# An Exceptionally Simple Theory of Everything **URL:** \ **Category:** Factual Questions\ **Created:** [November 16, 2007, 5:51am UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652 "2007-11-16T05:51:29Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [November 16, 2007, 11:04pm UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/21 "2007-11-16T23:04:30Z")
[QUOTE=jackdavinci] Surfer dude stuns physicists with theory of everything [/QUOTE] I was _so_ expecting a link to an Onion article with some some Spicoli-esque quotes about tasty waves and a cool buzz. ---
**Author:** ![Bytegeist](https://avatars.discourse-cdn.com/v4/letter/b/9dc877/32.png) [@Bytegeist](https://boards.straightdope.com/u/Bytegeist)\ **Post date:** [November 16, 2007, 11:22pm UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/22 "2007-11-16T23:22:16Z")
[QUOTE=ultrafilter] A group is a set G together with an operation \* that takes two elements of G and produces another one. There are a few properties that have to hold[ol][li]a \* (b \* c) = (a \* b) \* c[_]There is an element e in G such that for any element a, a \* e = e \* a = a.[_]For every element a in G, there is an element b such that **a \* b = b \* a = e**.[/ol]Note that we don’t require that **a \* b = b \* a** , although it’s always nice to work with groups where that does hold. [/li] [/QUOTE] Just to make sure I’m following along — the green **b** is not the same as the blue **b** , right? (The first one is specifically the inverse of **a** , but the second one is an arbitrary element.) ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [November 16, 2007, 11:31pm UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/23 "2007-11-16T23:31:58Z")
[QUOTE=Sean Factotum] Sidebar, your Honor. Doesn’t this just make string theory “a very neat idea” instead of a valid hypothesis? I mean, if you can explain away any inconsistencies, why even consider that it would be valid? [/QUOTE] There’s been several major books published over the last year or two arguing this in various ways. The one I read was [The Trouble With Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next, by Lee Smolin](http://www.amazon.com/Trouble-Physics-String-Theory-Science/dp/061891868X/ref=pd_bbs_sr_2?ie=UTF8&s=books&qid=1195255431&sr=8-2) who was a pioneering and now disillusioned string theorist. The book is an excellent introduction to all aspects of string theory for the layperson. However, as a layperson, I keep seeing numerous articles in the popular science magazines talking about possible testable results that string theory implies, and by testable I mean testable by current particle accelerators or astronomic results. Those may all still be just out of reach, or overblown, or trivial, but I had thought that the controversy raised by Solin and others had string theorists making a good rebuttal case that the lack of testable predictions of string theory was an overblown statement in itself. I of course invite rebuttal from Chronos on this. 🙂 ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [November 16, 2007, 11:48pm UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/24 "2007-11-16T23:48:06Z")
[QUOTE=Bytegeist] Just to make sure I’m following along — the green **b** is not the same as the blue **b** , right? (The first one is specifically the inverse of **a** , but the second one is an arbitrary element.) [/QUOTE] Yeah, sorry. I should’ve done the coding to write the inverse of a as a[sup]-1[/sup]. ---
**Author:** ![diggleblop](https://avatars.discourse-cdn.com/v4/letter/d/ac91a4/32.png) [@diggleblop](https://boards.straightdope.com/u/diggleblop)\ **Post date:** [November 16, 2007, 11:57pm UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/25 "2007-11-16T23:57:30Z")
[Slashdot](http://science.slashdot.org/comments.pl?sid=362251&cid=21373093) comments on this too. ---
**Author:** ![yelimS](https://avatars.discourse-cdn.com/v4/letter/y/54ee81/32.png) [@yelimS](https://boards.straightdope.com/u/yelimS)\ **Post date:** [November 17, 2007, 1:00am UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/26 "2007-11-17T01:00:54Z")
[QUOTE=cmyk] [An Animated Model of E8](http://deferentialgeometry.org.nyud.net:8080/anim/e8rotation.mov) I think I see my house in there, somewhere. Here’s [YouTube](http://www.youtube.com/watch?v=oycE0r_azP8) [/QUOTE] What exactly is this? And what is the significance of the symmetrical look of the video? I see that some of the dots and triangles change velocity and direction, what has that got to do with representing a matrix? Will my head hurt even more tomorrow? ---
