An Exceptionally Simple Theory of Everything

[marcus]

Yesterday the French newspaper LE MONDE had a pretty nice article and interview with Garrett. The article had some quotes from Carlo Rovelli and a range of other people.

Here's the interview, in printerfriendly version:
http://www.lemonde.fr/web/imprimer_element/0,40-0@2-3244,50-979854,0.html

Here's a Babelfish translation of the interview:
http://babelfish.altavista.com/babelfish/trurl_pagecontent?lp=fr_en&trurl=http%3a%2f%2fwww.lemonde.fr%2fweb%2fimprimer_element%2f0,40-0%402-3244,50-979854,0.html

==babelfish version of interview==
Anthony Garrett Lisi: "the theory is mathematically and aesthetically superb"
LEMONDE.FR | 19.11.07 | 14h00

Amateur physicist, Anthony Garrett Lisi, posted, at the beginning of November, on a webserver, a paper of 31 pages stipulating that all the laws of the universe would be described by one and the same theory. This 39 year old American, until now unknown, is attached to no university, any laboratory. His work is not less, since the beginning of November, at the center of sharp discussions in the scientific community.

How do you work ? Who finances your work?

I obtained my doctorate 10 years ago and I left the academic world to work with my own ideas on physics and surfer with Maui. I worked just enough to earn my living, dedicating the majority of my time to the equations and benefitting from the full air.

Then, one year ago, I applied for a grant at new private foundation, Foundational Questions in Physics and Cosmology (FQXi). I obtained it.

I have now a sufficient financing to live, make physics and to offer some boards of surfing to me. Without the support of FQXi, I would not have had sufficient time to devote me to physics and to achieve this work.

Since when do work you on this subject?

Since approximately 10 years. But progress was not continuous. I tried to build several other models which did not function and I had on several occasions all to begin again since the beginning.

If nature says to you that your ideas are false, it is useless to discuss. The "E8 theory" is mathematically and aesthetically superb and until now, it seems to correspond with physics that we know. But that is still new and can, of course, to prove to be false.

How are your work perceived by the physicists of the academic world?

By receiving the support of the foundation FXQi, I thought of having to communicate on my work. When I presented my work at conferences, several physicists of the academic world were immediately impressed by the theory as a whole. Even if I were an outsider, the ideas liked.

This favorable impression grew in the scientific community. And when I published paper, there were an astonishing interest and an attention. I was amazed.

There are also skepticism and criticisms, but that is necessary and healthy. Mathematics used is complex and that will take weeks with the best physicists to go fully at the bottom of the things. I know that mathematics is correct but more work and, then the experiment, will determine if this theory agrees with nature.

How many new particles are they predicted by your theory ? Some criticize reproach him not for predicting the mass of it...

In its current state the theory predicts the existence of 20 new particles. Because the theory is not completely developed, that can however change.

With this theory, it is "all or nothing". There are not a possibility of fudge the parameters or whimsical additional structures. Today, the theory has a satisfactory aspect, but there are still things to specify. With other researchers, we will work to improve the theory and the predictions will result from this.

Would you accept a station in a university?

Only if it is beside a beautiful mountain where to make snowboard.

Why not have carried out a traditional academic career?

I wanted to live in a beautiful place, where I could make surfing or snowboard and work on my physics, without other responsibilities.

I am a contemplative hedonist - I want life of the intense pleasures. And all that wants to say not to pass too much from time in a laboratory, but to find a balance between thinking and having fun.

==endquote==

Here's the main article, with the balance of opinion quotes from other physicists:

The main article, and printerfriendly version:
http://www.lemonde.fr/web/article/0,1-0@2-3244,36-979858@51-979860,0.html
http://www.lemonde.fr/web/imprimer_element/0,40-0@2-3244,50-979858,0.html

Fish translation of the article
http://babelfish.altavista.com/babelfish/trurl_pagecontent?lp=fr_en&trurl=http%3a%2f%2fwww.lemonde.fr%2fweb%2fimprimer_element%2f0,40-0%402-3244,50-979858,0.html
http://babelfish.altavista.com/babe...-0@2-3244,36-979858@51-979860,0.html&lp=fr_en

 

[chrisina]

Congratulations Garrett ! Hope you will get suport from as many researchers are needed to make the necessary calculations which will be needed. It is indeed a beautiful mathematical hypothesis, let's hope that it ends up being the real description of nature, at least it's definately a new avenue that is worthwile following.

One question I have, which I can't seem to get clear from the paper, how many degrres of freedom does the theory have in the end ? I mean, you explain that one should be able to derive the different mass relationships and coupling constants from the Higgs VEV, as well as the Cosmological Constant (which varies over time according to a relation to be derived I guess), so does that mean that all the parameters of the standard model, as well as the Lambda CDM densities could be theoretically derived from the Higgs VEV ?

Can you also be more precise with what you mean with the coupling constants "run".

Thanks.

 

[marcus]

Update.
Jacques Distler has gotten around to responding
http://golem.ph.utexas.edu/~distler/blog/archives/001505.html
http://golem.ph.utexas.edu/~distler/blog/archives/001505.html#more

sorry to cover up the preceding post, by chrisina, which has some questions addressed to Garrett.

=======================
BTW chrisina you asked G.L. what is meant by saying coupling constants run.
It is a usual thing in quantum field theories for the constants to vary with proximity or energy for example the usual value of alpha the fine structure constant in QED is 1/137.036...
but this is not correct for very close approaches. the true or "bare" value at extreme proximity or energy is larger.
as we reduce the energy and increase the scale the coupling constant runs down to it's usual value of around 1/137.

