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An Exceptionally Simple Theory of Everything

"An Exceptionally Simple Theory of Everything" is a unified field theory by Antony Garrett Lisi, aimed at describing all known fundamental interactions in physics. Proposed in November 2007,[1] it quickly stirred public interest in the topic and its author, and drew a wide range of academic reaction.The title is a pun on the algebra used for the model (E8), which is both a "simple" and an "exceptional" Lie group. It is generally agreed in public reviews that the model is not a complete Theory of Everything in its current form (e.g. it has not been quantized yet). In addition, it is unresolved whether or not certain open questions can be addressed. 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."[2]

Overview

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 Lisi, representing the largest (and arguably, most beautiful[3]) exceptional Lie group, was in part driven by 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."[1]

Proposing to form a theory of everything, 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. Much of this work is outstanding, in particular quantization and predictions of particle masses, and Lisi 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."[4] He further remarks: "This is an all-or-nothing kind of theory - it's either going to be exactly right, or spectacularly wrong."[5]

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 SU(3) subalgebra, and gravity in a SO(3,1) subalgebra of SO(7,1). The electroweak force is mapped to a SU(2)L + SU(2)R subalgebra of 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 UNIQ12e3e6017a9654-math-00000014-QINU).

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 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 fermion generations are "... related by triality in a way that is not presently understood well enough to write down."[1]

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. He remarks: "The lack of extraneous structures and free parameters ensures testable predictions, so it will either succeed or fail spectacularly."[1]

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.

Initial reception

After addressing an international meeting on loop quantum gravity at the Perimeter Institute for Theoretical Physics, Lee Smolin remarked on Lisi's work as "one of the most compelling unification models I've seen in many, many years." Quickly publicized,[4] Smolin had to clarify this as a spontaneous comment, and noted subsequent press coverage as premature.[6]

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 SM [Standard Model] interactions with gravity (he has to chose 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 SM (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."[7]

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."[8] 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.[9] After David Finkelstein, Emeritus Professor of the Georgia Institute of Technology, "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."[5] Marcus du Sautoy of the University of Oxford says, "There seem to be a lot of things still to fill in,"[10] and Luboš Motl, Assistant Professor at Harvard University (2004 - 2007) even comments: "Every high school senior excited about physics should be able to see that the paper is just a long sequence of childish misunderstandings."[11]

Criticism

Jacques Distler from the University of Texas at Austin was the first to demonstrate how it is not possible to embed fermion generations within E8 and concludes "...that 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."[12][13] He and Motl[11] 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.

Lisi responds 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.[14] 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.[15] Smolin further cautions against premature non-sequitur conclusions on Lisi's model, and writes: "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 ..." [16].

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 writes: "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."[11]

The role of non-constructive criticism and flaming in scientific debate was questioned, amongst others, by 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."[17]

Nevertheless, humorous remarks could also be found, e.g. by Peter Woit[18]: "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." Or Jacques Distler:[19]: "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."

• Grand unified theory
• Theory of Everything

References

1. ^ a b c d A. Garrett Lisi, An Exceptionally Simple Theory of Everything, Cornell University Library, Submitted on 6 Nov 2007
2. ^ Lisi on Jacques Distler's blog "Musings" (22 November 2007)
3. ^ Hermann Nicolai, in (AIM) Mathematicians Map E8 (retrieved 30 Dec 2007)
4. ^ a b Highfield, Roger. "Surfer dude stuns physicists with theory of everything", The Daily Telegraph, 2007-11-14. Retrieved on 2007-11-23.
5. ^ a b Is mathematical pattern the theory of everything? - fundamentals - 15 November 2007 - New Scientist. Retrieved on 2007-11-18.
6. ^ Lee Smolin on Cosmic Variance
7. ^ Sabine Hossenfelder's blog (retrieved 1 Jan 2008)
8. ^ A "theory of everything" causes trouble with the physicists, Le Monde, 19 November, 2007. (French)
9. ^ Baez, John. This Week's Finds in Mathematical Physics (Week 253).
10. ^ Fox News: Laid-Back Surfer Dude May Be Next Einstein
11. ^ a b c Motl, Lubos (2007-11-07). Garrett Lisi: An exceptionally simple theory of everything. Retrieved on 2007-11-23.
12. ^ Musings (Distler, 24 December; retrieved 30 Dec 2007)
13. ^ Musings (Distler, 9 December 2007; retrieved 30 Dec 2007)
14. ^ Backreaction (Hossenfelder; retrieved 30 Dec 2007)
15. ^ Lee Smolin: The Plebanski action extended to a unification of gravity and Yang-Mills theory on arXiv
16. ^ Lee Smolin on Cosmic Variance blog (17 Dec 2007; retrieved 5 Jan 2008)
17. ^ Lee Smolin on Cosmic Variance (retrieved 30 Dec 2007)
18. ^ Peter Woit on Cosmic Variance (retrieved 30 Dec 2007)
19. ^ Jacques Distler on Cosmic Variance (retrieved 30 Dec 2007)