An Exceptionally Simple Theory of Everything

[CarlB]

With that paragraph you quote, I was saying something I think is important, but might not be widely known by physicists. Conventional GR requires a metric to exist over the manifold -- this is kind of a strange object from the point of view of differential geometry. Nevertheless, physicists are used to thinking of GR as geometric and Yang-Mills as involving algebra. However, Lie algebra elements correspond to vector fields over the Lie group manifold. And a principal bundle can be described purely in terms of maps between vector fields, without a metric, using a tangent vector valued 1-form field over the entire space. In this way, the geometry of principal bundles is more natural than Riemmannian geometry. But this is a very subtle point, and I don't expect it to mean much to most readers.

Is this referring to the work by the Cambridge geometry group?

http://www.mrao.cam.ac.uk/~clifford/publications/abstracts/gravity.html

 

[garrett]

No Carl, you're not that lucky. I was referencing this:

http://deferentialgeometry.org/#[[Ehresmann principal bundle connection]]
http://en.wikipedia.org/wiki/Ehresmann_connection

 

[garrett]

Also, I'll be presenting a talk tomorrow, bright and early:

http://relativity.phys.lsu.edu/ilqgs/

The pdf for the talk just went up five minutes ago, but there seems to be some problem displaying them on windows machines. If anyone has any suggestions on how to fix that, it would be appreciated. (I have a mac)

 

[CarlB]

This windows machine displays the Acrobat file beautifully. It makes a good addition to the arXiv article. It used to be my experience that very large Acrobat files (the above is 1.8MB) should be downloaded rather than opened directly.

 

[Hans de Vries]

Also, I'll be presenting a talk tomorrow, bright and early:

http://relativity.phys.lsu.edu/ilqgs/

The pdf for the talk just went up five minutes ago, but there seems to be some problem displaying them on windows machines. If anyone has any suggestions on how to fix that, it would be appreciated. (I have a mac)

Success with your talk Garrett. You might say that you "have set the stage" now,
more then you probably would have imagined.


Regards, Hans

 

[garrett]

Thanks Hans, you're not kidding. I'm looking forward to going back to being a hermit again after tomorrow, playing with equations instead of with people.

I think we worked out the pdf problem. Thanks for the tip though Carl.

 

[jal]

E8 lives in 8D. Sure, it can be projected down to 3D.

Well ... it's better than dealing with 11D.
Believe me ... I'm trying with what I got ...?
From your statement I get a visual of a proton iceberg.
I looked at your slides ... it should give an interesting presentation.

 

[marcus]

...I'm looking forward to going back to being a hermit again after tomorrow, ...

It's been wonderful being able to watch the baby debut. thanks for being here at PF during.
Really smart of Jorge Pullin to invite you immediately to do ILQGS. It is already starting to be runup to next July QG².

On your sllde #45 in the concluding "discussion of E8 theory" section you say

Quantization:
* Coupling constants run.
* Large Lambda compatible with UV fixed point.
* Just a connection — amenable to LQG, spin foams, etc.

In Reuter's papers Lambda indeed gets large as k -> infty, so he has Lambda run in the right direction for E8 theory's needs.

But the other constant he has running is G_Newton which he has go to zero (!) as k -> infty. It seems like an unexpected thing that might cause a stumble, so I mention in case you get into discussing that bullet of slide 45.

Have fun with the ILQGS talk! it will be good for both theories and I hope they can converge some.

 

[strangerep]

Desitter space has no Smatrix, [...]
Read there is no apparent Smatrix in the theory!

Hi Haelfix,

I have some followup questions (for yourself, or anyone else who
knows the answers)...

Where can I read more about how DeSitter space has no S-Matrix?
I'm interested in the precise assumptions that lead to that conclusion.
Is the answer trivial in that, if one looks backwards in an expanding space,
there's no such thing as infinitely-separated effectively-free particles
for t \to -\infty? Or is there more to it than that?

If the former, I'm wondering how Garrett could get any cross-sections
out of such a theory which could be meaningfully compared with particle
physics experiments.

For that matter, what are the Casimirs and unitary irreps for the DeSitter
group? I tried some googling, but couldn't find a good exposition of this.

 

[marcus]

...Where can I read more about how DeSitter space has no S-Matrix?
...
Is the answer trivial in that, if one looks backwards in an expanding space,
there's no such thing as infinitely-separated ...

It'll be interesting to see what Haelfix says. Thanks for asking. About your guess of a trivial explanation, note that deSitter space contracts and then expands, so if you look back in time you can have infinitely separated paths.

but even without that, after two particles are a lightyear apart who cares? S-matrix could still be a good effective approximation, even if local reality is deSitter shaped. Just my two cents. We'll see what Haelfix says.

 

[Haelfix]

Bryce De Witt afaik did a lot of early work on DeSitter space, but I don't really feel like tracking down the references.

