#REDIRECT M-theory
M-theory is a solution proposed for the unknown theory of everything which would combine all five superstring theory and 11-dimensional supergravity together. According to Dr. Edward Witten, who proposed the theory, mathematical tools which have yet to be invented are needed in order to fully understand it. == M-theory's relation to superstrings and supergravity == M-Theory in various geometric backgrounds is associated with the different superstring theories (in different geometric backgrounds), and these limits are related to each other by the principle of dualism. Two physical theories are dual to each other if they have identical physics after a certain mathematical transformation. Type IIA string theory and type IIB string theory are related by T-duality, as are the two heterotic string theories. type I string and Heterotic SO(32) are related by the S-duality. Type IIB is also S-dual with itself. * The type II theories have two supersymmetries in the ten-dimensional sense, the rest just one. * The type I theory is special in that it is based on unoriented open and closed strings. * The other four are based on oriented closed strings. * The IIA theory is special because it is non-chiral (parity conserving). * The other four are chiral (parity violating). In each of these cases there is an 11th dimension that becomes large at strong coupling. In the IIA case the 11th dimension is a circle. In the HE case it is a line interval, which makes eleven-dimensional spacetime display two ten-dimensional boundaries. The strong coupling limit of either theory produces an 11-dimensional space-time. This eleven-dimensional description of the underlying theory is called "M- theory". A string's space-time history can be viewed mathematically by functions like
: that describe how the string's two-dimensional sheet coordinates map into space-time . One interpretation of this result is that the 11th dimension was always present but invisible because the radius of the 11th dimension is proportional to the string coupling constant and the traditional perturbative string theory presumes it to be infinitesimal. Another interpretation is that dimension is not a fundamental concept of M-theory at all. == Characteristics of M-theory == M-theory contains much more than just strings. It contains both higher and lower dimensional objects. These objects are called p-branes where p denotes their spatial dimensionality (thus, 1-brane for a string and 2-brane for a membrane). Higher dimensional objects were always present in superstring theory but could never be studied before the Second Superstring Revolution because of their perturbation theory (quantum mechanics) nature. Insights into non-perturbative properties of p-branes stem from a special class of p-branes called Dirichlet p-branes (Dp-branes). This name results from the Dirichlet boundary condition assigned to the ends of open strings in type I superstrings. Open strings of the type I theory can have endpoints which satisfy the Neumann boundary condition. Under this condition, the endpoints of strings are free to move about but no momentum can flow into or out of the end of a string. The T duality infers the existence of open strings with positions fixed in the dimensions that are T-transformed. Generally, in type II theories, we can imagine open strings with specific positions for the end-points in some of the dimensions. This lends an inference that they must end on a preferred surface. Superficially, this notion seems to break the relativistic invariance of the theory, possibly leading to a paradox. The resolution of this paradox is that strings end on a p-dimensional dynamic object, the Dp-brane. The importance of D-branes stems from the fact that they make it possible to study the excitations of the brane using the renormalizable 2D quantum field theory of the open string instead of the non-renormalizable world-volume theory of the D-brane itself. In this way it becomes possible to compute non-perturbative phenomena using perturbative methods. Many of the previously identified p-branes are D-branes ! Others are related to D-branes by duality symmetries, so that they can also be brought under mathematical control. D-branes have found many useful applications, the most remarkable being the study of black holes. Strominger and Vafa have shown that D-brane techniques can be used to count the quantum microstates associated to classical black hole configurations. The simplest case first explored was static extremal charged black holes in five dimensions. Strominger and Vafa proved