Re: Everything
- From: Rich <rembrandt4u@xxxxxxxxxxx>
- Date: Mon, 9 Mar 2009 02:59:44 -0700 (PDT)
On Mar 8, 10:36 pm, "Grand Mal" <ironw...@xxxxxxxxxxx> wrote:
"Rich" <rembrand...@xxxxxxxxxxx> wrote in message
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On Mar 8, 3:18 am, "Grand Mal" <ironw...@xxxxxxxxxxx> wrote:
"dearcilla" <dearci...@xxxxxxxxx> wrote in message
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On Mar 7, 4:45 am, Mark <blueriver...@xxxxxxxxx> wrote:
Everything is relative.
-Things that are not:
-Degrees Kelvin
-The speed of light
-Rest mass
Nothing is relative.
-That's old school. Get hip to the multidimensional
-string theory which advances Einstein's efforts.
There's no such thing.
"String theory is of interest to many physicists because it requires
new mathematical and physical ideas to mesh together its very
different mathematical formulations. One of the most inclusive of
these is the 11-dimensional M-theory, and in the M-theory way of
thinking, string theory requires spacetime to have eleven dimensions,
[1] as opposed to the usual three space and one time. The original
string theories from the 1980s describe special cases of M-theory
where the eleventh dimension is a very small circle or a line, and if
these formulations are considered as fundamental, then string theory
requires ten dimensions."'
http://en.wikipedia.org/wiki/String_theory
-
"It's the 21st century! Time to feed your mind"
http://www.superstringtheory.com
-Ads by Google Conspiracy Theories Physics G String Hawking Theory On
this page
Britannica Concise Encyclopedia: string theory
Sponsored LinksString Theory Made Easy
The Complete Idiots Guide to String Theory (and other unified
theories)
www.strings.musser.com
---
String theory
Any of a number of theories in particle physics that treat elementary
particles (see subatomic particle) as infinitesimal one-dimensional
"stringlike" objects rather than dimensionless points in space-time.
Different vibrations of the strings correspond to different particles.
Introduced in the early 1970s in attempts to describe the strong
force, string theories became popular in the 1980s when it was shown
that they might provide a fully self-consistent quantum field theory
that could describe gravitation as well as the weak, strong, and
electromagnetic forces. The development of a unified quantum field
theory is a major goal in theoretical particle physics, but inclusion
of gravity usually leads to difficult problems with infinite
quantities in the calculations. The most self-consistent string
theories propose 11 dimensions; 4 correspond to the 3 ordinary spatial
dimensions and time, while the rest are curled up and not perceptible.
For more information on string theory, visit Britannica.com.
Columbia Encyclopedia: string theory
Top Home > Library > Miscellaneous > Columbia Encyclopediastring
theory, description of elementary particles based on one-dimensional
curves, or “strings,” instead of point particles. Superstring theory,
which is string theory that contains a kind of symmetry known as
supersymmetry, shows promise as a way of unifying the four known
fundamental forces of nature. The strings are embedded in a space-time
having as many as 10 dimensions—the three ordinary dimensions plus
time and seven compactified dimensions. The energy-scale at which the
stringlike properties would become evident is so high that it is
currently unclear how any of the forms of the theory could be tested.
Bibliography
See P. C. W. Davies and J. Brown, ed., Superstrings (1988); L. Smolin,
The Trouble with Physics (2006).
--------------------------------------------------------------------------------
Science Dictionary: string theory
Top Home > Library > Science > Science Dictionary
In physics, a theory that views subatomic particles as string-like
objects floating in space-time rather than as point-like objects.
Space-time in string theory can have up to nine dimensions of space,
plus the dimension of time.
Wikipedia: String theory
Top Home > Library > Miscellaneous > WikipediaString theory
Superstring theory [hide]Theory
String theory
Superstrings
Bosonic string theory
M-theory (simplified)
Type I string · Type II string
Heterotic string
String field theory
Holographic principle
[show]Concepts
Strings · Branes
Calabi–Yau manifold
Kac–Moody algebra
D-brane
E8 Lie group
Related Topics
Supersymmetry
Supergravity
Quantum gravity
Scientists
Veneziano · Susskind · Ramond · Schwarz · Mandelstam · Scherk ·
Polyakov · Green · Witten · Gross · Polchinski · Vafa · Sen · Townsend
· Duff · Maldacena · Kaku
String theory is a still-developing approach to theoretical physics,
whose original building blocks are one-dimensional extended objects
called strings. String theory attempts to reconcile quantum mechanics
with general relativity in order to describe a quantum theory of
gravity.
Since its birth as the dual resonance model which described the
strongly interacting hadrons as strings, the term string theory has
changed to include any of a group of related superstring theories
which unite them. One shared property of all these theories is the
holographic principle. String theory itself consists of many theories
with different mathematical formulas. The logical coherence of the
approach, however, and the fact that string theory can include all
older theories of physics, have led many physicists to believe that
such a connection is possible. In particular, string theory is the
first candidate for the theory of everything, a way to describe all
the known natural forces (gravitational, electromagnetic, weak and
strong) and matter (quarks and leptons) in a mathematically complete
system. On the other hand, many detractors criticise string theory
because it has not yet provided experimentally testable predictions.
Like any other quantum theory of gravity, it is widely believed that
testing the theory experimentally would be prohibitively expensive,
requiring feats of engineering on a solar-system scale. Although some
critics concede that string theory is falsifiable in principle, they
maintain that it is unfalsifiable for the foreseeable future, and so
should not be called science.
String theory is of interest to many physicists because of the
mathematics involved, and because of the large number of forms that
the theories can take. String theory strongly suggests that spacetime
has eleven dimensions,[1] as opposed to the usual three space and one
time, but the theory can easily describe universes with four
observable spacetime dimensions as well.[2]
String theories include objects more general than strings, called
branes. The word brane, derived from "membrane", refers to a variety
of interrelated objects, such as D-branes, black p-branes and Neveu-
Schwarz 5-branes. These are typically extended objects that source
differential form generalizations of the vector potential
electromagnetic field. All such objects are known to be related to one-
another by a variety of dualities. For example, the black hole-like
black p-branes are identified with D-branes, upon which strings end,
through Gauge-gravity duality. Research on this equivalence has led to
new insights on quantum chromodynamics, the fundamental theory of the
strong nuclear force.
Overview
See also: Quantum gravity
String theory is a theory in which the electrons and quarks inside an
atom are not 0-dimensional objects, but 1-dimensional strings. These
string can move and vibrate, giving the observed particles their
flavor, charge, mass and spin. The strings make closed loops unless
they encounter surfaces, called D-branes, where they can open up into
one dimensional lines. The endpoints of the string can't break off the
D-brane, but they can slide around on it.
Levels of magnification:
1. Macroscopic level - Matter
2. Molecular level
3. Atomic level - Protons, neutrons, and electrons
4. Subatomic level - Electron
5. Subatomic level - Quarks
6. String levelString theory is a theory of gravity, an extension of
General Relativity, and the classical interpretation of the strings
and branes is that they are quantum mechanical vibrating extended
charged black holes. The overarching physical insight behind string
theory is the holographic principle, which states that the description
of the oscillations of the surface of a black hole must also describe
the space-time around it. Holography demands that a low-dimensional
theory describing the fluctuations of a horizon will end up describing
everything that can fall through, which can be anything at all. So a
theory of a black hole horizon is a theory of everything.
Finding even one consistent holographic description, a priori, seems
like a long-shot, because it would be a disembodied nonlocal
description of quantum gravity. In string theory, not only is there
one such description, there are several different ones, each
describing fluctuations of horizons with different charges and
dimensions, and all of them logically fit together. So the same
physical objects and interactions can be described by the fluctuations
of one-dimensional black hole horizons, or by three-dimensional
horizons, or by zero-dimensional horizons. The fact that these
different descriptions describe the same physics is overwhelming
evidence that string theory is consistent.
