For over a century, since Albert Einstein
published his first paper on the general theory of relativity in 1905, physicists have
struggled to resolve fundamental differences between quantum theory and the
continuum or yang miller field theory. The field approach should have no
singularities[big bang or big crunch]; but the quantum approach has only
singularities. Max Planck formulated quantum theory in 1900, and Einstein could
however successfully applied it in 1905 to electromagnetic radiation, when
Einstein first hypothesized the photon particle in Particle Physics, the
inheritors of quantum theory, used a paradigm of ballistic matter in
non-reactive flat space, that was originally fashioned using the Rutherford
atomic model for the fixed nucleus and its orbiting electrons, which was
patterned after the solar system by Rutherford to earn a Nobel prize. The laws
of conservation of momentum and energy, and orbital dynamics did not translate
well from the very large realm to the very small, resulting in necessary
modifications such as de Broglie waves. Relativity, the successor to field
theory, had been there after repeatedly tested and was proven using atomic
clocks, accelerated particles, and star light aberration of CS chandrasekhar. But other than explanations
involving passenger trains and observers as originally presented by Einstein,
relativity lacks a working visualization model like the Rutherford
atomic model, to explain interactions of matter at relativistic speeds
approaching "c" the speed of light. Very little is found in
scientific literature regarding common ground from which both particle physics
and relativity can be derived. All of theoretical physics suffers from the lack
of a definitive visualization model to guide research. The majority of
developments in theoretical physics are driven by purely mathematical concepts
and extensions of current theory.
The most recent attempt at achieving common
ground, that of String Theory, fell victim in this struggle and was reduced to
so called Super Symmetry String Theory ,being reinterpreted as super-short
string segments embedded within the theoretical quark particles. Each
miniaturized "super string" is supposed to have free ends whipping at
the speed of light. Exactly where the required string tension comes from to
support super high frequencies with unrestrained ends, and where the power
comes from to sustain the oscillations, is not addressed. Also left unanswered
is any relevance of whipping ends inside the theoretical sub-atomic quark, to
the transmission of light in free space. Compactifying string theory within the
unobserved quark particle effectively marginalized string theory and ended its
threat to the status quo.
What is time?
In physics, spacetime (or space–time)
is any mathematical model
that combines space and time into a single continuum.
Space-time is usually interpreted with space being three-dimensional
and time playing the role of a fourth dimension that is of a different
sort than the spatial dimensions. According to certain Euclidean space perceptions, the universe has three dimensions of space and one dimension of
time. By combining space and time into a single manifold, physicists have significantly
simplified a large number of physical theories,
as well as described in a more uniform way the workings of the universe at both
the super galactic
and subatomic
levels. The concept of space-time combines space and time within a single coordinate system, typically with three
spatial dimensions: length, width, height, and one temporal dimension: the time.
Dimensions are components of a coordinate grid typically used to locate a point
in a certain defined "space" as, for example, on the globe by latitude and longitude. In space time, a coordinate grid
that spans the 3+1 dimensions locates "events" (rather than just
points in space), so time is added as another dimension to the grid, and
another axis. This way, you have where and when something is. Unlike in
normal spatial coordinates, there are restrictions for how measurements can be
made spatially and temporally. These restrictions correspond roughly to a particular mathematical
model which differs from Euclidean space in its manifest symmetry. We live in a 3+1
dimensional space time with symmetry principles that, in the case of
special relativity, require that the laws of physics be invariant
under space time transformations. Symmetry and asymmetry have been
powerful organizing concepts in a host of disciplines, including
biology, art and mathematics. More than a century ago, van’t Hoff
pointed out a connection between molecular chirality and the
fundamental symmetries in physics . In the case of biology, Pasteur
was the first to recognize ‘‘symétrie’’ at the molecular level and
concluded from data on (+)- and (-)-tartaric acid that they
represented non super imposable mirror images of each other (Fig. 1
). Kelvin later introduced the
term chirality for this type of asymmetry
). Kelvin later introduced the
term chirality for this type of asymmetry 
Previously, from various important experiments at low speeds, time was
believed to be independent of motion, progressing only in forward direction, at
a fixed rate in all reference frames;
however, later in early mid 20th century, high-speed experiments
revealed that time can be slowed down at higher speeds (with such slowing
called "time dilation" explained in the
theory of Einstein "special theory of
relativity" . Many powerfull experiments later have confirmed time dilation, such as
in atomic clocks, on board a Space Shuttle running slower than
synchronized Earth-bound inertial clocks and at subatomic particles level the
relativistic decay of muons
from cosmic ray showers. So time is variable.
The duration of time can therefore vary for various events and various reference frames.
When dimensions are understood as mere components of a grid system, rather than
physical attributes of space, it is easier to understand the alternate
dimensional views as being simply the result of coordinate
transformations. The term spacetime
has taken on a generalized meaning beyond treating spacetime events with
the normal 3+1 dimensions (including time). It is really the combination of
space and time. Other proposed spacetime theories include additional
dimensions—normally spatial but there exist some speculative theories that
include additional temporal dimensions and even BY some those included some
other dimensions that are neither temporal nor spatial. How many dimensions are
needed to describe the visible universe is still an open question today.
Speculative theories such as string theory predict 10 [string
theory-3] or 26[string theory-1] dimensions ,when M-theory predicts 11 dimensions: 10
spatial and 1 temporal, but the existence of more than four dimensions would
only appear to make a difference at the subatomic level or micro universe
level. For physical reasons, a spacetime continuum is mathematically defined as
a four-dimensional, smooth, flat connected with Lorentzian manifold
(M,g). This means the smooth Lorentz metric g
has signature . The metric determines the geometry of space-time, as well as
determining the geodesics of particles and light beams.
About each point (event) on this manifold, coordinate charts are used to represent
observers in reference frames. Usually, Cartesian coordinates (x,y,z,t) are used. Moreover,
for simplicity's sake, the speed of light c
is usually assumed to be unity. A reference frame (observer) can be identified
with one of these coordinate charts; any such observer can describe any event p. Another reference frame may be identified by a
second coordinate chart about p. Two
observers (one in each reference frame) may describe the same event p but obtain different descriptions. Usually, many
overlapping coordinate charts are needed to cover a manifold. Given two
coordinate charts, one containing p
(representing an observer) and another containing q
(representing another observer), the intersection of the charts represents the
region of spacetime in which both observers can measure physical quantities and
hence compare results. The relation between the two sets of measurements is
given by a non-singular
coordinate transformation on this intersection. The idea of coordinate charts
as local observers who can perform measurements in their vicinity also makes
good physical sense, as this is how one actually collects physical
data—locally. For example, two observers, one of whom is on Earth, but the
other one who is on a fast rocket to pluto, may observe a comet crashing into
Jupiter or in pluto (this is the event p). In
general, they will disagree about the exact location and timing of this impact,
i.e., they will have different 4-tuples (x,y,z,t)
(as they are using different coordinate systems). Although their kinematic
descriptions will differ, dynamical (physical) laws, such as momentum
conservation and the first law of thermodynamics, will still hold. In fact,
relativity theory requires more than this in the sense that it stipulates these
(and all other physical) laws must take the same form in all coordinate
systems. This introduces tensors into
relativity, by which all physical quantities are represented.