for large values of the charges the entropy , where is equal to the number of quantum states that system can be in, agrees with the Black hole thermodynamics prediction (1/4 the area of the event horizon). This result has been generalized to black holes in 4D as well as to ones that are near extremal (and radiate correctly) or rotating, a remarkable advance. It has not yet been proven that there is any problematic breakdown of quantum mechanics due to black holes. Matrix theory (physics) is a promising formulation of M-theory. ==Further reading== * Duff, Michael J., ''[http://feynman.physics.lsa.umich.edu/~mduff/talks/1998%20-%20The%20Theory%20Formerly%20Known%20as%20Strings.pdf The Theory Formerly Known as Strings]'', Scientific American, February 1998, online at University of Michigan. * Gribbin, John. ''The Search for Superstrings, Symmetry, and the Theory of Everything'', ISBN 0316329754, Little, Brown & Company, 1ST BACK B Edition, August 2000, specifically pages 177-180. * Greene, Brian. ''The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory'', ISBN 0393046885, W.W. Norton & Company, February 1999 * Taubes, Gary. "String theorists find a Rosetta Stone." Science, v. 285, July 23, 1999: 512-515, 517. Q1.S35 ==External links== *[http://www.damtp.cam.ac.uk/user/gr/public/qg_ss.html M-Theory-Cambridge] *[http://www.theory.caltech.edu/people/jhs/strings/str154.html M-Theory-Caltech] *[http://www.pbs.org/wgbh/nova/elegant/program.html The Elegant Universe] Theoretical physics String theory simple:M-theory
April 27, 2004 Was bored, rewrote the whole thing. Unfortunately, I have a bad feeling the thing's completely incomprehensible now. Still, the simplified page is out there. It probably needs a lot of linking now. Feel free to change it back if it's hopelessly obscure. April 27, a bit later at night... Ugh. Changed it back. It needed too much work to be comprehensible, I think. If anyone else wants to grab from [http://en.wikipedia.org/w/wiki.phtml?title=M-theory&oldid=3357041 it] and make it better, they're more than welcome to it. ------- Note: add a mention to Vafa's F-theory with 12 spacetime dimensions (2 time, 10 space). Note 2: explain T-duality (between R and 1/R) and how it relates to energy; that there are two distinct measures for energy which give rise to different measures for dimensional size. == Please merge == This article is still poorly written (see my comments below); however, the article at M-theory (simplified explanation) is actually good. I suggest that this "simplified explanation" replace the current article. What little information is present in the current article and not in the other article could possibly be merged in. Stuff like the "Strominger and Vafa D-brane quantum microstates" Star Trek technobabble could possibly be merged or, even better, made nice like in the "simplified" article (really, not much simplified, just clearer.) If it stays as is, I might have a "moment of lucidity" and move the current article to "M-theory (obfuscated)" and move the simplified one to the current article. User:Loisel 04:31, 18 Apr 2004 (UTC) == 11d vs 12d == On the article it talks about 11-dimensional spacetime. Shouldn't this be a 12-dimensional spacetime with an eleven dimensional space? I don't know very much about M-theory, but I'm pretty sure that in string theory and Kaluza-Klein models in general, you need an even dimensional spacetime in order to allow left-handed and right-handed spins. Read this article. http://www.2think.org/t000104284.shtml . I'm not certain this helps. Will review my notes again. Remember I don't fully understand this, and to explain it is worse ! User:BF Hmm, that says 11-D spacetime, and some further searching confirms it. How very odd that that permits chiral asymmetry, but maybe some property of the 'branes allows it. Hmm. Sorry for the unwarranted questioning, and feel free to delete this conversation. ''There's no simple answer since the superstring theories are constructed on top of the bosonic string theory, which is 26 dimensional. So for all I know, chirality is related to dimensionality. I am curious where you got the idea though. -- ark'' == yet to produce testable predictions == "''yet to produce testable predictions" can only come from a qualified physicist who is working in the field.. sorry''" Boggle. WTF does that mean? Are you pulling rank? -- User:GWO Of course not. I am explaining that whoever added that part must be researching M-theory, unless they are quoting someone who is. once again, that deletion was made because the THEORY has already been scrutinized by fellows of Witten, and stands. Someone chooses to assume or fantasize they are part of the M-theory group of physicists, outside wiki. That tiny addition to the main page was unsubstantiated presumption on someone's part. Moreover, I have read some recent journal abstracts(some Japanese scientists) which use M-theory to expand into new areas of superstring, meaning it works. I found a site or paper (don't have it at hand) which had that section of the page (now moved/deleted) almost word for word. So I believe the person who wrote it was quoting a physicist, and not presuming to be a physicist. -- ark ==String theory is different.