Friday, June 1, 2007

Free math books

Here is a list of free math books.Yes free free math books.........
Professor Jim Herod's Multivariable Calculus
Calculus,by Gilbert Strang is made available through MIT's OpenCourseWare electronic publishing initiative.
Linear Methods of Applied Mathematics, by Evans Harrell and James Herod.
Yet another one produced at Georgia Tech is
Linear Algebra, Infinite Dimensions, and Maple, by James Herod.
One more recent one by
Professor Herod is Partial Differential Equations.
Complex Analysis, Complex Variables , by Robert Ash and W. P. Novinger. This is a substantial revision of the first edition of Professor Ash's complex variables text originally published in 1971.
Professor
E.H. Connell of the University of Miami has made available on the web his book Elements of Abstract and Linear Algebra. An introductory algebraic topology book, Algebraic Topology I, by Professor Allen Hatcher, of Cornell University, is available, and Professor Hatcher promises the second volume, Algebraic Topology II, will be ready soon.
The Geometry and Topology of Three-Manifolds, by William Thurston. This is an electronic edition of the 1980 lecture notes distributed by Princeton University.
Professor Jim Hefferon of Saint Michaels's College has made available his undergraduate textbook Linear Algebra.
Another elementary linear algebra textbook is
Elementary Linear Algebra, by Keith Matthews.
Introduction to Probability, by Charles Grinstead & J. Laurie Snell.
An Introduction to Probability and Random Processes, by Gian-Carlo Rota and Kenneth Baclawski. This is the 1979 manuscript of the work Professor Rota had been working on for some time. It is made available through the efforts of David Ellerman.
Professor Herbert Wilf (and the publisher, A. K. Peters) has made available his book generatingfunctionology.
Perhaps the greatest textbook of them all is
Euclid's Elements.
Originally published by
Springer-Verlag, the book A Course in Universal Algebra, by Stanley Burris, and H. P. Sankappanavar, is available online.
Professor Robert Ash has written and made available Abstract Algebra:The Basic Graduate Year.
Another one by
Professor Ash is A Course In Algebraic Number Theory.
Professor Ash has also completed and made available A Course in Commutative Algebra.
The Calculus Bible is an elementary calculus textbook from Professor G. S. Gill of the Brigham Young University Mathematics Department.
Calculus Without Limits, by John C. Sparks.
Originally published by Prindle, Weber & Schmidt but currently out of print,
Elementary Calculus: An Approach Using Infinitesimals, by Professor H. Jerome Keisler, is now freely available online.
Handbook of Applied Cryptography, by Alfred J. Menezes , Paul C. van Oorschot, and Scott A. Vanstone, is freely available thanks to the publisher, CRC Press.
Graph Theory, by Reinhard Diestel.
Available for self-study from
The Trillia Group is Basic Concepts of Mathematics, by Elias Zakon.
Another one from
The Trillia Group is An Introduction to the Theory of Numbers by Leo Moser.
Yet another from
The Trillia Group is Mathematical Analysis I, by Elias Zakon.
Thanks to Malaspina Great Books,
Mechanism of the Heavens (1831), by Mary Somerville, is available online. This second edition was prepared by Russell McNeil.
Lecture Notes on Optimization, by Pravin Varaiya. This is a re-issue of a book out of print since 1975. It is an introduction to mathematical programming, optimal control, and dynamic programming.
A Manual of Mathematical Ilustration, by Bill Casselman, shows, at several levels of sophistication, how to use PostScript for producing mathematical graphics.
Chebyshev and Fourier Spectral Methods (2nd. Edition), by John P. Boyd. This is the free online version of the Dover 2001 edition.
A Problem Course in Mathematical Logic, by Stefan Bilaniuk .
Concepts and Applications of Inferential Statistics, by Richard Lowry.
To be published soon by Cambridge University Press,
A Computational Introduction to Number Theory and Algebra, by Victor Shoup will nevertheless remain freely available on-line.
Out of print for sometime, but freely available is
Graph Theory with Applications, by J. A. Bondy and U. S. R. Murty.
Yet another one out of print, but now freely available is
Convergence of Stochastic Processes, by David Pollard.
Designed for undergraduate physics students is
Mathematical Tools for Physics, by James Nearing.
Elementary Number Theory, by William Stein.
A Modern Course on Curves and Surfaces, by Richard Palais.
A First Course in Linear Algebra, by Rob Beezer.
Group Theory, by Pedrag Civitanovic.
Shlomo Sternberg has written Theory of Functions of a Real Variable.
Lie Algebras Semi-Riemann Geometry and General Relativity
Advanced Calculus, by Lynn Loomis and Schlomo Sternberg
Originally published by Springer-Verlag and now out of print,
Non-Uniform Randon Variate Generation, by Luc Devroye is now, thanks to the author, freely available.
Difference Equations to Differential Equations, by Dan Sloughter.
The Calculus of Functions of Several Variables is another one by Professor Sloughter.
Notes on Differential Equation, by Bob Terrell.
Sets, Relations, Functions, by Ivo Düntsch and Günther Gediga.
Another one by
Düntsch and Gediga is Rough Set Data Analysis.
Predicative Arithmetic, by Edward Nelson.
Toposes, Triples and Theories, by Michaele Barr and Charles Wells.
Information Theory, Inference, and Learning Algorithms, by David J. C. MacKay is published by Cambridge University Press, but is, nevertheless, freely available online.
Linear Partial Differential Equations and Fourier Theory , by Marcus Pivato.
Another one by
Professor Pivato is Voting, Arbitration, and Fair Division: The Mathematics of Social Choice.
Introduction to Vectors and Tensors, Volume 1, Linear and Multilinear Algebra, and Introduction to Vectors and Tensors, Volume 2, Vector and Tensor Analysis by Ray M. Bowen and C.-C.Wang, are revised versions of books originally published by Plenum Press in 1976.
Another one by
Professor Bowen and originally published by Plenum Press is Introduction to Continuum Mechanics for Engineers.
Numerical Methods and Analysis for Engineers, by Douglas Wilhelm Harder.
Analysis of Functions of a Single Variable, by Lawerence Baggett, was originally written to be used for a one semester senior course, but the author suggests that it is more appropriate for first year graduate students.
Convex Optimization, by Stephen Boyd, and Lieven Vandenberghe is freely available thanks to Cambridge University Press.
Mathematics Under the Microscope, by Alexandre Borovik, is, according to the author, an attempt "to start a dialogue between mathematicians and cognitive scientists."
Introduction to Statistical Signal Processing, by R. M. Gray and L. D. Davisson is, according to Professor Gray, a "...much revised version of the earlier text Random Processes: An Introduction for Engineers, Prentice-Hall, 1986, which is long out of print." The current book is published by Cambridge University Press.
Not simply an online textbook, but certainly in the same spirit is the
Topology Webcourse project undertaken by Topology Atlas.
This is, I suppose, not a textbook, but nevertheless an interesting reference:
The Matrix Cookbook, by Kaare Brandt Petersen, and Michael Syskind Pedersen.
Not really a textbook either,
Constants, by Steven Finch, is, nevertheless, a nice collection of essays. The title pretty much describes the subject.
So you got your math books........

