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
Friday, November 19, 2010
Monday, June 28, 2010
An Explicit Embedding of Gravity and the Standard Model in E8
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
Saturday, October 24, 2009
SEED on-line
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/
Tuesday, February 3, 2009
Lisi's homepage & the EPE
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.
Thursday, January 29, 2009
Sunday, January 11, 2009
Question: What are the odds?
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)
Saturday, January 10, 2009
Happy New Year
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.
Monday, December 29, 2008
Suggested link...
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.
Sunday, August 24, 2008
An excellent little grant...
(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.
Saturday, March 15, 2008
Wired: ...Theory Leads to Fame, Backlash
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
Friday, February 22, 2008
Technocrat - a nice status update...
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?
Thursday, February 7, 2008
The Plebanski action extended to a unification of gravity and Yang-Mills theory
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
Wednesday, January 23, 2008
Symmetry Issues ??
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.
Sunday, December 23, 2007
Merry Xmas and/or Happy holidays
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...
Tuesday, November 27, 2007
What's all this 'Dimensions' stuff?
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.
Monday, November 26, 2007
Quote of the Day
"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
Tuesday, November 20, 2007
Must-see video on YouTube (New Scientist)
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)
Saturday, November 17, 2007
In the news (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...
ILQGS seminar talk - 13 November 2007
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.
Some more blogs and links and such
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...]
Some E8 links
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)
Links to Dr. Lisi
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.)
Attempts at humour found along the way...
"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!!!!!!"
Pre-canned Google search
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.
Lubos - a skeptical viewpoint...
Link= A skeptical viewpoint
(Warning, he comes across as a bit cranky.)
(Warning, he comes across as a bit cranky.)
'An Exceptionally Simple Theory of Everything'
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.
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).
Other potentially useful references
Link= 'The Significance of Numerical Coincidences in Nature'
[To be continued...]
[To be continued...]
Useful background knowledge
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
Friday, November 16, 2007
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