== String theory is different. Some people complain that it does not predict - but it in fact predicts a lot. To include gravity consistently to a quantum theory, we were forced to go to 10 dimensions, to discover supersymmetry, to allow topology change etc. Some people criticize string theory that it predicts nothing new, some people complain the string theory involves/predicts too much new stuff (excited strings, higher dimensions, SUSY etc.). Some critics happily belong to both categories and they do not realize how inconsistent their position is... ;-) (http://www.lns.cornell.edu/spr/2001-06/msg0033389.html) :Nice job cleaning up the article I originally wrote. The LD Learning Lab at Caltech does help a lot! I noticed some formulas painstakingly added with symbol fonts were removed by someone. This is very annoying to see on a science page. Not sure if wiki supports pdf yet, so restore the formulas, or I will. User:BF 22:55 Dec 12, 2002 (UTC) == Not well written == I'm a mathematician and I've written a number of articles about analysis, and sometimes people complain that my articles are too specialized and don't make any sense. (For instance, see Lebesgue integration or Riemann surface.) However, I'm almost certain you guys are doing a poorer job than I am. There are a zillion and a half technical terms that aren't defined at all. In fact, almost every word of every sentence is some undefined techincal term. Here's a specific example: ''The T duality infers the existence of open strings with positions fixed in the dimensions that are T-transformed.'' T duality? T transform? What does it mean to have open strings with positions fixed in whatever dimensions? Do you mean open as in f:[0,1]->X with f(0) \ne f(1) or as in f:(0,1)->X? Articles such as Riemann integral are long, not because the topic is complex, but because a more terse discussion missing numerous definitions is inappropriate, especially for an encyclopedia. I think a lot could be done to disambiguate, clarify and otherwise make this very interesting article even better. User:Loisel 00:06 Jan 30, 2003 (UTC) :I agree absolutely. Sentences like ''The theory requires mathematical tools which have yet to be invented in order to be fully understood'' make me instantly assume that the following paragraphs are not going to be too enlightening. If nobody understands the theory because we don't have the mathematical tools - well, what kind of theory is ''that''? User:Chas zzz brown 03:40 Feb 1, 2003 (UTC) ::Right, that sentence is not particularly good. Some fields of physics haven't been completely axiomatized yet, and sometimes many mathematical details are unproven (I believe this was the case for much of Witten's work, which was otherwise excellent and warranted a Fields medal.) So I would understand if some of the theory hasn't been worked out to a mathematician's satisfaction. However, with the article as it is now, much more profound changes are needed than an axiomatization. Right now, the article is unreadable to non-experts and probably useless to experts. == Extra Dimentions. == I read with interest the theory that extra spatial dimentions exist. However, this view is at variance with one expressed by Professor Stephen Hawking, who remarks that " if there were more than three spatial dimentions, the orbits of planets around the sun or electrons around a nucleus would be unstable and they would tend to spiral inward." Derek R Crawford. : [http://en.wikipedia.org/wiki/Talk:Why_10_dimensions#Extra_Dimentions. See an answer here]
See other meanings of words starting from letter:
Words begining with M-theory:
M-Theory
M-theory
M-theory
M-theory_(simplified)
M-theory_(simplified)
M-theory_(simplified_explanation)
M-theory_(simplified_explanation)
M-theory_Simplified
M-theory_Simplified
M-theory_simplified
M-theory_simplified
M-Theory
#REDIRECT M-theory
M-theory