Instead there's a readable bit by Witten on it
http://arxiv.org/PS_cache/hep-th/pdf/0106/0106109v1.pdf

Its a little short on details, but he's at least attempting to recover some notion of observables. Yes the main problem is there is there is no good notion of spatial asymptotia nor is their a conformal null boundary. The former could give you correlation functions on the boundary (alla AdS), the latter an SMatrix (Minkowski)

To quote

"The problem with de Sitter space can actually be divided into two parts. One aspect
is that because of the horizon experienced by an observer, one cannot hope to witness
the final state of the whole universe. The other side of the problem, which seems more
acute to me, is that, as indicated above, one also cannot in de Sitter space make sense
in a precise way of what we usually regard as local particle physics quantities. (...) However, an observer in such a universe would have to perform all
experiments with a finite supply of elementary particles and free energy stored up before
the acceleration progresses too far. Under these conditions, it seems doubtful that one
could perform asymptotically precise measurements."

DeSitter space is nasty indeed... Its the biggest theoretical problem imo of this century.

 

[marcus]

Hi Haelfix, I was wondering if you would quote that 2001 paper of Witten. Here is a long quote from the page before where you quoted, which explains WHY he is worried about civilization in the future being able to measure stuff with very high precision in an expanding universe, particularly one with positive cosmological constant.

==quote Witten==
In an eternal universe, in the absence of gravity, with a constant free energy supply generated by stars, this makes perfect sense. In a more realistic description of nature, taking the expansion of the universe into account, there are many pitfalls.

De Sitter space (or a cosmology asymptotic to it in the far future) is a particularly unfavorable case for achieving the usually assumed degree of precision. For example, if it is true that the dimension of the quantum Hilbert space is finite, this puts a limit on the conceivable complexity of any experimental apparatus or computational machinery. The
inflation that will occur in the future in de Sitter space puts a limit on the time in which the experiment must be conducted (or the computation performed) before the free energy supply runs down.

Even the concept of an observer in de Sitter space as a living creature making an observation has only limited validity. For life itself is only an approximation, valid in the limit of a complex organism or civilization. There might be a cosmology in which the approximation we call life is better and better in the future, but this requires a process of
adaptation to longer and longer time scales and lower and lower temperatures [15], neither of which is possible in de Sitter space (where inflation sets a maximum time scale, and the de Sitter temperature is a minimum temperature). The approximation we know as life thus breaks down in the far future in an asymptotically de Sitter world, and this will put an end to any measurement (or computation) performed by an observer or civilization in such a spacetime, and hence an upper bound to its precision.

==endquote==

As one can see, his argument is somewhat speculative. It does not present, as far as I can see, any problem with deSitter space or a universe with positive Lambda. Rather it points out problems inherent in human theories which depend on giving meaning to precise asymptotic measurement----measurement at infinity. They don't apply to the world we live in.

The sensible response would seem to be NOT to avoid a particular shape, if it fits our universe, but to go with the observed shape and FIX THE THEORY. I see that as the lesson to be drawn from Witten's paper. So I don't see Witten's paper as particularly relevant to present discussion of E8 theory. Do you agree?

the paper is http://arxiv.org/hep-th/0106109
an expanded version of the talk Witten gave to Strings 2001 at Mumbai, India.

for an updated view of what the future of scientific measurement looks like in the universe we got, see
http://arxiv.org/abs/0704.0221
The Return of a Static Universe and the End of Cosmology
Lawrence M. Krauss, Robert J. Scherrer
Gen. Rel. Grav. 39 (2007) 1545-1550

it seems considerably more dismal than the view Witten evokes

We demonstrate that as we extrapolate the current LambdaCDM universe forward in time, all evidence of the Hubble expansion will disappear, so that observers in our "island universe" will be fundamentally incapable of determining the true nature of the universe, including the existence of the highly dominant vacuum energy, the existence of the CMB, and the primordial origin of light elements. With these pillars of the modern Big Bang gone, this epoch will mark the end of cosmology and the return of a static universe. In this sense, the coordinate system appropriate for future observers will perhaps fittingly resemble the static coordinate system in which the de Sitter universe was first presented.

 

[marcus]

DeSitter space is nasty indeed... Its the biggest theoretical problem imo of this century.

I don't understand what you are saying. Witten's vision of scientific measurement in distant future applies to the standard LambdaCDM cosmology which describes the world we live in, in the same way it applies to the simplified deSitter model of it.

How can you call the real world nasty (as it must be by the same reasoning)? Maybe you are joking.

 

[Haelfix]

Strangerep asked me about the Smatrix in DeSitter space, so I gave him a paper that tries to explore that.

The relevance is there are no quantum observables (neither local, asymptotic or global) in quantum gravity in DeSitter space. People, like Witten (and others) look for some, but they are hard to construct. Some people use relational variables instead and so forth. Even the nature of the Hilbert space is under dispute (eg is it finite dimensional or infinite), nor do we know what the unitary reps are.

There is nothing speculative about this, that's the state of the art, and hasn't progressed that much for over 30 years b/c of the technical problems with dealing with the space.

The relevance to the E8 paper (which is essentially a classical paper) is in the quantum regime you want to seemlessly connect local DS to local Poincare for lambda --> 0 in the standard model limit. Which is hard to do! Not only b/c of the absence of an SMatrix in the gravity regime, but b/c it already seems like there is a discontinuity in the very action.