**Author:** ![Shagnasty](https://avatars.discourse-cdn.com/v4/letter/s/9dc877/32.png) [@Shagnasty](https://boards.straightdope.com/u/Shagnasty)\ **Post date:** [November 17, 2007, 1:35am UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/27 "2007-11-17T01:35:53Z")
[QUOTE=diggleblop] [Slashdot](http://science.slashdot.org/comments.pl?sid=362251&cid=21373093) comments on this too. [/QUOTE] I like the guys layman’s explanation even though I have no idea how right it is. I liked a comment below too: “So what you’re saying is that God doesn’t play dice with the universe, he plays fizzbin?” ---
**Author:** ![Siam\_Sam](https://avatars.discourse-cdn.com/v4/letter/s/d78d45/32.png) [@Siam\_Sam](https://boards.straightdope.com/u/Siam_Sam)\ **Post date:** [November 17, 2007, 1:58am UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/28 "2007-11-17T01:58:20Z")
The diagram of the universe in that article looks like something you get with one of those toys they came out with back in the 1960s. I can’t remember what it’s called, and it’s difficult to explain, but there was a hollow circle you’d pin down and other circles of varying sizes and different pen holes put inside. It would allow you to circle and spiral around, creating designs like that. Although I’ve not seen one that elaborate. ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [November 17, 2007, 2:16am UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/29 "2007-11-17T02:16:01Z")
What Ultrafilter didn’t say is what distinguishes a Lie (pronounced Lee, named after Norwegian mathematician Sophus Lie from the late 19th, early 20th century) group from an ordinary group. A Lie group has as its underlying pointset a manifold, which is (roughly speaking) is a space in which each point has a neighborhood that looks like a Euclidean space of some dimension. For a Lie group, this has to be what is called an analytic manifold (complicated explanation omitted) and the group multiplication has to be given by analytic functions (ditto). The simplest example of a simple Lie group–leaving commutative ones aside–is the group of complex n x n matrices with determinant 1 (for sufficiently large n, probably at least 5). As said above there are 4 infinite classes of simple Lie groups and five that don’t fit into one of the infinite classes. Of those “exceptional” groups, the largest is E8. I once studied this (nearly 50 years ago) but most of it has escaped my mind, what is left of it. Now what any of this has to do with elementary particles completely escapes me. ---
**Author:** ![Rysto](https://avatars.discourse-cdn.com/v4/letter/r/ecccb3/32.png) [@Rysto](https://boards.straightdope.com/u/Rysto)\ **Post date:** [November 17, 2007, 2:16am UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/30 "2007-11-17T02:16:09Z")
[QUOTE=Siam Sam] The diagram of the universe in that article looks like something you get with one of those toys they came out with back in the 1960s. I can’t remember what it’s called, and it’s difficult to explain, but there was a hollow circle you’d pin down and other circles of varying sizes and different pen holes put inside. It would allow you to circle and spiral around, creating designs like that. Although I’ve not seen one that elaborate. [/QUOTE] Spirograph? ---
**Author:** ![Siam\_Sam](https://avatars.discourse-cdn.com/v4/letter/s/d78d45/32.png) [@Siam\_Sam](https://boards.straightdope.com/u/Siam_Sam)\ **Post date:** [November 17, 2007, 2:18am UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/31 "2007-11-17T02:18:25Z")
[QUOTE=Rysto] Spirograph? [/QUOTE] Yeah, that sounds familiar. Probably. It looks like the guy did the design with one of those. as I said, I’ve not seen one that elaborate, but he had years to work on it. ---
**Author:** ![nd\_n8](https://avatars.discourse-cdn.com/v4/letter/n/439d5e/32.png) [@nd\_n8](https://boards.straightdope.com/u/nd_n8)\ **Post date:** [November 17, 2007, 3:53am UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/32 "2007-11-17T03:53:13Z")
I was a little confused because graphics of the relationships did not include gravity. Part of this confusion was eliminated by this part of the paper: > [@](#): > > It should be emphasized that the connection (3.1) comprises all fields over the four dimensional base manifold. There are no other fields required to match the fields of the standard model and gravity. The gravitational metric and connection have been supplanted by the frame and spin connection parts of _A_. The Riemannian geometry of general relativity has been subsumed by principal bundle geometry - a significant mathematical unification. Devotees of geometry should not despair at this development, as principal bundle geometry is even more natural than Riemannian geometry. A principal bundle with connection can be described purely in terms of a mapping between tangent vector fields (diffeomorphisms) on a manifold, with out the ab initio introduction of a metric. Is this E8 model stating that there may be no individually measurable occurance of _g_? That the only way to establish a metric for _g_ is to observe it’s effect on other, measurable particles and forces? I understand the probability that gravity may be neither an independant particle nor an independant force (a pseudo particle or force that only exists in relationship to actual particles and/or forces) but where would the gravitron fit into this view? Would the (hypothetical) gravitron be not the substance of \*g \* but actually the by-product of \*g-anything \* else that is refered to as _G2_? I forsee this as being an obsticle in building my time machine and taking over the world. -Please note that I am not a physicist. I work in a box factory for christ’s sake. Just an interested observer. ---
