E8 Lie group and E8 Lattice has sometimes been called the most beautiful mathematical structure in the world. Is it the theory of everything or the true nature of reality? It even has an entire research company behind it called "Quantum Gravity Research"
Note: E8 root system animation provided courtesy of David Madore - www.madore.org.
It is a 248 dimensional object, but it can also be thought of as an object that has 8 spatial dimensions, with 248 symmetries.
Why is this structure important? Well, it happens to show up in parts of String Theory. But also in 2007, a theoretical physicist Antony Garrett Lisi published a paper proclaiming that the mathematics of this structure contained all the particles and forces in the universe. He called it the “the exceptionally simple theory of everything” What Lisi did is he found a relationship between this object and all the forces and particles we know about.
According to the standard model, there are 4 fundamental forces in nature, strong force, weak force, electromagnetism and gravity. And there are 12 fundamental particles. In addition, each of these particles has a antiparticle of itself. In total, these make up all the elementary particles, and there are exactly 28 of them. 24 elementary particles, and 4 force carrier particles. Each of these distinct elementary particles has eight quantum numbers assigned to it, based on the charges each particle has.
This brings the number of distinct particles to 224.
Lisi found that he could mathematically equate all of these particles to one of the points in the E8 model.
But the model has 248 points, not 224. So what about the empty 24 extra points? He simply created 24 new theoretical particles.
Notice how the lines radiate from each point: Lisi also found patterns emerging between particles and forces like they happen in actual reality – for example, when photons interact with leptons, they create electrons. The same thing happens in the E8 lattice. The connections shown within points on the E8 match up to real, known connections between particles in our physical world.
One of the particles he assigned to this shape behaves very much like the force carrier for gravity – a graviton. And this is the key to Lisi claiming that this could be the “theory of everything.” – because it combines matter particles and gravity in one framework.
Lisi's theory does have some problems. One of the biggest problems with the theory is that Lisi combines the force carrying particles, Bosons with the matter particles. String theory does this too, but with the rigorous mathematics to go with it. This math is not present in E8, so Lisi combining these appears to be arbitrary.
In addition, a leading mathematician and expert on Lie groups, Skip Garibaldi wrote a paper in 2010 which mathematically disproved Lisi. But Lisi came back with counter arguments to that.
But the elephant in the room is the 24 new theoretical particles that come out of this the
