**A Geometric Theory of Everything**

*Deep down, the particles and forces of the universe are a manifestation of exquisite geometry*

By

**A. Garrett Lisi**and

**James Owen Weatherall**- November 29, 2010

Useful links regarding Garrett Lisi's 'An Exceptionally Simple Theory of Everything'

By

An Explicit Embedding of Gravity and the Standard Model in E8

A. Garrett Lisi

Submitted on 25 Jun 2010

The algebraic elements of gravitational and Standard Model gauge fields acting on a generation of fermions may be represented using real matrices. These elements match a subalgebra of spin(11,3) acting on a Majorana-Weyl spinor, consistent with GraviGUT unification. This entire structure embeds in the quaternionic real form of the largest exceptional Lie algebra, E8. These embeddings are presented explicitly and their implications discussed.

Here: http://arxiv.org/abs/1006.4908

A. Garrett Lisi

Submitted on 25 Jun 2010

The algebraic elements of gravitational and Standard Model gauge fields acting on a generation of fermions may be represented using real matrices. These elements match a subalgebra of spin(11,3) acting on a Majorana-Weyl spinor, consistent with GraviGUT unification. This entire structure embeds in the quaternionic real form of the largest exceptional Lie algebra, E8. These embeddings are presented explicitly and their implications discussed.

Here: http://arxiv.org/abs/1006.4908

SEED: HOW A PHYSICIST PUBLISHED AND VETTED HIS REVOLUTIONARY WORK SIGNALS THE POTENTIAL FUTURE OF AN OPEN, TRANSPARENT PEER REVIEW PROCESS. (from November 2008)

...

How does that group, referred to as E8, inform your theory, and is its structure really “in everything,” as stated by media?

In this E8 theory, it’s more accurate to say “everything” is in this particular Lie algebra. Three years ago I had gathered all known fields into one mess of algebra, describing particle interactions. This algebra included bosons interacting with fermions, and it looked unlike any Lie algebra I’d ever seen. It was a long time before I even considered that it might be part of some larger mathematical structure. Then one day I decided to look and see, and almost immediately found that it perfectly matched part of E8 — a truly beautiful mathematical object. It was a stunning realization. I had no reason to suspect that the collection of algebraic fields I had put together was actually part of a single mathematical object. And this object also seemed to have the two missing pieces I was looking for. So, to find it all fitting together like that, all at once — it was a bit overwhelming for me. One doesn’t get many days like that.

HERE: http://seedmagazine.com/content/article/garrett_lisis_exceptional_approach_to_everything/

...

How does that group, referred to as E8, inform your theory, and is its structure really “in everything,” as stated by media?

In this E8 theory, it’s more accurate to say “everything” is in this particular Lie algebra. Three years ago I had gathered all known fields into one mess of algebra, describing particle interactions. This algebra included bosons interacting with fermions, and it looked unlike any Lie algebra I’d ever seen. It was a long time before I even considered that it might be part of some larger mathematical structure. Then one day I decided to look and see, and almost immediately found that it perfectly matched part of E8 — a truly beautiful mathematical object. It was a stunning realization. I had no reason to suspect that the collection of algebraic fields I had put together was actually part of a single mathematical object. And this object also seemed to have the two missing pieces I was looking for. So, to find it all fitting together like that, all at once — it was a bit overwhelming for me. One doesn’t get many days like that.

HERE: http://seedmagazine.com/content/article/garrett_lisis_exceptional_approach_to_everything/

The homepage of A. Garrett Lisi has been improved.

See also the very cool Elementary Particle Explorer. I'm going to need to set aside some time to play with that one.

See also the very cool Elementary Particle Explorer. I'm going to need to set aside some time to play with that one.

If I understand it, the fundamental basis of this theory is the mapping of the fundamental particles to the E8 structure. Dr. Lisi mentioned that he had an extra 'variable' where he could assign his own value to make the particles hit the E8 vertices.

Here's my question:

How much geometrical freedom did he have to make the particles fit onto E8? Doesn't the fact that all the input data (the "God-given" already-known values) fit the E8 indicate something big? Or was there enough slack that any random collection of data can be made to fit. In other words, what are the odds of this mapping working if it isn't fundamentally true?

My gut tells me that it cannot be a coincidence if the known data for 200-some particles, with 7 of 8 variables constrained, lands perfectly onto the E8.