 

[marcus]

Also, I'll be presenting a talk tomorrow, bright and early:

http://relativity.phys.lsu.edu/ilqgs/

The pdf for the talk just went up five minutes ago, but there seems to be some problem displaying them on windows machines. If anyone has any suggestions on how to fix that, it would be appreciated. (I have a mac)

This new PDF is a big help. CarlB's comment was that "It makes a good addition to the arXiv article."

Here is the direct link to the PDF.
http://relativity.phys.lsu.edu/ilqgs/lisi111307_2.pdf
Here is the direct link to the audio.
http://relativity.phys.lsu.edu/ilqgs/lisi111307.wav

======EDIT TO REPLY TO NEXT=====
Thanks Carl, interested by the possible preon angle. I wrote you a PM in reply.

 

[CarlB]

Marcus, I'm beginning to suspect that there is a fairly simple preon model hiding behind the E8 here. The paper on octonions by Baez:
http://math.ucr.edu/home/baez/octonions/oct.pdf

shows that E8 is related to the isometries of OxO where O is the octonions. The octonions are not associative, but they are close. If you could adjust the signs in the multiplication table, they would be associative. They are called "alternative" instead of the more general non associative.

When you translate spinors into density operators, you take two of them at a time. This gets rid of arbitrary signs in the spinors, they cancel. This means that when you translate octonionic symmetry operations on spinors into octonionic symmetry operations on density matrices, you end up with a density operator theory that IS associative.

Associativity is important in density matrix theory because it translates into the fact that when you compute a path integral, it doesn't matter whether you start your analysis at the initial and final end.

Another way of saying the same thing is that when you compute the probabilities associated with a system that transitions through the sequence of states A, B, and C, it doesn't matter if you do the computation as (AB)C or A(BC), you should get the same result. And the octonions are compatible with this, when you apply them to density operators (as are required for virtual particles anyway).

So the OxO translates into E8 being a model of composite particles made from two quantum objects with |O| symmetry, where "|O|" symmetry is a density matrix type symmetry you get from (more or less) ignoring signs in the octonions.

 

[Thomas Larsson]

The relevance is there are no quantum observables (neither local, asymptotic or global) in quantum gravity in DeSitter space.

Unless, of course, we are missing something essential.

It should be an uncontroversial fact that diffeomorphism symmetry on the circle *is* compatible with locality, in the sense of correlators depending on separation, but only in the presence of an anomaly; unitary Virasoro reps with h > 0 exist, but only if c > 0. This observation was the main reason why I generalized the Virasoro algebra to higher dimensions.

With local observables, it does not really matter if de Sitter admits global observables or not.

 

[Hans de Vries]

Where can I read more about how DeSitter space has no S-Matrix?

Is the answer trivial in that, if one looks backwards in an expanding space,
there's no such thing as infinitely-separated effectively-free particles
for t \to -\infty? Or is there more to it than that?

It seems to be just that...

http://online.kitp.ucsb.edu/online/strings98/witten/

The thing what really does seem to hurt is this:

http://online.kitp.ucsb.edu/online/strings98/witten/oh/12.html

\Lambda = 0\ \Rightarrow\ \mbox{S-matrix}

\Lambda < 0\ \Rightarrow\ \mbox{AdS/CFT}

(\Lambda > 0\ \Rightarrow\ \mbox{no AdS/CFT...})

He's getting more cautious now here:
http://online.kitp.ucsb.edu/online/strings98/witten/oh/25.html


Regards, Hans

 

[ccdantas]

Audio for today's talk by Garrett Lisi is posted at
http://relativity.phys.lsu.edu/ilqgs

 

[marcus]

Audio for today's talk by Garrett Lisi is posted at
http://relativity.phys.lsu.edu/ilqgs

I've been listening! It's impressive and nicely done. I hear Jorge Pullin but not much interruption by questions so far.

the phrase "suggestively colored dark" commenting on slide #38 is suggestive

this was in reference to the "xPhi" and the "w" symbols at the bottom of the E8 Periodic Table on slide #38.

we have company coming and my wife insisted that I stop listening and help her bake an almond cake
so I only got to hear the first 38 of the 48 slides discussed.

 

[ccdantas]

There are questions at page 39 and also at the end, I'm almost finishing it. He also has time to continue with 3 extra slides at the end.

I recommend listening to the audio; the talk clarifies several points.

 

[ccdantas]

I think there was some joke right at the end?

I cannot understand it. Could someone tell me? ;)

 

[marcus]

i will go back and try to find the joke. what I remember is Abhay Ashtekar saying that the Coleman-Mandula no-go does not apply because it is a "totally different framework" and Garrett is kind of chuckling that at Sabine Hossenfelder blog the discussion has gone on to some 160 comments and the "string theorists and a few particle theorists" still have not understood that it is, as A.A. immediately perceived, a different framework, and are still hammering at him about C-M. Maybe there was an ironical chuckle there but I don't remember a burst of laughter. I will go back and look for something else.

