Garrett Lisi fills in E8 blanks

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Garrett Lisi fills in E8 blanks

Garrett Lisi, 39, has a doctorate but no university affiliation and spends most of the year surfing in Hawaii, where he has also been a hiking guide and bridge builder (when he slept in a jungle yurt).

In winter, he heads to the mountains near Lake Tahoe, Nevada, where he snowboards. "Being poor sucks," Lisi says. "It's hard to figure out the secrets of the universe when you're trying to figure out where you and your girlfriend are going to sleep next month."

Despite this unusual career path, his proposal is remarkable because, by the arcane standards of particle physics, it does not require highly complex mathematics.

Even better, it does not require more than one dimension of time and three of space, when some rival theories need ten or even more spatial dimensions and other bizarre concepts. And it may even be possible to test his theory, which predicts a host of new particles, perhaps even using the new Large Hadron Collider atom smasher that will go into action near Geneva next year.
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Lisi's inspiration lies in the most elegant and intricate shape known to mathematics, called E8 - a complex, eight-dimensional mathematical pattern with 248 points first found in 1887, but only fully understood by mathematicians this year after workings, that, if written out in tiny print, would cover an area the size of Manhattan.

E8 encapsulates the symmetries of a geometric object that is 57-dimensional and is itself is 248-dimensional. Lisi says "I think our universe is this beautiful shape."

What makes E8 so exciting is that Nature also seems to have embedded it at the heart of many bits of physics. One interpretation of why we have such a quirky list of fundamental particles is because they all result from different facets of the strange symmetries of E8.

Lisi's breakthrough came when he noticed that some of the equations describing E8's structure matched his own. "My brain exploded with the implications and the beauty of the thing," he tells New Scientist. "I thought: 'Holy crap, that's it!'"

What Lisi had realised was that he could find a way to place the various elementary particles and forces on E8's 248 points. What remained was 20 gaps which he filled with notional particles, for example those that some physicists predict to be associated with gravity.

Physicists have long puzzled over why elementary particles appear to belong to families, but this arises naturally from the geometry of E8, he says. So far, all the interactions predicted by the complex geometrical relationships inside E8 match with observations in the real world. "How cool is that?" he says.

The crucial test of Lisi's work will come only when he has made testable predictions. Lisi is now calculating the masses that the 20 new particles should have, in the hope that they may be spotted when the Large Hadron Collider starts up.
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His personal site is here.

I wish him good luck.
 
No comments? Was I born into the wrong time? Why can violent sports draw such large crowds, but this subject, even in a science forum, draws no comments.

More on the E8

- one of the largest and most complicated structures in mathematics.

- At the most basic level, the calculation is an arcane investigation of symmetry – in this case of an object that is 57 dimensional

- The group of symmetries of this strange geometry called E8 is one of the most intriguing structures that Nature has left for the mathematician to play with

- E8 is the symmetries of a geometric object that is 57-dimensional. E8 itself is 248-dimensional.

- E8 was discovered over a century ago, in 1887, and until now, no one thought the structure could ever be understood

- The new result is a complete list of these building blocks for the representations of E8, and a precise description of the relations between them, all encoded in a matrix, or grid, with 453,060 rows and columns. There are 205,263,363,600 entries in all, each a mathematical expression called a polynomial. If each entry was written in a one inch square, then the entire matrix would measure more than seven miles on each side.

- The result of the E8 calculation, which contains all the information about E8 and its representations, is 60 gigabytes in size. This is enough to store 45 days of continuous music in MP3-format.

- If written out on paper, the answer would cover an area the size of Manhattan

- The computation required sophisticated new mathematical techniques and computing power not available even a few years ago.

- understanding the inner workings of E8 is not only a great advance for pure mathematics, but may also help physicists in their quest for a unified theory
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So I want to know why they mean by matrix and "453,060 rows and columns". Is it a matrix or a tensor? When they say rows and columns I picture a square 2d matrix. When they say 248 dimensional, I can picture a data structure that can hold 248 dimensional data, but that doesn't give me a complete picture yet. A 2d matrix doesn't have to be square, it could be 10 rows and 2 columns. So to picture this thing I need more...
 
The E8 calculation is part of an ambitious project known as the Atlas of Lie Groups and Representations. The goal of the Atlas project is to determine the unitary representations of all the Lie groups. This is one of the great unsolved problems of mathematics, dating from the early 20th century. The success of the E8 calculation leaves little doubt that the Atlas team will complete their task.

The Atlas team consists of about 20 researchers from the United States and Europe.
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aimgroup04d.jpg

Atlas Project Members, 2004

More info about the Atlas project and the E8
 
Speaking for myself only, and my opinion, this is an area of mathematics where I can fully support some of the things Einstein believes about mathematics. Namely, this appears (to me) to be "math for math's sake". Granted, that could still be classified as science, but I admit to being biased... I am an engineer, and math is only useful to me with respect to how it helps me understand real, engineerable, physical situations. So far I haven't read much about this E8 stuff that grounds it into some usable form of physics.

God bless those "pure" theoretical physicists who work out there on the "bleeding edge". But until I can understand how the math can be used in an engineering sense ("put a bunch of knobs on it so we can control it"), then it doesn't have much use for me.

RMT
 
Not really TL. I hoped that someone would post a link to " E8 for dummies " so that I could gain a better understanding of what it's all about. The way GL talks about it has me on the edge of my seat more than any hockey game or episode of American Idol could ever have done.
 
damn, that wikipedia page is too complicated for me. I took a year of university, but here's a list of things that I think are important to know but I don't know...

- Lie Algebras
- mutually commutative degrees of freedom
- manifolds
- Root system/root vector
- All the sections after "Real forms" I'm like, err what?

So I need the "E8 for dummeries" then...

I do wonder though:
The most difficult case (for exceptional groups) is the split real form of E8 (see above), where the largest matrix is of size 453060×453060
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Is the reason this 248 dimensional structure can be in matrix form because of manifolds?


And I just find things like this,

There is a Lie algebra En for every integer n>3, which is infinite dimensional if n is greater than 8
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really cool, I don't know why.
 
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