Friday, August 01, 2014         


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Math theory key to more advances

By Richard Brill


One of the greatest failures of the new physics of the 20th century was its failure to reconcile quantum theory with general relativity.

This situation parallels that of 17th-century scientists who were trying to reconcile the way things fell on Earth with the greater motions of the planets.

Newton's laws of motion and gravitation solved both problems as they unified all aspects of motion.

It required him to visualize outside the flat Earth and into the three dimensions of space. Three centuries later, Einstein's general relativity explained gravity in a new way by linking space and time into a four-dimensional continuum called spacetime. This mathematical expansion of geometric dimensions taught us where to look but not exactly how.

Now we have one set of rules called the Standard Model which explains the behavior of tiny subatomic particles and another, general relativity, for giant objects like stars and galaxies. The two sets of math don't fit together as is, but a single theory of everything is a goal.

Such a theory of everything could bring us a step closer to understanding the creation of the universe and lead to advances that are beyond imagination, just as did Newton's physics. Scientists have spent billions of dollars and millions of hours over seven decades to understand and reconcile these basic forces that control the universe.

The electromagnetic forces and the weak and strong nuclear forces are reasonably understood, and work since the 1970s has led to unifying them.

As yet the graviton, a theoretical particle that carries gravitational force the way that photons carry electromagnetic force, exists only in mathematical equations.

Several mathematical models of unification have arisen that seem promising, but one in particular has piqued the interest of the cosmology community.

A Lie group is a mathematical shape that is a collection of circles twisting around one another in a specific pattern. Twisting circles 243 times produces a geometric shape called the Lie E8 group, the complexity of which cannot be appreciated in three dimensions.

Garrett Lisi, a theoretical physicist and Maui surf bum, found that the Lie E8 group describes the symmetry of the known elementary particles and the yet undiscovered gravitons.

The way the circles twist around each other in Lisi's theory mathematically describes the myriad ways in which the fundamental particles can interact with each other.

Now for the first time, someone has discovered a scheme in which gravity fits in with the other forces. Lisi calls it "An Exceptionally Simple Theory of Everything." It predicts the existence of several other particles that have not yet been observed, including the elusive and critical Higgs particle, which is thought to give mass to particles.

You might be wondering why this matters to us on a day-to-day basis.

No one in Newton's time could have predicted the many wonders that would flow out of Newtonian physics that have become second nature to our lifestyles.

Eventually some genius will reconcile these two worlds of the very small and the very large and open the doors to wonders that we can scarcely imagine.

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