New blog

Announcing my new (tentative) blog, Toy Universes.

News on Garrett Lisi’s E8 theory

Lisi posted this yesterday over at Physics Forums; I reproduce here:

Hello PF folk.

If you believe the Dirac equation in curved spacetime, and you believe Spin(10) grand unification, then a Spin(3,11) GraviGUT, acting on one generation of fermions as a 64 spinor, seems… inevitable.

Also, it’s pretty.

And it’s up to you whether or not to take seriously or not the observation that this whole structure fits in E8. Personally, I take it seriously. Slides are up for a talk I gave at Yale:

http://www.liegroups.org/zuckerman/slides.html

Best,
Garrett

I am not certain whether it addresses Distler’s previous objections (as I am not certain whether the issue was even settled at that time– see here and here, which goes as far as I could follow. More (older) personal opinions can be found here, here and here in reverse chronological order).

Edit: I forgot to add. I do find the theory beautiful and interesting. I hope it can be properly tested.

Edit: Here are further links that are relevant to this post.

There is no “Theory of Everything” inside E8 by Jacques Distler and Skip Garibaldi.

Here is Distler’s blog entry on his paper.

There was a discussion of Distler and Garibaldi’s paper at Physics Forums some time ago.

There was also a discussion at n-Category Café some time ago.

Quantum Gravity quote

A pessimist might say that combining string theory and loop quantum gravity is like combining epicycles and aether.

(John Baez, TWF281)

God said “Let Penrose be” and all was wrong

Roger Penrose Says: Physics Is Wrong, From String Theory to Quantum Mechanics.

First news from quantum gravity school in Corfu

Mathematical physicist John Baez has recently posted his “This Week’s Finds in Mathematical Physics” (Week 280) reporting his impressions of the school. It is a very nice summary and worth reading. See also this thread over at Physics Forums.

Questions and Answers about Perturbative quantum gravity

R. Woodard from the University of Florida will be talking at the International Loop Quantum Gravity Seminar tomorrow (September 22nd). His slides are already available.

See also a previous post.

News from LIGO

An upper limit on the stochastic gravitational-wave background of cosmological origin
The LIGO Scientific Collaboration & The Virgo Collaboration
Nature 460, 990-994 (20 August 2009)

Abstract

A stochastic background of gravitational waves is expected to arise from a superposition of a large number of unresolved gravitational-wave sources of astrophysical and cosmological origin. It should carry unique signatures from the earliest epochs in the evolution of the Universe, inaccessible to standard astrophysical observations. Direct measurements of the amplitude of this background are therefore of fundamental importance for understanding the evolution of the Universe when it was younger than one minute. Here we report limits on the amplitude of the stochastic gravitational-wave background using the data from a two-year science run of the Laser Interferometer Gravitational-wave Observatory (LIGO). Our result constrains the energy density of the stochastic gravitational-wave background normalized by the critical energy density of the Universe, in the frequency band around 100 Hz, to be <6.9 times 10^{-6} at 95% confidence. The data rule out models of early Universe evolution with relatively large equation-of-state parameter, as well as cosmic (super)string models with relatively small string tension that are favoured in some string theory models. This search for the stochastic background improves on the indirect limits from Big Bang nucleosynthesis and cosmic microwave background at 100 Hz.

Update: Now freely available in the arxiv. [0910.5772]

News from Fermi (formerly GLAST)

[Via Backreaction].

[arxiv:0908.1832]

Testing Einstein’s special relativity with Fermi’s short hard gamma-ray burst GRB090510
Authors: Fermi GBM/LAT Collaborations

Abstract: Gamma-ray bursts (GRBs) are the most powerful explosions in the universe and probe physics under extreme conditions. GRBs divide into two classes, of short and long duration, thought to originate from different types of progenitor systems. The physics of their gamma-ray emission is still poorly known, over 40 years after their discovery, but may be probed by their highest-energy photons. Here we report the first detection of high-energy emission from a short GRB with measured redshift, GRB 090510, using the Fermi Gamma-ray Space Telescope. We detect for the first time a GRB prompt spectrum with a significant deviation from the Band function. This can be interpreted as two distinct spectral components, which challenge the prevailing gamma-ray emission mechanism: synchrotron – synchrotron self-Compton. The detection of a 31 GeV photon during the first second sets the highest lower limit on a GRB outflow Lorentz factor, of >1200, suggesting that the outflows powering short GRBs are at least as highly relativistic as those powering long GRBs. Even more importantly, this photon sets limits on a possible linear energy dependence of the propagation speed of photons (Lorentz-invariance violation) requiring for the first time a quantum-gravity mass scale significantly above the Planck mass.