In the QG literature one finds widely scattered references to the idea that the gravity constant G could have a "bare" value relevant at very small scale which is different from the value we measure at macro scale. In other words a number of people seem to suspect that the G constant might run as well. Technically, I should be talking about a dimensionless form of G since I don't know what it means for a dimensionful quantity to run.

If you want to see how this idea is used, you could look up the most recent paper by Reuter and Bonanno. They make extremely bold use of the running (dimensionless) coupling constants idea in a gravity context. Use it to understand stuff about the early universe.

this is in case Garrett does not get around to replying immediately---something to think about in the meantime. Hopefully he'll straighten it out any misconceptions if I've made an error.
======EDIT TO REPLY TO NEXT=====

Hello again chrisina, you were asking G.L. about the number of free parameters in his model, in post #142.
I do not know of any free parameters. But I shouldn't interfere. G.L. is the only person who can really answer that.

My own take on it is there are no free parameters and you get "bare" values of stuff. Like he gets a definite value of Lambda the cosmological constant and he can't do anything about it.

You might want to look at the recent paper of Pereira and Aldrovandi. They also have a microscopic highenergy value of Lambda playing a role----and it would presumably run down to the macroscopic observed value that astronomers tell us they measure.

That is, the whole business is strange and new but G.L. isn't the only one for whom Lambda acts this way. And of course there is the whole Reuter Percacci AsymptoticSafety thing.

So in some sense you could say G.L. has no free parameters but you also have to say that he is in the early stages of developing the theory and deriving stuff, and maybe the present model does not govern how the constants run (making it among other things harder to test experimentally). But we'll see.

 

[chrisina]

thx Marcus, what about the number of free parameters ?

 

[Coin]

E8 is an exceptional Lie group, specifically a Lie group for an icosahedron, or 20-faced polyhedron, maybe looking up search terms with regards to that might help.

Thanks, I'm trying to look some of this stuff up, also the links garrett posted in the "layman" thread look useful. Just to be clear though-- I am seeing this reference in several places that E8 is the lie group of an icosahedron (and for that matter E6 is same for a Tetrahedron and E7 is the same for an octahedron). This seems like a very interesting way to approach E8, however I am not sure what we mean when we say it is the "lie group". Do we mean that it is the rotational symmetry group? An old Jacques Distler post says that the subgroup of SO(3) which is the icosahedron's rotational symmetry group "can be shown to map to" E8, but I am not sure if this means that they are isomorphic or just that there is an injection or what.

Wikipedia has an article on Icosahedral symmetry claiming the symmetry group of an icosahedron to be "I_H", and they describe a symmetry group that seems pretty different from E8. However they include reflection and translation in their symmetry group...

 

[member 11137]

First of all I want to apologize for what I shall say now.

I don't want to disturb the actual "euphory" but did some one heard about the conferences of Hawking:
"Is the end in sight for theoretical physics?" Cambridge april 1980

And :
"The edge of space time." (The new physics; Cambridge press, ...)

The only thing I want to note here is that the E8 theory was stil known at this time. Thus it is nothing really new I think.

Why so much noise ?

 

[notknowing]

Yesterday the French newspaper LE MONDE had a pretty nice article and interview with Garrett. The article had some quotes from Carlo Rovelli and a range of other people.

Here's the interview, in printerfriendly version:
http://www.lemonde.fr/web/imprimer_element/0,40-0@2-3244,50-979854,0.html

Here's a Babelfish translation of the interview:
http://babelfish.altavista.com/babelfish/trurl_pagecontent?lp=fr_en&trurl=http%3a%2f%2fwww.lemonde.fr%2fweb%2fimprimer_element%2f0,40-0%402-3244,50-979854,0.html

==babelfish version of interview==
Anthony Garrett Lisi: "the theory is mathematically and aesthetically superb"
LEMONDE.FR | 19.11.07 | 14h00


How many new particles are they predicted by your theory ? Some criticize reproach him not for predicting the mass of it...

In its current state the theory predicts the existence of 20 new particles. Because the theory is not completely developed, that can however change.

Indeed, many new particles are predicted and I really hope that these particels will indeed be found. What is disturbing though is that gravity also seems to be mediated by virtual particles. So, gravity is treated as an ordinary force whereas there are a number of indications that point in a different direction. Therefore, I think that this is a "theory of everything" - except for gravitation.

Rudi Van Nieuwenhove

 

[marcus]

possibly useful exchange on Jacques Distler's blog between J.D. and G.L.
http://golem.ph.utexas.edu/~distler/blog/archives/001505.html#c013271

 

[CarlB]

possibly useful exchange on Jacques Distler's blog between J.D. and G.L.
http://golem.ph.utexas.edu/~distler/blog/archives/001505.html#c013271

I think that Garrett is being very conservative in his rewriting of physics. He's trying to draw outside the lines by squinting a bit and that really doesn't work so well.

Instead of insisting that "New Physics" be completely compatible with all the theory of the "Old Physics", it needs to be compatible only with the experimental results of Old Physics. If the theory of old physics was perfect it wouldn't be so difficult to reconcile general relativity with quantum mechanics.

The essence of what the old physics knows about quantum mechanics is distilled into the Standard Model. If a new physics reproduces the standard model on a simpler set of assumptions than the old physics, you have to give more credit to that new physics than you gave to the old. Sure the old physics assumed restrictions such as Coleman-Mandula etc., but Coleman-Mandula is not an experimental result. It is a theoretical constraint that is built on a rather long and involved chain of reasoning. So long as a New Physics gets the standard model, you cannot use experimental arguments against it, only theoretical ones.