A related question that might clarify the previous:

Did the mapping reveal any fine adjustments to the values of any of these 'fundamental constants' related to the 7 variables? In other words, did he have to tweak any measured values ever-so-slightly to make them hit their E8 geometrical mark? If so, doesn't that mean that all these values are now known to infinite geometrical precision? If so, isn't that huge news?

Comments welcome.

(gently update for clarity 2009-02-09)

Here's my question:

How much geometrical freedom did he have to make the particles fit onto E8? Doesn't the fact that all the input data (the "God-given" already-known values) fit the E8 indicate something big? Or was there enough slack that any random collection of data can be made to fit. In other words, what are the odds of this mapping working if it isn't fundamentally true?

My gut tells me that it cannot be a coincidence if the known data for 200-some particles, with 7 of 8 variables constrained, lands perfectly onto the E8.

A related question that might clarify the previous:

Did the mapping reveal any fine adjustments to the values of any of these 'fundamental constants' related to the 7 variables? In other words, did he have to tweak any measured values ever-so-slightly to make them hit their E8 geometrical mark? If so, doesn't that mean that all these values are now known to infinite geometrical precision? If so, isn't that huge news?

Comments welcome.

(gently update for clarity 2009-02-09)

Happy New Year.

Yesterday, walking into in a toy store in Nova Scotia (Canada), I though I saw Garrett Lisi. Spittin' image. Exact twin. I'm sure it wasn't him - obviously - but it was a bit disconcerting.

By the way - the TED.com video recommended by Trent (see link in the previous post) is great. Well worth watching. You can even download a copy to keep for later viewing.

Yesterday, walking into in a toy store in Nova Scotia (Canada), I though I saw Garrett Lisi. Spittin' image. Exact twin. I'm sure it wasn't him - obviously - but it was a bit disconcerting.

By the way - the TED.com video recommended by Trent (see link in the previous post) is great. Well worth watching. You can even download a copy to keep for later viewing.

Trent suggested:

http://www.ted.com/index.php/talks/garrett_lisi_on_his_theory_of_everything.html

PS: Great video - well worth watching. Even if you're on dial-up, get it somehow. There are links to download, so let it run overnight.

http://www.ted.com/index.php/talks/garrett_lisi_on_his_theory_of_everything.html

PS: Great video - well worth watching. Even if you're on dial-up, get it somehow. There are links to download, so let it run overnight.

(early-August 2008) - The Foundational Questions Institute (FQXi) has announced that it has awarded theoretical physicist A. Garrett Lisi (of 'An Exceptionally Simple Theory of Everything' fame) a grant of $77,222 to work on his theory, which involves using a recently mapped 248-dimension mathematical structure called E8 to unify all the fundamental particles and forces, including gravity.

See New Scientist.

See New Scientist.

Nice article in Wired. Includes interview with Lisi.

Link= ...Theory Leads to Fame, Backlash

Also, linked from the above is this amusing gem:

Link= UnNews UnTechnica

And this one is more serious.

Link= The Daily Galaxy

Link= ...Theory Leads to Fame, Backlash

Also, linked from the above is this amusing gem:

Link= UnNews UnTechnica

And this one is more serious.

Link= The Daily Galaxy

So what's going on? Well, here is a good status update...

Link= Whither Garrett Lisi and the E8 theory of everything?

Link= Whither Garrett Lisi and the E8 theory of everything?

I'll post an indirect link first because it provides an explanation along the way.

Link= Physics Forums post by Marcus

Here is the direct link to this paper.

Link= The Paper on arXiv.org

Link= Physics Forums post by Marcus

Here is the direct link to this paper.

Link= The Paper on arXiv.org

Reportedly, they've found some symmetry issues with Lisi's theory.

"...Unfortunately, the consensus, after investigation, is that it is impossible to use E8 in the way Lisi was hoping and produce a consistent model that reflects reality."

Link= Telegraph.co.uk

The article linked above is very nearly content-free, and the author has a book to be released in less than two weeks. ...Rolls-eyes... Not a good first impression.

But I'll dig into the Physics Newsgroups (probably the ones linked in previous posts) in the next few weeks and see what I can decipher (if anything).

It'll be interesting to see Lisi's reaction to the consensus.

"...Unfortunately, the consensus, after investigation, is that it is impossible to use E8 in the way Lisi was hoping and produce a consistent model that reflects reality."

Link= Telegraph.co.uk

The article linked above is very nearly content-free, and the author has a book to be released in less than two weeks. ...Rolls-eyes... Not a good first impression.