An ordinary astronomical black hole does not have a convenient
holographic description, because it has a Hawking temperature. String
theories are formulated on cold black holes, which are those which
have as much charge as possible. The first holographic theory
discovered described the scattering of one-dimensional strings, tiny
loops of vibrating horizon charged with a two-form vector potential
which makes a charged black hole a one-dimensional line. Fluctuations
of this line horizon describe all matter, so every elementary particle
can be described by a mode of oscillation of a very small segment or
loop of string. The string-length is approximately the Planck length,
but can be significantly bigger when the strings are weakly
interacting.
All string theories predict the existence of degrees of freedom which
are usually described as extra dimensions. Without fermions, bosonic
strings can vibrate in a flat but unstable 26-dimensional space time.
In a superstring theory with fermions, the weak-coupling (no-
interaction) limit describes a flat stable 10-dimensional space time.
Interacting superstring theories are best thought of as configurations
of an 11 dimensional supergravity theory called M-theory where one or
more of the dimensions are curled up so that the line-extended charged
black holes become long and light.
Long light strings can vibrate at different resonant frequencies, and
each resonant frequency describes a different type of particle.[7] So
in string limits, any elementary particle should be thought of as a
tiny vibrating line, rather than as a point. The string can vibrate in
different modes just as a guitar string can produce different notes,
and every mode appears as a different particle: electron, photon,
gluon, etc.
The only way in which strings can interact is by splitting and
combining in a smooth way. It is impossible to introduce arbitrary
extra matter, like point particles which interact with strings by
collisions, because the particles can fall into the black hole, so
holography demands that it must show up as a mode of oscillation. The
only way to introduce new matter is to find gravitational backgrounds
where strings can scatter consistently, or to add boundary conditions,
endpoints for the strings. Some of the backgrounds are called NS-
branes, which are extreme-charged black hole sheets of different
dimensions. Other charged black-*** backgrounds are the D-branes,
which have an alternate description as planes where strings can end
and slide. When the strings are long and light, the branes are
classical and heavy. In other limits where the strings become heavy,
some of the branes can become light.
Since string theory is widely believed to be a consistent theory of
quantum gravity, many hope that it correctly describes our universe,
making it a theory of everything. There are known configurations which
describe all the observed fundamental forces and matter but with a
zero cosmological constant and some new fields. There are other
configurations with different values of the cosmological constant,
which are metastable but long-lived. This leads many to believe that
there is at least one metastable solution which is quantitatively
identical with the standard model, with a small cosmological constant,
which contains dark matter and a plausible mechanism for inflation. It
is not yet known whether string theory has such a solution, nor how
much freedom the theory allows to choose the details. Because of this,
string theory has not yet made practically falsifiable predictions
that would allow it to be experimentally tested.
The full theory does not yet have a satisfactory definition in all
circumstances, since the scattering of strings is most
straightforwardly defined by a perturbation theory. The complete
quantum mechanics of high dimensional branes is not easily defined,
and the behavior of string theory in cosmological settings (time-
dependent backgrounds) is not fully worked out. It is also not clear
if there is any principle by which string theory selects its vacuum
state, the space-time configuration which determines the properties of
our Universe (see string theory landscape).
Basic properties
String theory can be formulated in terms of an action principle,
either the Nambu-Goto action or the Polyakov action, which describes
how strings move through space and time. In the absence of external
interactions, string dynamics are governed by tension and kinetic
energy, which combine to produce oscillations. The quantum mechanics
of strings implies these oscillations take on discrete vibrational
modes, the spectrum of the theory.
On distance scales larger than the string radius, each oscillation
mode behaves as a different species of particle, with its mass, spin
and charge determined by the strings dynamics. Splitting and
recombinations of string correspond to particle emission and
absorption, giving rise to the interactions between particles.
An analogy for strings' modes of vibration is a guitar string's
production of multiple but distinct musical notes. In the analogy,
different notes correspond to different particles. The only difference
is the guitar is only 2-dimensional, you can strum it up, and down. In
actuality the guitar strings would be every dimension, and the strings
could vibrate in any direction. Meaning that the particles could move
through not only our dimension, but other dimensions as well.
String theory includes both open strings, which have two distinct
endpoints, and closed strings making a complete loop. The two types of
string behave in slightly different ways, yielding two different
spectra. For example, in most string theories, one of the closed
string modes is the graviton, and one of the open string modes is the
photon. Because the two ends of an open string can always meet and
connect, forming a closed string, there are no string theories without
closed strings.
The earliest string model, the bosonic string, incorporated only
bosons. This model describes, in low enough energies, a quantum
gravity theory, which also includes (if open strings are incorporated
as well) gauge fields such as the photon (or, more generally, any
gauge theory). However, this model has problems. Most importantly, the
theory has a fundamental instability, believed to result in the decay
(at least partially) of space-time itself. Additionally, as the name
implies, the spectrum of particles contains only bosons, particles
which, like the photon, obey particular rules of behavior. Roughly
speaking, bosons are the constituents of radiation, but not of matter,
which is made of fermions. Investigating how a string theory may
include fermions in its spectrum led to the invention of
supersymmetry, a mathematical relation between bosons and fermions.
String theories which include fermionic vibrations are now known as
superstring theories; several different kinds have been described, but
all are now thought to be different limits of M-theory.
Some qualitative properties of quantum strings can be understood in a
fairly simple fashion. For example, quantum strings have tension, much
like regular strings made of twine; this tension is considered a
fundamental parameter of the theory. The tension of a quantum string
is closely related to its size. Consider a closed loop of string, left
to move through space without external forces. Its tension will tend
to contract it into a smaller and smaller loop. Classical intuition
suggests that it might shrink to a single point, but this would
violate Heisenberg's uncertainty principle. The characteristic size of
the string loop will be a balance between the tension force, acting to
make it small, and the uncertainty effect, which keeps it "stretched".
Consequently, the minimum size of a string is related to the string
tension.
World***
For more details on this topic, see Relationship between string theory
and quantum field theory.
A point-like particle's motion may be described by drawing a graph of
its position (in one or two dimensions of space) against time. The
resulting picture depicts the worldline of the particle (its
'history') in spacetime. By analogy, a similar graph depicting the
progress of a string as time passes by can be obtained; the string (a
one-dimensional object — a small line — by itself) will trace out a
surface (a two-dimensional manifold), known as the world***. The
different string modes (representing different particles, such as
photon or graviton) are surface waves on this manifold.
A closed string looks like a small loop, so its world*** will look
like a pipe or, more generally, a Riemannian surface (a two-
dimensional oriented manifold) with no boundaries (i.e. no edge). An
open string looks like a short line, so its world*** will look like
a strip or, more generally, a Riemann surface with a boundary.
Interaction in the subatomic world: world lines of point-like
particles in the Standard Model or a world *** swept up by closed
strings in string theoryStrings can split and connect. This is
reflected by the form of their world*** (more accurately, by its
topology). For example, if a closed string splits, its world*** will
look like a single pipe splitting (or connected) to two pipes (often
referred to as a pair of pants — see drawing at right). If a closed
string splits and its two parts later reconnect, its world*** will
look like a single pipe splitting to two and then reconnecting, which
also looks like a torus connected to two pipes (one representing the
ingoing string, and the other — the outgoing one). An open string
doing the same thing will have its world*** looking like a ring
connected to two strips.
Note that the process of a string splitting (or strings connecting) is
a global process of the world***, not a local one: locally, the
world*** looks the same everywhere and it is not possible to
determine a single point on the world*** where the splitting occurs.
Therefore these processes are an integral part of the theory, and are
described by the same dynamics that controls the string modes.