But new physics theories have ALWAYS violated the theoretical restrictions of the old physics. That is why they are new. What new physics must do is to reproduce what is predictive in the old physics, it does not have to match exactly the methods for getting those predictions.

I think that Garrett did violate the theoretical limits of the old physics in packing the standard model plus gravity into E8. But I don't think this matters. If Einstein rolls over in his grave that's okay; hey, that's what new physics always does to old physics. If the people who staked their careers on understanding the exact details of the old physics scream bloody murder, that's even better.

History shows that when new physics arrives, it is never accepted by a majority of the old physicists. Instead, the battle is fought among the new generation. The old physicists eventually die. All you really need to know is that Garrett's theory is appreciated by a few; new physics never wins a majority (until there is an experiment that decisively supports one of its predictions).

 

[PhilosophyofPhysics]

"All truth goes through three stages. First it is ridiculed; then it is violently opposed; finally it is accepted as self-evident." -Schopenhauer

 

[10st1denTT]

sadly stages one and two do not determine a phase three outcome, right(?)
so your (schopenhauer's) apt observance qualifies better for a a posteriori musing (philosopher style... there is not much Predictive Power in it
The hard work has to be done now!
But not by me :)
The media frenzy garanties that the paper will be scrutenized (and sink to shame(?) or fly to glory). What will not happen is that it simply gathers dust in a dark basement shelf (as has fared to many a fine theory before).
So things are on a deterministic road now anyway.

 

[marcus]

"All truth goes through three stages. First it is ridiculed; then it is violently opposed; finally it is accepted as self-evident." -Schopenhauer

...
The media frenzy garanties that the paper will be scrutenized (and sink to shame(?) or fly to glory). What will not happen is that it simply gathers dust in a dark basement shelf (as has fared to many a fine theory before).
So things are on a deterministic road now anyway.

Lost I,
nice summary.

The issue of the huge wave of public admiration and media attention has come up.
1. is the publicity harmful to the longterm interests of science?
2. is it harmful to the development of E8 theory? (say, by making it less likely that other physicists will want to help Garrett Lisi work out the bugs, derive predictions, and complete the picture)
3. is it harmful to G.L. personally, if not to his theory's prospects?

Does anybody have thoughts about this?

My personal opinion is that the admiration and attention do no harm (aside from possibly provoking anger on part of those with competing demands for science media stature and glamor).

I think it's fine for the public to be exposed to attractive images of scientists. I don't see any harm in a short run of media enthusiasm. Things like this die down after a few weeks and leave no permanent expectations to be disappointed. What actually are we afraid of? What is supposed to be the harmful consequence to science?

I think the several decades of hyping string theory as a Theory of Everything, teaching a generation of adolescents to expect it to provide the final answers---a concerted effort involving public statements by many scientists---has been harmful to science. By debasing standards of empiricism and raising unreasonable expectations. But that is on a different scale.
==================

What I do think has been harmful is what I see as vindictive and relentless hammering of an incipient theory on a handful of science blogs.
I don't completely understand the motivation for all the anger I heard. Some of it came from string theorists, of course, and could have been motivated by jealousy---if they feel that the glamor of aspiring to a ToE, "realizing Einstein's dream", is their turf. If they felt that G.L. was infringing on public attention that was rightfully theirs. Maybe some string theorists feel that any sign of competition is an outrage and should be crushed.

But the outrage I heard in the science blogs didn't just come from envious or defensive string theorists. I think it contained a kind of puritanism and desire of some to control public reaction---a sense that publicity (especially when it gets out of their control) is somehow bad. Somehow G.L.'s infant theory was being given a whipping because it had made a media splash and that was BAD. It was out of control and it was a no-no.

I don't really understand but it seems to me that science blog-owners may think that they should be the gatekeepers and regulators of public attention.
Also the prominent ones are a new type of media personality. A little bit like science "talk show hosts". They have a kind of power. And that means that when things get out of control or where there is an issue of control, then the APPARENT issues (e.g. the degree of incompleteness of a new theory, the prospects for constructive revision, whether inconsistencies are fixable or fatal etc.) may not be what all the animosity is about. It may actually be more about issues of power.

Then there's the issue of conformity. Science is a community function that requires a balance of conformity and individuality. when the chips are down conformity has to win, and the ultimate sanction is ostracism. Ultimately the survival of the community trumps all other considerations. So that instinctive reflex has to be taken into account as well.

All in all, quite a fracas! Even you might call it a kind of minor street-riot.

====EDIT====
I wanted to include this valuable quote from S. Hossenfelder, because I strongly agree with almost everything said here and it is said very well and clearly, for the most part:
==quote Hossenfelder==
The hype of science in the media just reflects a general trend caused by information overflow. In today's world you have to scream really loud to be heard at all, and headlines are the better the fatter. I generally dislike this, as it leads to inaccurate reporting, unnecessary confusion, and bubbles of nothing. All of which obscures sensible discussions and is a huge waste of time.

However, despite this general trend, what worries me specifically about popular science reporting is how much our community seems to pay attention to it. This is a very unhealthy development. The opinion making process in science should not be affected by popular opinions. It should not be relevant whether somebody makes for a good story in the media, or whether he or she neglects advertising himself. What concerns me is not so much the media re-re-repeating fabulous sentences, but how many physicists get upset about it. This clearly indicates that they think this public discussion is relevant, and this should not be the case.

