An Exceptionally Simple Theory of Everything

"An Exceptionally Simple Theory of Everything" is a possible unified field theory, which attempts to describe all known fundamental interactions in physics, and to stand as a possible theory of everything (TOE). Posted to the physics arXiv by Dr. Antony Garrett Lisi in November 2007, the theory quickly stirred public interest and drew a wide range of reactions from other physicists. The title is a pun on the algebra used for the model (E₈), which is both a "simple" and an "exceptional" Lie group.

Overview

A visual representation of E₈ polytope, a manifestation of the structure of E₈.

The model by Lisi falls into the field of representation theory, which models unification of physical forces through gauge groups. It is conceptually a grand unification theory (GUT) with quantum gravity, similar to notable models such as left-right, Pati-Salam, Georgi-Glashow, SO(10), or E₆ based approaches. The choice of E₈ structure by Dr. Lisi, representing the largest (and arguably, most beautiful) exceptional Lie group, was in part driven by the proposition: "The mathematics of the universe should be beautiful. A successful description of nature should be a concise, elegant, unified mathematical structure consistent with experience."

Proposing to form a theory of everything that can stand versus the widely supported string theory and succeed where Albert Einstein failed in his late years, the model must eventually predict the exact number of fundamental particles, all of their properties, masses, forces between them, the nature of space-time, and the cosmological constant. Although being exceptional, much of this work is still on the conceptual stage, in particular quantization and predictions of particle masses, and Lisi himself acknowledges it as a work-in-progress: "The theory is very young, and still in development. Right now, I'd assign a low (but not tiny) likelihood to this prediction." He further remarks: "This is an all-or-nothing kind of theory - it's either going to be exactly right, or spectacularly wrong."

Description

In Lisi's model, the 240-element root system of E₈ is broken down according to the following schema:

$\mathrm {E} _{8}=\mathrm {F} _{4}+\mathrm {G} _{2}+(26\times 7)$

$\mathrm {F} _{4}~$ (graviweak)

$\mathrm {G} _{2}~$ (strong)

$(26\times 7)$

$\mathrm {SO} (7,1)~+~(8+8+8)$

$\mathrm {SU} (3)+3+{\bar {3}}$

$(8+8+8~+~1+1)$ $~~\times (3+{\bar {3}}+1)$

The strong force is embedded in the $\mathrm {SU} (3)$ subalgebra, and gravity in a $\mathrm {SO} (3,1)$ subalgebra of $\mathrm {SO} (7,1)$. The electroweak force is mapped to a $\mathrm {SU} (2)_{L}+\mathrm {SU} (2)_{R}$ subalgebra of $\mathrm {SO} (7,1)$, as in the Pati-Salam model. Notably, Lisi includes fermions along with bosons without using supersymmetry, and also proposes that the three generations of fermions of the standard model may be described by a triality rotation (relating to the three-fold symmetry of $\mathrm {SO} (8)$).

In order to specify dynamics, Lisi postulates a modified BF theory action,

$S=\int <{\overset {.}{\underset {=}{B}}}{\underset {=.}{F}}+{\frac {\pi G}{4}}{\underset {=}{B}}^{G}{\underset {=}{B}}^{G}\gamma -{\underset {=}{B}}'*{\underset {=}{B}}'>$,

and decomposes it to MacDowell-Mansouri action for gravity, electroweak and graviweak parts, and an $\mathrm {SO} (8)$ part that contains both "...gluons and a first guess at the action for the new fields." He also remarks that the actions for the second and third fermion generations are "... related by triality in a way that is not presently understood well enough to write down."

Note: the description provided above is just a brief summary. The full description is entailed in the paper in the physics arXiv.

Consequences

Lisi's model aims at reproducing all known fundamental fields and dynamics in nature through pure geometry. Aside from predicting proton decay (which is common amongst all grand unified theories), Lisi's model has 20 elements out of the 248 basis elements of E₈ that do not correspond to known particles or forces. These may include new quantum numbers, a new Higgs scalar, as well as fields that mix leptons and quarks and have forces that vary depending on fermion family. Lisi remarked that: "The lack of extraneous structures and free parameters ensures testable predictions, so it will either succeed or fail spectacularly."