Edit: Discussions are also going on over at Physics Forums.

A Brief Introduction to Loop Quantum Cosmology

A Brief Introduction to Loop Quantum Cosmology [arxiv:0907.5160]
Authors: Guillermo A. Mena Marugan

Abstract: In recent years, Loop Quantum Gravity has emerged as a solid candidate for a nonperturbative quantum theory of General Relativity. It is a background independent theory based on a description of the gravitational field in terms of holonomies and fluxes. In order to discuss its physical implications, a lot of attention has been paid to the application of the quantization techniques of Loop Quantum Gravity to symmetry reduced models with cosmological solutions, a line of research that has been called Loop Quantum Cosmology. We summarize its fundamentals and the main differences with respect to the more conventional quantization approaches employed in cosmology until now. In addition, we comment on the most important results that have been obtained in Loop Quantum Cosmology by analyzing simple homogeneous and isotropic models. These results include the resolution of the classical big-bang singularity, which is replaced by a quantum bounce.

Comments: 15 pages, published in AIP Conference Proceedings, Volume 1130, Geometry and Physics: XVII International Fall Workshop on Geometry and Physics

How Far Are We from the Quantum Theory of Gravity?

How Far Are We from the Quantum Theory of Gravity? [arxiv:0907.4238]

R. P. Woodard (University of Florida)

Abstract: I give a pedagogical explanation of what it is about quantization that makes general relativity go from being a nearly perfect classical theory to a very problematic quantum one. I also explain why some quantization of gravity is unavoidable, why quantum field theories have divergences, why the divergences of quantum general relativity are worse than those of the other forces, what physicists think this means and what they might do with a consistent theory of quantum gravity if they had one. Finally, I discuss the quantum gravitational data that have recently become available from cosmology.

Comments: 106 page review article solicited by Reports on Progress in Physics

FQXi prizes: not my time…

FQXi announced the prizes for the Essay Contest on the Nature of Time. Results are here.

My essay was not awarded.

Solvay Physics Conference 1927

Carver Mead: against Copenhagen

An interesting interview with Carver Mead, author of the (unconventional) Collective Electrodynamics: Quantum Foundations of Electromagnetism.

Weinberg on condensed matter matters

[Via Asymptotia]

Most of us do elementary-particle physics neither because of the intrinsic interestingness of the phenomena that we study, nor because of the practical importance of what we learn, but because we are pursuing a reductionist vision. All of the properties of ordinary matter are what they are because of the principles of atomic and nuclear physics, which are what they are because of the rules of the Standard Model of elementary particles, which are what they are because…well, we don’t know, this is the reductionist frontier, which we are currently exploring.

Weinberg, From BCS to the LHC

Unconventional computing

Just received.

…………………..

THE SCIENCE AND PHILOSOPHY OF UNCONVENTIONAL COMPUTING (SPUC09)

Cambridge (UK), March 23-25, 2009

SECOND CALL FOR PAPERS

We welcome submissions on topics normally classified under ‘natural computing’ or ‘unconventional computing’ or ‘hypercomputing’ including (but not restricted to) quantum computing, relativistic computing, biology-based computing, analogue computing, and also submissions on the philosophical implications of these new fields for topics including (but again not restricted to) philosophy of mind, philosophy of mathematics, the Church-Turing thesis.

Each presentation should last no more than 30 minutes; a further 10 minutes will be allowed for discussion.

Those wishing to make a presentation should submit by email a 250-word abstract of their paper to Mark Hogarth (mhogarth@cantab.net); enquiries to the same.

Registration fee (yet to be fixed) will be around £100.

Student bursaries are available.

