What Is E8 Good For?
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- Опубліковано 31 жов 2022
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We give an overview of the utilization of E8 in theoretical physics for applications to unified field theory. Concepts such as Lie groups, root systems, and exceptional Lie groups are introduced. A brief overview of spacetime symmetries for gravity and gauge symmetries for the standard model and beyond is provided. A history of exceptional Lie groups in physics is provided, with a highlight on the work stemming from Feza Gursey and his doctoral students. E8 grand unified theory, Garrett Lisi's E8 model, and E8 x E8 heterotic string theory are briefly reviewed. We conclude by discussing recent advances in applications of E8 to unified field theory.
This video was created as a submission to Curt's contest @TheoriesofEverything.
Find out more about emergence theory & E8 at quantumgravityresearch.org/
For more research on the subject matter:
Exceptional groups for GUTs and remarks on octonions - Feza Gürsey: doi.org/10.1063/1.32989
On tumbling E8 - Mehmet Koca: www.sciencedirect.com/science...
A universal gauge theory model based on E6 - F. Gürsey, P.Ramond, P.Sikivie: www.sciencedirect.com/science...
Quark structure and octonions - Murat Günaydin and Feza Gürsey: doi.org/10.1063/1.1666240
EFFECTIVE OCTONIONIC SUPERSYMMETRY IN HADRONIC PHYSICS - CATTO, SULTAN MEHMET: www.proquest.com/openview/01a...
Grand Unification with the Exceptional Group E8 - I. Bars and M. Günaydin: journals.aps.org/prl/abstract...
Asymptotically supersymmetrical model of a single interaction based on E8 - Konshtein and Fradkin: jetpletters.ru/ps/1432/article...
E8 family unification, mirror fermions, and new low-energy physics - S. M. Barr: journals.aps.org/prd/abstract...
An octonionic construction of E8 and the Lie algebra magic square - R. A. Wilson, T. Dray, C. A. Manogue: arxiv.org/abs/2204.04996v1
An Exceptionally Simple Theory of Everything - A. Garrett Lisi: arxiv.org/abs/0711.0770
An Explicit Embedding of Gravity and the Standard Model in E8 - A. Garrett Lisi: arxiv.org/abs/1006.4908
Lie Group Cosmology - A. Garrett Lisi: arxiv.org/abs/1506.08073
Super Yang-Mills in (11,3) Dimensions - Ergin Sezgin: arxiv.org/abs/hep-th/9703123
Evidence for F-Theory - Cumrun Vafa: arxiv.org/abs/hep-th/9602022
S-Theory - Itzhak Bars: arxiv.org/abs/hep-th/9607112
Geometrical Structures of M-Theory - Emil Martinec: arxiv.org/abs/hep-th/9608017
A magic pyramid of supergravities - A. Anastasiou, L. Borsten, M. J. Duff, L. J. Hughes, S. Nagy: arxiv.org/abs/1312.6523
Eric Weinstein’s Geometric Unity: geometricunity.org/
Krasnov on Spin(7,7): pirsa.org/speaker/Kirill-Krasnov
Tony Smith’s website: tony5m17h.net/TShome.html
A Clifford algebra-based grand unification program of gravity and the Standard Model: a review study - Carlos Castro Perelman: cdnsciencepub.com/doi/10.1139...
THE EXCEPTIONAL E8 GEOMETRY OF CLIFFORD (16) SUPERSPACE AND CONFORMAL GRAVITY YANG-MILLS GRAND UNIFICATION - CARLOS CASTRO PERELMAN: www.worldscientific.com/doi/a...
Octions: An E8 description of the Standard Model - Corinne A. Manogue, Tevian Dray, Robert A. Wilson: arxiv.org/abs/2204.05310
An E8⊗E8 unification of the standard model with pre-gravitation, on an octonion-valued twistor space - Priyank Kaushik, Vatsalya Vaibhav, Tejinder P. Singh: arxiv.org/abs/2206.06911
There is no "Theory of Everything" inside E8 - Jacques Distler, Skip Garibaldi: arxiv.org/abs/0905.2658
Articles by Piero Truini: arxiv.org/search/?searchtype=...
Beyond the standard model with six-dimensional spacetime - David Chester, Michael Rios, Alessio Marrani: arxiv.org/abs/2002.02391
The Geometry of Exceptional Super Yang-Mills Theories - Michael Rios, Alessio Marrani, David Chester: arxiv.org/abs/1811.06101#
Conformal Quasicrystals and Holography - Latham Boyle, Madeline Dickens, Felix Flicker: arxiv.org/abs/1805.02665
On the Emergence of Spacetime and Matter from Model Sets - Marcelo Amaral, Fang Fang, Raymond Aschheim, Klee Irwin: www.preprints.org/manuscript/...
An Icosahedral Quasicrystal and E8 derived quasicrystals - F. Fang and K. Irwin: www.researchgate.net/publicat... - Наука та технологія
Looking forward to going through this. Thank you for this submission to #PaCE1.
I feel a lot dumber... with all jokes aside, I appreciate what you are sharing here. The stuff is fascinating to me.
I am convinced that the underlying understanding and current exploration regarding the theoretics of E8 is the system closest to unraveling the theory of everything. It's incredibly exciting times 🤘
Been waiting for some progress on this and Garrett Lisi's TED talk from years ago
if energy=information, e8 looks for me like data structure of this information
Thank you David, great work.
Wishing you all a great Christmas !! And much success for the new year !!
Same to you!
Thank you for this awesome presentation
Glad you enjoyed it!
