You thought it was 42 didn’t you, well it seems like it could be E8 according to A. Garrett Lisi. (original paper) No, that’s not a part of Hackney but the E8 Lie algebra…
perhaps the most beautiful structure in mathematics.
I can hear the groans already but hang on to your hats this could be a fascinating trip.
You know how all the forces in the universe, nuclear, electowhatsit, gravity and the like are all described by pretty little equations of course you do, so far so good.
In his introduction to the paper Lisi sketches his mathematical approach to describing the universe.
Although It is interesting to consider that the universe may be the physical instantiation of all mathematics, there is a classic principle for restricting the possibilities… A successful description of nature should be a concise, elegant, unified mathematical structure consistent with experience. Hundreds of years of theoretical and experimental work have produced an extremely successful pair of mathematical theories describing our world. The standard model of particles and interactions described by quantum field theory is a paragon of predictive excellence. General relativity, a theory of gravity built from pure geometry, is exceedingly elegant and effective in its domain… Any attempt to describe nature at the foundational level must reproduce these successful theories, and the most sensible course towards unification is to extend them with as little new mathematical machinery as necessary. The further we drift from these experimentally verified foundations, the less likely our mathematics is to correspond with reality. In the absence of new experimental data, we should be very careful, accepting sophisticated mathematical constructions only when they provide a clear simplification. And we should pare and unite existing structures whenever possible…By considering these two theories and following our guiding principles, we will be led to a beautiful unification.
He’s off then on his merry way. The first subheading draws me in
A connection with everything
My kind of pizza. You may have a certain reluctance to follow the next few pages if your maths is a wee bit rusty but I defy you to ignore Figure 2 on page 17. The E8 root system, with each root assigned to an elementary particle field.
After a few more equations Lisi summarises his conclusions
The theory proposed in this paper represents a comprehensive unification program, describing all fields of the standard model and gravity as parts of a uniquely beautiful mathematical structure… Some aspects of this theory are not yet completely understood, and until they are it should be treated with appropriate skepticism. However, the current match to the standard model and gravity is very good. Future work will either strengthen the correlation to known physics and produce successful predictions for the LHC, or the theory will encounter a fatal contradiction with nature. The lack of extraneous structures and free parameters ensures testable predictions, so it will either succeed or fail spectacularly. If E8 theory is fully successful as a theory of everything, our universe is an exceptionally beautiful shape.
Now men, and it is usually men, who think they have the secret to the universe, and if you just let them have 4 hours of your time and provide them with lots of paper, will write out the equations in a very small hand in green ink. They are not uncommon. They are not quite as common as men who think they are the son of god, or even god! However, I don’t think this is in the same league.
Two points really:-
In an article in the New Scientist
Lee Smolin at the Perimeter Institute for Theoretical Physics (PI) in Waterloo, Ontario, Canada, describes Lisi's work as "fabulous". "It is one of the most compelling unification models I've seen in many, many years”…
A not inconsiderable achievement as one our prime ministers used to say. As I have mentioned before Lee Smolin seems to be a sharp cookie with a good overview
There is also testability. Those three letters LHC, the Large Hadron Collider, it is a big machine for hurtling particles at high energy towards each other. A very sophisticated way of finding out what stuff is made of. Just like kids bashing toys on the ground to see what’s inside! There are great hopes of finding the Higgs.
Now there is a theory, needs a bit more work and there is no guarantee guv, but it could be tested! So let's get bashing those poor old hadrons.