Supernova

Tuesday, May 1, 2007

Monday, April 9, 2007

A new way to test time travel

When i was searching for time travel at google i got an article at newscientist titeled
At last, a way to test time travel
But now that is not available.I suddenly found it at
http://bama.ua.edu/~physics/news/pas.txt
Here is the article:



THE title of Heinrich Päs's latest paper might not
mean much to you. To
those who know their theoretical physics, however,
"Closed timelike
curves in asymmetrically warped brane universes"
contains a revelation.
It suggests that time machines might be far more
common than we ever
thought possible.

Forget trawling the universe in search of rotating
black holes or exotic
wormhole tunnels that could supposedly let us hop
from one instant to
another. According to Päs, a physicist at the
University of Hawaii at
Manoa, and his colleagues, the door to a time
machine could be anywhere
and everywhere in our universe. And unlike most
other scenarios for time
travel, we can test this one here on Earth. "I
think the ideas presented
are wonderful and exciting," says Bill Louis,
a physicist at Los Alamos
National Laboratory in New Mexico and co-spokesperson
for the MiniBoone
neutrino experiment at Fermilab, near Chicago. "The
question is are they
true or not."

Louis is right to be cautious. Although nothing in
the laws of nature
appears to rule out time travel, physicists have
always been uneasy
about it because it makes a mockery of causality,
the idea that cause
always precedes effect. Violating causality would
play havoc with the
universe, for instance, allowing you to travel back
in time and prevent
your own birth.

Such paradoxes are what led Stephen Hawking to
propose his "chronology
protection conjecture". This basically says that
some principle of
physics, perhaps as yet undiscovered, will always
come to the rescue and
prevent time travel from happening. Yet no one
had been able to flesh
out the details until three years ago when several
groups of researchers
claimed that string theory, physicists' best stab
at a prospective
"theory of everything", was beginning to close the
door on time machines
(New Scientist, 20 September 2003, p 28).

All very well, except theoretical physicists are
notorious for never
taking no for an answer. Päs and his colleagues
Sandip Pakvasa of the
University of Hawaii and Thomas Weiler of Vanderbilt
University in
Nashville, Tennessee, have been re-examining
string theory. It views the
fundamental building blocks of the universe not
as point-like particles
but vibrating strings of energy; the faster the
vibration the greater
the mass of the particle.

Such vibrating strings can account for the myriad
interactions of all
the known subatomic particles, such as quarks and
electrons. But there
is a catch - it only works if the strings vibrate
in a space-time with
10 dimensions rather than the four with which we
are familiar.
Proponents of the idea maintain that the extra
dimensions are either so
fantastically small that we have not noticed them,
or so large and
warped in such a way that, again, they have remained
hidden from view.

This has led to the suggestion that our universe
may be like a
four-dimensional membrane or "brane" adrift in
a higher-dimensional
space-time. All of the particles and forces in
our universe would be
trapped in our brane like flies on fly-paper,
so we would have no
knowledge of any dimensions other than the four
we experience, even
though our brane might be floating in a 10-dimensional

space-time, or
"bulk". "If it is, then there is the possibility of
short cuts through
higher-dimensional space," says Päs. "It's such short
cuts that make
time travel possible."

?Time machines might be far more common than we
ever thought possible?

It is not too difficult to visualise such a short
cut. Suppose our
brane-universe is bent back on itself within a
large extra dimension,
making it the four-dimensional equivalent of a
pancake folded in two.
Then you could imagine leaving the brane at one
point, travelling a
short distance through the bulk and re-entering

the brane at a point far
away from your starting point.

There is a problem with this picture, however.
Although we can visualise
a universe where such a short cut is possible,
it cannot be our
universe. That is because the space-time of such
a severely folded brane
is not compatible with Einstein's special theory
of relativity, which
posits a "Euclidean geometry" where space is
perfectly flat. Since
numerous tests of special relativity have shown
that its predictions in
our locality are accurate to better than 1 part
in a million, it is very
unlikely that our universe is shaped like a folded pancake.

Instead Päs, Pakvasa and Weiler consider a space-time
where our universe
is a flat brane that is immersed in a bulk whose own
dimensions are
seriously warped. Because the brane is flat, special
relativity still
applies there. Yet in the bulk, Päs, Pakvasa and
Weiler have found that
the large dimensions can be distorted in such a
way that special
relativity does not apply within them. This means
that anything moving
through the fifth dimension can break one of the
founding principles of
special relativity: it can travel faster than the
speed of light as we
know it.

This has dramatic consequences for inhabitants stuck
on the brane. To
them, any entity that takes a short cut through the
bulk appears to
vanish and then pops up again at some point on the
brane far sooner than
it could have had it kept to the brane. For some
inhabitants of the
brane world, the entity appears to have travelled
faster than the speed
of light. Weirder still, to others it has also
travelled backwards in
time. That's because special relativity says that
from certain frames of
reference, faster-than-light travel is equivalent
to travelling
backwards in time. "Such off-brane short cuts can
appear as 'closed
timelike curves'," says Päs - again, that's code
for time machines.


