**Introduction To String Theory**

**General Relativity and Quantum
Mechanics**

**The two greatest achievements of 20th
century physics have been**

**General Theory of Relativity****Quantum Mechanics**

**While the former successfully describes the Universe
on a Large Scale, the latter solved mysteries of the world of small. Ever since
there has been a constant effort by the physicists to form a single Unified
Theory of Everything (TOE) which would describe the entire universe ranging from
quarks to black holes.**

**Obviously, such a TOE should essentially
incorporate within it the features of both General Theory as well as Quantum Theory. But the
very basic fact that these two theories disagree with each other has kept the
dream of a TOE away. There have been unsuccessful efforts to find a Quantum
Theory of Gravity that describes Gravity using the principles of Quantum
Mechanics.**

**One might wonder about the need to unify GR and QT
as both deal with the universe on completely different scales. Why not just use
GR when dealing with Gravity and Large scale Universe and use QT for the world
of the small?
The problem lies with certain parts of space time called Singularities. For ex: Blackhole
Singularities. These are the regions of spacetime with dimensions of the range
of an atom and at the same time with gravitational fields so strong
that the effect of General Relativity cannot be ignored. Thus, if we have to
describe singularities then, we must unite Quantum Mechanics and General
Relativity.**

**One of the fundamental issues on which General
Relativity (GR) and Quantum Theory (QT) disagree is Time. While GR rules out the
idea of absolute time, QT does not. However the absolute time of QT is not the
same as the classical Newtonian one, infact the absolute time of QT is not
measurable at all!**

**Also, unacceptable to GR is the microscopic universe
of QT filled with Quantum Foam. The world of the small is heavily chaotic with
the constant creation and annihilation of Quantum particles. The space here is
highly irregular and this is something which GR can't agree with. according to
GR, space might also be tightly curved, but it is always smooth and there
is absolutely no place for quantum irregularities. While Quantum Theory talks
about the occurrences of events in terms of probabilities, General Relativity
completely rules out probabilities, as Einstein put in his famous quote
"God never plays dice".**

**Thus the Quantum Theory and General Relativity are
completely inconsistent with each other.**

**String Theory Enters the Scenario:**

**String Theory has emerged as the most
promising candidate for the post of a Theory of Everything.**

**Originally String Theory was born to explain the interactions between
hadrons. In more simple terms, String Theory tried to explain Strong Nuclear
Force between particles like protons and neutrons. But the success of Quantum
Chromodynamics in explaining these interactions made physicists forget the
String Theory for quite sometime.**

**Once again String Theory entered into the picture, but now with a
completely different look when it was found that this could successfully prove
the existence of gravitons. Before going into the details of this...**

**What actually the String Theory all about?**

**We know that the quantum theory looks at the nature as particles and the
General relativity looks at the nature geometrically as a 4 dimensional
spacetime.
But String Theory insists that the basic entities of matter at the fundamental
level of the order of Planck's length are Strings
(see Fig 1) , similar to the Strings of a musical instrument like Veena or
Guitar, with different modes of vibration.
Fig 1. A String**

**The beauty of String Theory is the basic idea of explaining the different
fundamental particles of nature as the various modes of vibration of the same
string! While a string vibrating with a given mode becomes a top quark, the same
String when it starts to vibrates in some other mode might be a photon!**

**Things turn out more interesting when we look at the heavy mathematics of
this theory. As we look at the behavior of particles formed when a string
vibrates in different modes, there comes a particular mode of vibration at which
the resulting equations become exactly same as those of General Relativity! Thus
the particle formed at this particular mode of vibration is none other than our
old friend whom we have been searching for years together, The
Graviton.**

**One of the fundamental problems which the String Theory solved was the
infinity regarding the Inverse Square Laws. When the distance between two
particles are taken to be zero, both the Inverse Square Laws predict that the
respective Forces between the particles become infinite. For ex, if the distance
between two electrons is zero, then the Gravitational Force of attraction as
well as the Electromagnetic Force of repulsion becomes infinite and infinities
are not always welcome for us.**

This problem for
Electromagnetism was solved by Quantum Theory whose uncertainty principle
smears out the value r=0. But the problem remained unsolved in the case of
gravity. Remember that even Newton's Formula of Gravitation is not
incorrect, but is a good approximation of General Relativity. String
Theory solved this infinity problem immediately as there is no question of
Zero distance between two points here. Here interactions between Strings
always take place at a small but certainly finite distance. |

**The various String Theories we have today are based on the ideas like
whether a String is an open one or a closed one and even whether we want to
include fermions in the theory or not. **

**If we consider only bosons, i.e, the Force carrying
particles and both open as well as closed Strings, we get what is called the
Bosonic String Theory. This String Theory makes sense only in 26 dimensions! and
remember there is no room for fermions and hence for matter here. But then if
you look carefully, you find that this is not the Theory we are looking
for, due to the obvious reason that it doesn't deal with Fermions. To be a
Theory of Everything, it must explain everything! Also one more drawback with
the bosonic String Theory is that it explains a particle called Tachyon which
has imaginary mass! This is something which we cannot agree with.**

**So we will concentrate only on those String Theories which explain not
only bosons, but also fermions. But to do so, these theories demand a special
type of symmetry called supersymmetry to exist in nature. According to this,
each fermion has its bosonic partner. For ex: electron which is a fermion has
its bosonic particle called selectron! But then one has never found a selectron.
But that does not also mean that there are no selectrons!! perhaps they are
hidden in the extra dimensions! Yes even when we consider fermions the Universe
of String Theory still has more dimensions than our usual four. But unlike
bosonic String Theory which talks about 26 dimensions, here the numbers come
down to 10 i.e, 9 space dimensions and one time dimension (The science fiction
writers might be disappointed as the number of time dimensions continues to be
one!!). Nevertheless the other 6 space dimensions also are not the ones which we
can explore into as they are tightly compacted at subatomic distances.. So it
might be that only a few fundamental particles are able to wander around in
these extra dimensions!! or are they?? **

**The String Theories which talk about SuperSymmetry in nature and thus
explain bosons as well as fermions are called SuperString Theories. These
theories do not need Tachyons (The particles with imaginary mass which bosonic
String Theory explains) to exist. Currently physicists have filtered out five
different types of SuperString Theories called I, II A, II B, HO and HE.**

**While SuperString Theory I differs from the other in the respect that it
has both open as well as closed Strings, the other Super String Theories talk
only about closed strings. Unlike II A and II B, HO and HE are heterotic String
theories. In heterotic string theories the strings moving to right are different
from those moving left. heterotic string theories have emerged to be the most
promising candidates for a Theory of Everything. But still we have two of them
and still a lot needs to be done before we finally have a TOE.**

**Nowadays physicists love to call a TOE as M-Theory (Mother of all
theories!). Let us hope that we will find one very soon.**

** e-me at gurubangalore@rediffmail.com**

**Glossary:**

**Topology:**

This is a Mathematical Branch which deals with Shapes without going into the
Geometric details. To be more precise topology deals with Connectedness of
Shapes. Two shapes are to said to have the same connectedness if we can deform
one into another without tearing. For ex: a cup and a doughnut have the same
connectedness.

**Blackhole:
Region of spacetime so tightly curved by gravity that even light cannot escape.**

**Planck's Length:
is given by the formula (hG/c ^{3})^{1/2}**
,

**Graviton:
is a quantum particle zero mass of spin 2, which is believed to be the carrier
of the Gravitational Force.**

**Fermions:
are the particles that obey Pauli's Exclusion principle. These are the
fundamental particles that make up matter. Ex: electron**

**Bosons:
are the particles that do not obey **