[Jacques]

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An Exceptionally Simple Theory of Everything

Hi
I am just a layman and what I can read on it is that it is anything but simple...
What I can understand from that is only that this 'mathematical structure' (E8) describe well the world. Remind me a little bit of the epicicle:
It doesn't fit ? And more dimension...
Do I need to know QM to appreciate the simplicity ?

[Martin]

Jacques if you know what "in-joke" means, I would really like to know the French idiom for "inside joke".

Math and physics people always have these jokes and puns (double entendre?) that refer to the technical terminology of their specialites.

In the mathematics of Group Theory there is the technical concept of a simple group.

As it happens, E8 is a simple group. (it doesnt have to do with ordinary ideas of simplicity)

also E8 belongs to a small number of groups called the EXCEPTIONAL LIE GROUPS. It is the largest exceptional Lie group.

All the exceptional Lie groups are simple.

The moment I saw the title of Garrett's paper I started laughing because he had made a witty play on words----with some mockery or mild irony also.

It is not yet a complete Theory of Everything either, this term "ToE" has always been a gross exageration used by string theorizers. One of the extravagant promises that has never been fulfilled in over 20 years. So for Garrett to use "ToE" in his title was also a kind of subtle mockery.

He is a complex person. I took the title of the paper to be more witty than serious. But everyone can see it as they wish, there is certainly no one correct view.
============================

in case anyone is curious, a simple group G is intuitively one which cannot be collapsed down to a smaller group H

there is no non-trivial many-to-one mapping that preserves multiplication
that is, no group-mapping phi that goes G --> H, unless either it is one-to-one or H is the group with one element.
if you know Bourbakistic terms like surjection and injection then any nontrivial surjective homomorphism must be injective
and the same can be expressed in terms of subgroups----the non-existence of a certain type of subgroup of G.

the intuitive idea is that a simple group G has been collapsed down as far as it possibly can be collapse. all the air and water have been squeezed out and it is down to hard essential structure

but this does not make it simple in ordinary layman's language, only perhaps it is MORE simple than it MIGHT have been.
but still can be quite intricate!

[bascule]

Martin,

I saw a rather critical review of this paper, which unfortunately I cannot find anymore.

The critic cited descriptions in the paper which expressed sums of certain forces which the critic considered incompatible.

Have you seen anything along those lines?

[Martin]

Hi Bascule,
Sorry for not responding earlier. Holiday intervened and I didn't see your post until now.

G.L.'s first shot at a ToE does have serious flaws and he has been pretty frank about pointing out where he thinks it needs more work

I think the main question to be asking is whether or not there are some new ideas here that can be put to use.

There is a big discontinuity between the splash his paper made in the media (because interviewing Garrett makes good copy---for one thing he has a good sense of humor, plus of course the atypical lifestyle)
and the actual situation within the nonstring QG community.

Of course the stringfolks damned him fervently up and down non-stop. He infringed on their image.

But that doesnt matter. The real reason Garrett came out with his paper at this point----which he was thoroughly up front about----was it was time to get more people working on it.

He had made a good enough beginning that he thought he could recruit collaborators, and other people to help by working independently along similar lines. And there is a great deal of work to be done.

Not only does he have bugs to work out---but his entire theory (even assuming he gets all the glitches smoothed out---is not yet a quantum theory. What he has is a superstructure which it MIGHT be possible to graft onto LQG.

LQG is a quantum theory of geometry where the geometry is represented by a math object called a CONNECTION. Einstein described geometry with a distancefunction called a METRIC and later, at least by 1980s, people found out that you could drop the metric and use a connection instead.

Intuitively a connection is something that describes how structures twist and roll as you slide them about on the hypersurface---so it relates the tangentvectors at one point with the tangentvectors at a neighbor point. A connection lets you do parallel transport---it gives a meaning to that.

All this so far is CLASSICAL. What LQG did in the 1990s was formulate a quantum theory of connections, so you could have a hilbertspace of quantum states of the geometry of your continuum.

But the kind of connection that LQG deals with is quite rudimentary and only encompasses geometry (that was the original idea)

What Garrett offers is a much larger fancier type of connection that encompasses matter and forces. But it is not yet QUANTIZED.
(and it has other bugs which hopefully can be worked out, but that is the main lack that I see)

What he has basically done is apealed for LQG people to team up with him. This came out in the ILQGS (a conferencecall seminar called international LQG seminar) that was held soon after the appearance of his paper.

in a sense it is make or break now. It's a big job and he can't do it all. Either other people from nonstring QG community will join in, and his theory will mature and make some progress (whether ultimately right or wrong doesnt matter yet, tests are in the future) or it will not attract collaborators and it will fade from sight.

there have been some positive responses, but we won't know until we start seeing papers by new authors or by Garrett and others.

that's a quick assessment, may be quite wrong but that's my take at the moment.

have to go.