Space time in theory of special relativity : The geometry of spacetime in special relativity theory is described as the Minkowski
metric on R4. This spacetime there is called
Minkowski space. The Minkowski metric is usually denoted by η and can be written as a four-by-four matrix: where the Landau–Lifshitz
spacelike convention is being used. A basic assumption of relativity
is that coordinate transformations must leave spacetime intervals invariant.
Intervals are invariant
under Lorentz
transformations. This invariance property leads to the use of four-vectors (and other tensors) in
describing physics. Strictly speaking, one can also consider events in
Newtonian physics as a single spacetime. This is Galilean-Newtonian relativity, and the
coordinate systems are related by Galilean
transformations. However, since these preserve spatial and temporal
distances independently, such a spacetime can be decomposed into spatial
coordinates plus temporal coordinates, which is not possible in the general
case.
Space time in general relativity_: In general relativity theory, it is
assumed that spacetime is curved by the presence of matter (energy), this
curvature being represented by the Riemann
tensor. In special relativity, the Riemann tensor is identically
zero, and so this concept of "non-curvedness" is sometimes expressed
by the statement Minkowski spacetime is flat. Many spacetime continua
have physical interpretations which most physicists would consider bizarre or
unsettling. For example, a compact
spacetime has closed, time-like curves, which violate our usual ideas of
causality (that is, future events could affect past ones). For this reason,
mathematical physicists usually consider only restricted subsets of all the
possible spacetimes. One way to do this is to study "realistic"
solutions of the equations of general relativity. Another way is to add some additional
"physically reasonable" but still fairly general geometric
restrictions and try to prove interesting things about the resulting
spacetimes. The latter approach has led to some important results, most notably
the Penrose–Hawking singularity of the time
Quantized space time [3+1 spacetime] In general theory of relativity, spacetime is assumed to be smooth, flat
and continuous—and not just in the mathematics. In the theory of quantum
mechanics, there is an inherent discreteness present in physics. In attempting
to reconcile these two theories, it was sometimes postulated by some physicists
that spacetime should be quantized also at the very smallest scales. Current theory is focused on the nature of
spacetime at the Planck scale.
Causal sets, loop quantum
gravity string theory, and black hole
thermodynamics , all
predicts a quantized
spacetime with agreement order of magnitude. Loop
quantum gravity makes precise predictions about the geometry of spacetime at the Planck scale. Privileged
character of 3+1 spacetime Reasoning
about spacetime is always limited by the scientific evidence and technology
available. For example, in the latter 20th century, experiments with particle
accelerators revealed that protons gained mass when accelerated to
super high speeds, and the time required for particle decay and other physical
phenomena rose. Special relativity predicted this. Authors writing before
Einstein's discovery of special relativity were unaware of these facts, so that
their views were often mistaken, even fanciful. In the Universe, there
are two kinds of dimensions, spatial (bidirectional) and temporal
(unidirectional). Let the number of
spatial dimensions be N and the number of temporal dimensions be T.
That N=3 and T=1, setting aside the compactified dimensions
invoked by string theory
and undetectable to date, can be explained by appealing to the physical
consequences of letting N differ from 3 and T differ from 1. Immanuel Kant once argued that 3-dimensional space was a
consequence of the inverse square law of
universal gravitation. While Kant's argument is historically
important, John D. Barrow
today in 2002 says that it "...gets the punch-line back to front: it is
the three-dimensionality of space that explains why we see inverse-square force
laws in Nature, not vice-versa." This is because the law of gravitation
(or any other inverse-square law)
follows from the concept of flux, from N=3, and
from 3-dimensional solid objects having surface areas proportional to the
square of their size in a selected spatial dimension. In particular, a sphere
of radius r has area of 4πr2.
More generally, in a space of N dimensions, the strength of the
gravitational attraction between two bodies separated by a distance of r
would be inversely proportional to rN-1. In 1920, Paul Ehrenfest showed that if we fix T=
1 and let N>3, the orbit of a planet about its sun cannot remain stable. The same is
true of a star's orbit around the center of its galaxy Ehrenfest also showed that if N is even,
then the different parts of a wave impulse will travel
at different speeds. If N>3 and odd, then wave impulses become
distorted. Only when N=3 or 1 are both problems avoided. In 1922, Hermann Weyl showed that Maxwell's theory of electromagnetism works only when N=3
and T=1, writing that this fact "...not only leads to a deeper
understanding of Maxwell's theory, but also of the fact that the world is four
dimensional, which has hitherto always been accepted as merely
'accidental,'become intelligible through it. Finally, Tangherlini showed in
1963 that when N>3, electron orbitals around nuclei cannot be stable;
electrons would either fall into the nucleus or disperse. Max Tegmark expands on the preceding
argument in the following anthropic
manner. If T differs from 1, the behavior of physical systems could not
be predicted reliably from knowledge of the relevant partial
differential equations. In such a universe, intelligent life capable
of manipulating technology could not emerge. Moreover, if T>1,
Tegmark maintains that protons and electrons would be unstable and could decay
into particles having greater mass than themselves. (This is not a problem if
the particles have a sufficiently low temperature.) If N>3,
Ehrenfest's argument above holds; atoms as we know them (and probably more
complex structures as well) could not exist. If N<3, gravitation of
any kind becomes problematic, and the universe is probably too simple to
contain observers. For example, when N<3, nerves cannot overlap
without intersecting.In general, it is not clear how physical law could
function if T differed from 1. If T>1, subatomic particles
which decay after a fixed period would not behave predictably, because
time-like geodesics would not be necessarily maximal.
N=1 and T=3 has the peculiar property that the speed of light in a vacuum is a lower
bound on the velocity of matter; all matter consists of tachyons.Hence anthropic and other
arguments rule out all cases except N=3 and T=1—which happens to
describe the world about us. Curiously, the cases N=3 or 4 have the richest
and most difficult geometry and topology. There are, for example, geometric
statements whose truth or falsity is known for all N except one or both
of 3 and 4. N=3 was the last case of the Poincare conjecture
to be proved. For an elementary treatment of the privileged status of N=3
and T=1, of Barrow for deeper treatments, of Barrow and Tipler (1986)
and Tegmark String theory
builds on the notion that the "universe is wiggly" and hypothesizes
that matter and energy are composed of tiny vibrating strings of various types,
most of which are embedded in dimensions that exist only on a scale no larger
than the Planck length.
Hence N=3 and T=1 do not characterize string theory, whicha
embeds vibrating strings in coordinate grids having 10, even 26, dimensions
What is space time in the string theory?