Concerns about the public opinion arise from the fear it might affect the funding of some research areas. But it's not the media who creates fashions and hypes who is to blame. Neither is it the scientists who are not careful enough when talking to journalists who are to blame. To blame is everybody who tolerates that the funding in science is subject to irrelevant factors.
==endquote==

The boldface emphasis is in the original. There is some ambiguity. They should not think that the public discussion is relevant? (Because publicity does not affect the judgement of the agencies.) Or their fears are justified and indeed publicity affects the funding agencies and THIS should not be the case.

the last sentence may require some clarification, is it really true (as some people fear) that irrelevant factors do---and if so what factors. my impression was an oldboygirl network based on prestige and influence entirely within the community and there is some politics sure, but it is not public politics.

But on the whole, apart from some ambiguity, I agree very much with the middle paragraph---and include the rest for context.

 

[10st1denTT]

just want to pay you a compliment on the pithy way you sum things up.
//...//
Hope you keep striving towards conventional understandability, because you have something to say to us((my bold)).

Thanks marcus,
I think that was the kind of welcome on a board that anybody would wish for! In contrast to your last statement, i am somewhat sceptical though. I was mainly lured here by noticing that John Baez and Garrett Lisi had been dialoging here prior to the release of his now famous (read with a neutral tone) paper. My personal expertise on the matter at hand is Not deep. And my presents here is more about receiving than giving! I am well aware that you have been closely involved in the discussions of Lisi's ideas (dating back till 2005!). And i feel honoured to conversing with you now...
My ambition reaches not further than to abstain from disgracing these pages with too much stupidity. (My hope is that the "Lisi-ToE" was a valuable contribution (at least) and that the polemics around it will quiet down.)...

//(a child demands my attention

 

[marcus]

Hi Lost I.

I thought my initial response was immodestly cordial so I toned it down, in edit. But I am glad you saw and copied!

There is something that is more on-topic that concerns me a lot now, and I want to raise.

For several days I have had the suspicion that G.L. project of an E8 theory runs into trouble in part because it is not based on deSitter general relativity.

I have been reading Pereira etal paper 0711.2274 "de Sitter Relativity: a new road..." and trying to understand it.
It has a new form of Einstein's strong equivalence principle (that invokes deS local ambiances rather than the conventional Minkowski ones) and a new form of the Einstein field equation.

I keep struggling to understand the paper, and also why it is not picking up more notice. These guys are not nuts. They are top people by Brazil standards, at the Sao Paolo Institute for Theoretical Physics.
If you are going to unify QM with GR, then what General Relativity do you unify it with?

The conventional Minkowski space doesn't expand. deS space does. In a world with a positive cosmological constant it might be more realistic to work with a form of GR that is locally deS rather than locally Minkowski

So I have been expecting that if Garrett's approach is a good one then at a certain point someone will have a flash of insight and say "Wait! This fits better with deSitter General Relativity!" And then (if the approach is an overall good one) some of the kinks will get worked out, or so I have been imagining.

This is a dim hunch that you don't usually tell people.

 

[10st1denTT]

"subtle is the Lord"

In the end there will be a higher authority than the presently reigning DemiGods, that decides which fundamental theory is simply right and which one is Gloriously FALSE!
Somewhere in the basic foundations of reality there Must be beauty and (a kind of!) simplicity. There Must be logical consistency. And there Must be an answer to the question: Why had Everything to be the way it would?
Every once in a while there Will come an Individual who thinks deeper, abstracts more efficently (the bones from the flesh) and finally goes one step Further (for the mainstream to follow).
It's about time such a "Ferguson" showed up (flying in on a second hand kite or what ever!).
If Nature would be as intricate/convoluted/traversed/outre´/... as the string theoreticians figure, she would trip over her own TOEs at every single instance!
I think, however bad the state of morals in physics, there is enough space under the feet of the bestriding giants for a Ferguson to grow, thrive and bloom. (I think btw that she is sitting in a cold spartan room with a spartan bed and a raw spartan kitchen table and a lot of the Right books - and only a little, shabby computer- Right Now! - talking to herself, the physicists/mathematicians (alive or dead) from her books and to some Imagined/Fancied Higher Being also!)

((ExpectTheUnexpected))

 

[10st1denTT]

(this is going to be a funny game :) , we are seriously out of sync, isntit)
((i accommodate any style bytheby if i have the impression of a likable soul on the other side))
to your last post: I am a trained mathematician and conditioned to talk only things, i understand at least in their basic workings. You are presently talking over my head! I find the Lisi idea promising to think the Einstein world anew (demote the metric, think "connection"). I am just beginning to study MM. As I said, I am here to Learn!

 

[marcus]

Why the fabulous E8 connection could be fabulous.

The basic object in LQG is the SPIN NETWORK. Conceptually the spin network can be thought of as dual to the connection* idea. It only involves a finite (or sometimes countable) number of vertices, while a connection is defined over the whole continuum.
But it does give you information about what happens when you pass from one point to the other. Spin networks and connections are kindred ideas.

In LQG, quantum states of spatial geometry are described by spinnetworks. But so far only geometry is described by them, not matter. Matter fields can be stuck on, but they don't come free as part of the spinnet.

Lee Smolin's research group is embarked on trying to realize the standard particles of matter as TWISTS AND BRAIDS in spin networks. It is a risky and difficult venture. They have to show that patterns of braiding can propagate without getting unravelled, and that their interactions correspond to the known interactions of particles.

Twists and braids (in a network of tubes or wires) could turn out to be dual to a more complicated type of connection----analogous to how ordinary spinnet (without twists and braids) is dual to a simple geometrical connection.

Twists and braids are ALGEBRAIC things in the sense that you can combine them (doing two braids in sequence gives you a new braid) and sometimes one will UN-do another.