[Fred56]

I read a critic (I'll now be compelled to find this again -and I have to apologise pre-emptively because my pc is mid-mobo upgrade and I have 3 different 64-bit brand new linux (linuces?) I'm giving a tryout -phew): said that Lisi is mistakenly associating a non-transitive (or associative) group with a F8 sub-group that isn't. So he's whistling in the wrong key, according to this dude (I think I might have followed a link from a news feed).

Found it:http://motls.blogspo...-theory-of.html

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If you care how the forces and particles are supposed to be embedded into his group, it's like this. You start with a non-compact real form of E8. You embed a G2 into it. Its centralizer is a non-compact version of F4. Now, you embed the strong SU(3) into the G2 while the non-compact F4 acts as the source of a "graviweak" SO(7,1) group that contains SO(3,1), a "gauge group" that is now fashionable in the circles of amateur physicists to "describe" gravity, and SO(4), their source of cargo cult electroweak symmetry.

Of course, the SO(3,1) group mentioned a minute ago plays a different role (in the vielbein formulation of general relativity) than the Yang-Mills groups and the fact that these two kinds of a group cannot be merged is the content of the Coleman-Mandula theorem to be discussed at the end of my text. Moreover, the fermions clearly can't arise from the connection because they have a different spin and statistics and they don't transform in the adjoint representation. For people like A. Garrett Lisi, it is not hard to unify everything with everything else because they don't know any difference between different concepts in physics.

--Luboš Motl

P.S. Some (I won't say who) are rumbling away about various aspects of recognition and are waiting for Lisi's book...

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Can someone explain to me what E8 is?

Try to picture a spherically inverted multifaceted poly-dimensional plexoid of random size, add in an elemental variable thermal/mass coefficient linking system based on the gravitational and magnetic field enhanced rate of change fluctuations of sub-atomic particles and it all comes together like butter and honey on toast. Well, butter and honey don't really come together on toast but you get the idea...

--ROMRIX slashdot.org

[Norman Albers]

My good friend and colleague solidspin is doing handsprings and telling me to get with this. Frustratingly I am not yet at this level of mathematics.

[Fred56]

Question: Norman, or anyone, do you know what the difference is between E8 and F8 groups? Or is it maybe just someone's typo that got "ghosted" by the unfamiliar? I've found 1 or 2 refs to "F8", but most refer to "E8"...?:confused:

[Norman Albers]

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there is this very sensible question "who should read this paper?"
and I guess the simplest answer would be anyone who wants to follow what is going on with Quantum Gravity and Unification and they should scan it to find parts they can understand, and get an idea from other people as best they can
(because quite a lot requires extensive knowledge of Lie Groups and their representations, and the differential geometry of bundles and connections, so it isnt easy reading!)

the paper is in some sense "where it's at" right now and one should get from it at whatever depth one can.

Thanks, Martin. I was feeling bummed out.

[solidspin]

hello -

Fred - you may be referring to F2 - a subset of E8...you most likely found a typo. Lisi found the rules for colour/QED inside F2 - it's mesmerizing - see the Nov. issue of New Scientist for the story. It's sooooo simple, I still can't believe it.

Martin - the matrices he presents are, in fact, quantized, since they are normalized rotations and the extreme off-diagonals are all zeroes - only the Trace and the minor off-diags are left - gorgeous. This is the Clifford of rotations which we use in solid-state NMR. Same commutation rules apply, except that the rotational deconstructions are then manipulated (like |I> = Ix + Iy + Iz), since the whole spin, upon rotation, obviously does NOT commute, but the components do...so, for example, IxSy doesn't commute (standard commutation, right?), but IxSz of course, does. IzSz does, too, since L^2 is an observable - see Angular Momentum in Quantum Mechanics by A. R. Edmonds (ISBN 0691025894)

No singularities, no infinities - the (this) universe is a closed set. It's then likely that E(8) is, itself, part of a closed superset, with each E(n) representing a different set of rules...Read Munovitz for some practicals on rotations used in NMR and you'll see what I mean...