But I'll dig into the Physics Newsgroups (probably the ones linked in previous posts) in the next few weeks and see what I can decipher (if anything).

It'll be interesting to see Lisi's reaction to the consensus.

I hope that everyone has a happy and safe holiday season.

And remember: You are unique; just like everyone else.

PS: I've updated a few of the posts below with new links...

And remember: You are unique; just like everyone else.

PS: I've updated a few of the posts below with new links...

Let's start at the beginning:

A point has zero dimensions.

Move that point side-ways and it draws a one-dimensional line.

Next, drag the line (orthogonal, or 90-degrees, to the first motion) and it will create a two-dimensional square.

Then, pull the square up (orthogonal from both previous motions) and it will create a three-dimensional cube.

But we're not done.

Pull the 3-D cube into a fourth dimension (orthogonal to the other three) and it will create what is called a 'hypercube'. Each of the 8 corners moves along a new axis to create a new corner in the 4th dimension. So you can probably understand that a hypercube has 16 corners (or vertices).

Also, if you count the edges (12 in the original cube, 12 in the new cube, and 8 new edges linking the old vertices with the new vertices) it equals 32.

Have a look at the chart on Wiki and you'll see that our math is correct.

Link= Wiki on Hypercube

Also, enjoy the many Hypercube movies on YouTube.

Link= Hypercube on YouTube

We won't go past 4-D because the hypercube (or tesseract) is one of the simplest non-trivial polytopes. And E8 is the most complicated.

Once you see and understand the 'motion' of the hypercube, it is a wee bit easier to at least trust what is going on with the E8 movies.

A point has zero dimensions.

Move that point side-ways and it draws a one-dimensional line.

Next, drag the line (orthogonal, or 90-degrees, to the first motion) and it will create a two-dimensional square.

Then, pull the square up (orthogonal from both previous motions) and it will create a three-dimensional cube.

But we're not done.

Pull the 3-D cube into a fourth dimension (orthogonal to the other three) and it will create what is called a 'hypercube'. Each of the 8 corners moves along a new axis to create a new corner in the 4th dimension. So you can probably understand that a hypercube has 16 corners (or vertices).

Also, if you count the edges (12 in the original cube, 12 in the new cube, and 8 new edges linking the old vertices with the new vertices) it equals 32.

Have a look at the chart on Wiki and you'll see that our math is correct.

Link= Wiki on Hypercube

Also, enjoy the many Hypercube movies on YouTube.

Link= Hypercube on YouTube

We won't go past 4-D because the hypercube (or tesseract) is one of the simplest non-trivial polytopes. And E8 is the most complicated.

Once you see and understand the 'motion' of the hypercube, it is a wee bit easier to at least trust what is going on with the E8 movies.

"I feel like I should apologize to normal people that this E8 Theory is so complicated, despite being exceptionally simple as these things go. But, you know, I just live here. Complain to the management."

Garrett Lisi

Link= A. Garrett Lisi (blogger), Nov. 20, 2007

Garrett Lisi

Link= A. Garrett Lisi (blogger), Nov. 20, 2007

Link= Amazing YouTube Video

This video from 'New Scientist' is incredible. It is one of the first civilian-grade explanations of what is going on. Wow!! Nice.

Also, an image worth a closer look:

Image Link= When a gluon hits a quark

Source: NewScientist.com

(updated 24 Dec 07)

This video from 'New Scientist' is incredible. It is one of the first civilian-grade explanations of what is going on. Wow!! Nice.

Also, an image worth a closer look:

Image Link= When a gluon hits a quark

Source: NewScientist.com

(updated 24 Dec 07)

Link= 'Surfer dude stuns physicists...' @ The Telegraph, UK

Link= 'Is this the fabric...' @ The Telegraph, UK

Link= 'Surfer-Physicist...' @ Wired Science

Link= 'Laid-Back Surfer Dude...Next Einstein' @ Fox News

Link= 'Surfer makes waves...' @ CBC News

Link= 'Geometry is all' @ The Economist (added 24 Dec 07)

Link= 'Is mathematical...' @ NewScientist (added 24 Dec 07)

The story has broken, but I expect that the popular science media is just getting started. Watch this space...