In some string theories (namely, closed strings in Type I and some
versions of the bosonic string), strings can split and reconnect in an
opposite orientation (as in a Möbius strip or a Klein bottle). These
theories are called unoriented. Formally, the world*** in these
theories is a non-orientable surface.
Dualities
Main articles: String duality, S-duality, T-duality, and U-duality
Before the 1990s, string theorists believed there were five distinct
superstring theories: open type I, closed type I, closed type IIA,
closed type IIB, and the two flavors of heterotic string theory (SO
(32) and E8×E8)[8]. The thinking was that out of these five candidate
theories, only one was the actual correct theory of everything, and
that theory was the one whose low energy limit, with ten spacetime
dimensions compactified down to four, matched the physics observed in
our world today. It is now believed that this picture was incorrect
and that the five superstring theories are connected to one another as
if they are each a special case of some more fundamental theory
(thought to be M-theory). These theories are related by
transformations that are called dualities. If two theories are related
by a duality transformation, it means that the first theory can be
transformed in some way so that it ends up looking just like the
second theory. The two theories are then said to be dual to one
another under that kind of transformation. Put differently, the two
theories are mathematically different descriptions of the same
phenomena.
These dualities link quantities that were also thought to be separate.
Large and small distance scales, as well as strong and weak coupling
strengths, are quantities that have always marked very distinct limits
of behavior of a physical system in both classical field theory and
quantum particle physics. But strings can obscure the difference
between large and small, strong and weak, and this is how these five
very different theories end up being related. T-duality relates the
large and small distance scales between string theories, whereas S-
duality relates strong and weak coupling strengths between string
theories. U-duality links T-duality and S-duality.
Before the "duality revolution" there were believed to be five
distinct versions of string theory, plus the (unstable) bosonic and
gluonic theories.
String theories
Type Spacetime dimensions
Details
Bosonic 26 Only bosons, no fermions, meaning only forces, no matter,
with both open and closed strings; major flaw: a particle with
imaginary mass, called the tachyon, representing an instability in the
theory.
I 10 Supersymmetry between forces and matter, with both open and
closed strings; no tachyon; group symmetry is SO(32)
IIA 10 Supersymmetry between forces and matter, with closed strings
and open strings bound to D-branes; no tachyon; massless fermions are
non-chiral
IIB 10 Supersymmetry between forces and matter, with closed strings
and open strings bound to D-branes; no tachyon; massless fermions are
chiral
HO 10 Supersymmetry between forces and matter, with closed strings
only; no tachyon; heterotic, meaning right moving and left moving
strings differ; group symmetry is SO(32)
HE 10 Supersymmetry between forces and matter, with closed strings
only; no tachyon; heterotic, meaning right moving and left moving
strings differ; group symmetry is E8×E8
Note that in the type IIA and type IIB string theories closed strings
are allowed to move everywhere throughout the ten-dimensional space-
time (called the bulk), while open strings have their ends attached to
D-branes, which are membranes of lower dimensionality (their dimension
is odd — 1, 3, 5, 7 or 9 — in type IIA and even — 0, 2, 4, 6 or 8 — in
type IIB, including the time direction).
Extra dimensions
Number of dimensions
An intriguing feature of string theory is that it involves the
prediction of extra dimensions. The number of dimensions is not fixed
by any consistency criterion, but flat spacetime solutions do exist in
the so-called "critical dimension". Cosmological solutions exist in a
wider variety of dimensionalities, and these different dimensions—more
precisely different values of the "effective central charge", a count
of degrees of freedom which reduces to dimensionality in weakly curved
regimes—are related by dynamical transitions.[9]
Nothing in Maxwell's theory of electromagnetism or Einstein's theory
of relativity makes this kind of prediction; these theories require
physicists to insert the number of dimensions "by hand", and this
number is fixed and independent of potential energy. String theory
allows one to relate the number of dimensions to scalar potential
energy. Technically, this happens because a gauge anomaly exists for
every separate number of predicted dimensions, and the gauge anomaly
can be counteracted by including nontrivial potential energy into
equations to solve motion. Furthermore, the absence of potential
energy in the "critical dimension" explains why flat spacetime
solutions are possible.
This can be better understood by noting that a photon included in a
consistent theory (technically, a particle carrying a force related to
an unbroken gauge symmetry) must be massless. The mass of the photon
which is predicted by string theory depends on the energy of the
string mode which represents the photon. This energy includes a
contribution from the Casimir effect, namely from quantum fluctuations
in the string. The size of this contribution depends on the number of
dimensions since for a larger number of dimensions, there are more
possible fluctuations in the string position. Therefore, the photon in
flat spacetime will be massless—and the theory consistent—only for a
particular number of dimensions.[10]
When the calculation is done, the critical dimensionality is not four
as one may expect (three axes of space and one of time). The subset of
X is equal to the relation of photon fluxuations in a linear
dimension. Flat space string theories are 26-dimensional in the
bosonic case, while superstring and M-theories turn out to involve 10
or 11 dimensions for flat solutions. In bosonic string theories, the
26 dimensions come from the Polyakov equation.[11] Starting from any
dimension greater than four, it is necessary to consider how these are
reduced to four dimensional space-time.
Calabi-Yau manifold (3D projection)
Compact dimensions
Two different ways have been proposed to resolve this apparent
contradiction. The first is to compactify the extra dimensions; i.e.,
the 6 or 7 extra dimensions are so small as to be undetectable by
present day experiments.
To retain a high degree of supersymmetry, these compactification
spaces must be very special, as reflected in their holonomy. A 6-
dimensional manifold must have SU(3) structure, a particular case
(torsionless) of this being SU(3) holonomy, making it a Calabi-Yau
space, and a 7-dimensional manifold must have G2 structure, with G2
holonomy again being a specific, simple, case. Such spaces have been
studied in attempts to relate string theory to the 4-dimensional
Standard Model, in part due to the computational simplicity afforded
by the assumption of supersymmetry. More recently, progress has been
made constructing more realistic compactifications without the degree
of symmetry of Calabi-Yau or G2 manifolds.
A standard analogy for this is to consider multidimensional space as a
garden hose. If the hose is viewed from a sufficient distance, it
appears to have only one dimension, its length. Indeed, think of a
ball just small enough to enter the hose. Throwing such a ball inside
the hose, the ball would move more or less in one dimension; in any
experiment we make by throwing such balls in the hose, the only
important movement will be one-dimensional, that is, along the hose.
However, as one approaches the hose, one discovers that it contains a
second dimension, its circumference. Thus, an ant crawling inside it
would move in two dimensions (and a fly flying in it would move in
three dimensions). This "extra dimension" is only visible within a
relatively close range to the hose, or if one "throws in" small enough
objects. Similarly, the extra compact dimensions are only "visible" at
extremely small distances, or by experimenting with particles with
extremely small wavelengths (of the order of the compact dimension's
radius), which in quantum mechanics means very high energies (see wave-
particle duality).
Brane-world scenario
Another possibility is that we are "stuck" in a 3+1 dimensional (i.e.
three spatial dimensions plus the time dimension) subspace of the full
universe. This subspace is supposed to be a D-brane, hence this is
known as a braneworld theory. Some People believe that some
combination of the two ideas — compactification and branes — will
ultimately yield the most realistic theory.[citation needed]
Effect of the hidden dimensions
In either case, gravity acting in the hidden dimensions affects other
non-gravitational forces such as electromagnetism. In fact, Kaluza's
early work demonstrated that general relativity in five dimensions
actually predicts the existence of electromagnetism. However, because
of the nature of Calabi-Yau manifolds, no new forces appear from the
small dimensions, but their shape has a profound effect on how the
forces between the strings appear in our four-dimensional universe. In
principle, therefore, it is possible to deduce the nature of those
extra dimensions by requiring consistency with the standard model, but
this is not yet a practical possibility. It is also possible to
extract information regarding the hidden dimensions by precision tests
of gravity, but so far these have only put upper limitations on the
size of such hidden dimensions.