@@QuantumGravityResearch I wonder if there's some, as yet unknown, way to control the process of sonoluminescence to reverse the effect of gravitons. Do you know if there's any research into this possibility?
I know that Malcolm Bendall has been working on using sonoluminescence to generate a LENR. It seems like there might could be more possibilities for research of its quantum gravitational effects on water molecules.
Thank you ❤ that is great work!
Our pleasure! Thank you for watching!
Excellent mustache! It's important to recognize the significance of an excellent mustache.
100%.
Lie Tash group
Excellent!
How does this describe the transition boundary initiating the emergence of gravity at scale?
Very interesting
Great video.
Thanks for the visit!
Me: "What new geometry is this..?"
Gandolf: "An analog- an algebra of the ancient world... These maths are beyond any of you... RUN!"
Time and space are functions of ones conceptual scheme
I feel humbled and inspired. I got lost at 24 min. mark.
A lot further than me !
3:32.. I already failed matrices once, no need to experience that pain again
Read much? Wow! Did not know that I would be listening to an audio book...you are so smart, you can read other people's work.
holy mustache batman.... do you have some sinister motives here?
😆
😆 ded
Oh I get it
Dalí 🖌🎨
You shown like a politician.
Without love in the dream insanity's King.
I would not use Emergency here actually.
That is associated with System Science usually.
I know it gets me out of a false matrix into alignment if that helps anyone 🎉
Something is wrong with the audio!!!
Sorry, I'll try to get access to a better microphone next time!
no, it's you
to much sshh , nothing a thick sock could fix
Very interesting but real numbers don't exist. You'll have to start from zero, using rational numbers or dihedron numbers (the true complex numbers). Instead of octonions use 2x2x2x2 matrices of dihedron numbers.
why ? can use Geometric Numbers of corresponding Geometric Algebra. Real Clifford.
That said, Dihedrons (rational Split-Quaternions, not rational Split-Complex numbers) are interesting, and so are the other standard split composition algebras over rational numbers.
However there are VERY MANY (probably uncountable, if we allow those of infinite dimensions, such as various direct limits) field extensions and composition algebras over the rational numbers.
Not only can you do quadratic extensions with a new number that square to *any* square free integer (number 1 being a special case, and number 0 which is a square being another special case), and get a different non-isomorphic version of quadratic "complex" numbers, but you can also do cubic extensions, quartic extensions, quintic extensions etc ad infinitum and get higher dimensional versions of "complex" numbers, and split/non-division versions thereof. These are usually "hidden" within the Archimedean metric structure of real complex numbers, but they are VERY overt when working over the rational numbers as base field, and they are also overt yet unique when working over the prime finite fields.
Besides all these field extensions and other commutative associative ring extensions, there are lots of non-commutative associative ring extensions, and lots of alternative non-associative ring extensions of the rational numbers. Some of them are quadratic normed composition algebras, but even in those cases, there are infinite (countable) possibilities. Others are most likely "cubic normed composition algebras" or more complicated things, that cannot easily be defined over real numbers.
For rational quaternion algebras, choose two square free rational numbers q1 and q2. Set i^2 = q1, j^2 = q2, i*j = -j*i.
Then (assuming associativity) (i*j)^2 = i*j*i*j = -i*i*j*j = -i^2*j^2 = -q1*q2, i*(i*j) = q1*j and (i*j)*j = q2*i, so this is a four dimensional algebra, that with some work can be shown to be a quadratic normed composition algebra, i.e. supporting a quadratic norm form Q such that Q(x) is a rational number, and that Q(s*x) = s^2*Q(x) for all rational scalars s, and that there is a B such that Q(x+y) = Q(x) + Q(y) + B(x,y), where B is a symmetric bilinear form (orthogonal form). This quadratic norm form Q is usually constructed through a conjugate operation, which comes from the Galois groups (two element groups) of the quadratic field extensions for i and for j.
Namely given a Galois symmetry '_i that swaps i and -i, and a Galois symmetry '_j that swaps j and -j, we combine them into a conjugation that both swaps i and i', and swaps j and j', and also will swap i*j and -i*j, because we decide that it should be an anti-automorphism. It should also be linear. Then Q(x) is merely x*x'
This may be done through Pfizter forms also.
The reason i mention Galois symmetries at all is because these become important for cubic norm forms and more complicated things, where you best define the form as a product of factors related through Galois symmetries.
Well, yeah, obviously.
Wow! That's amazing! I just shaved a matting off my cat's rear-end that looked exactly like the matting on your head! The cat feels much better now with it shaved off...he is much "cleaner" and "presentable" now....prior to shaving it off, my cat was dirty and smelly.
All the mathematics in the world is futile if you can't come up with something to perform an experiment on. We want Star Trek physicists who can develop warp drive technology based on real experiments. Unless you can perform an experiment on E8 in the lab, then what good is it?
It could help to find a theory that gives finite results for quantum gravity. Even though most string theorists struggle to connect to reality, Joel Scherk wrote about how supergravity can lead to antigravitic effects. String theorists have been studying the idea of traversible wormholes more recently. Warp drive is challenging; I suspect understanding a single coherent theory that combines gravity and electromagnetism could help with those pursuits. This video was not about experimental validation of a single theory that involves e8, but rather focused on the mathematical foundations of e8 and attempted to give an overview of various different approaches for using e8 for theoretical physics. Of course, diving further into a single theory and discussing experimental implications would also be interesting. Cheers.
one cannot start doing experiments unless the theory is solid already.
think, how many decades it took for many physics theories to be verified by experiment...?
so patience. help or observe or pray silence.
A very fine moustache you got there good sir!