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A New Theory of Everything?
goatherder writes "The Telegraph is running a story about a new Unified Theory of Physics. Garrett Lisi has presented a paper called "An Exceptionally Simple Theory of Everything" which unifies the Standard Model with gravity — without using string theory. The trick was to use E8 geometry which you may remember from an earlier Slashdot article. Lisi's theory predicts 20 new particles which he hopes might turn up in the Large Hadron Collider."
The fact that he's a surfer dude deserves some mention as well - not everyday you see hard core mathematical physics coming from the beach!
Lubos Motl thinks it's pure bullshit ... so Lisi might
well be on to something :)
I think some people have an entirely different definition of 'Simple' than myself.
So it's not 42?
A set is a collection of things, such as the integers are a set of numbers.
A group is a set with an operation (and a couple of extra properties), such as the integers under addition.
The set of a symmetry group is the set of operations that you can perform to an object and have the object remain unchanged. For example, for an equilateral triangle, rotating it by 120 and 240 degrees leaves you with a triangle. So does flipping it around any of its three axes. Add the identity operation, which leaves the triangle untouched and you have the symmetry set for an equilateral triangle. Add an operation and you have a symmetry group.
The U(1) group is the group of all unitary, 1-dimensional operations that leave the inner (dot) product invariant.
The SU(2) group is the group of all unitary, 2-dimensional operations that leave the inner (dot) product invariant and have a determinant of 1.
The SU(3) group is the group of all unitary, 3-dimensional operations that leave the inner (dot) product invariant and have a determinant of 1.
The Standard Model obeys the symmetry found by combining the three above groups: SU(3)xSU(2)xU(1).
E8 is another group with some special properties. The author of the paper is claiming that E8 contains the Standard Model (SU(3)xSU(2)xU(1)), plus the symmetries belonging to gravity.
http://aimath.org/E8/e8.html
I found this site easier to understand than the wikipedia link. I warned my trig students about higher dimensions - wait till I tell them about 8-d vectors, they'll love it!
James Tiberius Kirk: "Spock, the women on your planet are logical. No other planet in the galaxy can make that claim."
Simply put, it's a complex dimensional algebra with lots of non-trivial, commutative degrees of freedom. It features symmetry groups, conjugation and adjoint representation, and comes with a free manifold which displays automorphism - so it can neatly fit into any space. For a small extra fee, we'll throw in some Vogon Polynomials and a Spin(16) (Z/Z2) which, fundamentally, gets your clothes drier, quicker. The best thing about the E8 is it's R8 Root System(TM), which, with the use of Euclidean Space Vectors is guaranteed(*) to make sure you don't get octonions on your breath. And if you order now, we'll send you a bonus 8x6 photo of Jacques Tits.
But honestly, I foud the wikipedia article pretty useless too. I'm not nerd enough.
Do it yourself, because no one else will do it yourself. [beta blockade 10-17 Feb]
I'm just waiting for Dvorak to denounce it. That'll be proof enough for me.
http://Communityville.com - A free place for new and old neighborhood webmasters to hang out.
Please see what a real physicist thinks of this. There's always a chance that he's stumbled onto something awesome of course, but odds are low. Basically he takes some stuff that looks cool and extracts physics from it in various ways.
:-) The author is not constrained by any old "conventions" and simply adds Grassmann fields together with ordinary numbers i.e. bosons with fermions, one-forms with spinors and scalars. He is just so skillful that he can add up not only apples and oranges but also fields of all kinds you could ever think of. Every high school senior excited about physics should be able to see that the paper is just a long sequence of childish misunderstandings.'
http://motls.blogspot.com/2007/11/exceptionally-simple-theory-of.html
'That's pretty cute!
"complex simple Lie algebras"?
Mathematics needs some new words, I think. And they need to stop using 'simple' in this kind of context. What about; instead of 'simple' they use 'mindbogglingly complicated' and instead of 'complex', 'totally headfucking' making the statement a more accurate 'totally headfucking mindboggleing complicated Lie algebras'.
Since you asked:
/O\ O
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The author of the paper is claiming
that E8 contains the Standard Model (SU(3)xSU(2)xU(1)),
plus the symmetries belonging to gravity.
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When I look at you, you make the
patterns in the floor tiles
vanish.
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If moderation could change anything, it would be illegal.
