In late 1960s, string theory
was firstly studied broadly.
In that span of time, it was studied
under the name of nuclear force.
Later on, the field of nuclear
force was left by this theory,
as this theory started
being applied on
various concepts of
quantum chromo-dynamics.
Therefore, the fact became
known that string theory is
not familiar to be applied
on nuclear physics theory,
which made it a thing of concern
for quantum theory of gravity.
Bosonic string theory was the earliest
version of modern string theory.
In that version, only the class of
particles were included and described.
These class were knows as bosons.
The subsequent version to Bosonic
string theory was super string theory.
Super string theory described
connections between
symmetry and bosons
(Class of particles);
this connection was referred as fermions.
In the time span of mid
1990s there were more than
five versions of super string
theory were developed.
However, they limited the scope
that is possessed by a whole
theory by dividing the theory into
various (Almost 11) dimensions;
this concept is known as M-theory.
Connection between string
theory and quantum
field theory was
developed in late 1997.
This connection or let us say relation is
well known as correspondence of AdS/CFT.
Fifth dimension in gravity
theory was introduced in 1914.
This introduction was carried
on by Gunnar Nordstrom, in
which he described both
electromagnetism and gravity too.
In this approach, he tried
to describe the concept of
electromagnetism with his
very own theory of gravity.
This is the first ever modification
attempted on string theory.
Later on, Einstein superseded this approach
by introducing non-symmetric matrix sensor.
In addition, later, actually
much later, Brans and Dicke
pursued this approach and
introduced their research
by developing the concept of
scalar component of gravity.
These consequences are said to be major
approaches in the field of string theory.
The original concept
of string theory was
produced in the time span
between 1960 and 1970.
In that, theorists did not
consider time the string theory.
As it was not able to provide complete help
for the problems surrounding to hadrons,
protons and neutrons (all are
subatomic particles), etc.
Despite of these early
researches, development or say
history of string theory is
divided between two phases.
The first one is knows as
first superstring theory.
Time span of this revolution
was between 1980 and 1994.
In beginning of this period, it was
discovered that neutrino (a chiral
fermino) could not be accommodate
by any quantum gravity theory.
Edward Witten played an important
role in this research.
As consequence, he collaborated
with Luis Alvarez Gaume and
pursued his studies further in
the field of conservation laws,
which is a part of
anomalies gravity theory.
Later on, a new anomaly was
discovered which these both missed.
As a result, to this foundation,
scope of a string theory
group, named gauge group was
restricted to be SO.
As a result, to this, Witten was
convinced that string theory
is a fully complete edition
of theory of quantum gravity.
He made is identity as a
high profile advocate
as a result thanks
to his researches.
Hundreds of physicist and
mathematicians pursued
their study taking Witten’s
researches as a base.
This all happened in the time span
of 1984 and 1986, this time period
is known as first superstring revolution
in the field of string theory.
In 1995, birth was given
to new 11-dimentional
theory that we now
know as M-theory.
The time period in which
M-theory was being developed
is knows as second
superstring revolution.
Fundamentals of String Theory
Almost all fundamental
interaction in which gravity
is also included, are a
part of string theory.
Thus, almost all theorists and physicists
believe that string theory is a theory
of everything and is able to describe
anything that is a part of our universe.
Currently research on
string theory is being
conducted in order to
find a valid solution
to the many problems related
to micro elementary
particles that has small
cosmological constants.
These constants contain dark matter
and a cosmic inflation mechanism.
Progress has been made in
order to achieve these goals.
Hence, it is not clear if the string theory
is really a universal theory or not.
As described above string theory has not
yet managed to give a complete definition
for a certain thing that can be applied
in any situation or circumstances.
This is said to be a big
fallback for string theory.
Until now string, theory is being
applied using a perturbative approach.
It is not yet discovered how to apply
this theory non-pertubatively.
To understand these
statements it is important
to understand fundamentals
of string theory.
Strings:
In Quantum field theory, practical
application of mechanics
to physical objects is
presented in an extended form.
In that theory, these concepts
are extended to space and time.
Various physical events are
calculated in the field of
quantum theory using
perturbation theory techniques.
To organize various calculations
perturbation theory uses Feynman diagram.
These diagrams are considered as
paths of point like particles.
These paths also indicate interaction of
particles along with particles themselves.
Bosonic theory is said to be the
most basic version of string theory.
The problem with that version was
that it described only bosons.
Bosons are particles classes that transmit
force between various matter particles.
They are known as fermions.
This version is replaced
by superstring theory.
This theory includes both
bosons and fermions too.
This theory incorporated
use of super symmetry.