Escape from the brane

The trouble with this idea is that it assumes there
is some way to
escape the confines of the brane and travel out into
the bulk. How could
we do this? Fortunately string theory provides a way
out. In the theory
almost all of the building blocks of matter are
represented by strings
whose ends are forever anchored to the brane.
This means they can never
escape into the fifth dimension and take a short
cut through space-time.
But there are two crucial exceptions: the hypothetical
carrier of the
gravitational force, called the graviton, and a fourth
type of neutrino
called a sterile neutrino (after the three ordinary
kinds of neutrino).
In string theory these are represented by closed loops
of string. Since
they have no ends attached to the brane, they are free
to leave and
travel into the bulk.

String theorists have pointed to this property of
gravitons to explain
why gravity is tremendously weaker than nature's
other fundamental
forces, such as electromagnetism. The idea is that
gravity is so weak
because a large proportion of gravitons leak away
into the extra
dimensions of the bulk. More intriguingly, however,
their ability to
take short cuts through the bulk also means gravitons
and sterile
neutrinos are potential time travellers. "If we can
manipulate them, we
can study time travel experimentally," says Päs.

None of this will be easy. No one has ever spotted a
graviton or a
sterile neutrino, and the odds of detecting them are
slim, to say the
least (New Scientist, 18 March, p 32). Trillions of o
rdinary neutrinos
pass through our bodies every second, yet we feel
nothing because they
so rarely interact with electrons and atoms.
Sterile neutrinos are even
less communicative because they are thought to
interact only via the
feeble gravitational force and the exchange of
the elusive Higgs boson -
an as yet undetected particle believed to endow
all particles with mass.

Päs and his colleagues point out that a quirk
of quantum mechanics could
save the day. According to the laws of quantum
physics, neutrinos can
flip from one kind to another. Experiments in
Japan and the US designed
to detect neutrinos on the rare occasions they
do interact with matter
have confirmed that neutrinos spewed out by the
sun and those from space
do indeed change type. This phenomenon should
affect sterile neutrinos
too, changing them into ordinary, detectable
neutrinos and back again.
What's more, the odds of this happening increase
whenever the density of
the material the neutrinos are travelling through
changes abruptly.

?A quirk of quantum mechanics could allow us to test
time travel right
here on Earth?

This has inspired Päs and his colleagues to propose
an experiment that
could test their ideas. They suggest sending a
beam of ordinary
neutrinos through the Earth, from a research station
at the South Pole
towards a detector located at the equator. When they
enter the ground,
some of the neutrinos will flip into sterile neutrinos.
Capable of
taking a short cut though the extra dimensions of the
bulk, these
sterile neutrinos will reach the other side of the
Earth first,
apparently having travelled faster than light. As
they pass out of the
ground into the air again, they will flip back into
ordinary neutrinos,
which can be detected. Because the Earth is rotating,
these
faster-than-light neutrinos can appear to have arrived
before they set off.

Such an experiment is beyond our current technological
capabilities but,
remarkably, Päs says it is a realistic proposition within
the next 50
years. Of course, it requires two things. The first is the
existence of
sterile neutrinos. While many physicists are keen on the
idea of sterile
neutrinos, they are barely beyond theoretical flights of
fancy. The
other is that we live in an asymmetrically warped space-time,
as Päs
prescribes. How plausible is this?

When Einstein's came up with his general theory of
relativity, he showed
us how space-time can be warped or flat, but his
equations tell us
nothing about the actual shape of our universe -
merely that different
shapes are possible. For instance, cosmologists have
no way of knowing
if space stretches out to infinity or curves back on
itself. This opens
the door to many different types of time machines,
some more plausible
than others.

One famous solution to Einstein's equations, formulated
by mathematician
Kurt Gödel, describes a universe that rotates rapidly.
Instead of
travelling in straight lines, light will appear to
travel in a spiral.
Gödel realised that this allows a traveller to outrun
light and return
to their starting point before they left. In other
words, Gödel's
rotating universe is a time machine. "But we know we
don't live in such
a universe," says Päs.

Another time machine exists inside rotating
black holes, where
space-time becomes so warped that space and time
change places. The
trouble is, as Päs points out, rotating black holes
are inaccessible to
us. Then there is the space-time surrounding an
infinitely long, rapidly
rotating cylinder, as proposed by physicist Frank
Tipler. Päs is quick
to dismiss it too. "It requires huge masses rotating
unphysically fast,"
he says.

Among the other leading contenders are wormholes,
microscopic tubes of
space-time that act as tunnels from one point to
another. But before you
climb into one, there is a problem: wormholes snap
shut in an instant
unless propped open by a supply of something called
exotic matter.
Unlike the familiar stuff found on Earth, which always
feels the pull of
gravity, this exotic matter has repulsive gravity,
halting the
wormhole's collapse. "We don't know whether such matter
exists and if it
is stable," says Päs.

Päs confesses that the scenario his team has examined
also requires
exotic matter to warp the fifth dimension, but he
still maintains that
it is more plausible than the other scenarios.
What sets their
space-time apart from wormholes is that the hypothetical
exotic matter
is hidden away in the higher-dimensional bulk instead
of roaming around
the brane. If it exists, this might explain why we have
never seen it.

Understandably, the idea is not without its critics.
Sydney Deser of
Brandeis University in Waltham, Massachusetts, is
convinced, as was
Einstein, that time machines are not possible and
does not like
"unphysical" exotic matter. He believes that concealing
it in the bulk,
as Päs's team suggests, is little better than a scenario
in which it is
out in the open. "It's only a matter of degree," he says.