Conference website: http://web.mac.com/mhogarth/Site/SPUC_Conference.html

ORGANISER

Mark Hogarth (Cambridge, UK)

CONFIRMED INVITED SPEAKERS

Selmer Brinsjord (New York, USA))

Jeff Barrett (Irvine, USA)

Philip Welch (Bristol, UK)

Tim Button (Harvard, USA)

Cristian Calude (Auckland, New Zealand))

István Németi (Budapest, Hungry)

Benjamin Wells (San Francisco, USA)

Hajnal Andréka (Budapest, Hungry)

Apostolos Syropoulos (Xanthi, Greece)

Susan Stepney (York, UK)

Bruce MacLennan (Tennessee, USA)

Peter Kugel (Boston, USA)

Mark Sprevak (Cambridge, UK)

Selim Akl (Kingston, Canada)

José Félix Costa (Swansea, UK)

ADVISORY PANEL

Mike Stannett (Sheffield, UK)

John Tucker (Swansea, UK)

Barry Cooper (Leeds, UK)

Sponsored by EPSRC through HyperNet (the Hypercomputation Research Network, EP/E064183/1)

Something I’d like to do if I were younger….

Just received.

…………………………………………………….

Dear Christine,

I am writing to ask for your assistance in drawing the attention of exceptional, highly motivated students to the Perimeter Scholars International (PSI) program.

PSI is an innovative, Masters level course designed to prepare students for cutting-edge research in theoretical physics. It provides a broad overview, allowing students to choose their preferred specialisation, and extensive tuition in formulating and solving interesting problems.

The due date for applications is February 1st: applications received after this date may still be considered but only as long as places remain available.

A number of outstanding lecturers have already signed up to teach, including for example Yakir Aharonov, Phil Anderson, Matt Choptuik, Nima Arkani-Hamed, John Cardy, Ruth Gregory, Michael Peskin, Sid Redner, Xiao-Gang Wen, and a number of Perimeter Institute research faculty. They will be supported by full-time tutors dedicated to the course.

All accepted students will be fully supported.

For further details, see www.perimeterscholars.org.

Thank you in advance for helping us to make this exciting opportunity known as widely as possible.

With my best wishes,

Neil Turok

Director
Perimeter Institute for Theoretical Physics
Waterloo, Ontario, Canada

Next talk at ILQGS

ILQGS

Tuesday, Jan 13th
Donald Marolf, UC Santa Barbara

Title: Unitarity and holography in gravitational physics

Selected papers of today (gr-qc) #2

Title: Transcending Big Bang in Loop Quantum Cosmology: Recent Advances
Authors: Parampreet Singh
[0901.1301]

Title: Black holes and entropy in loop quantum gravity: An overview
Authors: Alejandro Corichi
[0901.1302]

Black Holes and Loop Quantum Gravity

I have just received this message from the International Loop Quantum Gravity Seminar mailing list:

Valencia, March 26-28, 2009

The Workshop on Black Holes and Loop Quantum Gravity will take place in Valencia, Spain, from the 26th to the 28th of March, 2009. The purpose of the workshop is to bring together researchers working on quantum aspects of black holes, with emphasis on ideas that have originated in loop quantum gravity. A partial list of topics to be covered is as follows:

– Black hole entropy in LQG
– Spin foam approach to black holes
– Singularity resolution and information loss
– Prospects for a detailed description of the Hawking radiation
– Comparison between results from LQG and other approaches

This will be a ‘Discussion Workshop’. Therefore a significant time will be set aside for a critical evaluation of ideas that are being pursued in current research and on finding fertile directions for future work.

Selected papers of today (gr-qc)

Title: Quantum field theory on a cosmological, quantum space-time
Authors: Abhay Ashtekar, Wojciech Kaminski, Jerzy Lewandowski
[0901.0933]

Title: Quantum Gravity on the Lattice
Authors: Herbert W. Hamber
[0901.0964]

Title: Quantum theory, noncommutative gravity, and the cosmological constant
problem
Authors: T. P. Singh
[0901.0978]

Title: Singular sources in gravity and homotopy in the space of connections
Authors: E. Gravanis and S. Willison
[0901.1079]

Interesting papers by Salisbury et al.

For my record, I list here some interesting papers by Salisbury et al. which cover fundamental questions of relevance on, should I say, “pre-” quantum gravity matters.