Link= 'Is this the fabric...' @ The Telegraph, UK

Link= 'Surfer-Physicist...' @ Wired Science

Link= 'Laid-Back Surfer Dude...Next Einstein' @ Fox News

Link= 'Surfer makes waves...' @ CBC News

Link= 'Geometry is all' @ The Economist (added 24 Dec 07)

Link= 'Is mathematical...' @ NewScientist (added 24 Dec 07)

The story has broken, but I expect that the popular science media is just getting started. Watch this space...

Link= Slides in .pdf (about 8.1MB)

Link= Audio in .mp3 (about 7.4MB) *

If these links break, then Google the keyword:

Link= Google 'lisi111307'

* The seminar audio includes some telephone noises (ringing, dial tones, etc.) as people join the conference call a bit late.

Link= Audio in .mp3 (about 7.4MB) *

If these links break, then Google the keyword:

Link= Google 'lisi111307'

* The seminar audio includes some telephone noises (ringing, dial tones, etc.) as people join the conference call a bit late.

Link= democraticunderground

Link= iabervon (1971) @ SlashDot

Link= See God, Kai... blog

[To be continued...]

Link= iabervon (1971) @ SlashDot

Link= See God, Kai... blog

[To be continued...]

Link= E8 page on AIMath.org

Link= McMullen overview of E8

Link= Wikipedia - E8 Polytope

Link= ES Mathematics

Link= E8 on YouTube

Link= E8Rotation.mov (about 10.5 MB)

Link= McMullen overview of E8

Link= Wikipedia - E8 Polytope

Link= ES Mathematics

Link= E8 on YouTube

Link= E8Rotation.mov (about 10.5 MB)

Link= His homepage

Link= Deferential Geometry (*)

Link= FQXI Biography (.pdf)

(* For those on dial-up, this is a large page but well worth the wait. It is his personal Wiki where he stores ideas and information. He describes it as something like an extension to his brain.)

Link= Deferential Geometry (*)

Link= FQXI Biography (.pdf)

(* For those on dial-up, this is a large page but well worth the wait. It is his personal Wiki where he stores ideas and information. He describes it as something like an extension to his brain.)

"We shouldn't be surprised if string theory turns out to be false ... according to this, it's *all* a pack of Lies." [But 'Lie' is apparently pronounced 'lee'.]

"The Universe is a doily."

"Oh my God, it's full of dolies!"

"Oh - my - gawd... I was looking at comet 17P Holmes last night. I took a picture and analyzed it on my laptop. It's not a comet. It looks like a doily; an E8 doily. Oh my gawd, Garrett Lisi is right - THE UNIVERSE IS A DOILY !!!!!! ARGHHHHHHH!!!!!!"

"The Universe is a doily."

"Oh my God, it's full of dolies!"

"Oh - my - gawd... I was looking at comet 17P Holmes last night. I took a picture and analyzed it on my laptop. It's not a comet. It looks like a doily; an E8 doily. Oh my gawd, Garrett Lisi is right - THE UNIVERSE IS A DOILY !!!!!! ARGHHHHHHH!!!!!!"

In case your 'google-fu' is weak...

Link= Google it for yourself

As of 24 Dec 07, this very blog was at the bottom of Page 2 (#20 of 152000) - not bad. And the Google engine is doing a great job at putting the most important links right at the top of Page 1.

Link= Google it for yourself

As of 24 Dec 07, this very blog was at the bottom of Page 2 (#20 of 152000) - not bad. And the Google engine is doing a great job at putting the most important links right at the top of Page 1.

Link= A skeptical viewpoint

(Warning, he comes across as a bit cranky.)

(Warning, he comes across as a bit cranky.)

Link= 'An Exceptionally Simple Theory of Everything' (front page)

Sometimes .pdf files work better if you right-click and save a copy locally (instead of opening from within your browser).

Link= The paper in .pdf format <-Click the link The .pdf file is about 610KB, an easy download for anyone.

Sometimes .pdf files work better if you right-click and save a copy locally (instead of opening from within your browser).

Link= 'The Significance of Numerical Coincidences in Nature'

[To be continued...]

[To be continued...]

The following topics were recommended as prerequisites:

Link= Wikipedia - Group Theory

Link= Wikipedia - Symmetry Group

Link= Wikipedia - Differentiable Manifold

Link= Wikipedia - Lie Group

Link= AIMath - E8

Link= Wikipedia - Group Theory

Link= Wikipedia - Symmetry Group

Link= Wikipedia - Differentiable Manifold

Link= Wikipedia - Lie Group

Link= AIMath - E8

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