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........

## Friday, June 1, 2007

### Free math books

## Sunday, May 20, 2007

## Thursday, May 10, 2007

## Friday, May 4, 2007

## Tuesday, May 1, 2007

## Monday, April 9, 2007

### A new way to test time travel

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:**

**Extra dimensions:**

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:**

**The 11th dimension:**

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:**

**Image courtesy :**

### Large Hadron Collider

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

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

### Walking on 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

This problem appeared among the London Physics Olympics questions

### Halley's Planet

## Sunday, April 1, 2007

## Monday, March 19, 2007

### Wormhole

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

## Friday, March 9, 2007

### Cup of tea

## 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/