The lines of research are summarized as follows:

- preservation of general coordinate transformation and additional gauge symmetries in the transition from a Lagrangian to a Hamiltonian description;
- the nature of observables in classical general relativity, and their potential usefulness in the construction of an eventual quantum theory of gravity;
- construction of diffeomorphism invariants (observables) in general relativity;
- history of constrained hamiltonians.

The papers of relevance are the following:

- Realization in phase space of general coordinate transformations [Phys. Rev. D 27, 740, 1983];

- Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant theories [gr-qc/9612037 = PRDvol55,no2,658,1997]: establishes the general framework in which gauge variables are retained as canonical variables;

- Reduced phase space: quotienting procedure for gauge theories [math-ph/9811029]: describes an alternative algorithm to the Dirac-Bergmann constraint procedure for constructing a self-consistent Hamiltonian model;

- Gauge group and reality conditions in Ashtekar’s complex formulation of canonical gravity [gr-qc/9912085]: discusses Ashtekar’s complex connection approach to gravity;

- Gauge Transformations in Einstein-Yang-Mills Theories [gr-qc/9912086]: discusses gauge symmetries in Einstein-Yang-Mills models;

- The gauge group in the real triad formulation of general relativity [gr-qc/9912087]: discusses a real triad version of canonical gravity;

- Gauge symmetries in Ashtekar’s formulation of general relativity [gr-qc/0004013]: proposes a gauge averaging procedure modeled after an approach of Rovelli’s, though retaining gauge variables and recognizing the essential distinction between time evolution and realizeable canonical gauge symmetries;

- Quantum general invariance and loop gravity [gr-qc/0105097]: preliminary exploration into the construction of diffeomorphism invariants using dynamical field-dependent finite gauge transformations;

- Quantum General Invariance [Proceedings of the Ninth Marcel Grossmann Meeting held in Rome in 2000 ("Quantum general invariance", in Proceedings of the Ninth Marcel Grossmann Meeting, edited by V.G. Gurzadyan, R. T. Jantzen and R. Ruffini, (World Scientific, New Jersey, 2002), 1300-1301)]: continued the exploration of finite gauge transformations;

- The issue of time in generally covariant theories and the Komar-Bergmann approach to observables in general relativity [ gr-qc/0503013 = Phys.Rev. D71 (2005) 124012]: constructs local invariants through the use of intrinsic coordinates. This can be accomplished in the canonical framework in general relativity using Weyl curvature scalars, as was first suggested by Komar and Bergmann. One essential new observation in this work is the recognition that gauge variables become functionals of the non-gauge variables, and consequently in the quantum theory they become subject to fluctuations. In particular, in canonical quantum gravity the light cone is itself fluctuating [the authors supposedly show that there is no conceptual problem for the canonical formulation of generally covariant theories because the mathematical identification of the Hamiltonian as a gauge generator is erroneous (resolution of the time evolution versus gauge problem)];

- Rosenfeld, Bergmann, Dirac and the Invention of Constrained Hamiltonian Dynamics [physics/0701299]: In a paper appearing in Annalen der Physik in 1930 Leon Rosenfeld invented the first procedure for producing Hamiltonian constraints. He displayed and correctly distinguished the vanishing Hamiltonian generator of time evolution, and the vanishing generator of gauge transformations for general relativity with Dirac electron and electrodynamic field sources. Though he did not do so, had he chosen one of his tetrad fields to be normal to his spacetime foliation, he would have anticipated by almost thirty years the general relativisitic Hamiltonian first published by Paul Dirac.

Links will be added later [Edit: almost all included now]. It would be interesting to follow these matters in light of recent advances in canonical quantum gravity. Marcus over at Physics Forums have prepared a selection (actually, an invitation to a poll) of papers published in the arxiv in 2008 in canonical quantum gravity.

On the Nature of Time — essay competition

I have submitted an essay to the FQXi competition. If you are interested in reading it, click here.

Title: On the Nature of Time – Or Why Does Nature Abhor Deadlocks?

Essay Abstract

This essay aims at introducing a novel point of view on the nature of time, inspired by a synthesis of three seemingly unrelated concepts: Bergson’s notion of duration, Dijkstra’s notion of concurrency, and Mach’s notion of inertia.