Päs, however, points out that the kind of space-times
he and his
colleagues have considered can do away with a number
of problems that
have plagued general relativity. For instance,
faster-than-light
connections between far-flung parts of the cosmos
would have allowed
heat to flow back and forth across the early universe.
This would have
evened out any temperature variations, explaining the
uniformity that
cosmologists observe. This could provide an alternative
to the theory of
inflation, in which cosmologists believe space-time was
stretched
unimaginably fast after the big bang, and which would
also account for
the evenness in temperature. While the majority of
cosmologists believe
in inflation, no one has explained the detailed
physics behind it.

Others do not find asymmetrically warped space-times
so plausible. "I
certainly think the idea is interesting, but I have
some worries," says
Tony Padilla of the University of Barcelona in Spain.
"For a start, I
think it is premature to claim that these space-times
are 'natural'. One
needs to examine their stability first, and in this
case I would expect
the solution to be unstable, although I could be wrong."

Padilla concedes that it is possible that we may one
day find a stable
brane universe with the properties described by
Päs's team. "I'm just
not convinced we are there yet," he says.

John Cramer of the University of Washington in
Seattle agrees that the
work outlines some interesting ideas. "The scheme,
however, requires
asymmetrically warped brane universes - and our
universe may not be one
of these," he cautions. "Nevertheless, it's a
fascinating proposal."

Of course, if time travel is possible in the way
Päs envisages, it may
be accessible only to special particles like sterile
neutrinos and
gravitons, and therefore won't cause much havoc in
the everyday
universe. Päs takes a pragmatic view of all this.
As long as the
possibility of time machines remains, he believes it
is worth exploring
experimentally. "Even if time travel is not possible,
by manipulating
particles like sterile neutrinos we can explore the
physics that
intervenes to prevent it," he says.

?Anything travelling through the fifth dimension
can move faster than
the speed of light as we know it?

The first answers might come soon courtesy of the
MiniBoone neutrino
experiment at Fermilab. It could confirm the existence
of sterile
neutrinos and short cuts in extra dimensions as early as
this year. Then
again, if time travel really is true, maybe the answer
has already been
published.

From issue 2552 of New Scientist magazine, 22 May 2006,
page 34

Superstrings connect : What Happened Before The Big Bang



What is the fundamental thing that makes up matter? Do extra dimensions exist? If they do, where are they? Do parallel universes exist? How our visible universe was created?

Imagine you could find an explanation for everything in the universe, from the smallest events possible to the biggest. This is the dream which has captivated the most brilliant scientists since Einstein. But to make the dream true they needed “The theory of everything” which will unitie all the four fundamental forces into a single equation. The four forces (gravity, electromagnetism and the strong and weak nuclear forces) would be unified by an equation perhaps one inch long. During the last thirty years of his life Albert Eienstein sought, relentlessly for this theory and he came up empty handed and once said “Nature shows us only the tail of the lion”. But now scientists says that they have got that theory and that is the super string theory.

In the heart of string theory:
Think of a guitar that has been tuned by stretching the string under tension across the guitar. Depending on how the musical notes will be created by the string. These musical notes could be said to be excitation modes of that guitar string under tension.In similar manner, in string theory the elementary particles could be thought of as the musical note or excitation modes of elementary strings.So, roughly speaking everything in the universe in made of tiny strings, because the sub-atomic particles are really just resonance or vibrations of a tiny string.In string theory as in guitar playing, the string must be stretched under tension in order to become excited. The strings are floating at space time.If string theory is a quantum theory of gravity(it’s a theory which can unifie General Reletivity & Quantum mechanics, where general reletvity explains the largest events & quantum mechanics the smallest thing in the universe) then the average size of a string is about 10*-33 centimeters, or about a millionth of a billionth of a billionth of a billionth of a centimeter. Unfortunately, this means that the strings are too small to see by current or expected particle physics technology.There are both open & closed looped strings.
Extra dimensions:
We live in a universe of three dimensional space (3D), or can say four dimensional space-time. It means we can move back-front, up-down & left-right in these three ways. With these three dimensions adding time we get four dimensional (4D) space-time. But string theory says something different, strange and amazing.If a string has to oscillate properly if needs ten dimensions! Yes ten dimensions. But where are the extra six dimensions? Super string theory gives the answer. The extra six dimensions are compactified. The best way to draw this is to use complicated 6D geometry called Calabi-You manifold, in which all the intrinsic properties of elementary particles are hidden.There are infinite number of ways to wind a string around and extra dimension. Each way in topologically described by an integer called winding number, which can be positive or negative depending on the orientation of the string.
Five theories of everything!At first of early nineties there was total five distinct string theories in 10D space.The theories are So (32), Type I ,IIA,IIB & E8 X E8 heterotic.In that time string theory was said as “The theory of everything”. But it has five types. So it there are five theories of everything! and it is really impossible because we need only one. Besides Michel Duff (University of Michigan) and his team combined gravity and super symmetry which is called supergravity. Their equation said that totally there will be .11 dimensions where string theory said 10. So with everything string theory was in an embarrassing position. They were trying to add the eleventh dimension. It might rescue them.
Brane world:In 1995 Joe Polchinski of the University of California in Santa Barbara electrified the string-theory community with a major discovery that has subsequently impacted every field of physics. He discovered D-branes.D-branes are surfaces where the free ends of open strings are fixed. They come in various dimensions. 0.2-branes for example are two dimensional and can also be called D2-membranes, or super membranes. D0-branee are like particle like and D1-branes are string like. Higher dimensional objects can exist as well. D-branes are essential for making string-theory mathematically consistent, and have far-reaching implications for a theory of quantum gravity.

M-theory:
At last scientist’s were able to add the last one dimension, the eleventh dimension and something happened remarkable — the five theories turned out to be simply different manifestations of a more fundamental theory. It means in 11 dimensions looking from the mountain-top, looking down you could see string theory as being part of a much larger reality, reality of eleventh dimension.So with the addition of one extra dimension string theory made sense again, but it had become a very different kind of theory.Here the tiny invisible strings of string theory stretched and they combined. The astonishing conclusion was that all matter in the universe was connected to one vast structure: a membrane. In effect our entire universe is a membrane. The quest to explain everything in universe could begin again and at its heart would be this new theory. It was dubbed membrane theory or M-theory, but so enigmatic and profound did the idea seem that some thought ‘M’ should stand for other things as — magic, mystery, majesty, madness or mother theory. This is the mother of all superstring theories.

