An Exceptionally Simple Theory of Everything
Published on 1 Dec 2007 at 4:15 am.
1 Comment.
Filed under Physics, Research.
Garrett Lisi recently posted a paper to the arxiv (arXiv:0711.0770v1 [hep-th]) titled “An Exceptionally Simple Theory of Everything”. In it he proposes that the group E8 unifies all of the fields of the Standard Model with Gravity and predicts new particles.
In addition to the paper, here is an excellent blog that discusses the theory, its inspiration and implications:
BackReaction on Exceptionally Simple TOE
I cannot possibly do the topic justice, but allow me to attempt a watered-down, but relatively accurate description of what is going on here for those less versed in Quantum Gravity. The basic idea is that the elementary particles have properties that obey certain symmetries. These symmetries enable us to make diagrams that display the particles as vertices of symmetric graphs. Below is one such picture showing the symmetries of the what is known as the Baryon Octet. A Baryon is a particle made of three quarks. One set of axes denotes the charge Q of the particle (in units of electron charge), and the other set of axes indicates the number of strange quarks that compose the particle. The symmetries of the diagram represent the symmetries between the particle properties. The two particles on the top are the familiar proton and neutron.
However, these symmetries only goes so far since the particles have different masses. The fact that they have different masses breaks the symmetry. This is known as the problem of symmetry-breaking.
When you see a picture like this, it seems like we have a complete theory. However, some symmetries contain other symmetries. For instance, if you consider an equilateral triangle, you can rotate it 120 degrees and it looks the same. This symmetry happens to be contained within the hexagonal symmetry. But the hexagonal symmetry has more structure. It also is contained in the rotational symmetry of the circle. If we are trying to find a symmetry that contains the known symmetry of the equilateral triangle, but also contains new properties that can explain phenomena that we currently poorly understand, there is no obvious solution. There are many symmetries to consider (in this toy example the hexagon and circle are only two of them).
This is basically what is going on now in particle physics. We know some of the symmetries, but not all of them. The question is, which higher-order symmetries include and unite all of the symmetries we know about, while simultaneously introducing new symmetries that can explain effects that we currently have no theory for, such as uniting gravity with quantum mechanics.
Garrett Lisi is proposing that E8 does exactly that. It apparently contains all of the familiar symmetries, and unites gravity and the Standard Model of particle physics in a very satisfying way. As I understand it, this theory enables him to make testable predictions, which is a huge step forward. We will see if it is right…
For now, here is a movie that shows the symmetry of E8 while performing rotations in multiple dimensions. Here is a link to a much cleaner version (about 10 MB).
Particles related to the gravitational force are represented by green circles, particles related to the electroweak force are represented by yellow circles, particles related to the strong gauge fields are blue circles. The frame-Higgs particles are squares. Three generations of leptons (electrons, muons, tauons and their associated neutrinos) are yellow and gray triangles. Finally the quarks (rbg triangles) are related by triality (lines).
Albany NY
Don Rubottom on 18 Dec 2007 at 10:27 pm: 1
Thanks for an explanation for people with less than a PhD in Math or Physics, Kevin! I have a facebook group celebrating E8: E(8) Rules! Interested folks are welcome to join. I will post a link there to your discussion.