D-branes
Main article: D-brane
Another key feature of string theory is the existence of D-branes.
These are membranes of different dimensionality (anywhere from a zero
dimensional membrane — which is in fact a point — and up, including 2-
dimensional membranes, 3-dimensional volumes and so on).
D-branes are defined by the fact that world*** boundaries are
attached to them. Thus D-branes can emit and absorb closed strings;
therefore they have mass (since they emit gravitons) and — in
superstring theories — charge as well (since they emit closed strings
which are gauge bosons).
From the point of view of open strings, D-branes are objects to whichthe ends of open strings are attached. The open strings attached to a
D-brane are said to "live" on it, and they give rise to gauge theories
"living" on it (since one of the open string modes is a gauge boson
such as the photon). In the case of one D-brane there will be one type
of a gauge boson and we will have an Abelian gauge theory (with the
gauge boson being the photon). If there are multiple parallel D-branes
there will be multiple types of gauge bosons, giving rise to a non-
Abelian gauge theory.
D-branes are thus gravitational sources, on which a gauge theory
"lives". This gauge theory is coupled to gravity (which is said to
exist in the bulk), so that normally each of these two different
viewpoints is incomplete.
Gauge-gravity duality
Gauge-gravity duality is a conjectured duality between a quantum
theory of gravity in certain cases and gauge theory in a lower number
of dimensions. This means that each predicted phenomenon and quantity
in one theory has an analogue in the other theory, with a "dictionary"
translating from one theory to the other.
Description of the duality
In certain cases the gauge theory on the D-branes is decoupled from
the gravity living in the bulk; thus open strings attached to the D-
branes are not interacting with closed strings. Such a situation is
termed a decoupling limit.
In those cases, the D-branes have two independent alternative
descriptions. As discussed above, from the point of view of closed
strings, the D-branes are gravitational sources, and thus we have a
gravitational theory on spacetime with some background fields. From
the point of view of open strings, the physics of the D-branes is
described by the appropriate gauge theory. Therefore in such cases it
is often conjectured that the gravitational theory on spacetime with
the appropriate background fields is dual (i.e. physically equivalent)
to the gauge theory on the boundary of this spacetime (since the
subspace filled by the D-branes is the boundary of this spacetime). So
far, this duality has not been proven in any cases, so there is also
disagreement among string theorists regarding how strong the duality
applies to various models.
Examples and intuition
The most well-known example and the first one to be studied is the
duality between Type IIB supergravity on AdS5 S5 (a product space of
a five-dimensional Anti de Sitter space and a five-sphere) on one
hand, and N = 4 supersymmetric Yang-Mills theory on the four-
dimensional boundary of the Anti de Sitter space (either a flat four-
dimensional spacetime R3,1 or a three-sphere with time S3 R).[12]
This is known as the AdS/CFT correspondence, a name often used for
Gauge / gravity duality in general.
This duality can be thought of as follows: suppose there is a
spacetime with a gravitational source, for example an extremal black
hole. When particles are far away from this source, they are described
by closed strings (i.e. a gravitational theory, or usually
supergravity). As the particles approach the gravitational source,
they can still be described by closed strings; alternatively, they can
be described by objects similar to QCD strings, which are made of
gauge bosons (gluons) and other gauge theory degrees of freedom. So if
one is able (in a decoupling limit) to describe the gravitational
system as two separate regions — one (the bulk) far away from the
source, and the other close to the source — then the latter region can
also be described by a gauge theory on D-branes. This latter region
(close to the source) is termed the near-horizon limit, since usually
there is an event horizon around (or at) the gravitational source.
In the gravitational theory, one of the directions in spacetime is the
radial direction, going from the gravitational source and away
(towards the bulk). The gauge theory lives only on the D-brane itself,
so it does not include the radial direction: it lives in a spacetime
with one less dimension compared to the gravitational theory (in fact,
it lives on a spacetime identical to the boundary of the near-horizon
gravitational theory). Let us understand how the two theories are
still equivalent:
The physics of the near-horizon gravitational theory involves only on-
shell states (as usual in string theory), while the field theory
includes also off-shell correlation function. The on-shell states in
the near-horizon gravitational theory can be thought of as describing
only particles arriving from the bulk to the near-horizon region and
interacting there between themselves. In the gauge theory these are
"projected" onto the boundary, so that particles which arrive at the
source from different directions will be seen in the gauge theory as
(off-shell) quantum fluctuations far apart from each other, while
particles arriving at the source from almost the same direction in
space will be seen in the gauge theory as (off-shell) quantum
fluctuations close to each other. Thus the angle between the arriving
particles in the gravitational theory translates to the distance scale
between quantum fluctuations in the gauge theory. The angle between
arriving particles in the gravitational theory is related to the
radial distance from the gravitational source at which the particles
interact: the larger the angle, the closer the particles have to get
to the source in order to interact with each other. On the other hand,
the scale of the distance between quantum fluctuations in a quantum
field theory is related (inversely) to the energy scale in this
theory. So small radius in the gravitational theory translates to low
energy scale in the gauge theory (i.e. the IR regime of the field
theory) while large radius in the gravitational theory translates to
high energy scale in the gauge theory (i.e. the UV regime of the field
theory).
A simple example to this principle is that if in the gravitational
theory there is a setup in which the dilaton field (which determines
the strength of the coupling) is decreasing with the radius, then its
dual field theory will be asymptotically free, i.e. its coupling will
grow weaker in high energies.
Contact with experiment
This branch of string theory may lead to new insights on quantum
chromodynamics, a gauge theory which is the fundamental theory of the
strong nuclear force. To this end, it is hoped that a gravitational
theory dual to quantum chromodynamics will be found.[13]
In fact, a vague contact with experiment has already been claimed to
have been achieved[3][4][5][6], though currently the alternative
explanation for quark-gluon plasma behavior, Lattice QCD, is doing a
much better job and has already made contact with experiments in
various fields with good results,[14] though the computations are
numerical rather than analytic. Other possible experiments for string
theory have been proposed. One is the discovery of large cosmic
strings in space, formed when the high energies in the Big Bang
"stretched" some strings to astronomical proportions. Other possible
avenues of experiment which could help provide evidence for string
theory may take place at the newly built Large Hadron Collider. One is
the measurement of the strength of gravity on a microscopic scale,
which could provide evidence for extra dimensions; if gravitons (which
are closed strings) leak off the membrane, at small scales the force
of gravity should be much greater than at large scales where the
gravitons would have ample chance to leak away into the bulk. The
discovery of supersymmetry could also be considered evidence since
string theory was the first theory to require it, though other
theories have managed to incorporate supersymmetry as well. Also, the
absence of supersymmetric particles at energies accessible to the LHC
would not necessarily disprove string theory, since supersymmetry
could exist but still be outside the accelerator's range.
Unsolved problems in physics: Is there a string theory vacuum which
exactly describes everything in our universe? Is it uniquely
determined by low energy data?
Problems and controversy
Although string theory is an outgrowth of physics, some contend that
string theory's current untestable status means that it should
(strictly speaking) be classified as more of a mathematical framework.
