Bosonic string theory is the original version of
string theoryString theory is a developing branch of theoretical physics that combines quantum mechanics and general relativity into a quantum theory of gravity...
, developed in the late
1960sThe 1960s was the decade that ran from January 1, 1960, to December 31, 1969.The 1960s term also refers to an era more often called The Sixties, denoting the complex of inter-related cultural and political trends in the west, particularly United States, Canada, Argentina, Brazil, Spain, France,...
.
Although it has many attractive features, it has a pair of features that render it unattractive as a
physical modelA physical model is a smaller or larger physical copy of an object. The object being modelled may be small or large ....
. Firstly it predicts only the existence of bosons whereas many physical particles are fermions. Secondly, it predicts the existence of a particle whose mass is
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implying that it travels faster than light.
Bosonic string theory is the original version of
string theoryString theory is a developing branch of theoretical physics that combines quantum mechanics and general relativity into a quantum theory of gravity...
, developed in the late
1960sThe 1960s was the decade that ran from January 1, 1960, to December 31, 1969.The 1960s term also refers to an era more often called The Sixties, denoting the complex of inter-related cultural and political trends in the west, particularly United States, Canada, Argentina, Brazil, Spain, France,...
.
Although it has many attractive features, it has a pair of features that render it unattractive as a
physical modelA physical model is a smaller or larger physical copy of an object. The object being modelled may be small or large ....
. Firstly it predicts only the existence of bosons whereas many physical particles are fermions. Secondly, it predicts the existence of a particle whose mass is
imaginaryfrom blue area)|-||-||-||-| style="background:#cedff2;" | |-|style="background:#cedff2;" | |-|style="background:#cedff2;" | |-|style="background:#cedff2;" | |-||-||-||-| |-|}...
implying that it travels faster than light. The existence of such a particle, commonly known as a
tachyonA tachyon is a hypothetical subatomic particle that travels faster than the speed of light...
, would conflict with much of what is known about physics, and such particles have never been observed.
Another feature of bosonic string theory is that in general the theory displays inconsistencies due to the
conformal anomalyConformal anomaly is an anomaly i.e. a quantum phenomenon that breaks the conformal symmetry of the classical theory.In string theory, conformal symmetry on the worldsheet is a local Weyl symmetry and must therefore cancel if the theory is to be consistent...
. But, as was first noticed by Claud Lovelace, in a spacetime of 26 dimensions, with 25 dimensions of space and one of time, the inconsistencies cancel. Another way to look at this is that in general bosonic string theory predicts unphysical particle states called 'ghosts'. In 26 dimensions the no-ghost theorem predicts that these ghost states have no interaction whatsoever with any other states and hence that they can be ignored leaving a consistent theory. So bosonic string theory predicts a 26 dimensional spacetime. This high dimensionality is not a problem for bosonic string theory because it can be formulated in such a way that along the 22 excess dimensions, spacetime is folded up to form a small
torusIn geometry, a torus is a surface of revolution generated by revolving a circle in three dimensional space about an axis coplanar with and not touching the circle. Examples of tori include the surfaces of doughnuts and inner tubes. The solid contained by the surface is known as a toroid...
. This would leave only the familiar four dimensions of spacetime visible.
The universe is built on tiny vibrating quantized strings. The vibrational modes of these strings determine the characteristics that the strings display. These vibrational modes of strings in turn are controlled by the membranes they "live" in. We consider our strings to be vibrating on a D brane. The D brane is essentially a membrane wherein open strings can end within the Dirichlet Boundary conditions. The Dirichlet Boundary condition is a type of a boundary condition which when imposed on an ordinary or a partial differential equation, specifies the value which the solution of the equation must take on the boundary of the domain. The D branes are classified on the basis of their dimension, with a number written next to the letter D. For example D0 denotes a point or a dot D1 is called a line (which we refer to as a string) the D2 is a plane and the dimensions go on adding up to D26 for bosonic string theories and D10 for supersymmetric string theories.
For example, if we have two parallel D2-branes, we can easily imagine strings stretching from brane 1 to brane 2 or vice versa. (In most theories, strings are oriented objects: each one carries an "arrow" defining a direction along its length.) The open strings permissible in this situation then fall into two categories, or "sectors": those originating on brane 1 and terminating on brane 2, and those originating on brane 2 and terminating on brane 1. Symbolically, we say we have the [1\ 2] and the [2\ 1] sectors. In addition, a string may begin and end on the same brane, giving [1\ 1] and [2\ 2] sectors. (The numbers inside the brackets are called Chan-Paton indices, but they are really just labels identifying the branes.) A string in either the [1\ 2] or the [2\ 1] sector has a minimum length: it cannot be shorter than the separation between the branes. All strings have some tension, against which one must pull to lengthen the object; this pull does work on the string, adding to its energy. Because string theories are by nature relativistic, adding energy to a string is equivalent to adding mass, by Einstein's relation E = mc^2. Therefore, the separation between D-branes controls the minimum mass open strings may have.
We consider the case of "Entropy" of the black hole. Consider dropping an amount of very hot gas into the black hole. Since the gas cannot escape from the hole's gravitational pull, its entropy would seem to have vanished from the universe. In order to maintain the second law of thermodynamics, one must postulate that the black hole gained whatever entropy the infalling gas originally had. Attempting to apply quantum mechanics to the study of black holes, the legendary astrophysicist Stephen Hawking discovered that a Black hole should emit energy with the characteristic spectrum of thermal radiation. Now we come to our original statement which is describing a Black Hole using the string theory. From the above text, we can pretty much come to the conclusion that a black hole can be considered as a very long (thus very massive string).This model gives rough agreement with the expected entropy of a Schwarzschild black hole, but an exact proof has yet to be found one way or the other. The chief difficulty is that it is relatively easy to count the degrees of freedom quantum strings possess if they do not interact with one another. This is analogous to the ideal gas studied in introductory thermodynamics: the easiest situation to model is when the gas atoms do not have interactions among themselves. Developing the kinetic theory of gases in the case where the gas atoms or molecules experience inter-particle forces (like the van der Waals force) is more difficult. However, a world without interactions is an uninteresting place: most significantly for the black hole problem, gravity is an interaction, and so if the "string coupling" is turned off, no black hole could ever arise. Therefore, calculating black hole entropy requires working in a regime where string interactions exist
In the early 1970s,
supersymmetryIn particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
was discovered in the context of string theory, and a new version of string theory called
superstring theorySuperstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modelling them as vibrations of tiny supersymmetric strings...
(supersymmetric string theory) became the real focus. Nevertheless, bosonic string theory remains a very useful "
toy modelIn physics, a toy model is a simplified set of objects and equations relating them that can nevertheless be used to understand a mechanism that is also useful in the full, non-simplified theory....
" to understand many general features of perturbative string theory, and string theory textbooks usually start with the bosonic string. The first volume of
PolchinskiJoseph Polchinski is a physicist working on string theory. He graduated from Canyon del Oro High School in Tucson, Arizona in 1971, obtained his B.S. degree from Caltech in 1975, and his Ph.D. from the University of California, Berkeley in 1980 under the supervision of Stanley Mandelstam...
's
String Theory and Zwiebach's
A First Course in String Theory are good examples.