists to return to Einstein's idea - that there are no "forces", but rather all that we percieve to be "forces", are just the results of curvatures in spacetime.

    2) I am of the opinion that any one point on the T dimension ("time") corresponds to all points on the spacial dimensions. This is obviously true of the 3 spacial dimensions that we're used to, and I believe that it is true of all of them.
  6. Mar 18, 2003 #5


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    The Kalusa-Klein theory put a compacted fifth dimension onto the four dimensional spacetime of general relativity, and with a simple Lagrangean on the five dimensional manifold thus created, was able to build a unified theory of gravity and electromagnetism (Maxwell's equations).

    This would be an answer to everybody's prayers if it weren't for the quantum. The KK theory is completely classical, and the quantum, whatever groundlings want to believe, is very real.

    Plus there are the other two forces, the strong and the weak, which are not accomodated in this theory.

    The idea of compact dimensions was borrowed from KK theory by the string theorists.
  7. Mar 18, 2003 #6
    String Theory (and other ten-dimensional theories) incorporate all of the forces. Kaluza-Klein theory - quite simply - didn't have enough dimensions.
  8. Mar 18, 2003 #7
    The quantum problem?

    selfAdjoint, you mentioned that if it weren't for the quantum, Kaluz-Klein theories would be more acceptable. I don't understand this. Could you please explain why the quantum theory contradicts the higher-dimensional theories?
  9. Mar 18, 2003 #8
    I thought that if you wanted to understand higher dimensional objects you had to interprete the math,not visualize it,be cause the math shows you what it is because you cant precieve it with the minds eye
  10. Mar 18, 2003 #9

    Tom Mattson

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    Re: The quantum problem?

    The problem is not the higher-dimensions, the problem is that Kaluza-Klein is not quantum mechanical.

    It is basically a single classical field theory from which both GR and EM drop out. There are two reasons why this is not The Answer, and both reasons have to do with the quantum world:

    1. The fields are not quantized.

    We know for certain that the EM field is really a granular entity whose quanta are called photons. Kaluza-Klein does not share this feature. The EM that emerges from it is Maxwell's EM.

    2. The weak and strong interactions are not included.

    Moreover, they cannot be included, because there is no classical potential for gluons and W/Z bosons. Only quantum gauge field theories will do.
  11. Mar 19, 2003 #10
    to answer the question of the properties of the 5th dimension:
    i read it was another spatial dimension but of the same form as our normal 3, ie very long, which is SO not the proper way to describe it but i forget the terminology; like the rest of the 15 or so theorised dimensions would have to be curled up so small they wouldn't affect us. the 5th dimension would be big enough, however the only forve to interact with this dimension would be gravity.

    this is a great way to explain the fact gravity loses so much 'strength' after such short distances; it leaks away into this 5t dimension!
  12. Mar 19, 2003 #11


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    regular poligons and other small dimensional effects.

    As you mention the Tesseract, here is an insteresting property of dimension four and higher: the only regular poli"hedra" is the generalized cube. IE the Tesseract in four dimensions, and so on.

    It is interesting because we have infinite regular poligons in dimension two, five regular poli"gons" in dimension three, and only one in dimension four, five, six, etc... I have been told, at least.

    Other funny property of low dimensions relates to the permutation group. Fof n>4, the Symmetric Group S_n of permutations of n elements is not a solvable group (roughly, this property says that it can not be decomposed in interesting ways). This implies, for instance, that there are no algebraic formulae for a generic polinomial of degree 5, as it has five roots to play with and the solution depends on playing with permutations of the products.

    Other source of low dimensional effects comes from renormalization group. Via power-counting in the Gell-Mann RG, or scaling in the Kadanoff & Wilson approach, the dimensions D<= 4 are usually singled out as having particular properties, fixed points, etc. In some cases this can be an effect of the theories we are looking, but even so it is a remarkable thing.
  13. Mar 19, 2003 #12
    I am amazed at where my question has gone.
    Now may I add (or to point out) one of my questions.