**Author:** ![Sapo](https://avatars.discourse-cdn.com/v4/letter/s/ec9cab/32.png) [@Sapo](https://boards.straightdope.com/u/Sapo)\ **Post date:** [November 17, 2007, 4:43am UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/33 "2007-11-17T04:43:35Z")
[QUOTE=Rysto] Spirograph? [/QUOTE] Yes. Fun times, fun times. > **[Spirograph](https://en.wikipedia.org/wiki/Spirograph)** > > Spirograph is a geometric drawing device that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids. The well-known toy version was developed by British engineer Denys Fisher and first sold in 1965. > The name has been a registered trademark of Hasbro Inc. since 1998 following purchase of the company that had acquired the Denys Fisher company. The Spirograph brand was relaunched worldwide in 2013, with its original product configurations, by Kah... ---
**Author:** ![KGS](https://avatars.discourse-cdn.com/v4/letter/k/90ced4/32.png) [@KGS](https://boards.straightdope.com/u/KGS)\ **Post date:** [November 17, 2007, 5:05am UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/34 "2007-11-17T05:05:44Z")
So…if this model turns out to be correct, what happens to string theory? Does it mean that string theory is essentially bunk? [QUOTE=Diogenes the Cynic] “Holy crap, that’s it!” will be immortalized right alongside Archimide’s “Eureka!” [/QUOTE] Only if it becomes a rap song. 😉 ---
**Author:** ![Glazer](https://avatars.discourse-cdn.com/v4/letter/g/a88e57/32.png) [@Glazer](https://boards.straightdope.com/u/Glazer)\ **Post date:** [November 17, 2007, 5:38am UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/35 "2007-11-17T05:38:42Z")
My Google ad is for G-strings 😃 ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [November 17, 2007, 5:52am UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/36 "2007-11-17T05:52:09Z")
Spirograph was mentioned in the OP, incidentally… ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [November 17, 2007, 5:54am UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/37 "2007-11-17T05:54:22Z")
[QUOTE=Hari Seldon] What Ultrafilter didn’t say is what distinguishes a Lie (pronounced Lee, named after Norwegian mathematician Sophus Lie from the late 19th, early 20th century) group from an ordinary group. [/QUOTE] He kinda did, though not in any great technical detail: [QUOTE=ultrafilter] the operator \* has a derivative. That’s basically what you need to make it a Lie group (pronounced Lee, by the way), although the definition is a little bit more general. [/QUOTE] ---
**Author:** ![Omphaloskeptic](https://avatars.discourse-cdn.com/v4/letter/o/bcef8e/32.png) [@Omphaloskeptic](https://boards.straightdope.com/u/Omphaloskeptic)\ **Post date:** [November 17, 2007, 6:14am UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/38 "2007-11-17T06:14:02Z")
[QUOTE=Hari Seldon] Now what any of this has to do with elementary particles completely escapes me. [/QUOTE] I’ll try to explain this a little bit, and in the process explain a very little bit about the pretty Spirograph picture. In particle physics, elementary particles are thought of as states of some underlying field. And like states in ordinary quantum mechanics, these states transform among themselves like elements of some representation of the Lie group SU(n), representing some underlying symmetry. The cleanest example in the Standard Model is probably the “color” charge carried by the gluons, which is a representation of SU(3). The quarks come in three colors, which is a sloppy way of saying that they belong to the three-dimensional representation (usually just called “3”) of SU(3). Gluons, which transfer color charges, come in eight types, because they belong to the adjoint representation “8” of SU(3). The collective state space of several quantum particles is the tensor product of their individual representation spaces, and this tensor product generally decomposes as the direct sum of some irreducible representations. So a meson, formed of a quark and an antiquark, lies in a representation space “3x3=8+1.” (Here the numbers label the dimension of the representation; 8 is the adjoint representation and 1 is the singlet. The underline is usually typeset as an overbar and represents the complex-conjugate representation.) A baryon, formed of three quarks, lies in “3x3x3=10+8+8+1.” The reason that quarks combine in baryons and mesons, and not in other groups like qq, is that only color singlets (elements of the 1-dimensional representation of the color SU(3)) appear in nature at low energies. So both the meson and the baryon are actually restricted to lie in the color “1” in the products above. 