(I am not a particle physicist or a mathematician of the right sort, but I can kind of follow this sort of thing)
Okay, the context is that you've got particles, and they're fundamentally all the same, but they're "turned" in different ways. Think of a ball with 3-color LEDs inside: you can rotate it around three axes, and move it in three directions, and you can also cycle its color and change its blinking pattern. Particles are like that, except that the topology is weird: it's not back to the same orientation until you turn it around 720 degrees, instead of 360 like normal objects. The "gauge group" is the rules for how you can change things. For example, the total color of the universe is white: if you turn something from red to blue, you have to turn something else from blue to red; but you can also create a pair of a green and a purple (anti-green). They write all these rules up in math, and it's tricky because a lot of the features vary continuously (that is, you can rotate something an arbitrarily small amount). And due to the interaction of the rules for one property with the rules for other properties, there are only certain combinations of properties that you can get. They work out all the combinations that you can have and those are what you see as "different" particles that your experiments show. Of course, we don't know what the rules are, and we're trying to figure that out from what combinations of properties we've seen and which ones we're speculating are impossible. And it's hard and takes a lot of calculation to figure out what a candidate set of rules would even mean as far as results. And people are looking at known results and trying to describe them better than "we've done a billion things, and a billion things happened".
Now, the math of rules for how things can interact turns out to be sort of limited; there are basically 4 normal cases, which are boring, and then there are a few exceptional cases, which are interesting. Of these, the hardest to prove stuff about is E8, and it's just now becoming clear what combinations it allows. It's like one of those puzzles where you press a corner and lights change, and you have to turn off all the lights, but it's got dozens of corners and dozens of lights and every time you press a corner a bunch of things change at once, and there are different kinds of corners and it also matters exactly what angle you're holding it at, so there are hundreds of things you can say about each move.
And the mathematicians working on E8 recently said, "well, you can get positions like this and not like that", where "this" and "that" are big complicated lists. And this physicist read that paper and said, "hey, those lists are familiar; I made similar lists of particle interactions". So the proposal is that particles work like E8 in what kind of rules they follow. And it's a really nice theory, because E8 is essentially the most flexible set of rules you can have without it falling apart into just anything being possible (and some rules or properties just not mattering).
Since the 50s, particle physicists have found ways of classifying particles intro groups, much the way Mendelev classified elements into groups via the Periodic Table. When doing this, they discover "missing" particles that fit within a certain group but were not yet known, thus giving such groupings predictive power.
Different groups have different symmetries. E8 is a group in Lie algebra. The group is "exceptional" and "simple" which is why the article is entitled tongue-in-cheekishly "Exceptionally Simple". The power and beauty of the E8 group has been known for a long time, and it's featured in many theories of physics that have tried to provide an framework for explaining the bewildered world of particles and forces that make up the universe.
What this author has done is use E8 in a new way to come up with a potential new theory that unifies all the forces and fields. This is not *strictly* a theory of everything, as there's a lot more that has to be answered, but if true it provides a geometric model that can give us insight into the underlying principles that are involved, just the way the Periodic Table does for elements.
The guy is no kook, but his theory leaves a lot to be desired. One problem is that E8 and other lie algebras and their associated symmetries have been well-studied for decades, and most all of them have run into intractable problems or incorrect predictions, so this may just be another beautiful theory that doesn't fit reality. Lisi uses a little-known method called "BRST connections" to make it all seem to work, which most physicists are unfammiliar with. Another is that his theory actually forces something physicists call as "spontaneous symmetry breaking" into the calculations to make it fit what we know to be true in the "standard model". Many people feel this is putting the cart before the horse; they would prefer a theory where the symmetry is broken in a "nautral" way and the "standard model" of the universe just naturally falls out of it. Lisi's theory doesn't really tell us WHY this is the case, it just says it is, but here's the symmetry that underlies it and which you apply it to.
Another problem is that the theory is still new and doesn't have an quantitative predictions as of yet... there's a lot of math that needs to be done, and it's not clear that such calculation *can* be done given the contraints of his theory. At issue is something known as the "Coleman-Mandula" theorem, which basically says a lot of what Lisi does in his theory doesn't work if there are subgroups in the algenbra that are equivalent to what are known as Poincare groups. Lisi says this doesn't apply to his new theory because it posits that the vacuum of spacetime doesn't have Poincare symmetry but instead is deSitter space. Well, the idea of deSitter space is well-known and has been examined in theoretical physics for decades as well, but there are a lot of problems with it. One is that the "Smatrix", which physicists love so much in making calculations in theories with Poincare symmetries, no longer works and simply becomes an approximation.