I have to go, and don't have time to finish this thought. What I am driving at is that realizing the standar particles as twists and braids in a network as you go from one point to another could be akin to realizing the same particles in the Lie group of a connection. Each could provide helpful guidance for the other. This would be a fabulous duality, especially since the way is difficult on each side.*What is a connection? In ordinary differential geometry a connection specifies a way for tangent directions to change as you travel from one point to a neighboring one---a connection defined on a shapeless continuum can give it geometric shape just as well as defining a distance function (or metric) on it can. If defining the shape of a continuum by specifying a metric on it is the usual way, the practice of defining it with a connection is not far behind.

 

[10st1denTT]

I would simply like to add that i whole heartedly subscribe to your observances in post #152.
BTW, what irritated me in your post #154 was the passus

"it might be more realistic to work with a form of GR that is locally deS rather than locally Minkowski"

i thought i had learned from the (quite excellent) thread on SO(4,1) here on PF that "deS" (meant to be read deesse?) was locally Minkowski Anyway(!) (in perfect accord with what we know about space expansion and what we see in our labs)... Maybe i should have a look on that Pereira paper (ififindthetime

 

[jal]

How will E8 be tested?

3. Dynamics
The dynamics of a connection is specified by the action functional, S[ : A]. Classically, extremizing this action, constrained by boundary data, determines the value of the connection, : A(x), over a region of the base manifold. The value of the connection may also be used to infer topological properties of the base manifold. Quantum mechanically, the action of a connection over the base manifold determines the probability of experiencing that connection.[15] Since quantum mechanics is fundamental to our universe, it may be more direct to describe a set of quantum connections as a spin foam, with states described as a spin network. Under more conventional circumstances, the extensive methods of quantum field theory for a non-abelian gauge field may be employed, with propagators and interactions determined by the action.
In any case, the dynamics depends on the action, and the action depends on the curvature of the connection.
… 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 theory proposed in this paper represents a comprehensive unification program, describing all fields of the standard model and gravity as parts of a uniquely beautiful mathematical structure. The principal bundle connection and its curvature describe how the E8 manifold twists and turns over spacetime, reproducing all known fields and dynamics through pure geometry.

Everyone has their special model that they are working on and I assume, that is what they will be using to evaluate E8.
They will be looking at E8 to determine if their model is represented and will arrive at one of the following conclusions.

1. Yes, …. My model fits, therefore, E8 could be right.
2. No, …. My model does not fit in, therefore, E8 must be wrong.
3. Maybe, …. My model does not have or need all of the connections shown.
4. Maybe, …. My model needs more connections then what is shown by E8.

Then I expect that the next phase will be,
1. E8 says that it’s there but we cannot locate it in the noise.
2. My model says it’s there but we cannot locate in the noise.
--------
As a concrete example;
What would the following authors conclude?
http://arxiv.org/abs/0711.3910
SU(6), Triquark states, and the pentaquark
----------
jal

 

[cyberiantiger]

I love the theory, though "simple" is perhaps not a word I would choose to describe it.

I confess that my maths probably isn't up to understanding it yet, it seems that I really need to understand octonions and lie groups in order to get a real handle on this theory (I dropped maths 2 years into a university course for reasons I won't go into).

The majority of reviews on science blogs which tear the theory down for one reason or another are mostly flawed and if one reads around you can find alternative reviews which point out the same flaws (except for the one I read which claimed you couldn't add different types of quantity together - where the paper was quite obviously talking about vector maths and not actually adding different types of quantity together) but then added that though there were flaws they could be worked around. I gather that some of these blogs are owned by respected scientists, and I find this quite disturbing.

With regards to the mass media attention, I think it's probably done the theory more good than harm; Alternative theories historically have also initially suffered the same sort of acceptance by mainstream science, it's a shame mainstream science never learned the lesson that theories should be accepted solely on their ability to be proven or disproved.

The best summary I can see is that the paper is an incomplete alternative way of approaching solving some fundamental physics questions which string theory tried to address and mostly failed (Anything which by definition cannot be proven is a religion NOT science).

I will hopefully be spending some of my spare time trying to understand octonions, Lie groups and eventually E8, then I will reread the paper and hopefully understand the finer details and then unfortunately I will have to catch up my physics from a long way behind where it needs to be in order to start trying to apply this theory to anything meaningful.

Meanwhile I'll be sure to be keeping tabs on anything related to this topic, especially this thread.

The theory perhaps strikes a cord with me because what little physics I did led me to believe that there were probably 2 more forces on top of the standard 4 forces I learned about, mainly for reasons of symmetry with the fundamental particles. Well below the level this thread is at, did I mention my physics sucks ?

I suspect the theory will become more beautiful as I understand more about e8 and the Lie Groups, I also suspect the theory will become more flawed as I understand more about the physics side of it though ;)

Sorry for the long post, hopefully I'll have something more useful to contribute if I ever managed to catch up to the level this thread is at.

 

[Count Iblis]

In the interests of balance, we should probably point out that Lubos has savaged the paper.

What a surprise! http://insti.physics.sunysb.edu/~siegel/parodies/atchoo.html"

 

[Coin]

I love the theory, though "simple" is perhaps not a word I would choose to describe it.

The title was a pun. E8 is an Exceptional Simple Lie Group.

I will give you a few minutes to stop groaning

 

[marcus]

The title was a pun. E8 is an Exceptional Simple Lie Group.