Edit (June 9th 2009): Apparently, the essays on the nature of time are no longer available at the FQXi site. I have made a very few small corrections and modifications in my essay and a new version is available here (pdf file).

Physical limits of inference – Theories of almost everything?

There is a review at Nature’s News and Views section by P.-M. Binder about a recent article by David H. Wolpert from NASA Ames Research Center, entitled “Physical limits of inference“. Binder writes:

A provocative contribution to the logic of science extends the theorems of Kurt Gödel and Alan Turing, and bears on thinking about prediction, the standard model of particles, and quantum gravity.

From the abstract of the paper, one reads

We show that physical devices that perform observation, prediction, or recollection share an underlying mathematical structure. We call devices with that structure “inference devices”. We present a set of existence and impossibility results concerning inference devices. These results hold independent of the precise physical laws governing our universe. In a limited sense, the impossibility results establish that Laplace was wrong to claim that even in a classical, non-chaotic universe the future can be unerringly predicted, given sufficient knowledge of the present. Alternatively, these impossibility results can be viewed as a non-quantum-mechanical “uncertainty principle”.

[Yeah, Laplace was wrong even classically, according to my SF novel... ]

and

(…) We informally discuss the philosophical implications of these results, e.g., for whether the universe “is” a computer.

I find it very surprising that this was published in Physica D: Nonlinear Phenomena, and not in a philosophical journal. I have no criticisms against this work in particular (I did not read the paper in full), it is just that it does not seem, from a first impression, a physics paper per se, as much as interesting as it may seem.

Another (somewhat funny, I must admit, but it may be a reflection of my present pessimistic/sarcastic mood) excerpt from Binder’s review is this:

The other limitation is our inability to bring quantum mechanics and gravity into a single theory, although several viable alternative theories are being studied [9]. Quantum electrodynamics, a refinement of quantum mechanics, is defined by just two parameters (the charge and mass of the electron), whereas quantum gravity would require infinitely many parameters, and hence infinite experiments to determine those parameters, making it so far a meaningless theory.

BTW, Ref. [9] above is Wilczek’s book, The Lightness of Being.

Quantum gravity is not what we think!

At least, this is what Penrose says. You can find more about Penrose’s arguments (and other interesting talks) by watching the PIRSA videos of the recent conference “The Clock and the Quantum: Time and Quantum Foundations“.

LHC is on!

First beam of the Large Hadron Collider started today! See commissioning details and news here. News on the CMS detector (with photos) is here.

Back to my far far far away land, I feel like an ant-scientist. I can only fully recommend this paper by the young and clever russian Alexei Grinbaum:

- On the eve of the LHC: conceptual questions in high-energy physics

Requardt’s papers

Back in 2005, when I started to read more and more papers on quantum gravity, I have found one paper that really interested (and still interests) me a lot, and was the subject of one of my first posts back at my older blog.

- The Continuum Limit of Discrete Geometries, by Manfred Requardt [http://arxiv.org/abs/math-ph/0507017]

It is a well written paper, with lots of interesting mathematics (Gromov’s geometric group theory, random graphs, etc). As far as I know, it has not been much discussed in other blogs.

Recently, Requardt posted another interesting one, which I am presently reading:

- About the Minimal Resolution of Space-Time Grains in Experimental Quantum Gravity, by Manfred Requardt [http://arxiv.org/abs/0807.3619]

Abstract:

We critically analyse and compare various recent thought experiments, performed by Amelino-Camelia, Ng et al., Baez et al., Adler et al., and ourselves, concerning the (thought)experimental accessibility of the Planck scale by space-time measurements. We show that a closer inspection of the working of the measuring devices, by taking their microscopic quantum many-body nature in due account, leads to deeper insights concerning the extreme limits of the precision of space-time measurements. Among other things, we show how certain constraints like e.g. the Schwarzschild constraint can be circumvented and that quantum fluctuations being present in the measuring devices can be reduced by designing more intelligent measuring instruments. Consequences for various phenomenological quantum gravity models are discussed.

I like his writting style and the various points that he covers in his papers with sensible criticism.

Bertram Kostant on E(8)

I include here an email from Prof. Bertram Kostant to Ben Wallace-Wells on his view about the E(8) group and some considerations on Lisi’s theory. According to Lisi, this part of the email was permitted to become publically available.