Super symmetry is a mathematical
relation between bosons and fermions.
This relation can be found in
various physical theories.
Except supper symmetry, there are various
other versions of string theory.
Type I, type IIA, type IIB
are some of them, each
with its own new concepts
and theoretical approaches.
Type I includes both open
and closed strings where
types IIA and IIB describe
closed strings only.
Extra Dimensions:
Generally, there are
three dimensions in the
field of space, which we
are familiar with them.
These three dimensions are
height, weight and length.
However, Einstein treated
time as a dimension
in his general theory
of relativity.
In that theory, Einstein
formed a four-dimensional
space-time by merging
time and space.
To do so, he did not treated
time and space as individuals.
It is certain that space-time
which is a four dimensional
unit, describes universe in
a well-organized structure.
Still, other dimensions are considered
by many physicists in order to
achieve new methods in order to extent
approaches in this particular field.
It should be noticed that
to maintain consistency
in mathematical operations
in string theory,
one need to add an extra dimension that is
extracted from four-dimensional space-time.
In Bosonic, version
space-time has 26 dimensions;
the number reduces to 10
in superstring theory.
There have been many
approaches made in order to
reduce the number of extra
dimensions in space-time.
Physicist who made these approaches tend
strongly believes that observable universe
holds only 4-dimensional structure and
possesses a high dimensional space.
This concept is important
when one is trying to develop
real time physics by using
string theory as a base.
Dualities:
Almost every version of string theory
follows non-trivial was in their approach.
This kind of relationship
between various
versions of string theory
is called S-duality.
According to this relationship,
a set of particles that
strongly interact with each
other according to one theory
may have a very weak interaction
according a completely different theory.
Another relationship between various
string theories is T-duality, which
says that each string theory
circulates around an extra dimension.
Duality is a situation, in which
two different systems that possess
different physical concepts are
proven similar in a non-trivial way.
Here it should be notice that
duality relationship can be only
applied on concepts of string
theory or string theory itself,
as it does not provide
consistency in other fields.
Duality relationship means that if two
theories are in duality relationship,
one of them can be transformed
with some changes.
However, the operations
in two different theories
cannot be made similar as
they have different bases.
Duality describes that two
different theories possess same
phenomena yet have differences
mathematical operations.
As an example of S-duality
in the field of quantum
theories montanan and olive
duality can be considered,
in which AdS/CFT possesses
the duality the builds a
connection between quantum
theory field and string theory.
Branes:
In the field of string
theory and related
concepts, Branes is known
as a physical object.
This object is used to increase
the level of dimension
of a point particle by
generalizing its notion.
For instance, dimension level is zero for
particles and it is at level 1 for strings.
This is just an example;
however, Branes can posses
much higher dimension too.
Branes is considering as dynamic
objects that follow the rules and
regulations of quantum mechanics, in
order to operate through space-time.
They also possess attributes
such as charge and mass.
Branes are also studied in the
fields of pure mathematics.
In sting theory D-branes are
considered important class, as
the descriptively include open
strings in their concepts.
As string theory drives its
concepts through space-time,
it requires use D-branes
as a base of the process.
M-theory
In the beginning period of 1995, many
theorists had believed that there
are five versions in total of this
broad theory, which are as following:
Type I
Type IIA
Type IIB
Heterotic string theory-I
Heterotic string theory-II
This statement was proven wrong when
concept of M-theory was presented.
In 1995, Edward Witten suggested
that these five theories written
above are just limiting versions
of main 11-dimensional M-theory.
This announcement leads a huge
influence over physics field.
Many physicists rushed for further
research using M-theory as a base,
that multiple researches are now known
as second superstring revolution.
Unification of Various
Superstring Theories:
Super gravity theories
describe a combination
of general relativity
with super symmetry.
As a result, in 1970s, many
theorists and physicists
became interested in
this particular theory.
By the arrival of 1978, it
has been discovered that
if 11 is taken as maximum
number of dimensions,
it allows formulations of
consistent supper symmetry.
In the same period, it has
been proved that super
gravity cannot permit any
more dimensions than 11,
11 have been proven as a maximum number
of dimensions allowed by super gravity.
Thanks to these researches, many
physicists started to believe
that by using the concept of
super gravity with 11 dimensions
it would be possible to build real
time models of four-dimensional world.
They also hoped that these models
would help us descriptively
study fundamental elements
of four-dimensional world.
These elements are listed below:
Electromagnetism
Strong nuclear forces
Weak nuclear forces
Gravity
Chirality, which is a
phenomenon, caused a problem
in practical application
of 11-dimensional concept.