For a scientific theory to be valid it must be corroborated
empirically, i.e. through experiment or observation. Few avenues for
such contact with experiment have been claimed.[15] With the
construction of the Large Hadron Collider in CERN some scientists hope
to produce relevant data, though it is widely believed that any theory
of quantum gravity would require much higher energies, higher by
orders of magnitude[16], to probe directly. Moreover, string theory as
it is currently understood has a huge number of equally possible
solutions.[17] Thus it has been claimed by some scientists that string
theory may not be falsifiable and may have no predictive power.[18][19]
[20][21] String theory does predict, at least perturbatively, that at
sufficiently high energies—which are probably near the quantum gravity
scale—the string-like nature of particles should be apparent. For
example, there should be heavier copies of all particles corresponding
to higher string harmonics. However, it is unclear what these energies
are. In the limiting case, these energies would be one million billion
(ten followed by fourteen zeros) times higher than those accessible in
the newest particle accelerator, the LHC. String theory possesses many
features of mathematical interest and naturally incorporates all the
gross features of the Standard Model, such as non-abelian gauge groups
and chiral fermions. But because the theory will be difficult to test
in the foreseeable future, some theoretical physicists[22] have asked
if it can be called a scientific theory, as it is not yet falsifiable
in the sense of Popper.
It has also been suggested that string theory is better thought of as
a framework for building models, in the same way that quantum field
theory is a framework.[23]
String theory might not be truly fundamental in its present
formulation because it is background-dependent — string theory
describes perturbative expansions about fixed spacetime backgrounds.
Although the theory is conceptually background-independent, as
topology change is an established process in string theory, and the
exchange of gravitons is equivalent to a change in the background, the
mathematical execution of the theory relies on preselecting a
background as a starting point for calculations. This is because, like
many quantum field theories, much of string theory is still only
formulated perturbatively (i.e., as a series of approximations rather
than as an exact solution). Although nonperturbative techniques have
progressed considerably — including conjectured complete definitions
in space-times satisfying certain asymptotics — a full non-
perturbative definition of the theory is still lacking. While some see
background independence as a fundamental requirement of a theory of
quantum gravity, particularly since General Relativity is already
background independent, some string theorists disagree that background-
independence should be a guiding principle[citation needed]; most hope
that M-theory, or a non-perturbative treatment of string theory (such
as string field theory) will turn out to be background-independent,
giving as solutions the many different versions of string theory with
the different backgrounds.
A central problem for string theory's relevant application in physics
is that the best understood backgrounds of string theory preserve much
of the supersymmetry of the underlying theory, which results in time-
invariant space-times: currently string theory cannot deal well with
time-dependent, cosmological backgrounds. However, several models have
been proposed to explain supersymmetry breaking, such as the Randall-
Sundrum model, which suggests that our universe's brane interacts with
another brane which contains particles that break supersymmetry.
Another issue is that the vacuum structure of the theory, called the
string theory landscape, is not well understood. As string theory is
presently understood, it appears to contain a large number of
distinct, meta-stable vacua, perhaps 10500 or more. Each of these
corresponds to a different possible universe, with a different
collection of particles and forces.[17] What principle, if any, can be
used to select among these vacua is an open issue. While there are no
known continuous parameters in the theory, there is a very large
discretuum (coined in contradistinction to continuum) of possible
universes, which may be radically different from each other. Some
physicists believe this is a benefit of the theory, as it may allow a
natural anthropic explanation of the observed values of physical
constants, in particular the small value of the cosmological constant.
[24][25] The argument is that most universes contain values for
physical constants which lead to inhabitable universes (at least for
humans), and we happen to live in the most "friendly" universe. This
principle is already employed to explain the existence of life on
earth as the result of a life-friendly orbit around the medium-sized
sun among an infinite number of possible orbits (as well as a
relatively stable location in the galaxy). However, the cosmological
version of the anthropic principle remains highly controversial due to
the difficulty (if not impossibility) of testing it; many do not
accept it as scientific in the sense of Popper.
Following the appearance of two books claiming string theory is a
failure,[18][21] a hot media debate evolved in 2007.[26][27].
"For more than a generation, physicists have been chasing a will-o’-
the-wisp called string theory. The beginning of this chase marked the
end of what had been three-quarters of a century of progress. Dozens
of string-theory conferences have been held, hundreds of new Ph.D.s
have been minted, and thousands of papers have been written. Yet, for
all this activity, not a single new testable prediction has been made,
not a single theoretical puzzle has been solved. In fact, there is no
theory so far—just a set of hunches and calculations suggesting that a
theory might exist. And, even if it does, this theory will come in
such a bewildering number of versions that it will be of no practical
use: a Theory of Nothing."[28]
S. James Gates, Jr., Ph.D. strongly opposes the idea that string
theory would not be falsifiable: "So, the next time someone tells you
that string theory is not testable, remind them of the AdS/CFT
connection ..."[29]. The idea is that AdS/CFT permits the calculation
of the coupling of the "constants" of the four forces (gravitation,
electromagnetism, weak and strong nuclear forces). Namely, if the
electroweak unification happens before the electroweakstrong
unification, the supersymmetry model will be falsified. But, if all
three "constants" meet each other at the same energy in a "point"
wherein all three forces unite in a electroweakstrong unification
(without passing first through a electroweak unification),
supersymmetry will have resisted falsification[30]. Professor Gates
suggests that the LHC will be used for testing AdS/CFT, namely to
check if the electroweakstrong unification does happen as predicted,
and if it does happen at the energy computed according to AdS/CFT[31].
History
Main article: History of string theory
Some of the structures reintroduced by string theory arose for the
first time much earlier as part of the program of classical
unification started by Albert Einstein. The first person to add a
fifth dimension to general relativity was German mathematician Theodor
Kaluza in 1919, who noted that gravity in five dimensions describes
both gravity and electromagnetism in four. In 1926, the Swedish
physicist Oskar Klein gave a physical interpretation of the
unobservable extra dimension--- it is wrapped into a small circle.
Einstein introduced a non-symmetric geometric tensor, while much later
Brans and Dicke added a scalar component to gravity. These ideas would
be revived within string theory, where they are demanded by
consistency conditions.
String theory was originally developed during the late 1960s and early
1970s as a never completely successful theory of hadrons, the
subatomic particles like the proton and neutron which feel the strong
interaction. In the 1960s, Geoffrey Chew and Steven Frautschi
discovered that the mesons make families called Regge trajectories
with masses related to spins in a way that was later understood by
Yoichiro Nambu and Leonard Susskind to be the relationship expected
from rotating strings. Chew advocated making a theory for the
interactions of these trajectories which did not presume that they
were composed of any fundamental particles, but would construct their
interactions from self-consistency conditions on the S-matrix. The S-
matrix approach was started by Werner Heisenberg in the 1940s as a way
of constructing a theory which did not rely on the local notions of
space and time, which Heisenberg believed break down at the nuclear
scale. While the scale was off by many orders of magnitude, the
approach he advocated was ideally suited for a theory of quantum
gravity.
Working with experimental data, R. Dolen, D. Horn and C. Schmidt
developed some sum rules for hadron exchange. When a particle and
antiparticle scatter, virtual particles can be exchanged in two
qualitatively different ways. In the s-channel, the two particles
annihilate to make temporary intermediate states which fall apart into
the final state particles. In the t-channel, the particles exchange
intermediate states by emission and absorption. In field theory, the
two contributions add together, one giving a continuous background
contribution, the other giving peaks at certain energies. In the data,
it was clear that the peaks were stealing from the background--- the
authors interpreted this as saying that the t-channel contribution was
dual to the s-channel one, meaning both described the whole amplitude
and included the other.
The result was widely advertised by Murray Gell-Mann, leading Gabriele
Veneziano to construct a scattering amplitude which had the property
of Dolen-Horn-Schmidt duality, later renamed world-*** duality. The
amplitude needed poles where the particles appear, on straight line
trajectories, and there is a special mathematical function whose poles
are evenly spaced on half the real line--- the Gamma function--- which
was widely used in Regge theory. By manipulating combinations of Gamma
functions, Veneziano was able to find a consistent scattering
amplitude with poles on straight lines, with mostly positive residues,
which obeyed duality and had the appropriate Regge scaling at high
energy. The amplitude could fit near-beam scattering data as well as
other Regge type fits, and had a suggestive integral representation
which could be used for generalization.