I went back and there ARE a couple of bursts of laughter at just this point---where Garrett says he will not bother with the last slide, the Coleman-Mandula slide, unless someone insists and Jorge says "I insist!". And then there are some ironical remarks ("this has been discussed a lot mainly on the internet, but who reads that sort of thing ") and some more laughter. The basis of the joke is that C-M does not actually apply to what G.L. is doing, but on blog-threads he gets constantly harrassed by string/particle minded folks about the C-M---which they seem to think makes what he is doing illegal. And since C-M does not really apply he didn't want to discuss it, but Jorge twists his arm a little. The joke is that mentioning the C-M is extraneous to the talk, but he has to do it anyway because it has been raised as an issue.

Was that the laughter (right near the end) that you were asking about, Christine?

 

[marcus]

Here is the direct link to the PDF (this is to the second improved PDF with the extra slides.)
http://relativity.phys.lsu.edu/ilqgs/lisi111307_2.pdf
Here is the direct link to the audio.
http://relativity.phys.lsu.edu/ilqgs/lisi111307.wav

I now feel confident to recommend that everybody here at Beyond forum should listen to this talk, for me I should listen several times. Anybody at all interested in Unification and Quantum Gravity in the normal everyday number of spatial dimensions.

The main people besides the moderator Jorge who are commenting and asking questions are Abhay Ashtekar and Lee Smolin. I missed Rovelli, who often takes part in ILQGS

 

[jal]

Hi garrett!
From the way you organized your slides and audio I would say, to paraphrase bee, "... a little bit of german ...?
You said at bee's blog ...
"More technically, (I think) we're splitting E8 into the bosonic subgroup part:
SO(8) + SO(8) and the fermionic part is the coset space,
E8/(SO(8)+SO(8)) But I'm doing this on the Lie algebra level and haven't worked it out topologically."
---------
Lot's of work left to do.
Have you got a team of helpers? Or are you thinking that individuals will independently work on this E8 model without "... a little bit of german ...?
jal

 

[strangerep]

what I remember is Abhay Ashtekar saying that the Coleman-Mandula no-go does not apply because it is a "totally different framework" and Garrett is kind of chuckling that at Sabine Hossenfelder blog the discussion has gone on to some 160 comments and the "string theorists and a few particle theorists" still have not understood that it is, as A.A. immediately perceived, a different framework, and are still hammering at him about C-M.

I went back and there ARE a couple of bursts of laughter at just this point---where Garrett says he will not bother with the last slide, the Coleman-Mandula slide, unless someone insists and Jorge says "I insist!". And then there are some ironical remarks ("this has been discussed a lot mainly on the internet, but who reads that sort of thing ") and some more laughter. The basis of the joke is that C-M does not actually apply to what G.L. is doing, but on blog-threads he gets constantly harrassed by string/particle minded folks about the C-M---which they seem to think makes what he is doing illegal. And since C-M does not really apply he didn't want to discuss it, but Jorge twists his arm a little.

IMHO, discussion involving C-M is relevant, not deserving of ridicule, in the following sense...
The paper is titled "An Exceptionally Simple Theory of Everything". But there does not
seem to be a usable method to calculate scattering cross-sections. OK, C-M might not apply,
but how then can one wield the "theory" in any practical way? Is it perhaps premature to
call it a "theory"? Maybe "...towards a partial framework..." is a better way to describe it?

 

[marcus]

The paper is titled "An Exceptionally Simple Theory of Everything"...

I suppose ten years of string hype (if it was taken seriously) may have prepared some of us to read G.L.'s title with utter solemnity. My initial reaction, by contrast, was that the title was quite funny and contained two shameless puns as well as the obvious ironical reference to stringy promises of yore.
The group E8, which is the main actor, is technically a SIMPLE group and it is one of the EXCEPTIONAL groups. And "Theory of Everything" makes one immediately think of Brian Greene and a decade of unsupported hyperbole about fashionable but fruitless research.

So I took the title as witty and just a wee bit satirical---the gross puns making clear the burlesque element.

Here at PF I remember my first post on this thread was initially just laughing about the title, but after a few minutes that seemed like a superficial reaction, so I edited out my appreciation of the humor.

I would encourage all LQG authors, or more generally non-string QG authors, when they get around to including matter so that they are working with a quantum dynamics of geometry AND matter, to use the phrase "Theory of Everything" every chance they can, because it is such a nice ironical echo from the string glory days.

I hope you saw today's ILQGS seminar talk, which has another very funny title:

A CONNECTION WITH EVERYTHING

got to love it, right?

 

[garrett]

Exactly so.

 

[hch]

RG running

hi marcus,

i think the connection to the truncated flow RG running of QEG is not quite as nice as you seem to hope. as far as i remember, reuters biggest problem is the fine tuning issue of the real world RG trajectory. and per se, it would again require anthropic reasoning.

IF a theory predicts the correct starting point in the UV, THEN things should look much better. but again, as far as i understand these need to be extremely finely tuned initial conditions and i do not see at all that they come out from any kind of unified theory at the moment.