The 11th dimension:
With M theory it seemed at least there was a theory which might explain everything in the universe, but before they could decide if this was true the scientists needed to know more about this new eleventh dimension. It quickly became clear it was a place where all the normal rules of commonsense have been abandoned. For one thing it is both infinitely long but only a very small distance across.Scientists like Paul Steinhard (Princeton University) and Burt Or rut (University of Pennsylvania) tell that this 11th dimension exists only one trillionth of a millimetre away from every point in our three dimensional world. So it’s closer than your clothes to your body and yet we can not sense it. In this mysterious space our membrane universe is floating. At first no one could imagine how that worked. Then some suggested it might float like a thin rubber sheet. Others that it might be more like a bubble which vibrated as it was blown aimlessly across space. But is our universe alone or there are parallel universes? Let’s explore it. The journey began with Lisa Randall.

Parallel Universes:
Lisa Randall (Harvard University) had been fascinated by an apparently inexplicable phenomenon: the weakness of gravity.We know there are four fundamental force in our universes. If we assume the intensity of gravity ‘1′, then the intensity of weak Nuclear Force-10*30, strong Nuclear force- 10*40 and strong Nuclear force-10*42 (42 zero after 1). So gravity is extremely weaker than the other three forces. Now you might look around and say gravity does not seem weak, but if you think about if you have the entire earth pulling on you and yet can manage to pick things up.When M Theory emerged, Randall and Sundrum (John Hopkins University) wondered if it might be provide and explanation. Could gravity be leaking from our universe into empty space of the eleventh dimension?Randall tried to calculate how gravity could leak from our membrane universe into empty space, but she couldn’t make it work. Then she hard a theory that there might be another membrane in eleventh dimension. Now he had really strange thought. What if gravity was not leaking from our universe but to it? What if it came from that other universe? On that membrane or brain, gravity, would be as the other forces, but by the time it reached us it would only be a faint signal. Now when she reworked her calculations everything fitted exactly. So our gravity is just a weak signal leaking out of another universe into ours which spends most of the time near the other brane. We only feel the tail end of gravity.The weakness of gravity could at last be explained, but only by introducing the idea of parallel universe. Randall’s idea opened a pandora’s Box. Now suddenly physicists all over the world piled into the eleventh dimension trying to solve age-old problem and every time it seemed the perfect explanation was another parallel universe. Everywhere they looked it seemed they began to find more and more of them.within no time at all eleventh dimension seemed to be jam packed full of membranes. These membranes were possible other parallel universes. In those universes there may be people like us or not, may be different kinds of laws of physics.So M-theory was getting more and more stranger. But could it really be a theory which explained everything in our universe? Did it answered what caused the Bigbang, it mean the explosion from which our universe was created?

Before the Big bang:
Imagine there is an enormous ship standing at harbour which is 150 or 200ft high. This giant wave suddenly jumped from sea surface to air & crushed its windows. It means from 2d to 3d. Burt ovrut suggested our universe is moving through the eleventh dimension like giant, turbulent waves.Burt’s idea caught attention of the physicists and cosmologists. After a conference in Cambridge in which he explained this idea first time, Neil Turok (Cambridge University), Paul Steinhurdt and Burt decided to discuss about bigbang. Started to throw ideas. Suddenly they knocked at the right door and the mystery of bigbang opened.The idea was——-If two brains collide each other then it produces all the effects of early universe. It means Bigbang is the result of the collision of two brains or parallel universes. But the problem was things are not smooth out in our universe. In fact we have little clamps, we have galaxies & lumps of matter. Now they had to explain how the collision of two parallel universe could go on create these lumps of matter. Could they solve it?Yes, they solved it. They answer was — people tended to think of brains as being flat perfect sheets, geometrical plains, but the picture could not be correct. It cannot be perfectly flat. It has to ripple. When the rippling brains approach to each other and collide they don’t hit at exactly the same time, same place, but in fact they hit at different points and at different times. This rippling collision produces lumps of matter.So they finally had their complete explanation of the birth of our universe and the latest understanding of the universe is that there could be infinite number of universes each with a different laws of physics. Bigbangs probably take place all the time. Our universe co-exists with other universes which are also in process of expansion. Our universe could be just one bubble floating in an ocean of other bubbles. Perhaps out there in space there is another universe heading directly towards as — it may only be a matter of time before we collide.

Referance:
Elegent Universe-Brayan Greene
Superstrings-Leonerd Susskind http://www.physicsweb.com/
BBC science & nature
Image courtesy :

The Sun


Courtesy: Google images

Large Hadron Collider


At last after 20 years of preperation the mysterious ring is almost ready with its 1232 superconducting magnets to
guide the protons at almost the speed of light. Yes I am talking about theworld’s most powerful particle accilerator,LHC-
THE LARGE HADRON COLLIDER., which is scheduled to switch on in the November at CERN(EUROPEAN CENTRE
FOR NEUCLER RESEARCH) near Geneva, Switzerland. Physicists will then combine results from the LHC experiments
with insights from their theoretical investigations to explore phenomena whose effects are only detectable at small distances
and high energies. The theory known as the Standard Model of particle physics describes all known matter and the forces through
which it interacts. Experiments have thoroughly tested the Standard Model, and its basic ingredients are almost certainly
correct. But the Standard Model cannot be the final word: it leaves open important questions about the origin of elementary
particlemasses and puzzles such as the relative weakness of gravity. The LHC will help to resolve these mysteries, and
scientists all over the globe are busily preparing experiments they hope will provide answers to these questions. Perhaps
the most exciting proposal for extending and completing the Standard Model involves additional hidden dimensions of
space beyond the three dimensions with which we are all familiar: up-down, left-right, and forward-backward. The premise underlying particle physics is that elementary particles constitute the building blocks of matter.
Peel away the layers, and inside you will always ultimately find elementary particles. Because of Einstein's E=mc2 equation,
which states that energy (E) is equal to mass (m) multiplied by the square of the speed of light (c), we need high energies to create
particles with big masses. The LHC will produce enormous amounts of energy that can then be converted into particles
we would never find in any other way.