Over the next years, hundreds of physicists worked to complete the
bootstrap program for this model, with many surprises. Veneziano
himself discovered that for the scattering amplitude to describe the
scattering of a particle which appears in the theory, an obvious self-
consistency condition, the lightest particle must be a tachyon. Miguel
Virasoro and Joel Shapiro found a different amplitude now understood
to be that of closed strings, while Ziro Koba and Holger Nielsen
generalized Veneziano's integral representation to multiparticle
scattering. Veneziano and Sergio Fubini introduced an operator
formalism for computing the scattering amplitudes which was a
forerunner of world-*** conformal theory, while Virasoro understood
how to remove the poles with wrong-sign residues using a constraint on
the states. Claud Lovelace calculated a loop amplitude, and noted that
there is an inconsistency unless the dimension of the theory is 26.
Charles Thorn, Peter Goddard and Richard Brower went on to prove that
there are no wrong-sign propagating states in dimensions less than or
equal to 26.
In 1969 Yoichiro Nambu, Holger Bech Nielsen and Leonard Susskind
recognized that the theory could be given a description in space and
time in terms of strings. The scattering amplitudes were derived
systematically from the action principle by Peter Goddard, Jeffrey
Goldstone, Claudio Rebbi and Charles Thorn, giving a space-time
picture to the vertex operators introduced by Veneziano and Fubini and
a geometrical interpretation to the Virasoro conditions.
In 1970, Pierre Ramond added fermions to the model, which led him to
formulate a two-dimensional supersymmetry to cancel the wrong-sign
states. John Schwarz and André Neveu added another sector to the fermi
theory a short time later. In the fermion theories, the critical
dimension was 10. Stanley Mandelstam formulated a world ***
conformal theory for both the bose and fermi case, giving a two-
dimensional field theoretic path-integral to generate the operator
formalism.
In 1974, Tamiaki Yoneya discovered that all the known string theories
included a massless spin-two particle which obeyed the correct Ward
identities to be a graviton. John Schwarz and Joel Scherk came to the
same conclusion and made the bold leap to suggest that string theory
was a theory of gravity, not a theory of hadrons. They reintroduced
Kaluza-Klein theory as a way of making sense of the extra dimensions.
At the same time, quantum chromodynamics was recognized as the correct
theory of hadrons, shifting the attention of physicists and apparently
leaving the bootstrap program in the dustbin of history.
String theory eventually made it out of the dustbin, but for the
following decade all work on the theory was completely ignored. Still,
the theory continued to develop at a steady pace thanks the work of a
handful of devotees. Ferdinando Gliozzi, Joel Scherk, and David Olive
realized in 1976 that the original Ramond and Neveu Schwarz-strings
were separately inconsistent and needed to be combined. The resulting
theory did not have a tachyon, and was proven to have space-time
supersymmetry by John Schwarz and Michael Green in 1981. The same
year, Alexander Polyakov gave the theory a modern path integral
formulation, and went on to develop conformal field theory
extensively. In 1979, Daniel Friedan showed that the equations of
motions of string theory, which are generalizations of the Einstein
equations of General Relativity, emerge from the Renormalization group
equations for the two-dimensional field theory. Schwarz and Green
discovered T-duality, and constructed two different superstring
theories--- IIA and IIB related by T-duality, and type I theories with
open strings. The consistency conditions had been so strong, that the
entire theory was nearly uniquely determined, with only a few discrete
choices.
In the early 1980s, Edward Witten discovered that most theories of
quantum gravity could not accommodate chiral fermions like the
neutrino. This led him, in collaboration with Luiz Alvarez-Gaume to
study violations of the conservation laws in gravity theories with
anomalies, concluding that type I string theories were inconsistent.
Green and Schwarz discovered a contribution to the anomaly that Witten
and Alvarez-Gaume had missed, which restricted the gauge group of the
type I string theory to be SO(32). In coming to understand this
calculation, Edward Witten became convinced that string theory was
truly a consistent theory of gravity, and he became a high-profile
advocate. Following Witten's lead, between 1984 and 1986, hundreds of
physicists started to work in this field, and this is sometimes called
the first superstring revolution.
During this period, David Gross, Jeffrey Harvey, Emil Martinec, and
Ryan Rohm discovered heterotic strings. The gauge group of these
closed strings was two copies of E8, and either copy could easily and
naturally include the standard model. Philip Candelas, Gary Horowitz,
Andrew Strominger and Edward Witten found that the Calabi-Yau
manifolds are the compactifications which preserve a realistic amount
of supersymmetry, while Lance Dixon and others worked out the physical
properties of orbifolds, distinctive geometrical singularities allowed
in string theory. Cumrun Vafa generalized T-duality from circles to
arbitrary manifolds, creating the mathematical field of mirror
symmetry. David Gross and Vipul Periwal discovered that string
perturbation theory was divergent in a way that suggested that new non-
perturbative objects were missing.
In the 1990s, Joseph Polchinski discovered that the theory requires
higher-dimensional objects, called D-branes and identified these with
the black-hole solutions of supergravity. These were understood to be
the new objects suggested by the perturbative divergences, and they
opened up a new field with rich mathematical structure. It quickly
became clear that D-branes and other p-branes, not just strings,
formed the matter content of the string theories, and the physical
interpretation of the strings and branes was revealed--- they are a
type of black hole. Leonard Susskind had incorporated the holographic
principle of Gerardus 't Hooft into string theory, identifying the
long highly-excited string states with ordinary thermal black hole
states. As suggested by 't Hooft, the fluctuations of the black hole
horizon, the world-*** or world-volume theory, describes not only
the degrees of freedom of the black hole, but all nearby objects too.
In 1995, at the annual conference of string theorists at the
University of Southern California (USC), Edward Witten gave a speech
on string theory that essentially united the five string theories that
existed at the time, and giving birth to a new 11-dimensional theory
called M-theory. M-theory was also foreshadowed in the work of Paul
Townsend at approximately the same time. The flurry of activity which
began at this time is sometimes called the second superstring
revolution.
During this period, Tom Banks, Willy Fischler Stephen Shenker and
Leonard Susskind formulated a full holographic description of M-theory
on IIA D0 branes, the first definition of string theory that was fully
non-perturbative and a concrete mathematical realization of the
holographic principle. Andrew Strominger and Cumrun Vafa calculated
the entropy of certain configurations of D-branes and found agreement
with the semi-classical answer for extreme charged black holes. Petr
Horava and Edward Witten found the eleven-dimensional formulation of
the heterotic string theories, showing that orbifolds solve the
chirality problem. Witten noted that the effective description of the
physics of D-branes at low energies is by a supersymmetric gauge
theory, and found geometrical interpretations of mathematical
structures in gauge theory that he and Nathan Seiberg had earlier
discovered in terms of the location of the branes.
In 1997 Juan Maldacena noted that the low energy excitations of a
theory near a black hole consist of objects close to the horizon,
which for extreme charged black holes looks like an anti de Sitter
space. He noted that in this limit the gauge theory describes the
string excitations near the branes. So he hypothesized that string
theory on a near-horizon extreme-charged black-hole geometry, an anti-
deSitter space times a sphere with flux, is equally well described by
the low-energy limiting gauge theory, the N=4 supersymmetric Yang-
Mills theory. This hypothesis, complemented by converging work due to
Steven Gubser, Igor Klebanov and Alexander Polyakov, is called the AdS/
CFT correspondence and it is now well-accepted. It is a concrete
realization of the holographic principle, which has far-reaching
implications for black holes, locality and information in physics, as
well as the nature of the gravitational interaction. Through this
relationship, string theory has been shown to be related to gauge
theories like quantum chromodynamics and this has led to more
quantitative understanding of the behavior of hadrons, bringing string
theory back to its roots.