 

[marcus]

... reuters biggest problem is the fine tuning issue of the real world RG trajectory. and per se, it would again require anthropic reasoning.

IF a theory predicts the correct starting point in the UV, THEN things should look much better...

this is off-topic in this thread. Reuter and Percacci work on asymptotic safety is different from Lisi's work. We already have some threads about their work, where your post would be an interesting contribution---or we could start a new thread for critique of the asymptotic safety papers.

I think it is very appropriate to be scrutinizing Reuter's papers at this point and looking for gaps and weak spots. I hope you have read the recent papers from him and Percacci and want to explain, point me to specific pages where you think the problems are etc.
Let's find or set up a thread where that won't be a distraction from the main topic.

 

[hch]

this is off-topic in this thread. Reuter and Percacci work on asymptotic safety is different from Lisi's work. We already have some threads about their work, where your post would be an interesting contribution---or we could start a new thread for critique of the asymptotic safety papers.

I think it is very appropriate to be scrutinizing Reuter's papers at this point and looking for gaps and weak spots. I hope you have read the recent papers from him and Percacci and want to explain, point me to specific pages where you think the problems are etc.
Let's find or set up a thread where that won't be a distraction from the main topic.

sorry, it was not my intention to discuss asymptotic safety. i merely wanted to point out, that a theory that requires a large lambda at high scales, while it is in a sense compatible with asymptotic safety, is not automatically of any help there unless it is fine-tuned. i just found your optimistic statement, that this combines nicely with asymptotic safety a bit too bold.

 

[marcus]

...i just found your optimistic statement, that this combines nicely with asymptotic safety a bit too bold.

I dare say that something I said earlier in this thread COULD have been too bold, and in need of qualification.

If you wouldn't mind, please find the post you are referring to and press "quote". I looked back 20 or so posts and didn't see what you were talking about---could just be poor eyesight. If you find the post for me it will save me the effort of searching thru this lengthy thread for what you say is overbold. Thanks in advance.

I see you are a newcomer and want to extend an appreciative welcome, especially since not everyone here is as familiar with recent work on asymptotic safety. It's an interesting topic.

 

[arivero]

IMHO, discussion involving C-M is relevant, not deserving of ridicule, in the following sense...
The paper is titled "An Exceptionally Simple Theory of Everything". But there does not
seem to be a usable method to calculate scattering cross-sections. OK, C-M might not apply,

I agree, in a partial way: in a theory of everything with gravity, they should either have a G_Newton->0 limit, where scattering and C-M and all of QFT applies, or a way to show that the G_Newton->0 limit produces a trivial theory (for instance, that it also cancels all the other fields).
Similarly, they should have a gauge QFT ->0 limit, where only gravity survives, or a way to show that gauge->0 also cancels the gravity part.

In the case of triviality of the ->0 limits, a more complicated study is called for: large distances will emerge gravity only, short distances will emerge QFT only. It is more complicated because very short distances recall Planck length and thus gravity again.

 

[hch]

Here's the link to Bee's discussion
http://backreaction.blogspot.com/2007/11/theoretically-simple-exception-of.html

A point that comes out there, as I would interpret it, is that Garrett's "quantum E8 theory" requires a Lambda that is 16 orders of magnitude larger than observed but this could actually be a plus.

Bonanno Reuter's recent paper says Lambda true value, what it is at the UV FIXED POINT, before it runs down with decreasing energy and expanding scale, is in fact much larger than what we observe, and this, Bonanno Reuter say EXPLAINS INFLATION. Heh heh. They could be right!

Several of Reuter's papers say this, but here is the Bonanno and Reuter link, for one:
http://arxiv.org/abs/0706.0174

So assuming that's right, if you have a FUNDAMENTAL theory that determines a value of Lambda, then you want the determined fundamental value to be very large.

Apparently this idea is floating around and is shared by others besides the immediate Asymptotic Safety bunch. So we don't have to pin it on people like Percacci and Reuter if we don't want. But Garrett cites them lightly for some reason in his paper, so perhaps they have his blessing. An associate of Percacci, named Nesti, is mentioned in the acknowledgments.

I think it would be really great if some fundamental theory, like Garrett's, would peg the cosmological constant really high and in agreement with what shows up at the Asymptotic Safety people's fixed point. It would harmonize early inflation with late acceleration and make sense generally of the whole expansion history.

Here is Garrett's comment about the large Lambda, that he made a few minutes ago at Bee's blog:
http://backreaction.blogspot.com/2007/11/theoretically-simple-exception-of.html#c4837564169156800942

At 12:16 PM, November 07, 2007, Garrett said...

bee:

Yes, at first I considered the large value of the cosmological constant in this model to be a worrisome bug. But now this idea is in agreement with current theories of a large cosmological constant at high energy (ultraviolet fixed point) running to the tiny value we experience at low energies. So the bug now looks to be a feature...

as you are probably well aware, there is no shortage of theories that require lambda to be orders of magnitude above the observed value.

