The Dawn of M Theory
Carbon Dating the Birth and Evolution of String Theory
We, as human beings, have evolved just enough to let us equate observations with imaginations. This unique ability has led us towards the formulation of scientifically proven theories and mathematically sound laws. Starting from the early-man description of the five basic elements that governed nature, the progress in logical thinking and creativity have played a key role in advancing our skills in trying to understand and explain the stuff that the universe is really made of. Pythagoras, Copernicus, Galileo, Newton, Einstein and several others have attempted to get a better resolution of the pixelated truth of the universe. Each physical theory deals with a different facet of the universe that we're trying to understand. Until today, we've succeeded in sketching an asymptotic path in unifying physics.
The universe, as we know it, is more than a fabric of space-time woven by the nuanced laws of general relativity and quantum mechanics. This cosmic bubble that we are wrapped in might as well be a small unit of the bigger puzzle out there that is still an enigma to human perception. Recently, the universe has a new story to narrate which could possibly hint at the unification of all the physical laws. A brand new idea that was born amidst a neuronal Warfield - the brain of the brilliant physicist, Edward Witten, is a potential theory that could reshape all our intuitions by walking us through 'StringLand'.
The string theory developed as an outgrowth of a popular research program introduced by Werner Heisenberg in 1943. Documented as the S-matrix theory, the research proposal aimed at substituting the quantum field theory. The theory is concerned with complex particle interactions. The S-matrix theory is related to the holographic principle and the Anti-de Sitter (AdS)/ Conformal Field Theory (CFT) correspondence by a flat space limit. The ‘AdS/ CFT correspondence’, often termed as gravity/ gauge duality or Maldacena duality, deals with the relationship between two kinds of physical theories. The conjecture was first proposed by Juan Maldacena in 1997. Anti-de Sitter space is considered as the region of space that has negative curvature like a hyperbola and is likely to be associated with theories like quantum gravity. CFTs are closely related to QFTs ( Quantum Field Theories) that attempt hard to describe the elementary particles. The analogue of the S-matrix relations in AdS (Anti-de Sitter) space is the boundary conformal theory. The holographic principle is a congregation of the principle of string theories and a speculated property of quantum gravity. To break it down, the holographic principle states that the representation of a volume of space can be conceived of as encoded on a lower-dimensional boundary to the region similar to a gravitational horizon. Let’s see what a gravitational horizon looks like.
A gravitational horizon, in physics, is the apparent horizon surrounding a black hole. This is the region of space where light can evade the clutches of the black hole singularity. This boundary lies inside the event horizon’s boundary where light cannot escape. The holographic principle resolves the case of the black hole information paradox. Black holes are maximum entropy objects with their entropies being proportional to the areas of the respective event horizons. Non-Euclidean spherical geometry governs the trapping of light inside the horizons. When two geodesic trajectories of light graze through the edge of a black hole and eventually collide, the resultant would point towards the black hole’s core and make its way into its point of no return. Owing to the black hole information paradox, scientists believe that string theory could bear new insights into the perfect description of the stellar zombie. The S-matrix theory involved esoteric mathematics which made most of the physicists drop it over time. Reduction and simplifications of the very same theory has lead to what is known as the string theory.
The string theory gives a new kind of mathematical framework that attempts to replace all zero-dimensional points with one-dimensional lines, that is, to replace particles in particle physics with the notion of strings. According to this theory, the fundamental physical properties (mass, charge, frequency, etc) of the strings are the vibrations the strings themselves. There are several versions of the string theory which include the type I, type II and the heterotic string theory. Different versions of the string theory deal with different types of strings and the different symmetries of low energy string states exhibited in each of these theories. The type I string theory supports both open (segments) and closed (loops) strings while the rest of the theories support only closed strings. In Einstein’s theory of general relativity, the concept of space and time is described as a four-dimensional spacetime. In this framework, gravity is modelled as an effect of the geometry of spacetime. String theory supports 10 dimensions for mathematical consistency. Physicists prefer theories similar to string theory to help answer the unanswered questions that may lie beyond our perceptive abilities. The higher dimensions that couldn’t be traced out experimentally are theorised to be curled up and compacted. According to the mathematicians Eugenio Calabi and Shing-Tung Yau, the curled up dimensions may assume a shape similar to that of a complex geometric multidimensional figure called the Calabi-Yau manifold.
There are several valid versions of the string theory proposed. All these theories have come up as quests to try and solve different aspects of the same puzzle, to make up for the instability posed by each theory. The theories make sense when they are all put together as each version attempts to answer a specific question. These theories have to be woven to present the big picture. There are two kinds of dualities that explain the relationships between the different string theories. The S-duality presents a peculiar relationship which imposes the flexibility to consider the entire collection of strongly interacting particles in one theory to weakly interacting particles in another theory. The type I string theory and the SO(32) string theory, for example, are related by the S-duality. The T-duality relationship, on the other hand, mirrors two different string theories. The T-duality is based on the assumption that strings are wound around a circular extra dimension. The T-duality introduces the concept of the winding number. The number describes the number turns that a string makes around a circular dimension. In this duality, the quantitative properties are flipped between the two theories. For instance, the momentum p and the winding number n in one theory will correspond to momentum n and winding number p in the other theory related by the T-duality.
In string theory, the idea of a brane generalises the notion of a point to higher dimensions. Branes are important because they are dynamical objects that can propagate through spacetime according to the rules of quantum mechanics. The brane can be considered short for the membrane. Zero dimension is composed of zero-branes; one dimension is composed of one-branes or more plainly, strings; p dimensions are composed of p-branes. Branes possess all the attributes that a particle in Classical Mechanics possesses. A p-brane is expected to sweep through spacetime, a volume p+1 dimensions called the worldvolume. When considering open strings in string theory, D-branes are an important class of branes to be noted. The endpoints of an open string, when propagating through spacetime, are expected to lie on a D-brane which means that the open string has to be bounded by a mathematical limit given by the Dirichlet boundary condition. The letter D in D-brane stands for the name of the mathematical boundary condition. Study of the D-branes has led to the birth of the AdS/CFT correspondence. The connection between the mathematical and the physical notion of branes are given by algebraic geometry, symplectic geometry and representation theory.
By the year 1995, physicists filtered down the number of string theories to 5 consistent versions of the superstring theory. Edward Witten’s work changed the understanding of the string theories that the physicists had. Witten suggested that those 5 consistent theories were just special limiting cases of the 11-dimensional M-theory. This was regarded as the second superstring revolution. Thus the M-theory, an unification of all the superstring theories, was born. Supergravity theories combine general relativity and supersymmetry. Though general relativity applies to any number of dimensions, supergravity limits the number of dimensions. In 1978, Werner Nahm’s work showed that the maximum spacetime dimension in which one can formulate a consistent supersymmetric theory is eleven. Following Werner’s work, other prominent physicists showed that supergravity is elegant only in an eleven-dimensional spacetime. Hopes of describing the 4-dimensional spacetime using the 11-dimensional supergravity diminished as soon as it was learned that chirality can’t be preserved by curling up the extra dimensions. In the first superstring revolution, in 1984, the string theory was taken as a standard. In the second superstring revolution, in 1995, the M-theory was considered the standard.
