Physics Blogspeak : Part I Sunday, Jan 14 2007 

A collection of interesting posts from physics blogsphere :

Short Distances: Newton Still the Man (from Cosmic Variance by Sean)

Via Chad Orzel, I see that the latest constraints on short-distance modifications of Newton’s inverse-square law from the Eot-Wash group at the University of Washington have now appeared in PRL. And the answer is: extra dimensions must be smaller than 0.045 millimeters (in any not-too-contrived model)…


Undergraduate Theory Institute(from Cosmic Variance by Sean)

Sadly, I’m not here to announce that applications are now being accepted for students who would like to participate in this year’s Undergraduate Theory Institute. That’s because there is no such thing as the Undergraduate Theory Institute, at least as far as I know. (Google doesn’t know of one either.) But I think it would be a great idea — maybe if I post it here on the blog someone will start it.

It’s increasingly common for physics students to participate in some kind of research during their undergraduate years. The NSF has a very successful Research Experience for Undergraduates program, for example, that funds students to do summer research, typically at an institution other than their own. Getting involved in research as early as possible is a great idea for students, for a number of reasons. Most importantly, the flavor of doing real research, where the answers aren’t in the back of the book, is utterly different from almost any classroom experience or even self-study, where you are trying to learn material that someone else has already mastered. The move from following a course of study to striking out into the unknown is one of the hardest transitions to make during graduate school, and getting a head start is an enormous help. On a more prosaic level, it’s useful to work closely with an advisor who can end up writing letters of recommendation. And let’s not forget that it can be a lot of fun!..

Dancing Ball Lightnings in the Lab (from Backreaction Blog)

Ball lightnings are mysterious things: Small, bright balls of fire suddenly appear during a thunderstorm, swirl around, make sometimes funny noises, and leave behind a smell of ozone…

Since ball lightnings are not only spooky, but also very elusive, there has been a lot of speculation how to understand and explain them in a scientific way: People have suggested that it may be some ionised balls of plasma held together by their own magnetic fields, or even such exotic things as mini black holes leftover from the big bang…

A more “down to Earth” explanation was proposed in a 1999 Letter to Nature:..

From Griffiths to Peskin: a lit review for beginners (From “An American Physics Student in England” )

a.k.a. “How to get started learning QFT as an undergraduate.”

Quantum Field Theory (QFT) plays a key role in all branches of theoretical physics. For students interested in high energy theory, exposure to QFT at any early stage is slowly becoming the standard for top American graduate schools. This is already the case for the Mathematics Tripos at Cambridge…

An inspired student with adequate background should be able to take quantum mechanics in his/her second or third year and then progress directly to a ‘real’ QFT course with a bit preparation, without going through the rigmarole of a year-long graduate quantum mechanics course.

Instead, I present a rough guide to pedagogical QFT literature so that a motivated student can prepare for a graduate-level QFT course or a get started with a self-study during the summer after his/her undergraduate quantum mechanics course. As a someone who was in this position in the not-too-distant-past, I hope some personal experience with the pros and pitfalls of the listed texts will be helpful for other other students interested in doing the same….

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Happy Perihelion ! Wednesday, Jan 3 2007 

Via Bad Astronomy Blog, we are informed that

Today, January 3, on or about 20:00 Universal Time (2:00 p.m. Pacific time), the Earth will reach perihelion, its closest approach to the Sun. The distance from the Sun to the Earth will be roughly 147,093,600 kilometers (I have found several different distances on different sites, and this is an eyeball average).

with a statutory warning that

Remember, our distance from the Sun doesn’t affect our seasons (much).

So, Happy Perihelion ! 🙂

Don’t miss the The Top Ten Astronomy Images of 2006.

Now, last but not the least, via the same blog, I came across a treasure-trove for those who are interested in astronomy – What’s Up 2007 – 365 Days of Skywatching , a superb online book !

If somebody knows the present Astro-club co-ordinators, do pass on.

Ising model and Epsilon Expansion Monday, Jan 1 2007 

As one might know that topology plays an important role in the classical O(2) model in d=2 (i.e. x-y model in two dimension) becuase one can have non-trivial excitations, namely, vortices. These excitations, while having a huge energy, can contribute to the partition function at high temperatures becuase the entropy associated with them is also proportionately large. One can easily verify that perturbative epsilon-expansion (i.e. an expansion in no. of dimensions) fails here. The reason which is often cited is that such an expansion destroys all information related to topology since atleast till now there is no homotopy theory for fractional dimensions.

Considering an even simpler case, the ising transition in d=2 could be looked upon as condensation of domain walls which are again topological objects. My question is: why does an epsilon-expansion in this case works out quite nicely? (note: here one does an expansion near the lower critical dimension which is one). Is it that notion of domain walls can be extended to even fractional dimension in some way?