I will give you a few minutes to stop groaning

Yes! and puns aside, this might be a place to cover a few essentials of group theory (counting on Coin's help)

a simple group is sortofanalogous to a prime number in that you can't factor out any subgroup and collapse it down any further.
a simple group is one that contains no subgroup of a type that lends itself to factoring out (called a normal subgroup)
(like a prime number doesn't contain any factor you can divide by to make it smaller)

If the group can't be simplified that way, it is called simple (even if it's highly intricate, because it is already as simple as you can make it without totally trashing it).
=======================

Actually the source of Garrett's beautiful diagrams of E8 is another special kind of subgroup called a maximal abelian subgroup, or Cartan subgroup. A Cartan subgroup for E8 is 8 dimensional. that is the basic reason that all Garrett's E8 diagrams exist in 8D.
The Cartan subgroup is an easy concept to grasp and it's the key to how the larger group's structure is analyzed.

If anyone is curious about it, just ask. Coin, or myself, or half a dozen other people visiting PF Beyond forum these days, could possibly explain.

More difficult ideas, I personally don't make any guarantees or promises. But the Cartan subgroup is a babystep idea---and it's amazing how much structure it unlocks.

 

[dipstik]

please explain the cartan subgroup.

-thanks

 

[marcus]

I'd be happy if some of the others want to take over. But you know what a group is. If you know matrix multiplication you can think of a group of matrices----or pick up a book and think of the different ways to flip it, turn it etc.
Especially if it is square so there are more possible moves (i.e. symmetries. )

You can experiment with groups and find that not all moves commute.

But in any group you can find subgroups (even if it is only the trivial subgroup consisting of the identity) and in any group you can always find one or more commutative subgroups.

Like pick one element, and square it, and keep on multiplying it by itself. At least in a finite group that looks like it would generate a subgroup that is all commutative. Correct me if I'm wrong, or ask questions if you don't follow.

So you can start with one element and its powers (square, cube..) and you can keep picking other elements and trying to see if they commute with what you already have. So you can keep adding more and more and building up the subgroup until you have a maximal commutative subgroup. That means you can't add any more. Any other element you try will not commute with some element you already have.

It's like the maximal bunch of friends you can invite all to the same party at your house. So to sum up:

1. Not all groups are commutative. In some (like even the symmetries of a square) you find a pair of elements that it matters in which order you do them.

2. All groups have subgroups

3. Any group has at least one commutative subgroup.

4. At least under reasonable assumptions, I'd expect a group to have a maximal commutative subgroup.
================

That is basically what a Cartan subgroup is. now you can ask all kinds of questions like is it UNIQUE in some sense.
If you started building a commutative subgroup with different initial choices whould you get something that was at least the same size?
Questions of the sort mathematicians love to ask. don't let these intriguing questions distract us from the basic fact that we are talking about a very simple concept.

And another question is what about INFINITE groups, or what if the group is a continuum. A smooth manifold of a certain dimensionality----like 1, or 2, or 248.
Then what does maximal mean? And you want to know what the DIMENSION of the subgroup is, because you can't count discrete elements any more. And you want to know if maximal commutative subgroups are unique in what sense? At least they should have the same dimension.

Several other people are doubtless more familiar with this and could continue the discussion. my impulse is to consult Wikipedia on Cartan subgroups at this juncture.

But anyway to conclude this intro, E8 has a maximal commutative subgroup of dimension 8.
The whole group is a manifold of dimension 248. And it is not very commutative. But you can find a commutative subgroups of dimension 8.

And that turns out to be cool because you can then study how the small 8d subgroup ACTS on the group at large and...=====but OOPS! at this point we have to say what is a LIE ALGEBRA.
Groups that are manifolds are nice to study because a manifold has a tangent space at every point and if it is a group then it has a tangent space at the identity which the groups own multiplication projects a nice bit of algebra onto, making the tangent vectors at the identity into an algebra.

And then the Cartan subthing is going to act on the thing as a whole and it's linear (vectors, now) so there are going to be eigenvectors and eigenvalues====matrix stuff that you normally get a math package to do, but which is extremely useful.

If want to proceed, ask something. Then maybe somebody else besides me will take a turn.

=========EDIT TO REPLY TO NEXT============

Coin thanks! First of all for not leaving me dangling. Also for clarifying. And what you say is basically right

So the cartan subgroup of E8 would just be the largest subgroup wherein the lie bracket is everywhere 0? Is that right?

Right! (im not an authority but I would say largest subalgebra of e8 wherein the bracket is zero.------or the largest subgroup of E8 wherein ab = ba)

a useful confusion exists between a Lie group and its algebra---as between a diff manifold and its tangent space. one is linear with vectors you can add, and one isn't but they are intuitively much the same thing and should be thot of in the same mental breath :-)

To be circumspect about it, the only added complication here is keeping track of when we are talking about the group E8 and when we are talking about its Lie algebra, the tangentspace at the identity that has the bracket defined. that would normally be called e8. they tend to use caps for the group and lowercase for the algebra. but the two are so closely related that people often don't distinguish carefully and write E8 for the algebra as well as for the underlying group.

 

[Coin]

I'd be happy if some of the others want to take over. But you know what a group is. If you know matrix multiplication you can think of a group of matrices----or pick up a book and think of the different ways to flip it, turn it etc.
Especially if it is square so there are more possible moves (i.e. sym. )

You can experiment with groups and find that not all moves commute.

But in any group you can find subgroups (even if it is only the trivial subgroup consisting of the identity) and in any group you can always find one or more commutative subgroups.

To be clear, "commutative" and "abelian" mean the same thing.

So when marcus says a cartan subgroup is the "maximal abelian subgroup", he just means it is the largest subgroup where a*b=b*a is always true.

(I'm not specifically familiar with what constitutes a "cartan subgroup", though. Does it make any difference that in the case of e8, we're taking the Cartan subgroup of a Lie group? Also, isn't E8 already abelian? Wouldn't that make its maximal abelian subgroup just equal to E8 itself? Or does the subgroup have to be proper? Hm, now I'm confused...)