Space-time is defined there as an invisible, underlying matrix woven from a
double helix having one atomic diameter cross-section and infinite length,
always traveling at the speed of light "c" along its axis. It
is the power source and regulator of the entire universe. I can rather call
this invisible double helix the Space-time Helix (STH) because it defines the
limits and dimensions of space by its ubiquitous presence and extension. It
marks time at the most fundamental level by its resulting crest-to-crest sine
wave spacing (wavelength), while traveling at c; and the term
"helix" incorporates its cork-screw shape. The STH produces all known
rotational phenomena without actually rotating. A travelling helix gives the
appearance of rotation without actually rotating, yet it can induce rotation in
an intersecting plane of detection through which it slides. We tend to think of
a helix in terms of the Archimedes' screw in which a rotating screw lifts
water; the screw turns and the water doesn't. The STH works in the opposite
manner; the STH doesn't rotate but it causes rotation of the electrons and
nucleons formed by two intersecting space-time helices. If the STH were forced
to rotate, it would soon twist into a hopeless knot.As long as the double helix
travels longitudinally at speed c in a balanced state without lateral
displacement or vibration, it remains hidden and does not intrude into our
reality. Once the STH is disturbed laterally or longitudinally, by being struck
or forced out of balance, it is capable of producing all known vibrational
frequency particles, both short-lived and long-lived. The STH is the hidden
power source for all that exists and occurs in the universe. The STH is
described as follows –
1) The
Space-time helix can be illustrated by a ball of twisted yarn or by a twisted
ribbon of crepe paper with unequal edges (see Figure 1
2) The inner
helix has "positive
proto-charge" and "proto-mass" capable of producing a proton
when physically coupled with the inner helix of another intersecting Space-time
helix. Such coupling occurred one time only during the opening one (1) second
of the Big Bang event, creating instantly all the protons in the universe. The
sudden appearance of unbalanced, unbridled positive charge in the ultra-dense
compacted universe, which began smaller than a single pea, provided the
mutually repulsive force needed to explode the disassociated hydrogen H+ nuclei
into the ever expanding, cooling universe we know today.
- The inner
helix normally has an orbital diameter roughly equal to the nuclear diameter of
a hydrogen H nucleus; but the inner radius of gyration can be momentarily
displaced and expanded in its travels at c by a width ranging up to the
nuclear diameter of the heaviest possible element.
-- The
outer helix has "negative proto-charge" and "proto-mass"
capable of producing an electron when physically coupled with the outer helix
of another intersecting Space-time helix. The coupling of two inner helices and
two outer helices at a junction point or pair node produces a hydrogen H atom,
with an orbital proton and an orbital electron. According to the literature,
electron coupling first occurred 300,000 years after the Big Bang, when the
rapidly expanding chaotic H+ plasma cooled to the point that the two outer
helices of node-paired Space-time helices could capture each other as they whipped
around the proton-node already formed by the intersecting inner helices.
-- The outer
helix has an orbital diameter in free space roughly equal to the single
electron orbital diameter of a hydrogen H electron shell. The outer orbital
diameter can be momentarily displaced and expanded in its travels at c
by a width ranging up to the outer electron shell diameter of the heaviest
possible element. The outer helix is somewhat elastic and can assume a higher
or lower orbital diameter as it speeds through an intersecting atom-node. An
imbalance between the radii of gyration of a coupled proton and electron, at
the atom node, may contribute to chemical valence states, and provide some
basis for chemical bonding along the longitudinal axis of either paired helix
(see Figure
1 and Figure 2).
-- The
STH travels at c along its path throughout the universe in a dynamically
balanced state, so that the radii of gyration of the inner and outer helix
members are inversely proportional to their proto masses, which themselves are
proportional to the relative masses of the proton and electron, that being
1836.1 m(proton) :1 m(electron). By extrapolating from the
orbital frequency of a single electron in the hydrogen H atom, given as 6.6
million gigahertz, we can determine that the wave length of the STH at this
present point of universe expansion is about 4.54 x 10-6 cm.
[please
enlarge the all pictures by click on individual pictures and
then at format pictures and then on size
icons]
Time is nothing more than fixed periodicity
established at the most primal level. The basic time is the standard of the
entire material universe, shared by every atom, is the rotational frequency of
its constituent electrons, and the corresponding rotational frequency of its
nucleons that are paired to its electrons by the STH structure. Time
renormalizes at every electron, proton and neutron in the universe because an
STH imposes its rotational frequency on an intersecting node-paired STH, which
in turn is forced to the same rotational frequency by the STH it intersects.
That is why the universe, other than for spectral red shift or spectral blue
shift does not appear to radically depart from a common time base.
Relativistic time
dilation occurs when a pair
node (atom) is accelerated to speeds approaching the speed of light c.
At higher speeds the two space-time helices are drawn into a narrow
"V" trailing the atom, but each STH continues to course through the
atom from a lagging position toward the leading position. If one STH is
oriented by direction of flow opposite to the direction of travel of the atom,
this opposing STH folds to trail the atom, for the simple folk reason that it
is impossible to push a rope (see Figure
3). A rope can only be pulled because it is flexible, just like the
STH. The rope, in this case the STH opposing the direction of travel, folds as
the atom drags it along. In normal space-time, time can flow only one
direction, unless the STH is stiffened by an intense magnetic field As the
speed of the atom approaches c, both helices become more aligned in the
direction of travel. If it were possible to move an atom at speed c, the
two helices would become essentially overlaid and could be treated as a single
helix with uniform rotation. Rotation speed of the electron depends upon the
differential between the speed of the pair node (atom) through space, and the
speed of the STH which always travels at speed c. As the differential
decreases, the apparent rotational speed of the electron slows .At speed c,
the speed of the atom and electron would match the speed of the STH, so the STH
could no longer force the electron to rotate; time for the atom and electron
would stop, and the electron would become a stationary node riding the STH. An
atom cannot be pushed to speed c, because of relativistic mass increase which
prevents the atom from reaching speed c. The same behavior would be true
for nucleons in the atom. Time dilation is [shown in Equation as mentioned
bellow]relativistic which relates the
motion of one observer to another without benefit of an underlying matrix
common to both observers. The Clopton Model provides an inertial frame of
reference traveling at speed c that is common to both observers
The given formula for relatA = tB / sqrt (1- vBA2 / c2 )
tA = Time differential as measured by observer A
tB = Time differential as measured by observer B
vBA2 = Square of the difference in velocity between observer A and observer B
Relativistic mass
increase is linked to relativistic
time dilation. At higher speeds the two space-time helices are
drawn into a narrow "V" trailing the atom. As the moving atom
approaches speed c, the "V" narrows even more, so that the
atom is physically dragging along both of the space-time helices. It was
entirely possible that the universe is made of only one STH string, wrapped
countless times around the universe like a ball of yarn stretching and
expanding as a shell (Big Bang and the Shape of the Universe).