The problem was that basic
laws of physics were being
distinguishing between clockwise
and anti-clockwise phenomenon.
Later it was accepted that
11-dimensional concept is not
yet developed completely to
solve or cover this problem.
During the time period of
first superstring revolution,
many theorists and physicists
had accepted string theory as a
combination of particle physics
theory and quantum gravity theory.
Super gravity theory was not able
to solve the Chirality problem.
Unlike that theory, string theory
not only solved the Chirality
problem abut also provided an
updated version of gravity theory,
which also included the
concept of quantum effects.
However, in the time span of late
1990s, many physicists were arguing
if there are less than five super
symmetric versions of this theory.
It is proven that string theory has only
less than five consistent versions.
A combined version from these multiple
theories is yet to be developed.
However, as the research was
pushed further, physicists started
a close examination and deep
studies over string theory.
They eventually stumbled upon
the fact that these multiple
versions of string theory are
related with each other.
Some of them were related
through intricate
way and some were related
in non-trivial way.
Eventually, it had been
also discovered that
there are not much
difference between strongly
interacting strings and weakly interacting
strings except the level of interaction.
This fact or say phenomenon is known as
S-duality as described in a subtopic above.
After two years or three, T-duality
relationship was also discovered.
According to this relationship,
two equivalent strings can belong
to completely different space-time
and different geometries.
At the same time, handful physicists
were trying to apply string theory on
high dimensional objects and try to
describe properties of string theory.
In early 1987,
two-dimensional branes were
discovered as a part of
11-dimetional space.
Look of these objects was
very similar to sheets.
These sheets like objects
were found to be
propagating through
eleven-dimensional space-time.
Later on, a new concept was
developed in which one of
the dimensions was considered
as a curled up circle.
According to this concept,
it can be imagined that the
branes are wrapped around
that circular dimension.
Now consider that the radius of that
circle or dimension is small enough so
that on a 10-dimension level the branes
can be viewed as a whole string.
The pattern of these objects
were much similar to string
that appear in IIA version
of super string theory.
Matrix theory:
According to the definition provided by
mathematicians, matrix is an array of numbers
or other kind of data that is sorted in
a rectangular order of specific size.
The definition of matrix in physics is much
different from one given by mathematics.
According to physics, a particular
theory, which involves the notion
of matrix in its mathematical
formulation, is said to be a matrix.
A matrix model refers to
interaction between a set of
matrices that are a part of
quantum mechanics framework.
In 1997, through the BFSS
matrix an important example of
matrix model was presented by
a small group of researchers.
A set of nine large size matrices
was represented in that approach.
The proved that eleven-dimensional
super gravity is
responsible for the low energy
limit of any matrix model.
These results are enough to prove their
BFSS model much similar to M-theory.
As a result, in many
researches, BFSS matrix model
was used as a prototype
model of original M-theory.
The purpose of using that model was to
find exact formulation for M-theory.
Many physicists also used this model
deeply describe M-theory properties.
These researches were
helpful in the process
of linking matrix
models with M-theory.
They also constructed a
relationship between matrix
modes and geometry that has
a non-commutative nature.
By using these results as a base, many
physicists manage to discover important
relationships between non-commutative
geometry and multiple physical theories.
Concept of Black Holes
Generally, particular area or
region of space-time that possess
a super strong gravitational
field is known as black hole.
Their gravitational field is too strong
for any particle or radiation to escape.
As according current researches and most
accepted models, black holes are formed
when a massive or even a small star enters
its state of gravitational collapse.
It is said that there are super
massive black holes present
in the centre of each galaxy
that exists in the universe.
Back holes hold a specific theoretical
importance since in many researches;
theorists are using
them as a base to learn
quantum aspects that are
related to gravity.
String theory holds a framework of
thermodynamics, which is important for one
who is studying properties of black holes
based on their thermodynamics only.
Bekenstein-Hawking Formula:
Statistical mechanics is a
well-known branch of physics.
Entropy is a measure described
in statistical mechanics.
This measure is mainly used for randomness
or say disorder of any physical system.
It has been studied in late 1870s.
In that very same period,
it was discovered
by an Australian researcher
Ludwig Boltzmann
that combined properties of
multiple molecules of gas
can help to derive thermodynamic
properties of gas.
Not only had this but he also proved
that by tuning behavior of gas
molecules one could derive following
microscopic properties of gas:
Temperature
Volume
Pressure
Through his researches, he proved that
Entropy is a natural algorithm, which is
used to derive different states of the
molecules that are known as microstates.
These results lead many
theorists to discover
macroscopic features of
various physical objects.