EDIT: Okay, so I think I've got it: E8 is commutative under the group operation +, but it is NOT commutative under the lie bracket (since of course lie brackets are by definition anticommutative, meaning they must satisfy the [x,y] = -[y,x] property). So the cartan subgroup of E8 would just be the largest subgroup wherein the lie bracket is everywhere 0? Is that right?

 

[william donnelly]

Coin, you're getting closer, but you are confusing E8 (the Lie group) with e8 (its Lie algebra).

E8, the Lie group is a 248 dimensional manifold. It has a multiplication that is NOT always commutative. i.e. a*b != b*a.

e8, the Lie algebra is the 248 dimensional tangent space of E8. It has an addition, and addition is always commutative. It has a Lie bracket that is not necessarily zero, [a,b] != 0.

Sitting inside E8 is the Cartan subgroup, which is 8 dimensional and commutative. It's shaped like an 8-dimensional torus. It's a maximal Abelian subgroup, in the sense that there is no bigger Abelian subgroup that contains the Cartan subgroup.

Sitting inside e8 is the Cartan subalgebra, which is 8 dimensional. The Cartan subalgebra is the tangent space of the Cartan subgroup. It has a Lie bracket that is always zero.

 

[Coin]

William, thanks! While I have your attention, do you think you could maybe offer any help with my questions from page 8?:

From looking at wikipedia and this page (I think from the "atlas" people who "mapped" E8 awhile back?), the impression I get is that E8 consists of those vectors of length 8 that can be formed from adding together integral multiples of the members of a basis of "root" vectors. The group operation appears to be vector addition, and the "root" vectors consist of all 8-member vectors of the form
<±1, ±1, 0, 0, 0, 0, 0, 0>
or
<±0.5, ±0.5, ±0.5, ±0.5, ±0.5, ±0.5, ±0.5, ±0.5>
Because there are 8-vectors which it is not possible to construct by adding together these roots, E8 forms a proper subset of the set of {all 8-member vectors consisting of integer or half-integer values}.

Is all this correct? Okay, so: If so, is this the E8 Lie group or the Lie algebra? In either case, what is the corresponding algebra/group? And in the case of the algebra, what is the lie bracket? (The atlas page says only that the lie bracket for E8 is "very hard to write down". Oh.) And finally, is it "weird" that E8 is a lie group/algebra-- yet has only a countably infinite number of members, and is apparently constructed entirely of discrete structures? I've thus far only encountered lie groups which are continuous, where it makes sense to talk about things like "infinitesimal generators". There doesn't seem to be anything infinitesimal about E8 at all. (Mind you, I'm not complaining-- I have a CS background and I am WAY more comfortable with anything discrete than I am with anything continuous! It just seems jarringly different from the way I understood people to use lie groups/algebras previously, and I'm confused how I missed this.)

Past this, the biggest thing that is confusing me here are the "roots". First off, although this is probably not all that important, how on Earth were they chosen? That is to say, was someone just playing around with addition on different sets of basis vectors, and went "oh hey this particular combination of 248 vectors acts kinda weird, everyone else come look at this"? Or was E8 first discovered as some other kind of structure, and it was later realized that the 8-vectors above are a convenient representation of that structure? Second off and more importantly, I am dreadfully confused by these root "diagrams" such as one finds all over Lisi's paper. As far as I can tell, the idea is that we plot each of the roots as a point in eight-dimensional space. (I take it that we plot them by simply treating each 8-vector as a coordinate?) However, then we for some reason draw lines between some of the roots! Why on Earth do we do this? What do the lines mean?

I'm similarly a little bit confused by this "simple root" thing that wikipedia describes. As far as I can tell, the "simple root"s are an alternate integral basis for E8, consisting of the eight vectors found in the rows of this matrix:

Wow, that's convenient! What's confusing me here though is, why on earth do we bother using the 248 roots described above, when we could just use these 8 simple roots and be done with it? Another thing confusing me: Wikipedia offers a "dynkin diagram" (which I take it is different from the "root diagrams" used with the 248-root system) which looks very deep and beautiful:

http://upload.wikimedia.org/wikipedia/en/d/d3/Dynkin_diagram_E8.png

... but I can't for the life of me figure out what it's supposed to mean. Wikipedia says that this is a graph where vertices represent members of the simple root system, and edges are drawn between any two members of the simple root system (I assume this means a 120 degree angle when we treat the simple roots as coordinates in 8-space.) Okay, that's nice, but why? Why do we care which members of the simple root system are at 120 degree angles to one another?

I have a couple more questions related to what Garrett in specific is doing, but these are just my questions about the E8 [group? algebra?] itself. Any help in figuring these things out would be appreciated. In the meanwhile, something vaguely frustrating me is that there does not seem to be any specific information on E8 in the obvious places. It is clearly a well-researched subject but the best I can find is these very vague wikipedia-style summaries, and John Baez's writeups (which are invariably exhaustive and lucid, but everything I've found which Baez has written covering E8 seems to be primarily about other things, like octonions, and only indirectly concerned with E8). Is there some particular thing, perhaps a book, I would be best served by going and reading if I am curious about the mathematics of E8?

I take it from your comments that the 8-vector w/addition I describe above is the lie algebra. If this is the construction for the lie algebra, how are the members of the lie group constructed? And how do you find the members of the Cartan subgroup of the e8 lie group?

 

[william donnelly]

This 8d space is _a_ Lie algebra, but it's not the e8 Lie algebra, it's the Cartan subalgebra. The set of 240 8-dimensional vectors described in the link is the E8 root system, which lives inside the Cartan subalgebra.