 

[marcus]

as you are probably well aware, there is no shortage of theories that require lambda to be orders of magnitude above the observed value.

Not sure what the point of your remark is. There are some estimates based on conventional QFT which are way off. Unlike Reuter's treatment, they would predict that we should observe Lambda many orders of magnitude different from what is actually observed.

A treatment using RG flow trajectories and a UV fixed point (running scale-dependent Lambda) is an altogether different framework. If you require the distinction to be made clear then we really do need a separate thread. Discussing it here would take us far off topic. Would you like to start one, or shall I start a thread for you so we can talk about it?

==================

I see you have quoted my post #12, that mentions Reuter and other work involving running cosmological constant, and allows for the possibility that the work could be right or wrong. I don't see anything that needs additional qualification.

 

[marcus]

The discussion at Bee's blog has broken the 200 comment mark.
My last comment there was #200, Aaron Bergman's was #201.
It's like a loud party.
http://backreaction.blogspot.com/2007/11/theoretically-simple-exception-of.html

the person who is really missing in that discussion is John Baez

very good physics ideas can bring about the invention or recognition of new mathematics
(more often the recognition of already invented, and realization of its role in understanding nature)

G.L. E8 ToE in my humble opinion will eventually require the recognition of a new type of spacetime manifold and a new type of connection.

It could be a spacetime manifold that is locally deSitter instead of locally Lorentz.
Or where the local geometry is graded (i.e. energyscale dependent)

I guess in the best and free-est discussion people should be free to speak carelessly off-cuff and not suffer the chilling effect of being quoted, but I very much liked an off-the-cuff exchanged between G.L and Bee, and want to quote the essentials.
Garrett said the E8 theory under construction was neither top down or bottom up but, instead, might be described as
"top-down inspired, bottom-up". My punctuation.
that is it is being built up by hand from the ground of the standard models----to match GR and particle SM---but there is an overriding mathematical idea that inspires it.

Bee said "what is the top that the inspiration comes down from?" or words to that effect. It is a really good and persistent question and it points to where mathematical creativity could play a role.

I think the idea of naturalness at the top---or which is inspiring the construction of the theory---is that geometry and matter are the same thing and should be described by the same mathematical object.

however classical geometry dynamics (GR) the geomtry was described by the metric, the distancefunction played the role of geometry.

Garrett pointed out at the seminar that a CONNECTION is just as good a way to represent the geometry and in some ways more NATURAL. he mentioned that one can recover a metric from a connection and a connection is a more elegant or economical way---it describes the spacetime manifold's shape by how things roll and twist as you truck them around on it. With a metric you have to figure out how to do transport, by studying distances. But the connection just tells you how, with less fuss and bother. That's its job.

So a connection is an inertial compass trucking dingus that covers the metric's job and the bonus is that it gives a natural way to describe FIELDS and their allowed interactions.

so the overriding math idea (from whence the inspiration for the bottom-up buiding work) is that geometry and matter are the same thing so let's try to describe them both with a connection dingus, and get a classical and eventually quantum dynamics of geometry and matter in terms of that.

And there is the question of WHAT KIND OF 4D SPACETIME MANIFOLD it should be built on (because there are various definitions of manifold available in differential geometry, and of course one can invent new ones) and then WHAT KIND OF CONNECTION on what kind of bundle. A bundle is where you plant a copy of E8 at each point of the manifold and then talk about connecting them up. E8 is the egg of the universe, it is what defines our world of interacting matter and geometry, so naturally you want a copy of it at each point because that describes each point of our world. The nontrivial part is connecting.

These are just my inexpert reactions as a spectator. What I am anticipating is that a real mathematician will show up and say something like----hmmm Garrett's E8 doesn't have Lorentz flat symmetry in it, it has deSitter, so we have to do something about the underlying manifold. It might have a curved tangent space. And also it looks like Lambda is energyscale-dependent, so the manifold might be scale-graded in some sense. It might need to be able to have a dimensionality that varies with scale---so that it becomes fractal-like and lower dimensiony at very small scale...

We have this odd thing that in nature space expands----but the flat Minkowski space of special relativity doesn't. To be fundamental it seems intuitive that a theory could not be built on a manifold that is locally Minkowski. More likely one that is locally deSitter...

but these are my hunches and they don't matter, I just want to indicate some of the room outside the box. If it turns out that the E8 theory has the potential to GROW mathematics, like feet that require a new size of shoes, so as not to mis-shapen their ToEs.

 

[gnocchi]

I've started Wikipedia pages for http://en.wikipedia.org/wiki/Garrett_Lisi" if anyone wants to add to them.

 

[arivero]

http://reddit.com/info/60msi/comments/
http://science.reddit.com/info/60n0z/comments/

The discussion at Bee's blog has broken the 200 comment mark.
My last comment there was #200, Aaron Bergman's was #201.

Is bee going to close at #240?

http://backreaction.blogspot.com/2007/11/theoretically-simple-exception-of.html
the person who is really missing in that discussion is John Baez

It seems that the traditional role of E8 as GUT group is not reviewed in detail, so perhaps the remarks of Tony here and there are enough. But yep, you are right, some remark of Baez feels lacking.