THE LHC:

The collider is contained in a 27 km circumference tunnel located underground at a depth ranging from 50 to 150 metres The tunnel was formerly used to house the LEP an electron-positron collider. The 3 metre diameter, concrete-lined tunnel actually crosses the border between Switzerland and France at four points, although the majority of its length is inside France. The collider itself is located underground, with many surface buildings holding ancillary equipment such as compressors, ventilation equipment, control electronics and refrigeration plants.
The collider tunnel contains two pipes enclosed within superconducting magnets cooled by liquid helium, each pipe containing a proton beam. The two beams travel in opposite directions around the ring. Additional magnets are used to direct the beams to four intersection points where interactions between them will take place.
The protons will each have an energy of 7 TeV, giving a total collision energy of 14 TeV. It will take around 89 microseconds for an individual proton to travel once around the collider. Rather than continuous beams, the protons will be "bunched" together into approximately 2800 bunches, so that interactions between the two beams will take place at discrete intervals never shorter than 25 nanoseconds apart. When the collider is first commissioned, it will be operated with fewer bunches, to give a bunch crossing interval of 75 nanoseconds. The number of bunches will later be increased give the final bunch crossing interval of 25 nanoseconds.
Six detectors are being constructed at the LHC. They are located underground, in large caverns excavated at the LHC's intersection points. Two of them, ATLAS and CMS are large, "general purpose" particle detectors. The other four (LHCb, ALICE, TOTEM, and LHCf) are smaller and more specialized.
The LHC can also be used to collide heavy ions such as Lead (Pb) with a collision energy of 1150
LHC experiments
OUR ACHIEVEMENTS:

Physicists hope to use the collider to enhance their ability to answer the following questions:
Is the popular Higgs mechanism for generating elementary particle masses in the Standard Model violated? If not, how many Higgs bosons are there, and what are their masses? The Higgs boson is a hypothetical massive scalar elementary particle predicted to exist by the Standard Model of particle physics. It is the only Standard Model particle not yet observed, but plays a key role in explaining the origins of the mass of other elementary particles, in particular the difference between the massless photon and the very heavy W and Z bosons So it a particle of great importance.
Will the more precise measurements of the masses of baryons (In particle physics, the baryons are the family of subatomic particles which are made of three quarks. The family notably includes the proton and neutron, which make up the atomic nucleus, but many other unstable baryons exist as well.) continue to be mutually consistent within the Standard Model?
Do particles have supersymmetric ("SUSY") partners? Supersymmetry means every boson has a fermionic super partner Bosons are particles those transmit forces(photon,W,Z & graviton) & fermions makes up matter(electron,quark etc)
Why are there violations of the symmetry between matter and antimatter?
Are there extra dimensions, as predicted by various models inspired by string theory, and can we "see" them?
What is the nature of the 96% of the universe's mass which is unaccounted for by current astronomical observations which is called dark energy and dark matter and dark energy?
Why is gravity so many orders of magnitude weaker than the other three fundamental forces?

IS IT DISASTEROUS FOR EARTH & UNIVERSE?:

People both inside and outside of the physics community have voiced concern that the LHC might trigger one of several theoretical disasters capable of destroying the Earth or even the entire universe. These include:
Creation of a stable black hole(a place of high gravitational intensity from where nothing can scape.)
Creation of strange matter that is more stable than ordinary matter
Creation of magnetic monopoles that could catalyze proton decay In physics , a magnetic monopole is a hypothetical particle that may be loosely described as "a magnet with only one pole". In more accurate terms, it would have net magnetic charge. Interest in the concept stems from particle theories , notably Grand Unified Theories and superstring theories that predict either the existence or the possibility of magnetic monopoles.
CERN performed a study to investigate whether such dangerous events as micro black holes, magnetic monopoles could occur The report concluded, "We find no basis for any conceivable threat." For instance, it is not possible to produce microscopic black holes unless certain untested theories are correct. Even if they are produced, they are expected to be harmless due to the Hawking radiation process(particle-antiparticle pair to appear close to the event horizon of a black hole. One of the pair falls into the black hole whilst the other escapes. In order to fill the energy 'hole' left by the pair's spontaneous creation, energy tunnels out of the black hole and across the event horizon. By this process the black hole loses mass, and to an outside observer it would appear that the black hole has just emitted a particle.). Perhaps the strongest argument for the safety of colliders such as the LHC comes from the simple fact that cosmic rays of much higher energies than the LHC can produce have been bombarding the Earth, Moon and other objects in the solar system for billions of years with no such effects.
However, some people remain concerned about the safety of the LHC. As with any new and untested experiment, it is not possible to say with utter certainty what will happen. In academia there is some question of whether Hawking radiation is correct.

So the LHC is on its way.Its costing not too much,only US$ 8billion.We hope it will not be diasterous & will make mankind the lord of the mysterious ring by smashing open the mysteries.
Referance:

Interstellar Travel

In 1960 Bussard proposed an interstellar vehicle that would collect its fuel from interstellar medium. A large scoop would pick up protons present in space, and the protons would be fed into a fusion reactor where part of their mass would be converted into kinetic energy. How big would the scoop have to be in order to produce a constant 1g acceleration for a 3500-ton vehicle?

Walking on water

What is the minimal speed with which a person can run on the surface of the water.

(Please, no remarks about the gentelman who walked on the water (lake of Galilee) two thousand years ago.)

This question appears in the "Problems in Physics" by P.L. Kapitza

BIRD ON A TREE

How big does a seed on the ground have to be to justify a bird in flying off a tree branch to eat it?