As an accelerating atom approaches the speed of light and time slows for the
atom, it becomes mechanically coupled to the space-time helix, so that the atom
is actually attempting to drag the entire universe Relativistic
Time Dilation, above). The formula for relativistic mass
increase shows that the mass of any body becomes infinite at speed c, so
matter can never be accelerated to the speed of light.
What
is string theory? Why it is required?
Pythagoras could be called the first known string theorist. Pythagoras, an excellent lyre player, figured out the first known string physics -- the harmonic relationship. Pythagoras realized that vibrating Lyre strings of equal tensions but different lengths would produce harmonious notes (i.e. middle C and high C) if the ratio of the lengths of the two strings were a whole number. Pythagoras discovered this by looking and listening. Today that information is more precisely encoded into mathematics, namely the wave equation for a string with a tension T and a mass per unit length . If the string is described in coordinates as in the drawing below, where x is the distance along the string and y is the height of the string, as the string oscillates in time t,
then the equation of
motion is the one-dimensional wave equation
Pythagoras could be called the first known string theorist. Pythagoras, an excellent lyre player, figured out the first known string physics -- the harmonic relationship. Pythagoras realized that vibrating Lyre strings of equal tensions but different lengths would produce harmonious notes (i.e. middle C and high C) if the ratio of the lengths of the two strings were a whole number. Pythagoras discovered this by looking and listening. Today that information is more precisely encoded into mathematics, namely the wave equation for a string with a tension T and a mass per unit length . If the string is described in coordinates as in the drawing below, where x is the distance along the string and y is the height of the string, as the string oscillates in time t,
then the equation of
motion is the one-dimensional wave equation
where vw
is the wave velocity along the string.
When solving the equations of motion, we need to know the "boundary conditions" of the string. Let's suppose that the string is fixed at each end and has an unstretched length L. The general solution to this equation can be written as a sum of "normal modes", here labeled by the integer n, such that
When solving the equations of motion, we need to know the "boundary conditions" of the string. Let's suppose that the string is fixed at each end and has an unstretched length L. The general solution to this equation can be written as a sum of "normal modes", here labeled by the integer n, such that
The
condition for a normal mode is that the wavelength be some integral fraction of
twice the string length, or
The
frequency of the normal mode is then
The
normal modes are what we hear as notes. Notice that the string wave velocity vw
increases as the tension of the string is increased, and so the normal
frequency of the string increases as well. This is why a guitar string makes a
higher note when it is tightened. But that's for a nonrelativistic string,
one with a wave velocity much smaller than the speed of light. How do we write
the equation for a relativistic string?
According to Einstein's theory, a relativistic equation has to use coordinates that have the proper Lorentz transformation properties. But then we have a problem, because a string oscillates in space and time, and as it oscillates, it sweeps out a two-dimensional surface in spacetime that we call a world sheet (compared with the world line of a particle).
In the nonrelativistic string, there was a clear difference between the space coordinate along the string, and the time coordinate. But in a relativistic string theory, we wind up having to consider the world sheet of the string as a two-dimensional spacetime of its own, where the division between space and time depends upon the observer.
The classical equation can be written as
According to Einstein's theory, a relativistic equation has to use coordinates that have the proper Lorentz transformation properties. But then we have a problem, because a string oscillates in space and time, and as it oscillates, it sweeps out a two-dimensional surface in spacetime that we call a world sheet (compared with the world line of a particle).
In the nonrelativistic string, there was a clear difference between the space coordinate along the string, and the time coordinate. But in a relativistic string theory, we wind up having to consider the world sheet of the string as a two-dimensional spacetime of its own, where the division between space and time depends upon the observer.
The classical equation can be written as
where
and are coordinates on the string world sheet representing space and time
along the string, and the parameter c2 is the ratio of the string
tension to the string mass per unit length.
These equations of motion can be derived from Euler-Lagrange equations from an action based on the string world sheet
These equations of motion can be derived from Euler-Lagrange equations from an action based on the string world sheet
The space
time coordinates X of the string in this picture are also fields X
in a two-dimension field theory defined on the surface that a string sweeps out
as it travels in space. The partial derivatives are with respect to the
coordinates and on the world sheet and hmn is the
two-dimensional metric defined on the string world sheet.
The general solution to the relativistic string equations of motion looks very similar to the classical nonrelativistic case above. The transverse space coordinates can be expanded in normal modes as
The general solution to the relativistic string equations of motion looks very similar to the classical nonrelativistic case above. The transverse space coordinates can be expanded in normal modes as
The
string solution above is unlike a guitar string in that it isn't tied down at
either end and so travels freely through spacetime as it oscillates. The string
above is an open string, with ends that are floppy.
For a closed string, the boundary conditions are periodic, and the resulting oscillating solution looks like two open string oscillations moving in the opposite direction around the string. These two types of closed string modes are called right-movers and left-movers, and this difference will be important later in the supersymmetric heterotic string theory.
This is classical string. When we add quantum mechanics by making the string momentum and position obey quantum commutation relations, the oscillator mode coefficients have the commutation relations
For a closed string, the boundary conditions are periodic, and the resulting oscillating solution looks like two open string oscillations moving in the opposite direction around the string. These two types of closed string modes are called right-movers and left-movers, and this difference will be important later in the supersymmetric heterotic string theory.
This is classical string. When we add quantum mechanics by making the string momentum and position obey quantum commutation relations, the oscillator mode coefficients have the commutation relations
The
quantized string oscillator modes wind up giving representations of the Poincaré
group, through which quantum states of mass and spin are classified
in a relativistic quantum field theory.
So this is where the elementary particle arise in string theory. Particles in a string theory are like the harmonic notes played on a string with a fixed tension
So this is where the elementary particle arise in string theory. Particles in a string theory are like the harmonic notes played on a string with a fixed tension
The
parameter a' is called the string parameter and the square root of this number
represents the approximate distance scale at which string effects should become
observable.
In the generic quantum string theory, there are quantum states with negative norm, also known as ghosts. This happens because of the minus sign in the space-time metric, which implies that
In the generic quantum string theory, there are quantum states with negative norm, also known as ghosts. This happens because of the minus sign in the space-time metric, which implies that
So there
ends up being extra unphysical states in the string spectrum.
In 26 space-time dimensions, these extra unphysical states wind up disappearing from the spectrum. Therefore. bosonic string quantum mechanics is only consistent if the dimension of spacetime is 26.
By looking at the quantum mechanics of the relativistic string normal modes, one can deduce that the quantum modes of the string look just like the particles we see in space time, with mass that depends on the spin according to the formula
In 26 space-time dimensions, these extra unphysical states wind up disappearing from the spectrum. Therefore. bosonic string quantum mechanics is only consistent if the dimension of spacetime is 26.
By looking at the quantum mechanics of the relativistic string normal modes, one can deduce that the quantum modes of the string look just like the particles we see in space time, with mass that depends on the spin according to the formula
Remember
that boundary conditions are important for string behavior. Strings can be
open, with ends that travel at the speed of light, or closed, with their ends
joined in a ring.