The theory also predicts a very LARGE cosmological constant, which is contrary to observation, but there are other theories that explain how this is not actually a problem, so that might not be an issue. Perhaps the largest obstacle of the theory, once the calculations can be figured out, is that it pretty much obsoletes all of String Theory in favor of something like Loop Quantum Gravity. This will make a LOT of string physicists very unhappy.
Lisi's theory will probably not be the last work in physics, but it might bring us a step closer to a real "Theory of Everything". The truth is physicists have been toying with similar geometric approaches and arrange particles in tables and trying to tie in gravity for decades now and every new theory looks great but never quite actually works out. The fact that the universe can *almost* be described via these methods probably tells us we're on the right track, but a true
Try to picture a spherically inverted multifaceted poly-dimensional plexoid of random size, add in an elemental variable thermal/mass coefficient linking system based on the gravitational and magnetic field enhanced rate of change fluctuations of sub-atomic particles and it all comes together like butter and honey on toast. Well, butter and honey don't really come together on toast but you get the idea...
for a double major in two hard science disciplines. This isn't some foo-foo private university where they'll graduate you in 4 no matter what you do, it's two degrees from a University of California campus. Lots of classes that are required are taught only once a year -- or sometimes even every other year. If you can't get a spot in the class, tough. You get to spend an extra year. God forbid you have two required courses that are only taught once a year -- and they're scheduled at the same hour. It's not uncommon for people to get "out of sequence"... and spend an extra year. (I speak from experience on that front)
Warning: grossly inaccurate and oversimplified.
He's not saying space has 248 dimensions, he's describing the geometry of a polygon. If you read the paper, he's only invoking 3 spatial dimensions and one time dimension to define our universe.
Let's say you've got a cube, and each corner of the cube represents the properties of a subatomic particle. You can have a total of 8 subatomic particles and you can create a direct line between any point on the cube and any other.
E8 is a 248-dimensional set of lines connecting the points of a 57-dimensional imaginary object. What he has done is merge the E8 "object" with the various subatomic particles and used the remaining unassigned points to predict the features of those particles we have yet to detect. In essence, he's created a math representation of a periodic table of subatomic particles.
People with Ph.D's in mathematics aren't expected to understand the theory. People with Ph.D's in particle physics aren't expected to understand the theory.
Quite frankly, there's a serious audience of around one hundred people on the planet that can actually grasp what he's saying, and they seem to be divided about it and its ramifications.
~ J. Barrett
The 248-dimensions that he is talking about are not like the time-space dimensions, which particles move through. They describe the state of the particle itself - things like spin, charge, etc. The standard model has 6(?) properties. Some of the combinations of these properties are allowed, some are not. E8 is a very generalized mathematical model that has 248-properties, where only some of the combinations are allowed. What Garrett Lisi showed is that the rules that describe the allowed combinations of the 6 properties of the standard model show up in E8, and furthermore, the symmetries of gravity can be described with it as well.
Now, there are other valid combinations of properties within E8 beyond the ones that represent the particles in the standard model, and these combinations would represent new particles that we have not seen before, if the model is correct.
Clifford Algebras, Grassman Algebras, Spacetime Algebra, and Geometric Algebra are a group of mathematics notations that are related to the ones being used here. The notation in use has interesting properties that make it more likely that an equation will be valid in any number of dimensions, embeds the behavior of complex numbers, quaternions, hypercomplex numbers in a purely real system, etc.
I have read of ideas for unifying physics by using these notations for their superior ability to reason with space. (David Hestenes has good examples.) A good physical theory should be like a consistent programmer's interface. If the "code" continues to become unwieldly over time, then a point will be reached where rewrites must be done in order to eliminate special cases and bring out hidden symmetries.
This particular paper may end up failing important tests, but it does seem clear that at some point Clifford Algebras will end up being the thing that ended up simplifying physics.
So what you're saying is that God doesn't play dice with the universe, he plays fizzbin?
Yah, OK, so please, you try it.
-Garrett
Holy crap! - I can read all the words, but none of it makes any sense. It's like the took regular English words and gave them all different meanings. I haven't felt this uncomprehending in a loooong time - and even the dumbness felt from quantum chemistry pales to this. Well, a lot of it falls out of this:
http://en.wikipedia.org/wiki/Group_theory
Which then gets you here:
http://en.wikipedia.org/wiki/Symmetry_group
Once you get those two, you can hit:
http://en.wikipedia.org/wiki/Differentiable_manifold
and you're very close to a general understanding of the shape (no pun intended) of what E8 is all about, and can dive into:
http://en.wikipedia.org/wiki/Lie_group