3x3=6+3, containing no singlet, so the diquark cannot appear. But apart from this prediction, this SU(3) is rather boring, since everything we see is just a singlet. Things get more interesting when you consider other transformations. For example, there is an approximate flavor symmetry called isospin, transforming between up and down quarks; and an even more approximate symmetry called strangeness, transforming between down and strange quarks. Putting these symmetries together gives an approximate SU(3) symmetry among these three lightest quark flavors. This is the explanation for the diagrams of Gell-Mann’s “Eightfold Way.” A “Cartan subgroup” of the Lie group is an abelian subgroup which is as large as possible. The dimension of the Cartan subgroup of the Lie group is called its rank (this is the subscript in the Cartan classification). In the language of quantum mechanics, the operators in the Cartan subgroup are simultaneously diagonalizable and form a complete set of commuting observables. Because this SU(3) symmetry is only approximate, a Cartan basis may be chosen so that each basis element corresponds to a quantum number. The rank of SU(3) is 2; in the Eightfold Way the quantum numbers are isospin (or charge) and strangeness. Particle multiplets are under this flavor SU(3) are often drawn with isospin on a horizontal axis and strangeness increasing upward (usually at 120°, for reasons I won’t get into here). Now a baryon containing only up, down, and strange quarks transforms, under this approximate flavor SU(3) symmetry, as 3x3x3=10+8+8+1. So we expect to find, for example, a group of 10 baryons with similar properties. This “baryon decuplet” is what Gell-Mann discovered: he placed nine then-recently-discovered baryons in 9 of the 10 positions in the 10-dimensional representation of SU(3), like this: ```auto Delta- Delta0 Delta+ Delta++ * * * * Sigma- Sigma0 Sigma+ * * * Xi- Xi0 * * * ``` Then he predicted the existence and properties of the tenth, “Omega-,” which was quickly discovered. Other particles then quickly fell into other multiplets. The particles in the same row often have the same name. This is because the SU(2) isospin symmetry is good enough that these particles are often quite similar (with masses differing by only a few MeV); the “strangeness” symmetry is less good, and it is not as obvious that the Delta and Sigma are related. This idea can obviously be extended; once charmed particles were discovered, it was natural to extend the approximate flavor symmetry to SU(4), and so on. As a quantitative predictive tool, this doesn’t add much, since the c, b, and t are so heavy they tend to decay very rapidly. But the idea of grouping similar particles together as elements of some larger space, with a symmetry broken somehow at the low energies we perceive, has persisted. The electroweak unification used a similar idea, for example. Now the rank of E[sub]8[/sub] is 8, so each particle in a representation of E[sub]8[/sub] has eight associated quantum numbers, and can be plotted in an eight-dimensional space. This is what the spirograph picture is: a plot of all of the elements of some representation (in this case a 240-dimensional representation) of E[sub]8[/sub], being rotated in eight-dimensional space and then projected down to two dimensions. ---
**Author:** ![diggleblop](https://avatars.discourse-cdn.com/v4/letter/d/ac91a4/32.png) [@diggleblop](https://boards.straightdope.com/u/diggleblop)\ **Post date:** [November 17, 2007, 7:15am UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/39 "2007-11-17T07:15:37Z")
[QUOTE=Shagnasty] I like the guys layman’s explanation even though I have no idea how right it is. I liked a comment below too: “So what you’re saying is that God doesn’t play dice with the universe, he plays fizzbin?” [/QUOTE] I got a kick outta that too. ha ---