References
^ M. J. Duff, James T. Liu and R. Minasian Eleven Dimensional Origin
of String/String Duality: A One Loop Test Center for Theoretical
Physics, Department of Physics, Texas A&M University
^ Polchinski, Joseph (1998). String Theory, Cambridge University
Press.
^ a b H. Nastase The RHIC fireball as a dual black hole BROWN-
HET-1439, ArXiv: hep-th/0501068, January 2005,
^ a b H. Nastase More on the RHIC fireball and dual black holes BROWN-
HET-1466, ArXiv: hep-th/0603176, March 2006,
^ a b H. Liu, K. Rajagopal, U. A. Wiedemann An AdS/CFT Calculation of
Screening in a Hot Wind, MIT-CTP-3757, July 2006,
^ a b H. Liu, K. Rajagopal, U. A. Wiedemann Calculating the Jet
Quenching Parameter from AdS/CFT, Phys.Rev.Lett.97:182301,2006
^ To compare, the size of an atom is roughly 10-10 m and the size of a
proton is 10-15 m. To imagine the Planck length: you can stretch along
the diameter of an atom the same number of strings as the number of
atoms you can line up to Proxima Centauri (the nearest star to Earth
after the Sun). The tension of a string (8.9×1042 newtons) is about
1041 times the tension of an average piano string (735 newtons).
^ S. James Gates, Jr., Ph.D., Superstring Theory: The DNA of Reality
"Lecture 23 - Can I Have that Extra Dimension in the Window?",
0:04:54, 0:21:00.
^ Simeon Hellerman, Ian Swanson: "Dimension-changing exact solutions
of string theory". e-Print: hep-th/0612051; Ofer Aharony, Eva
Silverstein: "Supercritical stability, transitions and (pseudo)
tachyons". Physical Review D 75:046003, 2007. e-Print: hep-th/0612031
^ The calculation of the number of dimensions can be circumvented by
adding a degree of freedom which compensates for the "missing" quantum
fluctuations. However, this degree of freedom behaves similar to
spacetime dimensions only in some aspects, and the produced theory is
not Lorentz invariant, and has other characteristics which don't
appear in nature. This is known as the linear dilaton or non-critical
string.
^ "Quantum Geometry of Bosonic Strings – Revisited"
^ Aharony, O.; S.S. Gubser, J. Maldacena, H. Ooguri, Y. Oz (2000).
"Large N Field Theories, String Theory and Gravity" (subscription
required). Phys. Rept. 323: 183–386. doi:10.1016/S0370-1573(99)
00083-6, http://arxiv.org/abs/hep-th/9905111. . For other examples
see: [1]
^ For example: T. Sakai and S. Sugimoto, Low energy hadron physics in
holographic QCD, Prog.Theor.Phys.113:843-882,2005, ArXiv: hep-th/
0412141, December 2004
^ See for example Recent Results of the MILC research program, taken
from the MILC Collaboration homepage
^ M. R. Douglas,Are There Testable Predictions of String Theory?
February 2007 Texas A&M
^ See e.g. E. Kiritsis, String theory in a nutshell. Introduction to
Modern String theory, Princeton University Press, Princeton, N.Y.
(2007)
^ a b S. Kachru, R. Kallosh, A. Linde and S. P. Trivedi, de Sitter
Vacua in String Theory, Phys.Rev.D68:046005,2003
^ a b Peter Woit's Not Even Wrong weblog
^ P. Woit (Columbia University) String theory: An Evaluation,February
2001, e-Print: physics/0102051
^ P. Woit, Is String Theory Testable? INFN Rome March 2007
^ a b Lee Smolin's The Trouble With Physics webpage
^ Prominent critics include Philip Anderson ("string theory is the
first science in hundreds of years to be pursued in pre-Baconian
fashion, without any adequate experimental guidance", New York Times,
4 January 2005), Sheldon Glashow ("there ain't no experiment that
could be done nor is there any observation that could be made that
would say, `You guys are wrong.' The theory is safe, permanently
safe", NOVA interview), Lawrence Krauss ("String theory [is] yet to
have any real successes in explaining or predicting anything
measurable", New York Times, 8 November 2005), Peter Woit (see his
blog, article and book "Not Even Wrong", ISBN 0-224-07605-1) and Carlo
Rovelli (see his Dialog on Quantum Gravity)
^ David Gross, Perspectives, String Theory: Achievements and
Perspectives - A conference
^ N. Arkani-Hamed, S. Dimopoulos and S. Kachru, Predictive Landscapes
and New Physics at a TeV, SLAC-PUB-10928, HUTP-05-A0001, SU-ITP-04-44,
January 2005
^ L. Susskind The Anthropic Landscape of String Theory, February 2003
^ John Baez and responses on the group weblog The n-Category Cafe
^ John Baez weblog
^ Unstrung: The New Yorker
^ S. James Gates, Jr., Ph.D., Superstring Theory: The DNA of Reality
"Lecture 21 - Can 4D Forces (without Gravity) Love Strings?",
0:26:06-0:26:21, cf. 0:24:05-0:26-24.
^ Idem, "Lecture 19 - Do-See-Do and Swing your Superpartner Part II"
0:16:05-0:24:29.
^ Idem, Lecture 21, 0:20:10-0:21:20.
Further reading
Popular books and articles
Davies, Paul; Julian R. Brown (Eds.) (July 31 1992). Superstrings: A
Theory of Everything? (Reprint edition ed.). Cambridge: Cambridge
University Press. pp.244. ISBN 0-521-43775-X.
Gefter, Amanda (December 2005). "Is string theory in trouble?". New
Scientist. Retrieved on December 19, 2005. – An interview with Leonard
Susskind, the theoretical physicist who discovered that string theory
is based on one-dimensional objects and now is promoting the idea of
multiple universes.
Green, Michael (September 1986). "Superstrings". Scientific American.
Retrieved on December 19, 2005.
Greene, Brian (October 20 2003). The Elegant Universe: Superstrings,
Hidden Dimensions, and the Quest for the Ultimate Theory (Reissue
edition ed.). New York: W.W. Norton & Company. pp.464. ISBN
0-393-05858-1.
Greene, Brian (2004). The Fabric of the Cosmos: Space, Time, and the
Texture of Reality. New York: Alfred A. Knopf. pp.569. ISBN
0-375-41288-3.
Gribbin, John (1998). The Search for Superstrings, Symmetry, and the
Theory of Everything. London: Little Brown and Company. pp.224. ISBN
0-316-32975-4.
Halpern, Paul (2004). The Great Beyond: Higher Dimensions, Parallel
Universes, and the Extraordinary Search for a Theory of Everything.
Hoboken, New Jersey: John Wiley & Sons, Inc.. pp.326. ISBN 0-471-46595-
X.
Hooper, Dan (2006). Dark Cosmos: In Search of Our Universe's Missing
Mass and Energy. New York: HarperCollins. pp.240. ISBN
978-0-06-113032-8.
Kaku, Michio (April 1994). Hyperspace: A Scientific Odyssey Through
Parallel Universes, Time Warps, and the Tenth Dimension. Oxford:
Oxford University Press. pp.384. ISBN 0-19-508514-0.
Musser, George (2008). The Complete Idiot's Guide to String Theory.
Indianapolis: Alpha. pp.368. ISBN 978-1-59-257702-6.
Penrose, Roger (February 22 2005). The Road to Reality: A Complete
Guide to the Laws of the Universe, Knopf. pp.1136. ISBN
0-679-45443-8.