M-theory is a solution proposed for the unknown theory of everything which would combine all five superstring theory and 11-dimensional supergravity together. According to Dr. Edward Witten, who proposed the theory, mathematical tools which have yet to be invented are needed in order to fully understand it. == M-theory's relation to superstrings and supergravity == M-Theory in various geometric backgrounds is associated with the different superstring theories (in different geometric backgrounds), and these limits are related to each other by the principle of dualism. Two physical theories are dual to each other if they have identical physics after a certain mathematical transformation. Type IIA string theory and type IIB string theory are related by T-duality, as are the two heterotic string theories. type I string and Heterotic SO(32) are related by the S-duality. Type IIB is also S-dual with itself. * The type II theories have two supersymmetries in the ten-dimensional sense, the rest just one. * The type I theory is special in that it is based on unoriented open and closed strings. * The other four are based on oriented closed strings. * The IIA theory is special because it is non-chiral (parity conserving). * The other four are chiral (parity violating). In each of these cases there is an 11th dimension that becomes large at strong coupling. In the IIA case the 11th dimension is a circle. In the HE case it is a line interval, which makes eleven-dimensional spacetime display two ten-dimensional boundaries. The strong coupling limit of either theory produces an 11-dimensional space-time. This eleven-dimensional description of the underlying theory is called "M- theory". A string's space-time history can be viewed mathematically by functions like
: that describe how the string's two-dimensional sheet coordinates map into space-time . One interpretation of this result is that the 11th dimension was always present but invisible because the radius of the 11th dimension is proportional to the string coupling constant and the traditional perturbative string theory presumes it to be infinitesimal. Another interpretation is that dimension is not a fundamental concept of M-theory at all. == Characteristics of M-theory == M-theory contains much more than just strings. It contains both higher and lower dimensional objects. These objects are called p-branes where p denotes their spatial dimensionality (thus, 1-brane for a string and 2-brane for a membrane). Higher dimensional objects were always present in superstring theory but could never be studied before the Second Superstring Revolution because of their perturbation theory (quantum mechanics) nature. Insights into non-perturbative properties of p-branes stem from a special class of p-branes called Dirichlet p-branes (Dp-branes). This name results from the Dirichlet boundary condition assigned to the ends of open strings in type I superstrings. Open strings of the type I theory can have endpoints which satisfy the Neumann boundary condition. Under this condition, the endpoints of strings are free to move about but no momentum can flow into or out of the end of a string. The T duality infers the existence of open strings with positions fixed in the dimensions that are T-transformed. Generally, in type II theories, we can imagine open strings with specific positions for the end-points in some of the dimensions. This lends an inference that they must end on a preferred surface. Superficially, this notion seems to break the relativistic invariance of the theory, possibly leading to a paradox. The resolution of this paradox is that strings end on a p-dimensional dynamic object, the Dp-brane. The importance of D-branes stems from the fact that they make it possible to study the excitations of the brane using the renormalizable 2D quantum field theory of the open string instead of the non-renormalizable world-volume theory of the D-brane itself. In this way it becomes possible to compute non-perturbative phenomena using perturbative methods. Many of the previously identified p-branes are D-branes ! Others are related to D-branes by duality symmetries, so that they can also be brought under mathematical control. D-branes have found many useful applications, the most remarkable being the study of black holes. Strominger and Vafa have shown that D-brane techniques can be used to count the quantum microstates associated to classical black hole configurations. The simplest case first explored was static extremal charged black holes in five dimensions. Strominger and Vafa proved for large values of the charges the entropy , where is equal to the number of quantum states that system