The main alternative theory of the origin of the structures of the universe are the cosmic strings or super heavy strings which are predicted too form in the early universe by the Grand Unified Theory (GUT) in inflationary “ Big Bang model. Loops of cosmic strings were the seed of the galaxies. They were super heavy strings, formed at phase transition or condensation that took place when the universe was cooled after GUTS in the very early universe. Kibble had suggested that GUTS strings played an important role in the evolution of the Universe and the strings provided the inhomogenity leading to the formation of galaxies. In the very early universe Strings were predicted to be formed at symmetry breaking phase transition by those in grand unified theories (GUTS) in which vacuum had the appropriate topology. Cosmic Strings were the configuration of the matter fields, which owe their topology of the space of degenerate vacuum, produced in the phase transition, in the early universe. Let us ignore the internal structure of the strings and treat them as one-dimensional object with tension. In the resting frame of the strings, the mass per unit length μ to the tension. The equality of the line of the density and the tension caused the typical velocity associated with large vibration on the strings to be close to speed of light. The strings cannot end but can either close on themselves or can be extended to infinity. The closed strings are loops.
Whenever two long strings cross each other, they exchange ends, or `intercommute' (case (a) in the figure below). We had already encountered this apparently strange fact when we discussed the strings in the context of nematic liquid crystals. In particular, a long string can intercommute with itself, in which case a loop will be produced (this is case (b) below).
As with any object in tension, strings would also accelerate so as to try to become straight. Damping of the string motion was due to their non gravitational interaction with other matter, those become negligible as soon as the strings were formed. Strings that extended outside the horizon were conformably stretched by the cosmic expansion. Thus at a given epoch, these strings were straight on their length & scale, but were smaller then the horizon size, but was quiet convoluted on large scale lager then this. The typical velocity was associated with the straightening of a string and was close to the speed of light and the velocity field of the string extending outside the horizon was relativistic and approximately constant over scale much smaller than a horizon size. Once a loop entered the horizon it no longer expanded but rather started oscillate with a period comparable to light travel time across it. This motion was damped by gravitational radiation causing the size & period of the loop to decrease approximately linearly with time The Fractional decrease in size, period,& mass of the strings in one oscillation was given by equation* Gμwhere G is Gravitational constant. A string will decrease to zero size in a finite amount of time loosing its energy by Gravitational Radiation. The distribution of strings in our universe was not quite so well understood
Example
1]
These pictures show
1) a full three-dimensional simulation of the intercommoning of two cosmic strings... The reconnection and `exchange of partners' when two strings intersect. In this three-dimensional simulation, the strings approach each other at half the speed of light. Notice the radiation of energy and the production of a small interaction loop in the aftermath of the collision
[ Picture By Rupak Bhattacharya].
2]
The scattering of two vortices is highly non-trivial; the two vortices approach and form a donut from which the emerge at right-angles have `exchanged halves'
3]
Both long cosmic strings and small loops will emit radiation. In most cosmological scenarios this will be gravitational radiation, but electromagnetic radiation or axions can also be emitted in some cases (for some specific phase transitions). Here is a single, oscillating piece of string
4]
Radiation fields from the oscillating shown
above. A transverse cross-section of the fields has been made at the point of
maximum amplitude. Notice the four lobes of the radiation (a quadrupole
pattern) which is characteristic of all cosmic string radiation5]
The
effect of radiation is much more dramatic for loops, since they lose all their
energy this way, and eventually disappear. Here you can see what happens in the
case of two interlocked loops. This configuration is unlikely to happen in a
cosmological setting, but it is nevertheless quite enlightening. Notice the
succession of compicated dynamic processes before the loop finally disappears. After formation, an initially high density string network begins to chop itself up by producing small loops. These loops oscillate rapidly (relativistically) and decay away into gravitational waves. The net result is that the strings become more and more dilute with time as the universe expands. From an enormous density at formation, mathematical modelling suggests that today there would only be about 10 long strings stretching across the observed universe, together with about a thousand small loops!
In fact the network dynamics is such that the string density will eventually stabilize at an exactly constant level relative to the rest of the radiation and matter energy density in the universe. Thus the string evolution is described as `scaling' or scale-invariant, that is, the properties of the network look the same at any particular time t if they are scaled (or multiplied) by the change in the time. This is schematically represented below:
After the phase transition, the strings were formed in a random
network of self-avoiding curves/loops. Some of the strings were in closed loops
and some were as infinite strings. The distribution of strings so happened that
a constant number of loops entered the Horizon. If the infinite strings would
simply straighten out, then the numbers of open strings across the horizon-sized volume would also increase
with time and strings would soon come out to dominate the density. Velenkin .A [Physics Review D23, p852;
1981] showed that the geometry produced by the gravitational field near a
length of straight string is that of Minkowski space with a three dimensional
wedge taken out of each space like slice. The vertex of the wedge lies along
the length of the string and the angle subtended by missing wedge lies in rest
frame of the string and is equated asδπGμThe two exposed faces of the strings
are thus identified. Thus the Space Time remained
flat everywhere except along the Strings, where it was
highly curved. If Gμ<<1, then the stress energy of the strings would
produce only small (lenier) perturbations
from the metric of rest of the
universe. Because the matter
in the Universe did not produce significant purturbation from the Minkowski metric Space ,on scale ,less then horizon,
the Gravitational field at a point much closer
to a length of a string would be essentially then the same
as gravitational field at a
similarly located point in Minkowski
space. In the rest of frame of the strings, all
particles were when passing , the strings were deflated by an angle 8πG μ with respect to all particles passing
on other side of the strings. The magnitude of discontinuity
in temperature(While passing of particles) across the string was δT/T= 8πGβ, where β=Transverse Velocity of the strings which was typically was close to Unity. This Jump of temperature
persisted on angular distance away from
the string, corresponding to the present angular size of the radius of
curvature of the strings. The magnitude of temperature jump was then
independent of the Red shift (Z) at which Light Rays reaching to us, passed by the strings. If we calculate the general properties of microwave sky anisotropy in string mode , then let us assume that microwave photons were last scattered at Red shift Z
1s. In a perfectly homogenious
Universe ,the matter became
mostly neutral and optically then at Z˜ 1000. However
in a Universe with strings, there will be large amplitude in homogeneity on
small scale and the heat output from objects forming at or before
Zγee may re -ionize the plasma. If the plasma were
kept fully ionized then Z1s>10 and we have 1000>Z1s>10,the angle
subtended by a horizon-sized volume space at Z1c is o1s-1/2<<1.
One would do expect to see on a round patch of sky of strings per horizon volume at red shift Z, will project to one length of string of
angular size o if z<z1s. These strings will be moving
relativistic ally,
as they were unable to straighten themselves out of these length scale.