Dear Ben Wallace-Wells,

The following is my response to your queries. In order to answer your question about the Lie group E(8), I found it necessary in the first paragraph to add some historical context. I hope it is not too burdensome to read.

Lie (pronounced Lee) group theory was developed by mathematicians towards the end of the 1800′s. An important accomplishment at that time was also a classification of the simple Lie groups. It turned out there were 4 infinite families and 5 exceptional Lie groups, the largest (containing all the others) of which is E(8). There is an unfortunate double usage here of the word “simple”. There is of course, the everyday usage (eu) meaning easy to understand and a technical use (tu) meaning not built up from other groups. For example, the title of Lisi’s paper is “An Exceptionally Simple Theory of Everything”. His use of Exceptionally Simple is a pun. The exceptional refers to the exceptional Lie groups and simple is (tu). Lie groups started entering physics in a serious way at the beginning of the twentieth century. Perhaps more prominent was Einstein’s theory of special relativity, where the Lie group involved was the Lorentz group. This is a (eu) group and occupies only a very tiny sliver of something as sophisticated as E(8). Also Bohr’s theory of atomic spectra uses the rotation group SO(3) and again is an (eu) and a very tiny sliver of E(8). For the most part, Lie groups were more or less put on the “back burner” by both mathematicians and physicists until the middle of the twentieth century, At that time, it became a serious object of study by mathematicians. I should make it perfectly clear that I am a research mathematician and not a physicist. My speciality is Lie groups and any use of physics terminology here is only what is common knowledge. On occasion I have been motivated by physics – for example, the marvelous development of quantum mechanics by physicists in the 1920′s. I believe that there were some stirrings about Lie groups by physicists in the middle of the twentieth century. I have the following prescient story to tell. I was a visiting member of Princeton’s Institute for Advanced Study in 1955. It was a Good Friday in April and Einstein was looking for the Institute bus to take him back home to 112 Mercer Street. Being Good Friday, the driver was on holiday amd I offered to drive him home. We had a wonderful conversation and at one point he asked me what I was working on. I told him Lie groups. He then remarked, wagging his finger, that that will be very important. Actually, I was quite surprised that he knew who Lie was. About a week later Einstein was dead. In the middle of the twentieth century, physicists developed what is called quantum field theory (Feynman, Schwinger, etc.) Also at that time, the powerful accelerators were producing a zoo of new particles. To deal with this menagerie of particles and to carry forward Einstein’s program of finding a unified field theory (unifying all 4 forces of nature), physicists came up with what is called the Standard Model (Weinberg, etc.) This involved what is called a gauge group. In fact, in the Standard Model, the gauge group is a (eu) simple Lie group. A more refined development was the grand unified theory (GUT) of Glashow and Georgi. Here the gauge group (SU(5)) was more interesting. The GUT theory happily confers a desired fractional electric charge on such exotic particles as quarks. These theories also unified three of the four forces of Nature.

The latter part of the twentieth century also saw the development, by physicists, of string theory. String theory has had vast consequence for mathematics (excluding Lie groups). However, as far as I know, there have been no experimental verifications of the physics involved. (For his work in this area, the mathematical physicist Ed Witten was awarded the most prestigious prize in mathematics.)