**Author:** ![KGS](https://avatars.discourse-cdn.com/v4/letter/k/90ced4/32.png) [@KGS](https://boards.straightdope.com/u/KGS)\ **Post date:** [November 17, 2007, 7:24am UTC](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652/40 "2007-11-17T07:24:19Z")
[QUOTE=Omphaloskeptic] I’ll try to explain this a little bit, and in the process explain a very little bit about the pretty Spirograph picture. In particle physics, elementary particles are thought of as states of some underlying field. And like states in ordinary quantum mechanics, these states transform among themselves like elements of some representation of the Lie group SU(n), representing some underlying symmetry. The cleanest example in the Standard Model is probably the “color” charge carried by the gluons, which is a representation of SU(3). The quarks come in three colors, which is a sloppy way of saying that they belong to the three-dimensional representation (usually just called “3”) of SU(3). Gluons, which transfer color charges, come in eight types, because they belong to the adjoint representation “8” of SU(3). The collective state space of several quantum particles is the tensor product of their individual representation spaces, and this tensor product generally decomposes as the direct sum of some irreducible representations. So a meson, formed of a quark and an antiquark, lies in a representation space “3x3=8+1.” (Here the numbers label the dimension of the representation; 8 is the adjoint representation and 1 is the singlet. The underline is usually typeset as an overbar and represents the complex-conjugate representation.) A baryon, formed of three quarks, lies in “3x3x3=10+8+8+1.” The reason that quarks combine in baryons and mesons, and not in other groups like qq, is that only color singlets (elements of the 1-dimensional representation of the color SU(3)) appear in nature at low energies. So both the meson and the baryon are actually restricted to lie in the color “1” in the products above. 3x3=6+3, containing no singlet, so the diquark cannot appear. But apart from this prediction, this SU(3) is rather boring, since everything we see is just a singlet. Things get more interesting when you consider other transformations. For example, there is an approximate flavor symmetry called isospin, transforming between up and down quarks; and an even more approximate symmetry called strangeness, transforming between down and strange quarks. Putting these symmetries together gives an approximate SU(3) symmetry among these three lightest quark flavors. This is the explanation for the diagrams of Gell-Mann’s “Eightfold Way.” A “Cartan subgroup” of the Lie group is an abelian subgroup which is as large as possible. The dimension of the Cartan subgroup of the Lie group is called its rank (this is the subscript in the Cartan classification). In the language of quantum mechanics, the operators in the Cartan subgroup are simultaneously diagonalizable and form a complete set of commuting observables. Because this SU(3) symmetry is only approximate, a Cartan basis may be chosen so that each basis element corresponds to a quantum number. The rank of SU(3) is 2; in the Eightfold Way the quantum numbers are isospin (or charge) and strangeness. Particle multiplets are under this flavor SU(3) are often drawn with isospin on a horizontal axis and strangeness increasing upward (usually at 120°, for reasons I won’t get into here). Now a baryon containing only up, down, and strange quarks transforms, under this approximate flavor SU(3) symmetry, as 3x3x3=10+8+8+1. So we expect to find, for example, a group of 10 baryons with similar properties. This “baryon decuplet” is what Gell-Mann discovered: he placed nine then-recently-discovered baryons in 9 of the 10 positions in the 10-dimensional representation of SU(3), like this: ```auto Delta- Delta0 Delta+ Delta++ * * * * Sigma- Sigma0 Sigma+ * * * Xi- Xi0 * * * ``` Then he predicted the existence and properties of the tenth, “Omega-,” which was quickly discovered. Other particles then quickly fell into other multiplets. The particles in the same row often have the same name. This is because the SU(2) isospin symmetry is good enough that these particles are often quite similar (with masses differing by only a few MeV); the “strangeness” symmetry is less good, and it is not as obvious that the Delta and Sigma are related. This idea can obviously be extended; once charmed particles were discovered, it was natural to extend the approximate flavor symmetry to SU(4), and so on. As a quantitative predictive tool, this doesn’t add much, since the c, b, and t are so heavy they tend to decay very rapidly. But the idea of grouping similar particles together as elements of some larger space, with a symmetry broken somehow at the low energies we perceive, has persisted. The electroweak unification used a similar idea, for example. Now the rank of E[sub]8[/sub] is 8, so each particle in a representation of E[sub]8[/sub] has eight associated quantum numbers, and can be plotted in an eight-dimensional space. This is what the spirograph picture is: a plot of all of the elements of some representation (in this case a 240-dimensional representation) of E[sub]8[/sub], being rotated in eight-dimensional space and then projected down to two dimensions. [/QUOTE] Dang…if this is the “Exceptionally Simple” theory, I’d hate to see the complicated one. 😃 [Previous page](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652.md?page=1) [Next page](https://boards.straightdope.com/t/an-exceptionally-simple-theory-of-everything/426652.md?page=3)