It is generally agreed in public reviews that in its current form, the model by itself is not yet a complete theory of everything. For example, it has not been quantized. Lisi acknowledges certain issues, but states: "I consider this to be a developing theory that is worth my time to work on, as a long shot."

Publicity and controversy

Lisi's paper was quickly publicized after its release on 6 November 2007, and spun-off a variety of mostly controversial debates across various blogs and online discussion groups. Numerous news sites from all over the world reported this new theory, noting the personal background of Dr. Lisi.

Initial reception by the scientific community

After addressing an international meeting on loop quantum gravity at the Perimeter Institute for Theoretical Physics, Lee Smolin, who sits on the advisory panel at FQXI (the institute that funded Lisi's research), remarked on Lisi's work as:

One of the most compelling unification models I've seen in many, many years.

Quickly publicized, Smolin had to clarify this as a spontaneous comment, and noted subsequent press coverage as premature.

Sabine Hossenfelder, who helped arrange for Lisi's participation, also clarifies that while she believes "... Garrett's paper has the potential to become a very important contribution, and his approach is worth further examination", she also notes:

Given today's status, Garrett's model does not naturally lead to a unification of the Standard Model interactions with gravity (he has to choose the action by hand that contains both), it does not allow us to understand quantum gravity (since there's nothing said about quantization), it does not explain the parameters in the standard model (since there isn't yet a mechanism for symmetry breaking), it does not explain the cosmological constant or its value (as said above, to claim there has to be one, it would be necessary to show there's no way to do it without one), it does not explain the hierarchy problem (and I see no way to do so), it does not explain why we live in a spacetime with 3 spatial and 1 timelike dimensions, it does not in my very humble opinion yet qualify being called a Theory of Everything.

Other preliminary feedback was mixed: Carlo Rovelli, a leading quantum gravity physicist, commented:

When I started to read the article I was a sceptic. When I'd finished it, I asked myself why I hadn't had the idea before.

John Baez described the theory as speculative. While stating that he felt it was more mathematically natural to combine bosons and fermions within a Z₂ grading of an E₆ Lie group rather than within a Z₂ grading of an E₈ Lie group, he added that only time will tell. He has recently said,

[Lisi] certainly makes no serious attempt to get the Standard Model Lagrangian in all its detail. Nor does it seem possible (without further feats of genius). For example, his Lagrangian has no place for the ∼25 adjustable constants contained in the Standard Model: particle masses, coupling constants, etc. Nor does he attempt to derive these constants.

David Finkelstein, emeritus professor of the Georgia Institute of Technology said:

Some incredibly beautiful stuff falls out of Lisi's theory, I think that this must be more than coincidence and he really is touching on something profound.

Criticism

Jacques Distler from the University of Texas at Austin demonstrated that it is not possible to embed the fermions of the Standard Model within E₈ and concludes:

The overlap between the set of people who know some group theory and those who are (still) interested in giving Lisi’s 'Theory of Everything' a passing thought is empty.

Luboš Motl, assistant professor at Harvard University (2004–2007) commented:

Every high school senior excited about physics should be able to see that the paper is just a long sequence of childish misunderstandings.

Distler and Motl also argue that it is impossible to have a theory with internal and external symmetries unified in any non-trivial way, as this violates the Coleman-Mandula theorem.

Dr. Lisi responded in Distler's blog on fermion embedding:

I have discussed this inadequacy clearly in the paper, going so far as to explicitly state it is currently the main problem with the theory." He also believes the Coleman-Mandula theorem to not be applicable for his theory.

Related to this issue is the embedding of particles of different spin (spin 1/2 fermions, spin 1 gauge bosons, and spin 2 gravitons) in the same group representation, as proposed by Lisi. One point of concern, the action of the model not actually being E₈-symmetric, has since been addressed by Lee Smolin, by proposing a way to obtain the bosonic part of Lisi's action (plus higher-order terms) from a fully E₈-symmetric theory. Smolin wrote:

Does Lisi’s proposal survive Distler’s second post? Even if there is some truth to Distler’s argument, is the result the end of Lisi-like proposals or are there alternatives which evade it? For example, by going to the complexification? Or might it be that Lisi’s proposal works for the Euclidean spacetimes but not for Lorentzian? Might it be that it only works if only part of the Lorentz algebra is gauged, as in the Ashtekar or Thiemann formulations? All these are interesting possibilities...