A word about E(8). In my opinion, and shared by others, E(8) is the most magnificent “object” in all of mathematics. It is like a diamond with thousands of facets. Each facet offering a different view of its unbelievable intricate internal structure. It is easy to arrive at the feeling that a final understanding of the universe must somehow involve E(8), or otherwise put, (tongue in cheek) Nature would be foolish not to utilize E(8). There was a good deal of publicity about E(8) in the last few years when a team of about 25 mathematicians, using the power of present computers and a very complicated program, succeeded in determining all of the vast number of (to use a technical term) characters associated with it. Incidentally, one of the main leaders of the team was an ex-student of mine, David Vogan. It was Vogan who told me about Lisi’s paper. Another person involved here is John Baez. Baez, (a relative of the singer Joan Baez) is a professor of mathematics at the Riverside campus of the University of California. Baez performs a great service to the Math-Physics community by publishing a very engaging weekly report on doings of mathematicians and physicists – explaining latest results in physics to mathematicians and latest results of mathematics to physicists. His week 253 report deals with Lisi’s paper. In effect Lisi is saying that E(8) is the ultimate gauge group. Lisi’s theory makes some astounding claims. Among them is that E(8) “sees” all the elementary particles in the Universe. In addition, Lisi claims that his theory unifies all 4 forces in Nature (the last being gravity) and thereby achieves Einstein’s dream of a unified field theory. String theorists, by and large, heartily dismiss Lisi’s theory. But among some prominent nonstring theorists (e.g., Lee Smolin), the paper has been acclaimed. Incidentally, string theorists utilize E(8), but not as a gauge group. According to Baez’s week 253 report, one of Lisi’s motivations in going to E(8) was that the Glashow-Georgi GUT theory “sees” only one generation of fermions. Apparently there are 3 “generations” of such particles. The Lie group E(8) has a triality construction and I believe that Lisi thought that this may be used to give all 3 generations. Since I had something to do with this triality construction, I became interested in Lisi’s paper. I remind you, I am not a physicist and cannot comment one way or another on the physics involved. However, mathematically, I was able to show, using beautiful results of such finite group theorists as John Thompson, Robert Griess, Alex Ryba and an important input from Jean-Pierre Serre, together with some old results of mine, that E(8) not only “sees” GUT in a natural way, but in fact is itself (viewed through one of the facets) a composite of two copies of GUT. This is the subject matter of what I have been lecturing about. One such lecture was at UC Riverside, which was filmed and put on line by John Baez.

Having seem the film, Lisi sent me an enthusiastic E-mail, saying my results were brand new to him and speculating on what the meaning of the second GUT might be. I am too happy to forward Lisi’s E-mail letter to you, if you wish to see it. At any rate, if there is any physical validity to E(8) as a gauge group, the ball is in the court of physicists to interpret what this doubling up of GUT might mean.

I am happy to cooperate with you on your New Yorker article. However, I think it is best to do this by E-mail and not via phone conversations. I wish to avoid all the misquotations attendant to the New Yorker publication having to do with the solution of the Poincare conjecture.

Bertram Kostant Professor Emeritus of Mathematics at MIT

Garrett Lisi and Jacques Distler: debates revived — Part II

The text below was extracted from the original post by Distler over at the n-Category Café:

——–
[Begin of Distler's comment excerpt]

This is my summary of Lisi’s programme (at least, as best I have been able to understand it).

1. Choose an embedding of Spin(3,1)×SU(3)×SU(2)×U(1) in (noncompact) E 8. The generators of the Lie algebra, e 8, then transform as some representation of this subgroup.

* In particular, the action of the center of SL(2,ℂ)≃Spin(3,1) gives a ℤ 2 grading on e 8. The generators of e 8 which transform in spinorial representations of Spin(3,1) are “odd”; the generators which transform in tensorial representations are “even.”

* There is a similar ℤ 2 grading on the fields of any QFT: fermions are “odd” and bosons are “even.” The spin-statistics theorem requires that these be the same grading.

* While Lisi say that he doesn’t want to envoke a ℤ 2 grading, one is clearly physically required, and mathematically provided by the aforementioned embedding of Spin(3,1). He might as well say that he doesn’t want to speak in prose.

2. Use this ℤ 2 grading to build a Schreiber superconnection. The bosonic fields transform as 1-forms with values in various tensor representations of Spin(3,1); the fermionic fields transform as 0-forms in spinor representations of Spin(3,1).

* Lisi says that he isn’t using a Schreiber superconnection. Instead he’s doing ‘standard’ BRST. I can’t make head or tails of his usage of the term “BRST.” In the end, to each generator of e 8, he associates either a bosonic or a fermionic field. Spin-statistics dictates that he do this in a fashion compatible with the ℤ 2 grading. Which is to say that his fields comprise a Schreiber superconnection. Protestations to the contrary he, again, seems to be speaking in prose.

3. Use this Schreiber superconnection to build an action.

4. Quantize that action.

5. Try to extract some quasi-realistic physics from it.

Unfortunately, the construction falls down at step 1.

* Lisi wants there to be 192 odd generators, with respect to some embedding of Spin(3,1). This, of course, is impossible.