can be in, agrees with the Black hole thermodynamics prediction (1/4 the area of the event horizon). This result has been generalized to black holes in 4D as well as to ones that are near extremal (and radiate correctly) or rotating, a remarkable advance. It has not yet been proven that there is any problematic breakdown of quantum mechanics due to black holes. Matrix theory (physics) is a promising formulation of M-theory. ==Further reading== * Duff, Michael J., ''[http://feynman.physics.lsa.umich.edu/~mduff/talks/1998%20-%20The%20Theory%20Formerly%20Known%20as%20Strings.pdf The Theory Formerly Known as Strings]'', Scientific American, February 1998, online at University of Michigan. * Gribbin, John. ''The Search for Superstrings, Symmetry, and the Theory of Everything'', ISBN 0316329754, Little, Brown & Company, 1ST BACK B Edition, August 2000, specifically pages 177-180. * Greene, Brian. ''The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory'', ISBN 0393046885, W.W. Norton & Company, February 1999 * Taubes, Gary. "String theorists find a Rosetta Stone." Science, v. 285, July 23, 1999: 512-515, 517. Q1.S35 ==External links== *[http://www.damtp.cam.ac.uk/user/gr/public/qg_ss.html M-Theory-Cambridge] *[http://www.theory.caltech.edu/people/jhs/strings/str154.html M-Theory-Caltech] *[http://www.pbs.org/wgbh/nova/elegant/program.html The Elegant Universe] Theoretical physics String theory simple:M-theory
M-theory
April 27, 2004 Was bored, rewrote the whole thing. Unfortunately, I have a bad feeling the thing's completely incomprehensible now. Still, the simplified page is out there. It probably needs a lot of linking now. Feel free to change it back if it's hopelessly obscure. April 27, a bit later at night... Ugh. Changed it back. It needed too much work to be comprehensible, I think. If anyone else wants to grab from [http://en.wikipedia.org/w/wiki.phtml?title=M-theory&oldid=3357041 it] and make it better, they're more than welcome to it. ------- Note: add a mention to Vafa's F-theory with 12 spacetime dimensions (2 time, 10 space). Note 2: explain T-duality (between R and 1/R) and how it relates to energy; that there are two distinct measures for energy which give rise to different measures for dimensional size. == Please merge == This article is still poorly written (see my comments below); however, the article at M-theory (simplified explanation) is actually good. I suggest that this "simplified explanation" replace the current article. What little information is present in the current article and not in the other article could possibly be merged in. Stuff like the "Strominger and Vafa D-brane quantum microstates" Star Trek technobabble could possibly be merged or, even better, made nice like in the "simplified" article (really, not much simplified, just clearer.) If it stays as is, I might have a "moment of lucidity" and move the current article to "M-theory (obfuscated)" and move the simplified one to the current article. User:Loisel 04:31, 18 Apr 2004 (UTC) == 11d vs 12d == On the article it talks about 11-dimensional spacetime. Shouldn't this be a 12-dimensional spacetime with an eleven dimensional space? I don't know very much about M-theory, but I'm pretty sure that in string theory and Kaluza-Klein models in general, you need an even dimensional spacetime in order to allow left-handed and right-handed spins. Read this article. http://www.2think.org/t000104284.shtml . I'm not certain this helps. Will review my notes again. Remember I don't fully understand this, and to explain it is worse ! User:BF Hmm, that says 11-D spacetime, and some further searching confirms it. How very odd that that permits chiral asymmetry, but maybe some property of the 'branes allows it. Hmm. Sorry for the unwarranted questioning, and feel free to delete this conversation. ''There's no simple answer since the superstring theories are constructed on top of the bosonic string theory, which is 26 dimensional. So for all I know, chirality is related to dimensionality. I am curious where you got the idea though. -- ark'' == yet to produce testable predictions == "''yet to produce testable predictions" can only come from a qualified physicist who is working in the field.. sorry''" Boggle. WTF does that mean? Are you pulling rank? -- User:GWO Of course not. I am explaining that whoever added that part must be researching M-theory, unless they are quoting someone who is. once again, that deletion was made because the THEORY has already been scrutinized by fellows of Witten, and stands. Someone chooses to assume or fantasize they are part of the M-theory group of physicists, outside wiki. That tiny addition to the main page was unsubstantiated presumption on someone's part. Moreover, I have read some recent journal abstracts(some Japanese scientists) which use M-theory to expand into new areas of superstring, meaning it works. I found a site or paper (don't have it at hand) which had that section of the page (now moved/deleted) almost word for word. So I believe the person who wrote it was quoting a physicist, and not presuming to be a physicist. -- ark ==String theory is different.