Marcus du Sautoy of the University of Oxford said: "There seem to be a lot of things still to fill in." Sautoy continues in The Telegraph: "Garrett Lisi: This surfer is no Einstein... the media went wild. However, in the last few weeks several physics blogs have uncovered a problem with Lisi's idea: it doesn't work," but this remark is not substantiated.

Secondary debates

In addition to debate over the model, Lisi's paper has sparked several secondary discussions, often laced with hostile and insulting remarks, about blogging, scientific etiquette, and the non-peer review endorsement system of ArXiv that supported Lisi's publication.

In his blog, Luboš Motl wrote:

This paper by A. Garrett Lisi had to be endorsed by someone. If you read the acknowledgements, it is not hard to see possible answers. Some of those people such as Lee Smolin may endorse any crackpot paper because they are both endorsers and crackpots at the same moment. Moreover, they have a vested interest to increase the proportion of similar papers on the arXiv because this is where they belong. As Lee Smolin recently pointed out, irrationality has been extremely useful for him in the past.

The role of non-constructive criticism and flaming in scientific debate was questioned, amongst others, by Lee Smolin:

I entered this discussion hoping we could find resolution, what I encountered was a toxic and nasty atmosphere in which it was impossible to get a simple yes/no answer to a simple question without facing a lot of blustering and nastiness. [...] What has happened is that one very smart, but intellectually isolated young theoretical physicist has made a bold and risky proposal for unification of physics. Due to his personal circumstances, he got much too much media attention - something everyone including him agrees about and several of us including myself tried to stop. A bunch of people who think they own the territory of unification are enraged. They react with all the classic symptoms of territory defense that the sociologists of science have catalogued.

Nevertheless, humorous remarks could also be found, e.g. by Peter Woit:

As far as I can tell, there seems to be a consensus among the CV [Cosmic Variance] commenters that: 1. We think denigrating and insulting people is a legitimate part of a scientific discussion. 2. We think doing this anonymously is fine too. 3. We don’t understand why it is so hard to have serious discussions about physics on blogs. We suspect it is because PW [Peter Woit] keeps interfering with them.

Jacques Distler commented:

Allow me to make four predictions for 2008. (1) There will be several further followups to Lisi’s paper. (2) The protagonists will insist (if ever challenged on the matter) that no flaws in Lisi’s or Lee’s paper were ever proven. (3) Anyone who attempts to say otherwise will be denounced as (a) rude, (b) a “string theory partisan”, with suspicious motives. (4) Peter Woit will chime in, to announce that the whole affair reflects badly on the string theorists.

The Telegraph reports, "Garrett Lisi: This surfer is no Einstein... The media went wild. However, in the last few weeks several physics blogs have uncovered a problem with Lisi's idea: it doesn't work."

Putting the theory to the test

Template:Future scientific facility Garret Lisi's theory will be put to the test by the Large Hadron Collider (LHC) particle accelerator, which is currently under construction near Geneva, Switzerland. Once the test results are evaluated and concluded, this theory of everything will either be proved or refuted, as Lisi himself has stated.

Garrett Lisi's theory makes no concrete numerical predictions, as noted by physicists including Lee Smolin, Peter Woit, and Garrett Lisi. As the theory does not calculate anything, it cannot be tested by the LHC.

External links

• "A Connection with Everything" Slides for ILQGS seminar talk by Lisi, 13 November 2007. Audio available in various formats. Slides also on Lisi's wiki
• Animation of lattice E8 explaining the theory
• Semi-technical exposition at the New Scientist.
• (FQXi) An exceptionally simple FAQ Lisi's answers to questions about his paper asked by newspaper reporters.
• Discussion on the blog of Peter Woit of Columbia University
• Discussion at the blog BackRe(Action)
• Discussion and Q&A with Dr Lisi at advancedphysics.org
• An Exceptionally Technical Discussion of AESToE - a thread on PhysicsForums.com, started by Garrett Lisi, devoted to discuss mathematics used in the AESToE paper.
• Review at Ars Technica
• A little group theory... A critical blog by Jacques Distler
• Non-technical exposition at The Economist