* Moreover, in his paper, Lisi embeds Spin(3,1)×SU(3)×SU(2)×U(1) via a D 4×D 4 subgroup of E 8. I classified all such embedding. They all lead (via the above prescription) to a non-chiral fermion spectrum. The closest one can come to the Standard Model spectrum of fermions is to get 1 generation and 1 anti-generation.

* This, in fact, is completely general. Any embedding SL(2,ℂ)×SU(3)×SU(2)×U(1)↪E 8 yields a nonchiral spectrum of fermions, with — at best — a generation and an anti-generation of Standard Model particles.

None of these statements is particularly hard to prove. In fact, once you know that there’s no ℤ 2 grading of e 8 with more than 128 odd generators, you know that it’s impossible to accommodate 3 generations. The best you could get is 2, but even that proves not to be possible.

That said, there is something kinda cool about the elements of the construction:

1. An embedding of Spin(d−1,1) in G gives a ℤ 2 grading on 𝔤.

2. Using the corresponding Schreiber superconnection, one naturally gets a theory with fermions, corresponding to the odd generators of 𝔤, transforming as spinors Spin(d−1,1).

It would be mildly interesting to see what sort of actions one could build with this construction.

[End of Distler's comment excerpt]
—————–

Although that site is perfectly adequate for rigorous discussions on the matter using mathematical language, I leave here a welcome space for comments on the above intrepretation by Distler in layman terms.

I have previously posted over at n-Cat café the following:

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Do I understand correctly that the “other stuff” that sits in the odd part is considered important for Distler (it is the “anti-generation” which for him is one of the points that would make the whole approach doomed to be incorrect), whereas for Lisi the “other stuff” – whatever it is – can be worked out, eventually avoiding a possible invalidation? Is this the point of tension?

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I have also posted the following remark (slightly edited):

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If I understand it correctly, it is agreeded on both parts that Lisi’s model as a whole results in a non-chiral spectrum (net number of generations = 0). Furthermore, Distler appears to have shown that there are no decompositions of E8 allowing the inclusion of the 3 SM generations. (Does Lisi agree with the latter?)

So, I was wondering – is it really all there is to be concerning the use of E8 (or any other group, for what is worth)?

I mean, on speculative grounds, is it possible that simply using the group “as it is” is not the whole story, but actually one could gain more room for analysis or insight by seeing the group from a different “perspective”?

What I have in mind here comes from something I was reading superficially about, groups of polynomial growth and the work of Gromov. Does E8 have any relation to such groups? If so, would it be possible to prove whether the “net # gen = 0” feature shown by Distler for the E8 is preserved (or not) when considering related groups of polynomial growth (if that is possible at all), in which the group is “seen from infinity”?
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I keep these posts here for personal record.

[Part I of the present post here.]

Lowest cost, highest benefit book ever

This is the book with the lowest cost ($7.95), highest benefit ever, in the physical sciences (in my opinion):

You submerge into Dirac’s mind and learn about his general Hamiltonian formalism with constraints, which is a great start for a subsequent, more modern treatment, given in (the much more expansive) Henneaux and Teitelboim‘s book.

There are, of course, other low cost, high benefit books, specially coming from Dover publications (several come to my mind). But Dirac’s book is presently my favorite in that respect.

A very concise, brilliant and rich little book that it’s easy to carry everywhere and keep your mind busy with important concepts and how to work towards new approaches and developments.

Garrett Lisi and Jacques Distler: debates revived

Debates on Lisi’s theory are back being discussed over at n-Category Café from this post on chronologically, so that you can check the exchange progress.

However, it is difficult to tell ahead the end of this story. It appears that some sort of agreement is slowly and painfully being reached, but it is clear that there is still a long way to go.

[Previous posts on Lisi's theory can be found here.]

[Edit 19-Jul-08: An interesting summary by Distler is found in a previous entry from the above mentioned exchange, dated May 22, 2008, and pointed out by Urs Schreiber. It is interesting not only for being a summary of what he interprets from Lisi's theory and the points that he indicate as being problematic, but also because he actually finds what he calls "something kinda cool about the elements of the construction" and that it "would be mildly interesting to see what sort of actions one could build with this construction".]