Dr. N.L. Kachhara
In order to appreciate field theory we must know about two important developments in physics - quantum mechanics and the theory of general relativity. Quantum mechanics is a fundamental branch of theoretical physics that replaces classical mechanics and classical electromagnetism at the atomic and sub atomic levels. Along with general relativity, quantum mechanics is one of the pillars of modern physics. Quantum mechanics is a more fundamental theory than Newtonian mechanics and classical electromagnetism, in the sense that it provides accurate and precise descriptions for many phenomena that these "classical" theories simply cannot explain on the atomic and subatomic level. For example, if Newtonian mechanics governed the working of an atom, electrons would rapidly travel towards and collide with the nucleus. However, in the natural world the electron normally remains in a stable orbit around a nucleus seemingly defying classical electromagnetism.
The foundations of quantum mechanism were established during the first half of the twentieth century. In 1900, the German physicist Max Plank introduced the idea that energy is quantized, in order to derive a formula for the observed frequency dependence of the energy omitted by a black body. In 1905 Einstein explained the photoelectric effect by postulating that light energy comes in quanta called photons. In 1913 Neil Bohr explained the spectral lines of the hydrogen atom, again by using quantization. In 1924, the French physicist Louis De Broglie put forward his theory of matter waves by stating that particles can exhibit wave characteristics and vice versa. These theories are collectively known as the old quantum theory.
Modern quantum theory was born in 1925, when the German physicist Werner Heisenberg developed matrix mechanics and the Austrian physicist Erwin Schrödinger invented wave mechanics and the non-relativistic Schrödinger equation. Heisenberg formulated his uncertainty principle in 1927. The Uncertainty Principle states that both the position and the momentum cannot simultaneously be known with infinite precision at the same time. Quantum mechanics does not pinpoint the exact values for the position or momentum of certain particles in a given space in a finite time, but rather, it only provides a range of probabilities of where that particle might be. The Copenhagen interpretation of quantum mechanics took shape in 1927. According to it, the probabilistic nature of quantum mechanics predictions cannot be explained in term of some other deterministic theory, and does not simply reflect our limited knowledge. Quantum mechanics provides probabilistic results because the physical universe is itself probabilistic rather than deterministic.
Starting around 1927 Paul Dirac began the process of unifying quantum mechanics with special relativity by proposing the Dirac equation for the electron. During the same period, Hungarian polymath John von Neumann formulated the rigorous mathematical basis for quantum mechanics as the theory of linear operators and Hilbert spaces. Beginning in 1927, attempts were made to apply quantum mechanics to fields rather than simple particles resulting in what are known as quantum field theories. Early workers in this area included Dirac, Pauli, Weisskopf, and Jordan. This area of research culminated in the formation of quantum electrodynamics by Feynman, Dyson, Schwinger, and Tomonaga during the 1940s. Quantum electrodynamics is a quantum theory of electron, positron, and the electromagnetic field, and served as a role model for subsequent quantum field theories. This theory represents the interactions of charged particles mediated by force carrier photons. The quantum field theory of the strong nuclear force is called quantum chromo dynamics, and describes the interactions of the sub nuclear particles quarks and gluons.
In 1967, two Americans Sheldon Glashow and Steven Weinberg and a Pakistani Abdus Salam proposed independently a theory unifying electromagnetism and the weak nuclear forces. This unified theory was governed by the exchange of four particles the photon for electromagnetic interaction, and a neutral Z particle and two charged w particles for weak interaction. Their theory was given experimental support by the discovery, in 1983, of the Z and W bosons at CERN by Carlo Rubbia's, team.
The next logical step towards the unification of the fundamental forces of nature was to include the strong interaction with the electroweak forces in a theory called the Grand Unified Theory (GUT). The strong interaction acts between quarks via the exchange of gluons. There are eight types of gluons, each carrying a colour charge and an anti-colour charge. Based on this theory, Sheldon Glashow and Howard George proposed the first grand unified theory in 1974, which applied to energies above 1000 GeV. Since then there have been several proposals for GUTs, although none is currently universally accepted. A major problem for experimental tests of such theories is the energy scale involved, which is well beyond the reach of current accelerators. However, there are some falsifiable predictions that have been made for low energy processes that do not involve accelerators. One of these predictions is that the proton is unstable and can decay. It is at present unknown if the proton can decay although experiments have determined a lower bound of 1035 years for its lifetime. It is therefore uncertain, at the present time, whether any GUT can provide an accurate description of matter.
Gravity has yet to be included in a theory of everything. Theoretical physicists have been so far incapable of formulating a consistent theory that combines general relativity and quantum mechanics. The two theories have proved to be outstanding problem in the field of physics. In recent years the quest for a unified field theory is largely trusted on string theory.
Relativistic quantum field theory has worked very well to describe the observed behaviors and properties of elementary particles. But the theory itself only works well when gravity is so weak that it can be neglected.
String theory is believed to close this gap. By this theory we can combine quantum mechanics and gravity and we can talk sensibly about a string excitation that carries the gravitational force. Think of a guitar string that has been tuned by stretching the string under tension across the guitar. Depending on how the string is plucked and how much tension is in the string, different musical notes will be created by the string. In a similar manner, in string theory, the elementary particles we observe in particle accelerators could be thought of as the "musical notes" or excitation modes of elementary strings. The average size of a string is about 10-35 meter. This means that strings are way too small to see by current or expected particle physics technology.
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 fermion in string theory, there must be a special kind of symmetry called super symmetry, which means for every boson there is a corresponding fermion. Super symmetric partners have so far not been observed in particle experiments, but scientists are hopeful of finding evidence for highenergy super symmetry in the next decade.
There are several kinds of string theories. The bosonic string theory deals with bosons only with both open and closed strings. A superstring theory deals with super symmetry between forces and matter. There are five kinds of superstring theories one of which uses both open and closed strings and four use closed strings only. For bosonic strings the quantum mechanics can be done sensibly if the space-time dimensions number 26. For super strings the space-time dimensions are 10. Attempts are on way to collapse all the string theories into one theory, which people want to call M theory, for it is the mother of all theories. We still don't know the fundamental M theory but a lot has been learned about the eleven dimensional M theory and how it relates to superstrings in ten space-time dimensions.
Discovery of a theory is only part success. According to Stephan Hawking "Even if we do discover a complete unified theory, it would not mean that we would be able to predict events in general, for two reasons. The first is the limitations that the uncertainty principle of quantum mechanics sets on our powers of prediction. There is nothing we can do to get around that. In practice, however, this first limitation is less restrictive than the second one. It arises from the fact that we could not solve the equations of the theory exactly, except in very simple situation. We already know the laws that govern the behaviour of matter under all but the most extreme conditions. In particular, we know the basic laws that underline all of chemistry and biology. Yet we have certainly not reduced these subjects to the status of solved problems. We have, as yet, had little success in predicting human behaviour from mathematical equation! So even if we do find a complete set of basic laws, there will still be the intellectually challenging task of developing better approximation methods, so that we can make useful predictions of the probable outcomes in complicated and realistic situations. A complete, consistent, unified theory is only the first step. Our goal is a complete understanding of the events around as, and of our own existence."
