E8 – An Exceptionally Simple Theory of Everything

In 1915 Albert Einstein proposed a new interpretation for gravity in his theory of General Relativity. Until that point, the classical interpretation of gravity provided by Newton in 1687 was the guiding theory. Newton basically described gravity as a force of attraction between objects. In Einstein’s new interpretation, mass and energy distort the geometry of spacetime, creating the illusion of force as objects fall through bent spacetime. Einstein’s theory of gravity prevails as the modern interpretation for gravity and is used to predict the planetary motions, the orbits of artificial satellites, GPS triangulation and other applications.

Similarly, the Standard Model of quantum mechanics, created in the first decades of the 20th century and refined during the subsequent decades, has allowed scientists to relate all the other forces of nature under a common set of equations, proving that three of the four known forces are different representations of the same fundamental force.  Electromagnetism, the nuclear weak and strong forces are all part of the Standard Model. However, gravity is not included. Gravity lies outside of the realm of present Quantum Theory. Einstein’s theory of General Relativity and the Standard Model seem incompatible, as they philosophically differ in regards to what constitutes a force.

Almost since the inception of the Quantum Theory, scientists of all walks of life have strived to come up with a Theory of Everything (TOE) that unifies all the forces into a Grand Unified Theory, but with no success so far. Many potential candidates have been proposed. Some of these theories are incredibly complex, requiring multiple space dimensions. And, for the most part, they exist outside the realm of experimentation rendering them unverifiable. String Theory and Super Symmetry are examples of such theories and have been held as candidates for the TOE since the 70’s.

Superstring theory representation of 6-dimensional spacetime

In 2007 a new candidate was put forth by an unlikely proponent. The new theory comes from a surfer dude/snowboarding scientist named Garret Lisi, who splits his time between surfing in Hawaii and skiing the slopes of Lake Tahoe and Colorado.  Lisi was not affiliated with any university at the time he proposed his theory, and, for many years, had resisted falling in line with the conventional wisdom of his peers that held String Theory as the most likely candidate for the TOE. Lisi has taken known geometrical representations known as Lie Groups (which seem to relate known particles) a few steps forward. His development proposes that all known subatomic particles are related to each other and fit nicely within the construct of the E8 Lie Group.

The E8 Lie group is a structure with complex dimension in eight-dimensional Euclidean space, that is considered by many as the most beautiful structure in mathematics. In his paper “An Exceptionally Simple Theory of Everything” Lisi proposes a Unified Field Theory that combines a Grand Unification Theory of particle physics with Einstein’s description of gravity, using the largest Lie algebra group, E8. The E8 structure incorporates the interaction of all known particles and predicts 24 new particles.

First identified in 1887, E8 has 248 dimensions and cannot be observed or even drawn in its complete form. The E8 is the largest and most complex of the five exceptional Lie groups. According to Lisi’s theory, the E8 contains four subgroups that are related to the four fundamental forces of nature: the electromagnetic force; the strong force (which binds quarks that comprise protons); the weak force (which controls radioactive decay); and the gravitational force.

The E8 is expressed as a 248-dimensional object.  However; it can also be expressed as an eight-dimensional object with 248 symmetries. Lisi located the 224 known particles as points within the E8 structure using their charge as coordinates in eight dimensions. The remaining 24 places were reserved for yet-to-be observed particles with predicted properties of charger and spin.

E8 graph as a 2-dimensional orthogonal projection

Lisi found that when he rotated the E8 filled with the quantum particles, patterns emerged between particles and forces. Photons interacted with leptons to create electrons and other known connections between particles in the physical world. The E8 also includes gravity. If correct, the E8 would show how macro-scale gravity interacts with the other three forces.

Lisi’s model is incredibly elegant and beautiful, linking all know particles in the Standard Model and grouping them in a way that has been corroborated previously by testing of the Standard Model. It also predicts new particles, as any true theory should, and these particles might soon be observed at the Large Hadron Collider (LHC), the largest particle accelerator in the world located beneath the Franco-Swiss border.

As Lisi himself has indicated, this is an all or nothing theory. If true it can portend the final unification of all natural forces. If not, then it will be just another idea – an elegant one at least.

Lisi’s idea of positioning known particles within a Lie group is not new. Previous physicists had noticed that all currently known matter particles fit nicely and carry the correct observed changes in three copies of the smallest group representations of SU(5).  This is one of the reasons why Lisi’s idea may actually be a Grand Unified Theory.

The fact that particles in the Standard Model can already be positioned in simpler structures such as SU(5) and that the E8 can be visualized in 3 dimensions by other representations such as G421 and F4, points in the direction that these simpler shapes are only parts of a larger and more complex structure, such as E8. In his newest model, only 20 particles remain unknown to complete the puzzle and these new particles might resolve the apparent excess of invisible mass and energy that the universe seems to posses which today we call Dark Matter and Dark Energy. We have come a long way already in the subatomic realm of quantum physics and this might be the next big step towards converging the physics of the subatomic world with the macro physics of the cosmos.

The forces of nature have always seemed to follow mathematical rules. It seems right and befitting that nature would have chosen a structure such as the E8 to create order from chaos. Even if E8 is eventually proven flawed, Lisi’s geometrical interpretation of the natural order merges Einstein’s geometrical view of space time and the quantum mechanics particle world. It seems only fair that a Grand Unifying Theory should incorporate geometry among the apparent chaos of the quantum world.

“Nature’s grand book, which stands continually open to our gaze, is written in the language of mathematics. Its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth.”

Galileo Galilei 1623

Achieving a Unified Theory of Everything would be extremely exciting. New physics invariably lead to the understanding of previously unknown phenomena and new potential technological applications. Just like Einstein’s Special Theory of Relativity launched humanity into the atomic age, the final understanding of gravity could lead to applications as mundane as new transportation methods and as far reaching as interstellar travel. It has been 95 years since Einstein introduced the concept of space time and the equivalence of energy and mass providing a new understanding of the physical world not seen since Newton’s apple. We might be seeing a new apple falling from the tree.