This problem appeared among the London Physics Olympics questions

Halley's Planet

Not so many years ago there was no order of magnitude estimate of the age of the planet Earth. Edmund Halley (yes, that's the "comet guy") wrote an article in Philosophical Transactions of the Royal Society of London, 29, 296 (1714), where he observed that lakes that emit no rivers (such as Dead Sea, or Caspian Sea) are very salty, and thus it is reasonable to assume that rivers bring salt into the lakes. He further claimed that "'tis not improbable that the ocean it self is become salt from the same cause." Consequently, by measuring the salinity of the oceans and by determining the amount of salt brought by rivers every year, one could estimate the age of the Earth. Halley lacked the data to actually perform an estimate of the age of the Earth using his method. Halley's assumptions are wrong, but nevertheless it was a nice try for his time. What would be the age of Earth according to Halley's method?

Sunday, April 1, 2007

Monday, March 19, 2007

Wormhole

Anyone who has more than a passing interest in science fiction will be aware of "wormholes". They linked the Stargates in the series (and movie) of the same name. They sucked John Crichton and Farscape 1 through to some "distant galaxy". They even appeared in some of the eleventy-billion episodes of Star Trek, putting the Gamma Quadrant in Deep Space 9's back yard. In other words, they're a standard response to the problem of covering interstellar distances. Intriguingly, they may actually exist.

A black hole is a produced when a particularly heavy star runs out of fuel and collapses in on itself. Every object exerts a force, called gravity, on every other object in the universe (although because it follows an inverse square rule, unless the object is particularly massive, or you're very close to it, that force is essentially negligible). In order to escape from an object's gravity, you need to be going very fast - and that speed, called the "escape velocity", is a function of the size and gravity of an object.

A black hole is black because it is so small and heavy that the escape velocity required to escape its gravityish grasp exceeds the speed of light. Because Einstein's theory of General Relativity says that nothing can travel faster than the speed of light (299,792,458 m/s), it is impossible for anything to go fast enough to escape from a black hole. At the centre of the black hole is a singularity, but the distance at which the escape velocity equals the speed of light is called the event horizon (no, not the movie), and it's impossible to see past the event horizon.

No one has actually seen a black hole (because, like space, it's black), but there are plenty of spots where effects are seen which are consistent with the presence of a black hole. But the research linked above suggests that a wormhole may actually produce an effect similar to a black hole, so what we think are black holes may actually been wormholes.

Wormholes essentially punch a whole through space, and may link two distant bits of space (or even time), so they may be a way to explore the galaxy. Or they may just rip your atoms into bits and turn you into singularity soup. So they may one day aide space travel, but much like the first person to eat an oyster, the first person to attempt to travel through a wormhole is going to be taking one hell of a leap of faith.

The article linked above suggests that the new generation of particle accelerators may actually be able to create tiny little wormholes, which may be able to be distinguished from black holes by the absence of Hawking radiation. It's times like this that I wish I was good enough at maths to have contemplated following a career in physics - instead of sitting here at a boring desk I could be creating black holes and laying the foundations to future human exploration of the universe (or possibly destroying the world - either is cool with me).
Originaly posted at Anyone who has more than a passing interest in science fiction will be aware of "wormholes". They linked the Stargates in the series (and movie) of the same name. They sucked John Crichton and Farscape 1 through to some "distant galaxy". They even appeared in some of the eleventy-billion episodes of Star Trek, putting the Gamma Quadrant in Deep Space 9's back yard. In other words, they're a standard response to the problem of covering interstellar distances. Intriguingly, they may actually exist.

A black hole is a produced when a particularly heavy star runs out of fuel and collapses in on itself. Every object exerts a force, called gravity, on every other object in the universe (although because it follows an inverse square rule, unless the object is particularly massive, or you're very close to it, that force is essentially negligible). In order to escape from an object's gravity, you need to be going very fast - and that speed, called the "escape velocity", is a function of the size and gravity of an object.

A black hole is black because it is so small and heavy that the escape velocity required to escape its gravityish grasp exceeds the speed of light. Because Einstein's theory of General Relativity says that nothing can travel faster than the speed of light (299,792,458 m/s), it is impossible for anything to go fast enough to escape from a black hole. At the centre of the black hole is a singularity, but the distance at which the escape velocity equals the speed of light is called the event horizon (no, not the movie), and it's impossible to see past the event horizon.

No one has actually seen a black hole (because, like space, it's black), but there are plenty of spots where effects are seen which are consistent with the presence of a black hole. But the research linked above suggests that a wormhole may actually produce an effect similar to a black hole, so what we think are black holes may actually been wormholes.

Wormholes essentially punch a whole through space, and may link two distant bits of space (or even time), so they may be a way to explore the galaxy. Or they may just rip your atoms into bits and turn you into singularity soup. So they may one day aide space travel, but much like the first person to eat an oyster, the first person to attempt to travel through a wormhole is going to be taking one hell of a leap of faith.

The article linked above suggests that the new generation of particle accelerators may actually be able to create tiny little wormholes, which may be able to be distinguished from black holes by the absence of Hawking radiation. It's times like this that I wish I was good enough at maths to have contemplated following a career in physics - instead of sitting here at a boring desk I could be creating black holes and laying the foundations to future human exploration of the universe (or possibly destroying the world - either is cool with me).
Anyone who has more than a passing interest in science fiction will be aware of "wormholes". They linked the Stargates in the series (and movie) of the same name. They sucked John Crichton and Farscape 1 through to some "distant galaxy". They even appeared in some of the eleventy-billion episodes of Star Trek, putting the Gamma Quadrant in Deep Space 9's back yard. In other words, they're a standard response to the problem of covering interstellar distances. Intriguingly, they may actually exist.

A black hole is a produced when a particularly heavy star runs out of fuel and collapses in on itself. Every object exerts a force, called gravity, on every other object in the universe (although because it follows an inverse square rule, unless the object is particularly massive, or you're very close to it, that force is essentially negligible). In order to escape from an object's gravity, you need to be going very fast - and that speed, called the "escape velocity", is a function of the size and gravity of an object.