== String theory is different. Some people complain that it does not predict - but it in fact predicts a lot. To include gravity consistently to a quantum theory, we were forced to go to 10 dimensions, to discover supersymmetry, to allow topology change etc. Some people criticize string theory that it predicts nothing new, some people complain the string theory involves/predicts too much new stuff (excited strings, higher dimensions, SUSY etc.). Some critics happily belong to both categories and they do not realize how inconsistent their position is... ;-) (http://www.lns.cornell.edu/spr/2001-06/msg0033389.html) :Nice job cleaning up the article I originally wrote. The LD Learning Lab at Caltech does help a lot! I noticed some formulas painstakingly added with symbol fonts were removed by someone. This is very annoying to see on a science page. Not sure if wiki supports pdf yet, so restore the formulas, or I will. User:BF 22:55 Dec 12, 2002 (UTC) == Not well written == I'm a mathematician and I've written a number of articles about analysis, and sometimes people complain that my articles are too specialized and don't make any sense. (For instance, see Lebesgue integration or Riemann surface.) However, I'm almost certain you guys are doing a poorer job than I am. There are a zillion and a half technical terms that aren't defined at all. In fact, almost every word of every sentence is some undefined techincal term. Here's a specific example: ''The T duality infers the existence of open strings with positions fixed in the dimensions that are T-transformed.'' T duality? T transform? What does it mean to have open strings with positions fixed in whatever dimensions? Do you mean open as in f:[0,1]->X with f(0) \ne f(1) or as in f:(0,1)->X? Articles such as Riemann integral are long, not because the topic is complex, but because a more terse discussion missing numerous definitions is inappropriate, especially for an encyclopedia. I think a lot could be done to disambiguate, clarify and otherwise make this very interesting article even better. User:Loisel 00:06 Jan 30, 2003 (UTC) :I agree absolutely. Sentences like ''The theory requires mathematical tools which have yet to be invented in order to be fully understood'' make me instantly assume that the following paragraphs are not going to be too enlightening. If nobody understands the theory because we don't have the mathematical tools - well, what kind of theory is ''that''? User:Chas zzz brown 03:40 Feb 1, 2003 (UTC) ::Right, that sentence is not particularly good. Some fields of physics haven't been completely axiomatized yet, and sometimes many mathematical details are unproven (I believe this was the case for much of Witten's work, which was otherwise excellent and warranted a Fields medal.) So I would understand if some of the theory hasn't been worked out to a mathematician's satisfaction. However, with the article as it is now, much more profound changes are needed than an axiomatization. Right now, the article is unreadable to non-experts and probably useless to experts. == Extra Dimentions. == I read with interest the theory that extra spatial dimentions exist. However, this view is at variance with one expressed by Professor Stephen Hawking, who remarks that " if there were more than three spatial dimentions, the orbits of planets around the sun or electrons around a nucleus would be unstable and they would tend to spiral inward." Derek R Crawford. : [http://en.wikipedia.org/wiki/Talk:Why_10_dimensions#Extra_Dimentions. See an answer here]
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MA | MB | MC | MD | ME | MF | MG | MH | MI | MJ | MK | ML | MN | MO | MP | MR | MS | MT | MU | MW | MX | MY | MZ |Words begining with M-theory:
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M-theory
M-theory
M-theory_(simplified)
M-theory_(simplified)
M-theory_(simplified_explanation)
M-theory_(simplified_explanation)
M-theory_Simplified
M-theory_Simplified
M-theory_simplified
M-theory_simplified
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