Actually constructing the Lie group E8 is apparently quite complicated, and I have no idea how to do it. John Baez talks about it in TWF 253: http://math.ucr.edu/home/baez/week253.html.

To find the Cartan subgroup, one thing you can prove is that the Cartan subgroup has a single vector, that when you take all multiples of this vector you can recover the whole Cartan subgroup. So if you can find this one vector, you get the whole Cartan subgroup. I'm not sure how you would get this vector though, other than by just trying all of vectors.

 

[rntsai]

root labels

There's a standard way to label the 240 roots in Table 9
of Lisi's paper as weights of the adjoint rep of e8.
The rep is 248 dimensional; it has a weight [0,0,0,0,0,0,0,0]
with multiplicity 8 that corresponds to the cartan subalgebra.
The remaining 240 weights have multiplicty 1 and can be listed as :

[ [ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, -1 ],
[ 0, 0, 0, 0, 0, 0, 1, -1 ],
[ 0, 0, 0, 0, 0, 0, -1, 1 ],
[ 0, 0, 0, 0, 0, 1, -1, 0 ],

... <deleted 230 of 240 nonzero weights>

[ 1, 0, -1, 0, 0, 1, -1, 0 ],
[ -1, 0, 1, 0, 0, 0, -1, 1 ],
[ 1, 0, -1, 0, 0, 0, 1, -1 ],
[ -1, 0, 1, 0, 0, 0, 0, -1 ],
[ 1, 0, -1, 0, 0, 0, 0, 1 ] ]

so each "particle" is represented by 8 integer values.
Actually it looks like only (-2,-1,0,1,2) occur in the list.
This representation is different from the coordinates
of the polytope mentioned in the paper.

Table 9 includes 8 labels :

(1/2i)w_T^3,(1/2)w_S^3,U^3,V^3,w,x,y,z

These are probably more physically meaningful than the
above integral weights. There should be a map between the
two which would be good to have explicitely worked out.

 

[Unbeliever]

Even if Dr. Lisi's model turns out to be other than the long-sought TOE - if it merely points others in fruitful directions - it will have performed its appointed task, and have followed Galileo's Dictum, and contributed to science. And, who knows, maybe we're all in at the ground floor of historic science! I, for one, am happy to be so close to the edge of the envelope of the search for knowledge. I'm not by any means a physicist, only an interested layman, but I enjoy being here. Thanks for having such a fun discussion!

 

[marcus]

Even if Dr. Lisi's model turns out to be other than the long-sought TOE - if it merely points others in fruitful directions - it will have performed its appointed task, and have followed Galileo's Dictum, and contributed to science...

I share your attitude. Win or lose, a testable theory---one that makes new predictions that can be checked---can help advance understanding. especially if it stirs people up and gives them ideas of things to try and not try.

At the moment I can't think what Galileo's dictum might be. Can someone help me out?
I thought the programme of empirical science was laid out by Francis Bacon, early 1600s. A contemporary of Shakespeare and an early martyr to the frozen food business.
(he died after an unfortunate experience with a chicken.)
============================

Online conversation between two science writers: George Johnson and John Horgan
discussing AESTOE among other things
http://bloggingheads.tv/video.php?id=471

the first two minutes is about Horgan's list of the 70 greatest science books, but then they get into a 14 minute discussion of E8 and events surrounding its arrival on the scene. Savvy science journalists, especially George Johnson IMO. They made some astute comment on the academic and media reaction. Then they got on to other (most likely sillier) science stories of the past week.

 

[Unbeliever]

At the moment I can't think what Galileo's dictum might be. Can someone help me out?

I got that from Bertolt Brecht's, The Life of Galileo:

Science knows only one commandment: contribute to science.

I read somewhere else that this is known as Galileo's Dictum.

 

[marcus]

Brecht deserves a lot of respect as a playwright and it is a good dictum.
But there may be two famous Galileo dicta. I googled and found this other saying that the universe is a great book:

"this grand book . . . is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures."

http://findarticles.com/p/articles/mi_m0425/is_n1_v55/ai_18299591/pg_3

and something like that in Italian
Per Galileo l'universo è un libro, il «grandissimo libro che continuamente ci sta aperto innanzi agli occhi …, ma non si può intendere se prima non s'impara a inteder la lingua, e conoscer i caratteri, ne' quali è scritto. Egli è scritto in lingua matematica, e i caratteri sono triangoli, cerchi, ed altre figure geometriche, senza i quali mezzi è impossibile a intenderne umanamente parola».
http://www.italialibri.net/arretratis/apr00.html
This has the same quote and also a great quote from Johannes Kepler.
http://www.phyast.pitt.edu/~micheles/notabili.html
The Italian Wikipedia begins its Galileo article with this same quote
http://it.wikipedia.org/wiki/Galileo_Galilei

 

[arivero]

A secondary reference is a kind of paperback answer to Horgan's "End of Science" (I guess it because it was contemporary and the editors used the same format and cover colours; it could be reverse, or unrelated)

https://www.amazon.com/dp/0316648280/?tag=pfamazon01-20
https://www.amazon.com/gp/product/0805073493/?tag=pfamazon01-20

The Amazon review of this book contains Brecht's reference. It is taken from the second page of the introduction, and then again from the first quote in first part of the book. So it comes, in some sense, from the editor, Edmund Blair (is he related to Eric Blair, or is it a very common name in England?).

If I were to abstract Brecht to a single quote, it could be
“Of all the days that was the one /
An age of reason could have begun”
But note this is also reductionist; to get an idea of Brecht's arguments, one should at least to read the whole speech of Galileo to Viviani in the last act, if not the whole work with some dense introduction about the text.