In the modern Gauge theories of fundamental interaction of the Vacuum was far from being
nothing. Rather it is now recognized as a dynamical object
that was in different state. The current state of vacuum affects the
properties such as masses and interaction of any particles put into it. Although the vacuum is thought to lie in it’s ground state ,that
with the lowest state of energy, this state had not always been the same. Thus in the early universe
when the particle component [ordinarily matter and radiation] was at a very high temperature, the
vacuum adjusted it’s state in doing so modified
the properties
of particles so as to minimize the free energy of the entire system. [Vacuum
plus particles. ] e i. the vacuum went into higher energy state in order to
lower the energy of hot plasma by even
greater amount. As the universe cooled to keep the entire
system at the lowest possible
energy at a given temperature , the
vacuum had to change eventually, ending
up in it’s present state which is nearby the true or zero temperature vacuum. It
was possible in early universe that as the
Universe expanded , the
cooling happened too rapidly for the vacuum to find it’s true ground state and the vacuum was frozen into
ground state with defects. Defects that probably could occur in a three
dimensional space could be Zero dimensional (Monopoles), Two dimensional
(Domain walls) or One dimensional (Strings). The
Strings are macroscopic objects. In most cases of cosmological interest they
have no ends and are either infinitely long or closed in a loop 
At GUT’s the Strong, Weak and Electromagnetic forces behaved as if, they had equal strength, much as line defects found in the crystal. They formed as a net work across the space& time. The GUT”s predicts that strings were formed at a temperature of about 1015 to ~1016 Gev. at a Cosmological time of about 10̃35 Second. The Cosmic Strings were formed at the mass scale of GUTs Symmetry breaking (Mx-̃ 2x1015 Gev) was typified by a mass per unit length μG/c2̃̃ ~ 2x10 6 in dimensionless unit.[ G= Gravitational Constant, C= speed of Light, which is corresponding to μ= ~ 2.6X10 21, Kgm-1~ 4x107 MOPC-1 where MO= Mass of Sun . Or in other words the strings were formed with a mass per unit length of about 1020 kg-1. They have a mass per unit length μ=ε/G [where ε= ~( <φ>/ mp)2 is the dimensionless amplitude of their Gravitational potential, mp is the Plank Mass and the Vaccum Expectation value of Higgs field is φ.] Because of their enormous tension ε/G , the net work of the Strings were formed in the phase transition. In this Theory the Strings contributed only a small fraction of mass of the Universe. The Galaxies were formed by Accreating of ordinary matter about the Strings. The Strings were stretched by subsequent expansion of the Universe on waves, on a given scale and began to oscillate then. The strings underwent Oscillation in which the Transverse intertia acted as weight and the restoring forces were provided by longitudinal tension of the strings. As a result of oscillation in such that the scale entered the particles horizon and whenever the strings crossed itself and exchanged particle partners and produced closed Oscillating loops of the Strings with long life(Peebles. P.G. Z- large scale Structure of the
The Strings actually underwent Oscillation in which the
Transverse inertia acted as weight and the
resting force was provided longitudinal tension of the strings. The gravitational field of these strings loops caused
accretion of matter around them. Brosche. P.J in the
journal of Astrophysics stated that angular
momentum of an astronomical object is proportional directly t square of mass
and constant of proportionality is comparable to String Theories, which suggest
that the Universe had evolved through hecrchial breaking of rotating or
oscillating strings and the angular momentum with mass between various classes
of different objects ranging from planets to super clusters (brosche.PZ.J-Astrophysics Vo 57; P143; 1963). For the past
three decades, a variety of Grand Unified Theories (GUT’S) had been developed
to unify the strong and electro weak interactions at an energy scale of 1016
Gev. GUTs are Gauge invariant point field theories (yang Mills), which do not
incorporate Gravitational forces and henceforth there remains few theoretical
constrains on the possible internal symmetry group. The
most favored Guts theories are based on the special unitary group Su (5), the
special orthogonal Group SO (10) or the Exceptional Group E6. In
such Guts theories “Quark’ and “Leptons” make up three of these families, are
unified in one family. Super symmetries an important ingredient in Guts. It is
a symmetry that relates to “Fermions” and particles of different spins. But supper symmetry is not an internal symmetry but amounts to
an extension of the Space &time in super space that includes extra
spinorial anti commuting co-ordinates as well ordinary co-ordinates. Super Symmetry requires particles Known as” s-quarks”, s
leptons”, winos, Zinos, or Rupak –particles( a near zero mass particle from
where mass came] which have yet to be discovered through LHC. Super gravity
theories are point field theories that incorporate local or gauged supper
symmetry and thereby enlarging Einstein Theory of relativity. The basic idea of Gauge theory is that a continuous Symmetry or
global invariance properties of Lagaragian field theory that can be made into a
local invariance by introducing compensating gauge field in to the theory. This
means that given a field theory, which possesses symmetry such as U1
(1), Su (2), Su (3) or any other Ugroup. The theory can be extended to a gauge
theory, which has the symmetry at each part in the space-time individually. The
new symmetry is then called gauge symmetry because it implies that we can choose
our measuring standard gauge differentiate through out space-time without
changing physics of the theory. The most familiar example of a gauge theory is
Electromagnetism. In Quantum
Electrodynamics the quantum field theory of electromagnetic interactions are
charged particles and Boson (photon) is the most successful gauge theory. The
behavior of a relativistic String moving in space-time differs significantly
from that of a structure less point particle. Unlike a point particle, a
classical relativistic string has an infinite number of vibrational modes with
arbitrarily high frequencies and angular momentum. This means that in quantum
theory, a single string has an infinite number of states with masses sand spins
which increases without limit. The string theories were developed in early
1970s as model of strong interaction physics. A Meson has thought of as a
string with a quark attached to one end while an antiquark to the other end.
The string tension (T) was supposed to be _1Gev2 and the excited states
of the string were supposed to be hadrons. The main theories were “Boson
Theory” [Boson particle are particles in the name of Prof. S.N. Bose of
kolkatta, India
[http://www.nature.com/news/2011/110922/full/news.2011.554.html#comment-id-27107]
[http://www.nature.com/news/2011/110922/full/news.2011.554.html#comment-id-27107]
- not the neutrinos. It has been that
photon(light particle is no more fastest p[article in the universe). Super string theories, that evolved from spinning string
theories, that incorporated supper-symmetry and had no Tachyonic ground states.
Super string theories hence offered the possibility of constructing a
consistent quantum theory that unifies all interactions including the gravity
and natural mass scale set by string tension (T) in Planck scale [ T1/2 =109Gev] The excited states were so massive that they
could be taken to be infinitely heavy and the theory can be approximated by an
effective point field theory of the mass less state only. At energy scale
bellow the plancks scale the string looks like a point. One of the constrains
in any string theory is that all string theories contain mass less spin-1 and
Spin-2 particles which are associated with
“yang( He was a NL in physics]
mills Gauge Boson” and Gravitation.