By the beginning of 20th century,
the very same concept was
applied to black holes by many
researchers and physicists.
They used gases and entropy
scales for such application.
In 1970s, it has been proved
that entropy is related
with the surface are of event
horizon of any black hole.
This concept was represented
by Jacob Bekenstein.
Event horizon of a black hole is the
boundary, where matter, particles or
radiation is lost due to the super strong
gravitational attraction of black hole.
By combining the result of his researches
with the results of Stephen Hawking,
Bekenstein presented a formula to
find mathematical value of entropy S:
S=c³kA/4hG
Values presented in the formula
above are as following:
C= Speed of light
K= Boltzmann’s constant
H= reduced value of Planck constant
G= Newton’s constant
A= Surface area of even horizon
of related black hole.
Every black hole has relative entropy
like any other physical object or system.
It is related to different microstates.
These microstates offer very same
macroscopic features as described above.
This formula is capable enough to find
expected value of any black hole.
However, in 1990s physicist attempted
to count microstate in the theory of
quantum gravity, as a result they lacked
a derivation for the very same formula.
Thus, it is considered important to find
such a derivation, which is similarly
important for the viability of any quantum
theory say especially for string theory.
Concept of Phenomenology
String theory is a collection of multiple
frameworks with different purpose.
Some of its models are also used to
construct real world physics models.
These models are used to
construct a combination
of particle physics and
general relativity.
Phenomenology is one of the many
branches of theoretical physics.
This branch describes how
one can build real-time
models with abstract
theoretical ideas.
In the field of string theory, it
is known as string phenomenology.
In this concept, it describes
how real-time or semi real-time
models can be constructed by using
only string theory as a base.
There is no practical evidence to prove
these models practically correct.
There are two reasons for such failure:
1. Theoretical and
mathematical difficulties
2. To test these facts
practically, a high
amount of extreme high
energies are required.
Due to this, this approach
has been criticized
by many communities or
individual experts.
Some also doubt on the
unification of questions
and values derived
through this approach.
Particle Physics:
Standard models of particle physics is the
most accepted theory in current time.
This theory contains
descriptive information
about particles and
their interactions.
In this very same theory,
three fundamentals forces of
nature are covered and studied,
which are as following:
Strong nuclear forces
Weak nuclear forces
Electro magnetism
However, this model has failed to
provide complete description of
real-time objects, despite of its
descriptive information and resources.
Main reason behind its failure
was that it failed to
perform a complete incorporation
of the force of gravity.
There were also minor problems
such as hierarchy problems.
This model could describe neither fermions
mass structure nor dark matter completely.
Crossing the limits of standard
models, models of particle physics
can be also built using concepts
described deeply in string theory.
Compactification is used as a base
for construction such models.
Physicists managed to
postulate a shape for extra
dimension by starting with
10/11-dimensional space-time.
By applying/using this shape
in proper method similar
models to the standard
model can be constructed.
These models also include
undiscovered particles.
If one wants to derive real-time physics
from string theory, one needs to
start applying Heterotic theory by
assuming 10-dimensional space-time.
It should also be assumed
that there is extra
space for almost six
extra dimensions.
This techniques offer multiple
approaches and methods that
help a lot to derive real-time
physics from string theory.
Real or semi real model for
four-dimensional universe can be
also constructed with the same
method with minor changes.
Thus, this technique can be
also applied in M-theory.
Cosmology:
The Big Bang theory is said to be the
earliest known cosmological model.
It covers a subsequent and
large scale of evolutions.
In this successful and
well-structured theory, following
features of universe are
observed and explained:
Galactic red-shifts
Hydrogen and helium as a relative
abundance of light elements
Proving the reality behind cosmic microwave
However, big bang theory
could not answer many
questions and they are
unanswered until the date.
Some questions whose answers are not
found in big bang models are as follows:
Why universe tends to be
equivalent in each direction?
On very large distance scales,
why universe becomes flat?
What is the reason for not using
magnetic monopoles and other
hypothesized particles in practical
implementation or experiment?
An alternative theory to big bang
concept was developed by multiple
experts in 1980s, which is known
as theory of cosmic inflation.
The cosmic theory includes and accepts all
the concepts of big bang theory being
true, but it also include explanation for
some unanswered features of universe.
According to this theory, cosmic
microwave radiation was spread
around 380,000 years after the
events of big bang theory.
This incident was responsible to
fill the sky, says inflation theory.
Criticism upon Approaches of String Theory
Number of solutions:
It is important to specify a certain shape
for extra dimension in space-time in order
to construct real time physics model that
are completely based on string theory.