    "Does the 5TH spacial dimension have anything to do with the tunneling properties of high-energy particles?"

    Now if I may add a thought?
    Mayby by taking a tesseract and visualizing the movement, then taking it one step further into the 5TH spacial dimension I began to visualized the consepts of multiple planes of existence in one spacetime continum.

    As I tried to describe the properties I thought of 'in font of' and 'behind'.
    THis was the only wy I could think of for describing what consepts I visualized. The consept might help somebody somewhere. I hope.
  14. Mar 19, 2003 #13
    "Does the 5TH spacial dimension have anything to do with the tunneling properties of high-energy particles?"
    No... not if you mean *observed* tunneling properties.

    Touching on S_n, S_6 is also a very weird case: it is the only S_n that has an outer automorphism, and also the only S_n not isomorphic to its automorphism group. :)
  15. Mar 20, 2003 #14
    Could somebody please explain to me what he just said?
    As in: 'S_n, S_6'; and 'automorphism and isomorphism'
  16. Mar 20, 2003 #15
    Highly unpredictable algebra...(and complex)...
    It's something you'll learn in school probably next year...
    These Ss...are groups of "transformations" represented by matrices...S means that the sum of the color "charges" is 0...
    Damn complicated...
  17. Mar 20, 2003 #16
    Re: Re: The quantum problem?

    So Einstein was wrong? Forces are not just curvature?

    It appears that String Theory unites the Quantum view of "forces" with Einstein's view. String theory states that a certain vibration of the string alters spacetime in a certain way, so that - while the force is still caused by a particle/wave - the percieved force is still the result of a curvature (on one of the dimensions).
  18. Mar 20, 2003 #17


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    Avempt, S_n is standard for the group of permutations of n elements. So for instance S3 is the group of six posible exchange operations (123)-----> (123) (213) (132) (321) (231) (312). It
    must no be confused with the label "S" in a Lie Group, which indicates "Special" in the sense of being a matrix group with determinant always equal to 1.

    The S_n groups are also seen as coming from the A_n groups, the groups of even permutations of n elements.

    In any case, they could be relevant in the thread because permutations are important when defining a volume form or any other differential form. For instance, the external product is sensible to permutations: dx ^ dy = - dy ^ dx.

    As for the weirdness of S6, I was not aware of it. Damgo is claiming that it is possible to map S6 onto itself with a transformation which is not an element of S6, and that it is the only permutation group having this property. I had never heard of this.
  19. Mar 21, 2003 #18
    Offering some help

    I have a theory that revolves around there being four dimensions, and having time as a state of being as opposed to a dimension, and I thoroughly believe that time is NOT a dimension. If you want to check out my theory, it is in the theory development area of this site.
  20. Mar 22, 2003 #19
    Yup, basically. The proof for n>6 is IIRC not particularly short and pretty, but you can find it in the first couple chapters of Dummitt&Foote. The counterexample for n=6 maps something is an outer isomorphism that takes the two-cycles (a b) to triads (c d) (e f) (g h)... you can find it spelled out online I think.
  21. Mar 24, 2003 #20
    This is a grossly overly complicated subject, get down to the simplicity of reality.
    Every measurement of distance we make is made using the EM spectrum. We cannot measure inside a SF body and any attempt to do so results in pushing the SF body to one side. We can of course measure from side to side using the EM spectrum but we cannot measure inside. Exactly the same arguement applies to gravitons. SF particles are to strong and gravitons are to weak both are pushed aside by our EM instruments. The same arguements would apply if we were made of SF or gravitons.
    Each force has its own Length, Breadth and Height dimensions that do not overlap, giving a total of nine dimensions so far. To this must be added Time, the dimension of history; and infinity, the dimension of the vaccum frame.Time and the vacuum frame are common to all force fields. This gives a total of eleven dimensions all of which fit into Quantum theory and Relativity as they stand without any need for strings, white or black holes, or other magical terms.
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