A black hole is black because it is so small and heavy that the escape velocity required to escape its gravityish grasp exceeds the speed of light. Because Einstein's theory of General Relativity says that nothing can travel faster than the speed of light (299,792,458 m/s), it is impossible for anything to go fast enough to escape from a black hole. At the centre of the black hole is a singularity, but the distance at which the escape velocity equals the speed of light is called the event horizon (no, not the movie), and it's impossible to see past the event horizon.

No one has actually seen a black hole (because, like space, it's black), but there are plenty of spots where effects are seen which are consistent with the presence of a black hole. But the research linked above suggests that a wormhole may actually produce an effect similar to a black hole, so what we think are black holes may actually been wormholes.

Wormholes essentially punch a whole through space, and may link two distant bits of space (or even time), so they may be a way to explore the galaxy. Or they may just rip your atoms into bits and turn you into singularity soup. So they may one day aide space travel, but much like the first person to eat an oyster, the first person to attempt to travel through a wormhole is going to be taking one hell of a leap of faith.

The article linked above suggests that the new generation of particle accelerators may actually be able to create tiny little wormholes, which may be able to be distinguished from black holes by the absence of Hawking radiation. It's times like this that I wish I was good enough at maths to have contemplated following a career in physics - instead of sitting here at a boring desk I could be creating black holes and laying the foundations to future human exploration of the universe (or possibly destroying the world - either is cool with me).
originaly posted at
http://thekillfile.blogspot.com/2007/04/wormhole-extreme.html

Thursday, March 15, 2007

FALLING CLOUDS

Clouds are made of water droplets, and water is about 800 times denser than air. Why don't clouds fall like a rock to the ground?

Friday, March 9, 2007

Cup of tea

When you finish stirring sugar into your cup of tea the water comes to rest in a few seconds. Is the decay of the water's rotation caused primarily by the walls of the cup or by its bottom?

Sunday, March 4, 2007

1300 blackholes


Every dot of light in that image is a black hole, hundreds of millions and even billions of light years away. Before you say, "Say wha?", this will take some explanation.

The black holes themselves are black (duh). But as matter falls into them, it can settle into a disk, called an accretion disk. If you remember your college physics — you did take college physics, right? — as something falls into a black hole, it acquires a huge amount of kinetic energy (for you pedants, it actually converts gravitational potential energy to kinetic energy). Think of it this way: when you hold a rock up over the ground, it has potential energy– the potential to move due to gravity. When you let go, that potential energy becomes kinetic energy– the energy of motion. If you don’t think it has energy, then let it hit your toe. The kinetic energy will be converted to a loud crunching sound, and you will potentially have to go to the hospital.

So matter falling into gravity can gather energy, and matter falling into a black hole can get a lot of energy. This is converted to motion and heat, and as the matter piles up into the accretion disk it gets terribly, terribly hot: as hot as millions of degrees. There are also associated magnetic fields and other forces which can make the matter in the disk light up, getting it extremely bright. The bigger the black hole, the brighter this disk can get.

Astronomers think that in the center of every big galaxy there is black hole with millions or even billions of times the Sun’s mass. Guess how bright they can get?

Answer: pretty damn bright. In fact, as long as they are actively feeding, black holes like this are the brightest sustained objects it the Universe. We call them "active galaxies". They’re so bright they they can be spotted when they are billions of light years away. And hey, didn’t I say that the spots in the image above were at that distance?

Yes, good! You’re paying attention. The image at the top of this entry is from the orbiting Chandra X-ray Observatory — it’s only one part of a bigger image revealing 1300 black holes at the centers of galaxies.

When matter gets heated to millions of degrees, it gives off X-rays, so Chandra is a great telescope to spot black holes, especially the supermassive monsters in the centers of galaxies. We’re still trying to figure out just how many galaxies are active, and how many are quiescent like the Milky Way (our central black hole has 4 million times the mass of the Sun, but is not currently feeding, so it’s not active).

Also, we’re not completely sure what the structure of the accretion disk is like near a hole. The current theory is that near the black hole it’s very flat and thin, but farther out it puffs up into a torus or doughnut (or bagel if you’re from New York City). But think about this: imagine putting a pea in the center of a donut hole. From most viewing angles, the pea is hidden. If you view it face-on you can see the pea, but at an angle the donut blocks your view. From edge-on you’re looking through a lot of doughnut and can’t see the pea at all.

This model explains a lot about what we see with these active galaxies, but is it right?

Maybe. Maybe not.

The new observations from Chandra are very interesting. If we see a black hole torus face-on, we expect to see X-rays of all energies, since they are free to get to us. But if we see one edge-on, only the highest-energy X-rays can penetrate the obscuring torus, so we’d expect to see only those high-energy X-rays and no low energy ones. So, looking at 1300 black holes as Chandra did, you’d expect to see a few that are face-on, a few edge-on, and most ranging in between. In other words, the observations should show most black holes sending out a mix of high and low energy X-rays.

Oops. They didn’t. They reveal lots of high-energy-X-ray-emitting-galaxies, and lots of low-energy-X-ray-emitting-galaxies, but very few in between, the opposite of what the model predicted.

Does this mean the model is completely wrong? No, because in fact the model does very well predicting what we see from black holes in a whole bunch of other obsrevations, hundreds and even thousands of them. So what these new data really mean is that the details of the model need to be worked on more. Maybe in active galaxies the torus doesn’t puff up as much. Maybe the disks are bigger than we thought, or there isn’t as much dust in the torus, or a hundred other reasons.

The devil, that rascal, is always in the details. And if there is any actual place in the Universe that could be described as Hell, it’s the gaping maw of a black hole and the swirling maelstrom surrounding it. So there will always be devilish details to hammer out.

One final note: these active galaxies can pour out gamma rays as well– gamma rays have even higher energy than X-rays. NASA and the Department of Energy are building GLAST, an observatory whose main mission is to investigate these supermassive black holes (I’ve written about GLAST several times). It’s due for launch in November, so by this time next year we’ll have a lot more data, and a lot more answers. But we’ll have a lot more questions, too! This is truly the game that never ends, which is one reason it’s so much fun.

Originally posted at http://www.badastronomy.com/bablog/2007/03/12/1300-black-holes/