Randall, Lisa (September 1 2005). Warped Passages: Unraveling the
Mysteries of the Universe's Hidden Dimensions. New York: Ecco Press.
pp.512. ISBN 0-06-053108-8.
Smolin, Lee (2006). The Trouble with Physics: The Rise of String
Theory, the Fall of a Science, and What Comes Next. New York: Houghton
Mifflin Co.. pp.392. ISBN 0-618-55105-0.
Susskind, Leonard (December 2006). The Cosmic Landscape: String Theory
and the Illusion of Intelligent Design. New York: Hachette Book Group/
Back Bay Books. pp.403. ISBN 0-316-01333-1.
Taubes, Gary (November 1986). "Everything's Now Tied to Strings"
Discover Magazine vol 7, #11. (Popular article, probably the first
ever written, on the first superstring revolution.)
Vilenkin, Alex (2006). Many Worlds in One: The Search for Other
Universes. New York: Hill and Wang. pp.235. ISBN 0-8090-9523-8.
Witten, Edward (June 2002). "The Universe on a String". Astronomy
Magazine. Retrieved on December 19, 2005. – An easy article for
everybody outside physics wanting to understand the very basics of the
theory.
Woit, Peter (2006). Not Even Wrong - The Failure of String Theory And
the Search for Unity in Physical Law. London: Jonathan Cape &: New
York: Basic Books. pp.290. ISBN 0-224-07605-1 & ISBN
978-0-465-09275-8.
Textbooks
Binétruy, Pierre (2007). Supersymmetry: Theory, Experiment, and
Cosmology, Oxford University Press. ISBN 978-0-19-850954-7.
Dine, Michael (2007). Supersymmetry and String Theory: Beyond the
Standard Model, Cambridge University Press. ISBN 0-521-85841-0.
Paul H. Frampton (1974). Dual Resonance Models, Frontiers in Physics.
ISBN 0-805-32581-6.
Gasperini, Maurizio (2007). Elements of String Cosmology, Cambridge
University Press. ISBN 978-0-521-86875-4.
Michael Green, John H. Schwarz and Edward Witten (1987). Superstring
theory, Cambridge University Press. The original textbook.
Vol. 1: Introduction. ISBN 0-521-35752-7.
Vol. 2: Loop amplitudes, anomalies and phenomenology. ISBN
0-521-35753-5.
Kiritsis, Elias (2007). String Theory in a Nutshell, Princeton
University Press. ISBN 978-0-691-12230-4.
Polchinski, Joseph (1998). String Theory, Cambridge University Press.
A modern textbook.
Vol. 1: An introduction to the bosonic string. ISBN 0-521-63303-6.
Vol. 2: Superstring theory and beyond. ISBN 0-521-63304-4.
Johnson, Clifford (2003). D-branes. Cambridge: Cambridge University
Press. ISBN 0-521-80912-6.
Zwiebach, Barton (2004). A First Course in String Theory, Cambridge
University Press. ISBN 0-521-83143-1. Errata are available
Katrin Becker, Melanie Becker and John H. Schwarz (2007). String
Theory and M-Theory: A Modern Introduction , Cambridge University
Press. ISBN 0-521-86069-5
Leonard Susskind, (2006). The Cosmic Landscape: String Theory And The
Illusion Of Intelligent Design, Little, Brown & Company ISBN
0-316-15579-9
Szabo, Richard J. (Reprinted 2007). An Introduction to String Theory
and D-brane Dynamics, Imperial College Press. ISBN 978-1-86094-427-7.
External links
Superstring Theory Perimeter Institute for Theoretical Physics
Schwarz, Patricia (1998). "The Official String Theory Web Site".
Retrieved on December 16, 2005.
WGBH Educational Foundation (2003). "The Elegant Universe". PBS
Online, NOVA. Retrieved on December 16, 2005. – A Three-Hour
Miniseries with Brian Greene by NOVA (original PBS Broadcast Dates:
October 28, 8-10 p.m. and November 4, 8-9 p.m., 2003). Various images,
texts, videos and animations explaining string theory.
Troost, Jan (2002). "Beyond String Theory". Vrije Universiteit
Brussel, Theoretical Physics (TENA). Retrieved on December 16, 2005. –
An ongoing project by a string physicist, working for the French
CNRS.
Dialogue on the Foundations of String Theory at MathPages
Pierre, John M. (1999). "Superstrings! String Theory Home Page".
Retrieved on December 16, 2005. – Online tutorial.
Motl, Luboš; Screiber, Urs. "SCI.physics. STRINGS newsgroup". Harvard
High Energy Theory Group. Retrieved on December 16, 2005. – A
moderated newsgroup for discussion of string theory (a theory of
quantum gravity and unification of forces) and related fields of high-
energy physics.
Schwarz, John H. (2000). "Introduction to Superstring Theory".
arXiv.org e-Print archive. Retrieved on December 22, 2005. – Four
lectures, presented at the NATO Advanced Study Institute on Techniques
and Concepts of High Energy Physics, St. Croix, Virgin Islands, in
June 2000, and addressed to an audience of graduate students in
experimental high energy physics, survey basic concepts in string
theory.
Witten, Edward (1998). "Duality, Spacetime and Quantum Mechanics".
Kavli Institute for Theoretical Physics. Retrieved on December 16,
2005. – Slides and audio from an Ed Witten lecture where he introduces
string theory and discusses its challenges.
Kibble, Tom (2004). "Cosmic strings reborn?". arXiv.org e-Print
archive. Retrieved on December 16, 2005. – Invited Lecture at COSLAB
2004, held at Ambleside, Cumbria, United Kingdom, from 10 to 17
September 2004.
Marolf, Don (2004). "Resource Letter NSST-1: The Nature and Status of
String Theory". arXiv.org e-Print archive. Retrieved on December 16,
2005. – A guide to the string theory literature.
Ajay, Shakeeb, Wieland et al. (2004). "The nth dimension". Retrieved
on December 16, 2005. – A comprehensive compilation of materials
concerning string theory. Created by an international team of
students.
Woit, Peter (2002). "Is string theory even wrong?". American
Scientist. Retrieved on December 16, 2005. – A criticism of string
theory.
Woit, Peter (2004). "Not Even Wrong". Columbia University Mathematics
Department. Retrieved on December 16, 2005. – A blog critical of
string theory.
Veneziano, Gabriele (May 2004), "The Myth of the Beginning of Time",
Scientific American, http://www.sciam.com/article.cfm?chanID=sa006&articleID=00042F0D-1A0E-1085-94F483414B7F0000
McKie, Robin (2006-10-09), "Setback as string theory of the universe
is de-bunked", The Hindu, http://www.hindu.com/thehindu/holnus/008200610091240.htm
Harris, Richard (2006-11-07). "Short of 'All,' String Theorists
Accused of Nothing". National Public Radio. Retrieved on 2007-03-05.
A website dedicated to creative writing inspired by string theory.
George Gardner (2007-01-24). "Theory of everything put to the test".
tech.blorge.com. (Web link). Retrieved on 2007-03-03.
Minkel, J. R. (2006-03-02), "A Prediction from String Theory, with
Strings Attached", Scientific American,
http://www.sciam.com/article.cfm?chanId=sa003&articleId=1475A684-E7F2-99DF-355B95296BE6031C
Chalmers, Matthew (2007-09-03). "Stringscape". Physics World.
Retrieved on September 6, 2007. — An up-to-date and thorough review of
string theory in a popular way.
Smolin, Lee. The Trouble With Physics: The Rise of String Theory, the
Fall of a Science, and What Comes Next (2006), Houghton Mifflin. ISBN
978-0-618-55105-7.
http://www.answers.com/topic/string-theory
-Everything is absolutely relative.
-Including perspective.
Including nothing?
Yeah...right, stupid ol geezer.
This conversation is over.
----
Rich
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