I know it has been taken seriously with string theory and other dimensions have been shown plausible through math. I was wondering where I can find specific writings on these things. a proof is even better. the only proof I have found so far has been on the famous "Poincaré Conjecture."
2007-12-21 07:51:05 · 5 answers · asked by sunscour 4 in Science & Mathematics ➔ Physics
A fun reading that tackled this subject is "Flat Land: A Romance of Many Dimensions" written by Edwin Abbott Abbott. Its a neat book that gets you thinking about dimensions greater than the ones we live in.
2007-12-21 07:54:39 · answer #1 · answered by Anonymous · 1⤊ 1⤋
If you are looking for proofs, you are in the wrong section. Physics is not math and the only accepted "proof" is an experiment.
So far nobody has found any experimental proof for anything string theory has ever predicted... and it has not really predicted that much.
We have to wait for LHC to produce first results in 2008 and 2009 before there can be anything much said about this. From what I have heard from people who are actually immersed in this theoretically, the expectation levels are rather low at this point. But then, nature knows how to surprise physicists!
On the other end of the spectrum the experiments in Washington could shed light on large compactified dimensions if they find deviations from Newtonian gravity at distances of 10um-100um. There seems to be little, if any effect in the 1mm range... which is where some people have expected to see something. That game is not quite over, but it is looking increasingly bleak. You will hear a scream go through the physics world is they find something. That would be a real game changer.
The Poincare conjecture is mostly important for mathematicians. It will not apply directly to any observed physics, although it might play a crucial role in the structure of potentially self-consistent field theories. I would not rule that out... but it is way too high for me to address.
2007-12-21 16:06:11 · answer #2 · answered by Anonymous · 0⤊ 1⤋
Since space is multidirectional, any point in space can be expressed as a mlutidirectional vector ,called Tensor.
If an event is expressed in terms of Radom variables ,then it can be represented as the integral of "n"space dimensions.
However , after all said and done it all boils down in reality as a space volume of 3 dimensions and time as an indicative quantity how fast a mass volume moves. In the same way no matter how many root solutions to a differential equation only a 2nd order solution predominates.
Einstein got the Ideas from The Henri Poincare conjecture for his Field equation of General relativity. The Field equation diferential equations represent solution on the basis of a space manifold. Hence it is possible to represent the Universe as abstract mathermatical volume of the Universe in terms of any arbitrary dimensions.
The last Fermat conjecture was such a case.
Hence there is a fine line between mathematics proofs and Sanity.
2007-12-21 16:13:22 · answer #3 · answered by goring 6 · 0⤊ 0⤋
In mathematics, no definition of dimension adequately captures the concept in all situations where we would like to make use of it. Consequently, mathematicians have devised numerous definitions of dimension for different types of spaces. All, however, are ultimately based on the concept of the dimension of Euclidean n-space E n. The point E 0 is 0-dimensional. The line E 1 is 1-dimensional. The plane E 2 is 2-dimensional. And in general E n is n-dimensional.
A tesseract is an example of a four-dimensional object. Whereas outside of mathematics the use of the term "dimension" is as in: "A tesseract has four dimensions," mathematicians usually express this as: "The tesseract has dimension 4," or: "The dimension of the tesseract is 4."
Historically, the notion of higher dimensions in mathematics was introduced by Bernhard Riemann, in his 1854 Habilitationsschrift, where he considered a point to be any n numbers , abstractly, without any geometric picture needed nor implied.
The rest of this section examines some of the more important mathematical definitions of dimension.
2007-12-22 02:34:31 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Why limit yourself to integer dimensions? You can look at Fractals, and realize that Hausdorff-Besicovitch dimension can be any value that is a real number.
E.g. the Sierpinski triangle has fractional dimension ln 3 / ln 2, or approximately 1.58
2007-12-21 16:05:06 · answer #5 · answered by Charles M 6 · 1⤊ 0⤋