 

[AzMa]

Two Questions:
I recently stumbled on a comment made by kkenn on reddit that goes as follows: ""Stuns" in the sense of "Wha? How is this a theory of everything?"

From what I can see, he has proposed a way to rearrange the particle content of the standard model into representations of E_8. This is not new in concept, people do this all the time in grand unified theories.

The new part is that he is claiming that he can embed all of the particle content of the standard model plus gravity into E_8.

However, he does not yet have a full theory of the interactions (quantized Lagrangian) which can be studied and compared to existing predictions. Only once you have this is it reasonable to say you have "a theory". Up until this point, you just have some patterns that you have observed which might emerge from a theory.

Historical note: this happened in the 1960s in the development of QCD: Gell-Mann noticed that particles could be assembled into representations of SU(3); this was not itself a theory of the strong interactions, but it helped point the way to the development of one. So this approach is not new, and in fact theoretical physicists have been trying to apply it to grand unified theories for 4 decades.

However, in this case, in order to fit the representations together into E_8 he is doing some things which are, on the face of it, mathematically extremely dubious and should give serious doubt about whether the his formulae make any sense at all.

For example, his expressions combine bosons and fermions as if they can be simply added. But these fields have opposite statistics (commuting vs anti-commuting), so it makes no sense to just add them; the resulting mathematical object makes no sense. In blog comments he keeps pointing to BRST symmetry as an example of where physicists do this, but has not addressed the basic point that in BRST symmetry the fermions are "ghosts" with the wrong statistics, and there is a way to make mathematical sense of this case. This problem is well-known to other physicists working on grand unified theories, but here it is just avoided by assuming there is some kind of "formal" structure in which it makes sense.

This kind of confusion probably comes from being extremely imprecise about the definitions of various quantities that are being manipulated throughout the paper, and an attempt at notational simplicity (very few of his formulae are written with indices, which is OK as long as you are very careful to check that they make sense - leaving indices in makes expressions notationally more complex but is an easy consistency check that you are not doing something silly).

I suspect this is misleading him into writing expressions that fit the concepts that the author wants, but do not make mathematical sense as an expression of those concepts.

Another fundamental theorem (the Coleman-Mandula theorem) is also ignored by asserting that it does not apply (even though it must, in the regime where space is approximately flat). This theorem is a basic mathematical result that says that what the author is attempting is fundamentally not possible once he starts to introduce interactions between his fields, and to just wave it away like that is also quite disingenuous. Again, there is 4 decades of research into this theorem, and one should be extremely skeptical when an author claims it does not apply to them.

Some other problems (basically, all the hard problems of whether -- once the author actually has a theory that he can begin to calculate with -- it will match with the extremely precise data required of it) are swept under the rug with the assumption that they will magically work out once he actually has the full theory. At this stage he can perform no such calculations because there is no theory to calculate with."

Now I would love to know if this is actually reasonable criticism of the theory or if it's merely a load of BS from I guy who only thinks he know what he is talking about.

Secondly, does this new theory allow for other universes (as in a multiverse)?

*If these seem like incredibly stupid questions, I apologize. Other than the general concept, this stuff has always been way over my head (probably because I'm only a junior in high school). But of course, that doesn't mean I'm not interested.

 

[staf9]

Kind of a novice-ish question here:
With gravitational so(3,1), I'd assume we're using a Lorentzian manifold signature there. Is that assumption right? If so it couldn't be DeSitter. If we do describe the universe as locally DeSitter, I always believed that it could lead to a theory of faster-than-light travel (due to constant exponential inflation) which doesn't sound very plausible anyway.

One more thing, since the paper describes bosons and fermions which are being represented as Grassman valued fields, shouldn't we use some other form of Lie algebra instead of just a simple Lie algebra because of the Grassmans involved?

 

[CarlB]

The one thing I haven't seen mentioned here is that when physics finds nice pretty symmetries that explain the known particles, it seems that they end up replacing the idea with a theory of more elementary particles. The most recent time this occurred was with the quarks, which started out as an application of SU(3).

 

[jal]

Who is going to be able to show that the “other theories/models” fit into E8?
“They” won’t do the work it has to be done by an E8 team.
Here is what I found for a recent search of arxiv.org

http://arxiv.org/find/hep-ph/1/au:+Forkel_H/0/1/0/all/0/1
Holographic glueball structure
Authors: Hilmar Forkel
------------
http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.2259v1.pdf
The Pion Cloud: Insights into Hadron Structure
Anthony W. Thomas
Jefferson Lab, 12000 Jefferson Ave., Newport News VA 23606 USA and
College of William and Mary, Williamsburg VA 23187 USA
14 Nov 2007
-------------
http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.1703v1.pdf
Probing the nucleon structure with CLAS
Highlights of recent results.
Volker D. Burkert, for the CLAS collaboration.
Jefferson Lab, Newport News, Virginia, USA
November 12, 2007
----------
http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.2048v1.pdf
Nucleon Structure from Lattice QCD
David Richards
Jefferson Laboratory, 12000 Jefferson Avenue, Newport News, VA 23606, USA
November 12, 2007[/color]

 

[garrett]

One more thing, since the paper describes bosons and fermions which are being represented as Grassman valued fields, shouldn't we use some other form of Lie algebra instead of just a simple Lie algebra because of the Grassmans involved?