Furthermore the original “Bosonic String
Theory” required 26 space time dimension whereas super string theory only ten(10) dimensional space Time. We live
in only three (3) dimensional Universe and we can at best imagine Four (4)
dimensional space-time. Then where are these Extra Six Dimension in super
string theory? Or extra 22 dimensions Bosonic String theory? May be these extra
dimensions are curled up [they may be as large as our three dimension] coiled
up and finally became very small by compactification in super string theory.
There are three types of Super String theories. Type 1 super string theory describe the dynamics of open strings that have their free end
points. The string carries quantum numbers in the n-dimensional,
defining representation of a classical group G=S0 (n) or the simplistic group
USP (n) at their end points SU (n). This is similar to the way in which “quark
quantum numbers” were incorporated in the original string picture of mesons.
Inflation was the only way of explaining several of otherwise
extra ordinary initial conditions of the universe. But for fine tuning of
inflation required a critical density of the universe. Thus at
least 85% of the universe could not be then the baryons matter and more then
60% of the matter of this Universe so did not cluster into galaxies. The
density of the matter on the universe must be greater then the baryonic upper
limit .To make the things a little more difficult, it was said, that” the
special co-relation function of rich cluster of galaxies had revealed strong
clustering of very large scale up to 150 MPC.” This co-relation function of
clustering of galaxies was 18 times stronger then the special co-relation function of galaxies. It was also found that the largest scale of the universe
seem to look filamentous [Strings are filamentous] with large voids and large
clumps . With the GUTs an excellent way appeared to produce the
distribution of size of universe. In normal generation and application of GUTs
[a fluctuational spectrum with equal powering all scale formed naturally] it
was assumed that there was no special co-relation between large scale and small
clumps. They each had a random probability of occurring anywhere in the
universe. On the other hand, it means, that strings
are still produced in the some spectrum, somewhere, &in some size.
Different proposals so had been put to solve the problem. But no models could
solve it, as long as it was assumed that the primordial fluctuation had random
phases. For example- a model based on Neutrinos produces both critical density
and large-scale structure [filaments, voids, cluster co-relation function] but
did not account for early formation of galaxies (Bachcall.N- J Astrophysics Vol
270; p20; 1983). Models evoking heavy or slow moving particles [like Gev mass
photinos, gravitinos, ax ions, planetary mass black holes] however fits the
small scale structure galaxy co-relation function, formation of time &so
forth as well as building hierarchal to yield clusters but it do not allow
critical density of the universe to be reached.]. Even the hybrid models, -
with low- mass and huge - mass ions also runs problem, because of low- mass
particles smear out the small-scale structure of universe. A more natural solution of the problem might be non-random
phases of string model. J.E Peebles (Nature Vol-311; P517; 1984) noted that the
non random phases of string model of the Universe yields large scale filaments
and voids, as super heavy strings attract galaxies and cluster and gives string
cluster- cluster co-relation. Work by J.E. Peebles showed that a
model based on clustering of galaxies about filaments [here strings] fit higher
3 and 4 points co-relation function for
galaxies as well as hierarchical clustering. This model also enables density
growth in some areas without producing a large universal background anisotropy
and so could enable baryons to be dark matter on
galaxy and cluster state with non-baryonic stuff being
a critical density background. The
degree of random to nonrandom
phases in such a model depends upon density of strings in the space. In the
limit of space being completely filled with strings, the strings picture also
gives random phases. Even if strings densities are large enough to
randomize phases, their mere existence would still alter galaxy –in formation,
calculation, because it were the strings rather then matter that would carry
the fluctuation.
The basic
things of string theory say that-:
*we live in
accelerating and expanding universe today** String theory support the inflation theory
where a period of rapid expansion happened in the early universe history.
*** Most of
the theories in the string theory are focused on understanding of theory of
unbroken super-symmetry. ****In string theory De-Sitter Space can arise only when
super-symmetry is broken( Rupak Bhattacharya, Ritwik Bhattacharya & prof
Pranab kumar Bhattacharya’s Theory). Breaking supper-symmetry in the
string theory requires us to come face
to face with problem of moduli stabilization. In string theory Vacuum with N≥2
super-symmetry, there are many flat direction or modules. The energy as we go
along these direction of space time, there are many flat direction. In field the
space is constant and in fact vanishes identically. There are 100
flat directions in compactification. The flat directions are however
very bad in cosmology. Flat directions cause however problems in standard model.
They ruin the successful prediction of Big Bang Theory.
The big Question hat one of author of this
article Mr. Rupak Bhattacharya once raised
“ Does the
string theory allows De sitter Universe? Vacuum with negative cosmological
constant to anti de-sitter space and Inflation theory of Big Bang?”
This was of course a great question, exactly not yet solved probably.
Interested readers can read the Threads and discussion at http//www.bautforumtoday.com of BAD Astronomy & Universe Today forum under
the threads “ String theory- De sitter Universe and Inflation’ in astronomy
forum and in thread by Fraser “ Superstrings could be detectable as they decay”
in Universe Today & story Comments forum
It is known that the de- Sitter space can only
arise if super symmetry is broken. In string theory
with≥2 super-symmetry there are many flat directions. The energy as we go along
these spaces is a constant & in fact vanishes identically and these flat
directions are bad news from the part of Big Bang cosmology. Cosmology flat
directions cause problems in standard model of Big Bang and ruin the successful
prediction of Big bang nucleo-synthesis. In these compactifications besides
curling up the extra dimensions preserved in the string theory to small size,
fluxes are also turned on along the compactified directions. The fluxes
includes higher form generalization of magnetic fluxes in the electromagnetism
turning them on charges, the potential in moduli spaces, so that new minima
arise in regions or field space where the potential can be calculated with
control. The value of Cosmological constant in this minima can also be can also
be calculated with a positive value give rise to De-Sitter universe.
There remain always a fundamental asymmetry in the distribution of the constituents of the universe. That is, there appears to be an excess of normal matter over antimatter in the most current and compelling models of the universe (cold dark matter [CDM]). The origin of this asymmetry remains yet unexplained before us as do the nature of both dark matter and dark energy. Dark matter and dark energy are required by the latest CDM models that have recently been shown to be very much in accord with the findings of the cosmic background surveys . However, most intriguingly, this fundamental cosmic asymmetry appears to manifest itself by way of other asymmetries observed in other more complex systems of universe. For example, there has been a much discussed thesis that the left-right symmetry encountered in simple as well as complex multicellular organisms, including human laterality and cerebral symmetry, are a consequence of symmetry at the molecular level . This, in turn, is thought to arise from asymmetry at the level of elementary particles. However, although connecting links between molecular—and subatomic—chirality and macroscopic handedness and asymmetry are not established, the implications of this asymmetry for biologic processes and evolution are profound. We today now know that proteins in life forms consist (almost) exclusively of L-
-amino acids, whereas nucleic
acids contain only the D-isomers of ribose or deoxyribose. Although
there exists considerable controversy concerning the questions of
when and how this homochirality arose in world, but it appears to be
the fundamental, but incompletely tested, assumption that life as we
know it could not have arisen without it. Much less attention seems
to have been paid in recent years to the reasons for homochirality
and its connection to the origin of life. Older studies have held
that the structure-destabilizing effects of ‘‘chiral defects’’
(i.e., the incorporation of D-amino acids or L-nucleotides into
their respective polymers would render them incapable or unable to
participate in ‘‘biology’’). However, although newer studies
confirm some destabilization, they also indicate that there is more
ability to accommodate unnatural enantiomers than was previously
appreciated. These findings provide new insights into the
constraints imposed on life’s origin with respect to chiral purity.
