Tuesday, April 3, 2007

Unified Field Theory---String Theory & Causal Dynamical Triangulation (CDT)

A recent article in Scientific America renewed my interest in the Unified Field Theory after a long time. When I left my post-graduate physics class some twenty years back, we were still trying to solve the equations derived from Quark Theory and had just started to get some explanation on Black Holes. Though the wheels for postulating a unified theory had been in motion for many years, things looked still very vague.Last few decades have seen a great progress in explaining most of the universe as it exists today and the dream of unified field theory may actually come true, though we may not be able to validate it for few more centuries. Let me try to explain, this highly complex and mathematical world in words.

There are four fundamental forces in the universe:
gravity, electromagnetism, and the weak and strong nuclear forces. Each of these is produced by fundamental particles that act as carriers of the force. It has been the endeavor of all theoretical physicists to explain all four fundamental forces by a unified theory--- the ultimate goal for some of them is a unified framework for all fundamental forces—a "theory of everything". Standard Model (Quantum Mechanics) of particle physics, describes both the fundamental building blocks out of which the world is made, and the forces through which these blocks interact. There are twelve basic building blocks. Six of these are quarks--- they go by the interesting names of up, down, charm, strange, bottom and top. The other six are leptons--- these include the electron and its two heavier siblings, the muon and the tauon, as well as three neutrinos. But Standard model cannot explain the: Gravity. In the last few decades physicists have formulated, what may be called a quantum theory of gravity and String theory was so far as the most promising candidate for a microscopic theory of gravity and it is possible to derive the Standard Model (which has been verified experimentally with incredible precision) from a theory of strings. In string theory, the elementary particles we observe in particle accelerators could be thought as excitation modes of elementary strings. The average size of a string should be somewhere near the length scale of quantum gravity,called the
Planck length =
String theories are classified according to whether or not the strings are required to be closed loops, and whether or not the particle spectrum includes fermions. In order to include fermions in string theory, there must be a special kind of symmetry called supersymmetry, which means for every boson (particle that transmits a force) there is a corresponding fermion (particle that makes up matter). So supersymmetry relates the particles that transmit forces to the particles that make up matter.
One of drawbacks with earlier String Theory; being set against a fixed background was over come with loop quantum gravity, which describes space as a network of tiny volumes of 10-35 meters. But this approach still does not explain the how the jumbles of volumes come together to form the familiar four –dimensional space-time of our everyday world.
Causal Dynamical Triangulation (CDT) which is less than 10 years old is gaining lot of acceptance. This approach that like loop quantum gravity is background independent. CDT constructs space-time geometries from simple triangular structures. The basic building block is a 4-simplex, the equivalent of a tetrahedron (A tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex) but in four dimensions. Each simplex though geometrically flat can be glued together in a variety of patterns to produce curved space-time. Using some extensive computer simulations, theorist successful constructed model of universe from thousands of four dimensional simplexes.