Each individual shape is related
to a possible universe.
Collection of particles and forces
vary from unit to unit for such shape.
There are around 10500
knows vacuum states or
possible universes according
to string theory.
They are enough to derive
any phenomena that
are observed through two
different energies.
Many critics are concerned
about the large
number of possible universes
in string theory.
Critics argue that because of
large variety of universes
string theory is almost
useless to predict anything.
If someone pickups certain
option among them his
result would be only
related to that universe.
However, some experts also
see this number as a virtue.
As a reason, they say that a large
number of available universes
allow the examiner to observe
values of physical constant closely
and extract natural observation
through it and that too about
cosmological constant, that
holds a particular small value.
Many string theorists accept
these facts, but they
do not claime string theory
to be completely wrong.
Some of them see this as a virtue
and some as an error or say bug.
None of them supports critics
claiming the theory completely wrong.
Background independence is one
of the fundamental properties of
general theory of relativity,
which was presented by Einstein.
Background independence means that to
formulations contain in a particular
theory with this independence cannot
refer to particular space-time geometry.
Some critics argued that string theory
fails to maintain such independence.
According to string theory,
a fixed reference to
geometry or space-time
needs to be specified.
Thus, any other geometrical
calculations are
described as reference
to this fixed one.
Critics argue that string theory
badly fails to maintain this
important general activity for each
tern described in string theory.
These facts were rejected
by some string theorists.
One of these string theorists, Polchinski
pointed out that quantum gravity
theory has a major problem in developing
holographic description for gravity,
which is why it does not require
gravitational field to be anti-de sitter.
Moreover, this is the
exact reason why string
theory does not possess
background independence.
As a response to Polchinski, Smolin
said that the facts presented
by Polchinski are unproven future
results rather than being facts.
He noticed that the whole concept of
general relativity and quantum gravity is
based on global symmetries because geometry
of space-time is completely dynamical.
Sadly, this debate is still going on
and the truth is still to be found.
Many critics are trying to understand string
theory even better to find and explain
bugs in it, and vice versa, some theorists
are studying it to fill the holes.
Sociological issues:
String theory has been considering a valuable
and useful resource for the studies of
high-energy theoretical physics since the
first and second superstring revolutions,
those who took place
between 1980s and 1990s.
Many string theorists believe that
there is not any similar theory that
can answer fundamental questions
of physics as string theory does.
They strongly believe
that there are no viable
alternative for string
theory are available.
Many critics have responded
negatively to these
kinds of statements from
multiple string theorists.
Despite of the popularity of string theory
among physicists Peter Woit considers
string theory as an unhealthy and
detrimental for the future of pure physics.
He thinks that financial structure of
academia and fierce competition to
scarce resources are main reason behind
the popularity of string theory.
Many critics use his thought to build up
their own opinion about string theory.
Statements stated by Woit
are wildly accepted.
Even some string theorists
accepted them as a fallback.
A critic Penrose believes that many young
researchers prefer using premade bases
to establish a new research rather than
building new resources on their own.
He claims this statement as
a reason for which string
theory is very popular among
physicists and researchers.
Lee Smolin says that the rise
of string theory discourages
foundation of physics despite the
theory being all about physics.
He prefers to follow loop quantum
gravity theory, which (according
to him) encourages the fundamentals
of physics and radical thinking.
Until the date, any critic
or string theorists have
not managed to prove their
self completely right.
In simple words, no critic has
proved string theory completely
wrong and no theorist has proved
string theory completely right.
The debate is endless until now.
However, some experts have
hope that one day it will
end and they will have a
conclusion to the topic.
Some accept the loop holes
in the theory and strongly
believe that this debate is
never going to meet an end.
As described through various
chapters and concepts, string theory
describes almost all fundamental
concepts of modern and pure physics.
Yes, there are many loopholes
in this broad theory,
for which solutions are
still to be found.
Some string theorists believe
that one day by constant
researches the theory would
be turn out to be complete.
On the other hand, some of them have
accepted string theory as it is.
It is same with the critics.
Some are trying to prove it completely
wrong from the base and some have accepted
it in incomplete form and believe that there
are no more unknown errors left in it.
As a researcher, student,
or practitioner, one
must accept the theory
as an incomplete one.
This way, he can fulfill his purpose
of practicing string theory.
Ignoring all the criticism will
help the practitioner a lot
to accept the concepts and
facts presented in the theory.
If criticism is concerned, then no
concept in the theory is left complete.
Critics have covered almost every concept
present in the theory, thus it is strongly
recommended to learn the
theory as a complete
theory with certain
errors or say exceptions.