We should note, however, that this is a subject that has attracted
considerable interest and has been reviewed in the past . Indeed,
one can even use one’s nose
and establish that stereo isomers can smell different 
Or on a more tragic note, the story of thalidomide where the R isomer is a teratogen while the S isomer is a tranquilizer. The primary amino acid sequence determines the structure and function of a protein. The two most common structural motifs are the
-helix and ß-sheet. Although -helices are now
more abundant in proteins than ß-sheets, it is thought that the
ß-sheet occurred earlier during chemical evolution . Generally,
L-amino acids form a right-handed helix; a right-handed helix
exhibits optical rotation of its own. Similarly, ß-sheets are not
flat but, if made of L-amino acids, exhibit a right-handed twist
when viewed along their strands. This right-handedness of turn
arises from energetic constraints in the bonding of L-amino acids; a
chain consisting of D-amino acids would produce sheets with a left-handed
twist . Indeed, the circular dichroism (CD) spectrum
produced by the all-D enantiomer of the full-length ß-amyloid
peptide (42 amino acid residues) was a mirror image of the spectrum
obtained with the natural all-L enantiomer, indicating that the
two enantiomers had opposite optical rotation . Furthermore, there
are indications that such mirror image conformation translates into
functional stereospecificity. When the D- and the L-enantiomer of
the complete enzyme HIV-1 protease were chemically synthesized, they
were found to have identical covalent structure and CD spectra of
equal, but opposite, optical rotation . These data suggest that the
folded forms of the D- and L-protease enzymes are mirror images when
viewed in three dimension 
. Most notably, the enantiomers exhibited reciprocal chiral specificity, the L-enzyme cleaving only the L-substrate and the D-enzyme showing activity only for the D-substrate. Although protein macromolecules are carriers of function, DNA macromolecules are the transgenerational informational carriers of most contemporary organisms . RNA plays the role of an intermediary between DNA and proteins in eukaryotes and can take on both informational as well as functional roles. As in proteins, the monomeric units of DNA and RNA are homochiral, each of the nucleotides containing either D-ribose or D-deoxyribose. Also like proteins, nucleic acids are able of taking on a variety of secondary structures, most famous among them the double helix. Both RNA and DNA are matrices for the assembly of a complementary replica, and homochirality has been postulated to be an absolute necessity for complementarity . Molecular modeling was interpreted as indicating that incorporation of a single T of the opposite chirality in double-stranded poly(A)/poly(T) would prevent base coupling, thereby destroying the template property and the ability to act as an information carrier . This does not, however, appear to be entirely correct. An NMR study with a dodecadeoxynucleotide containing a single nucleotide with a L-deoxyribose (the G4 residue) formed a stable base pair with the natural C-9 residue within a right-handed B-form conformation . Similarly, although substitution of a D-nucleotide with an L-nucleotide somewhat destabilized a short DNA duplex, the D-isomer could nonetheless be accommodated via changes in some of the backbone torsion angles around the phosphates and the glycosidic bond . Others have confirmed that cooperative binding between mixed L/D-oligodeoxynucleotides and single-stranded DNA and RNA is possible despite the destabilizing effect of L-substitutions . The magnitude of this destabilization was found to depend on the position and type of the nucleotide . In addition, there appears to be a limit to the number of substitutions that a sequence can tolerate .
Links to see other sites
Acknowledgement- To our late parent diseased
late Mr. Bholanath Bhattacharya and late Mrs. Bani Bhattacharya of residence 7/51
purbapalli, Po-Sodepur, Dist 24 parganas (north) , Kolkata-110,WestBengal , India
” ……….because his idea on Space time concept
involved a triple helix structure as the "thread of time" in the
"fabric" structure of the universe, with triple helices spiraling
around a time axis at all possible straight lines in the universe. And He
believe that this structure might be responsible for our experiencing three
spatial arrows of dimensions plus the dimension of time as a matter and energy
travel along these helices with time. he envision the spatial progression of
these time lines as the expanding universe, and photons on the time line would
have zero velocity relative to the time line from the point of the Planck
moment of Big bang. his envision the particles bound to this triple helix are
any of the individual members from the three families of quarks that make up
protons (which are reportedly proven to be in a 2-d triangular configuration)
traveling through time along the three "spines" of the helix……………………………….)
Copy
Right-
Strictly reserved to Professor Pranab Kumar Bhattacharya and first five authors
only as per IPR copy Right Rules and Protect Intellectual Property [PIP]
Act/law of 2012 of USA
Professor and Head of Pathology now convener In-charge of DCP &DLT course of WBUHS School of Tropical Medicine 108 CRAvenue Kol-73 , and EX Professor&HOD Ophthalmic pathology RIO, CR Avenue kol-73 and also of WBUHS and EX Professor of Pathology, Ex In charge of Histopathology unit, in charge of Blood Banks VCCTC, in charge of Cytogenetics ,Human Tech DNA & Gene cloning laboratoriesat Institute of Post Graduate medical Education & Research,244a AJC Bose Road, Kolkata-20.India, Member of Board of Studies Undergraduate, Post Graduate& post Doctoral Courses in Pathology of West Bengal University of HealthSciences(WBUHS), India
The author of this letter great fully
acknowledges contributions of late Mr. Bholanath Bhattacharya B.Com(cal), FCA,
SAS(Ind.) - his diseased[ 2009] retired
Father, His diseased[2006] Mother late Mrs BaniBhattacharya, his only sweet
daughter Miss Upasana Bhattacarya, and his youngest twin brothers Mr. Rupak Bhattacharya Bsc(cal)Msc(JU), Mr. Ritwik Bhattacharya B.Com(cal), Nice Miss Rupsa Bhattacharya,
Nephew Somuyak Bhattacharya BHM Msc Student- all of Residence 7/51 purbapalli,
PO-Sodepur, Dist 24 Parganas(north) , KOl-110, West Bengal, Mrs Dahlia mukherjee BA(hons) cal, and Mr.
Debasis Mukherjee BSC(cal) of Swamiji Road, Po- South Habra, 24 Parganas(north)
and of Miss Upasana Bhattacharya- his only sweet daughter as he took many of
their concept and discussions to write this letter to Prof. Robbie York,
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