The connection involves only Lie algebra valued 1-forms and Lie algebra valued Grassmann numbers. Nothing fancier.

 

[CarlB]

In Baez's paper on the octonions:
http://math.ucr.edu/home/baez/octonions/oct.pdf
which I think really needs to be read in conjunction with Garrett's, the most interesting description of E_8 to me is on page 48:

With 248 dimensions, E_8 is the biggest of the exceptional Lie groups, and in some ways the most mysterious. The easiest way to understand a group is to realize it as as symmetries of a structure one already understands. Of all the simple Lie groups, E_8 is the only one whose smallest nontrivial representation is the adjoint representation. This means that in the context of linear algebra, E_8 ismost simply described as the group of symmetries of its own Lie algebra!

In the usual state vector formalism of QM, this is just an interesting factoid. But if you represent quantum states in the density operator or density matrix formalism, it begins to make a little intuitive sense.

In the state vector formalism, states are represented by state vectors. These are operated upon by operators. In the density operator formalism, both the states and operators are operators.

Now if you define "quantum state" as a thing which is defined by its symmetry, and you also require a density operator formalism, then E_8 is the only choice if you demand that the same objects represent the quantum states and also the symmetries of the quantum states.

If you start with something smaller, it will have to grow. If you start with something larger, it will not be simple and it will have undetermined coefficients.

 

[marcus]

I'm concerned about simple question-answering fatigue. (Not on my part. I'm laid back and quite often let questions go for a day or two.)

the two that keep coming up, though answered by G.L. many times at Bee's, are
1)adding fermions and bosons
2) Colemandula

Abhay Ashtekar, the wise old Elephant of quantum gravity, has given us plenty with which to beat down the Colemandula objection if we just get up the gumption to do it.
He said it was a "completely different framework". He's smart and saw this right away.

But there are some string theorists who are slow to get it (like AzMa's kken on reddit, and like some at Bees blog). Read my lips, says Ashtekar: Colemandula does not apply here.

the other question I have the feeling CarlB could explain to me why 'tis not a problem.
I keep hearing about Z₂ graded algebras. That is a very simple mathematical idea, just a direct sum of two and a rule that when multiplying you add the grades mod 2.
I have this idea, please tell me if I am wrong, that it would ease things if only everyone in discussion was familiar with the idea of a Z₂ graded algebra. If I'm wrong, don't bother to explain why, just tell me I'm on the wrong tack.
===================

Ashtekar said another really wise thing at the seminar: "You have to solve problems one at a time."

I think that means that a theory is developed by successive approximations. If some facet looks almost right, you leave it for the moment and go fix something else. The next time round, with the next version, it's better and so on.
Something the present version seems to have in spades is predictivity. Instead of yelling all these reasons why they think the theory can't possibly work (which tend to be based on misunderstanding) you'd think we could all accept the fact that it MIGHT work and wait politely to see some of the predictions, which are surely going to be derived.

 

[Mephisto]

slightly off-topic,
an article about this theory was posted on digg today and generated a lot of buzz with almost 6000 diggs in 10 hours, which as a regular reader, I can tell you, is pretty rare and quite great; Especially considering that this is a highly technical subject. A direct link:
http://digg.com/general_sciences/Surfer_Dude_Stuns_Physicists_With_Theory_of_Everything_2

I'm only an undergrad in physics so I'm lost in the details, but I am really excited about your theory, and I hope you are right. Deriving laws of physics by geometric means like this seems really nice, elegant and strangely mysterious.

 

[christianjb]

Writing as someone who doesn't understand this paper at all:

The more I read about this work the more exciting it seems. I'd like to offer my congratulations to Lisi. It makes me happy to be a member of the human species when I see how imaginative we can be.

Even if this turns out to be wrong- it's inspiring to see scientists trying to find deep symmetries in physical law.

Lisi seems like a great guy and I hope his work continues to bring inspiration to others like me who can only gaze in awe at all of this.

 

[Ivan Seeking]

This is all very exciting!

Congratulations Garrett, and good luck!

[we may need to create a Big Kahuna medal... ]

 

[marcus]

[we may need to create a Big Kahuna medal... ]

Nice idea. i wonder what it would look like.
Another idea would be just turn on the avatar image option (as for an honorary so-and-so) and see what iconic device he devises.

 

[arivero]

slightly off-topic,
an article about this theory was posted on digg today and generated a lot of buzz with almost 6000 diggs in 10 hours, which as a regular reader, I can tell you, is pretty rare and quite great;

Yep, the reactions in digg, reddit (quoted some messagges before) and meneame are very curious. In any case, it proves that the people writing newspapers has some knowledge about what is going to connect with the public.