Btw, one might like to visit the website http://www.math.princeton.edu/~aizenman/OpenProblems.iamp/index.html  which contains a collection of open problems in mathematical physics. Coming to a problem related to this post (though somewhat remotely), one might be surprised to find through this link that the perturbative result of O(N > 2) model in d=2 being always in a single disordered phase at all temperatures has actually not been rigourosly proved. Infact, it is even disputed by some numerical results (though I don’t claim any understanding of these). See for example, http://prola.aps.org/abstract/PRB/v54/i10/p7177_1.

2006 – Year of Maxwell ? Sunday, Dec 17 2006 

maxwell_j_c.jpg
I just realised(via a physicsweb article ) that this year is supposed to be the 175th anniversary of the birth of James Clerk Maxwell. Quite in the year to realise it I suppose 😉

So what impression of Maxwell would you have gained if you had met him in his prime, as a young Scottish undergraduate Donald MacAlister did in Cambridge in 1877? You would surely have been charmed, but perhaps also surprised to meet – as MacAlister put it – “a thorough old Scotch laird in ways and speech”. As the proprietor of an 1800 acre Scottish estate, Maxwell had all the qualities of the better kind of Victorian country gentleman: cultivated, considerate of his tenants, active in local affairs, and an expert swimmer and horseman too.

Few would have guessed that this “Scotch laird”, so disarmingly old-fashioned even in 1877, was a scientist whose writings remain astonishingly vibrant in 2006 and the greatest mathematical physicist since Newton. In addition to his work on electromagnetism, Maxwell also contributed to eight other scientific spheres: geometrical optics, kinetic theory, thermodynamics, viscoelasticity, bridge structures, control theory, dimensional analysis and the theory of Saturn’s rings. He also worked on colour vision, producing the first ever colour photograph…

Even if his achievements are somewhat overshadowed in the public’s eye by those of Einstein, whose successes were marked by a great series of events last year, it is a measure of Maxwell’s standing that 2006 – the 175th anniversary of this birth – has been dubbed Maxwell Year.

Anyway, this gives me an excuse to return back to writing about Maxwell about whom Feynman famously remarked

From a long view of the history of mankind — seen from, say, ten thousand years from now, there can be little doubt that the most significant event of the 19th century will be judged as Maxwell’s discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade.

I guess I should add that the revolt of 1857 would also pale into provincial insignificance….

Since I have already linked once to peoms by Maxwell , I will now link to one of the oldest biographies of Maxwell – the one written by Lewis Campbell and William Garnett (Link to PDF file).

The 1997 Digital Preservation of “The Life of James Clerk Maxwell”

..There are very few biographies of Maxwell. The most comprehensive biography was written by a life-long friend, Lewis Campbell with help from William Garnett. It is considered a primary historical reference on Maxwell. Published in 1882, shortly after Maxwell’s death, it is today found only in the rare book rooms of large libraries. However, now the entire text of the book with figures included is available here…

It is a long and interesting book filled with a lot of anecdotes written at a time when mechanical theories of ether were still in vogue. This of course, does not undermine its significance in History of physics . …

To quote what Weinberg wrote three years ago in his “Four Golden Lessons” addressed to a Scientist

Finally, learn something about the history of science, or at a minimum the history of your own branch of science. The least important reason for this is that the history may actually be of some use to you in your own scientific work. For instance, now and then scientists are hampered by believing one of the over-simplified models of science that have been proposed by philosophers from Francis Bacon to Thomas Kuhn and Karl Popper. The best antidote to the philosophy of science is a knowledge of the history of science.

More importantly, the history of science can make your work seem more worthwhile to you. As a scientist, you’re probably not going to get rich. Your friends and relatives probably won’t understand what you’re doing. And if you work in a field like elementary particle physics, you won’t even have the satisfaction of doing something that is immediately useful. But you can get great satisfaction by recognizing that your work in science is a part of history.

Torus subgroups Saturday, Dec 2 2006 

This is the report of the presentation I gave for the Group Theory Course.

It is basically a complete proof of a very important and curious result in compact connected groups which states that all maximal connected abelian subgroups( tori) are conjugate to each other and the union of all these conjugates cover the entire set.

The proof is quite long and somewhat involved but nonetheless there are some very interesting ideas that go into it. A glimpse of that can be seen in the section where I have proved some theorems that would be required in the main proof.

Maximal Tori In Compact Connected Groups

Salam Tuesday, Nov 21 2006 

salam.jpg

Ten years ago, on 21st of Novomber, 1996, Abdus Salam, who was among the co-founders of the Standard Model died at his home at Oxford.

For those who don’t know him, he was one of the recipient of the Nobel Prize in Physics(1979) “for their contributions to the theory of the unified weak and electromagnetic interaction between elementary particles, including, inter alia, the prediction of the weak neutral current” in short, for what physicists call the Glashow-Salam-Weinberg Model (which along with Quantum Chromodynamics and Classical General Relativity form the foundations on which all physics stands).

Was just reminded of him as I was doing some calculation with the Salam-Strathdee Superfield Formalism in (Supersymmetric extension of) Glashow-Salam-Weinberg Model. It is amusing how pursuit of science brings back names from far away…

As Salam himself mused before beginning his Nobel Lecture

Scientific thought and its creation is the common and shared heritage of mankind. In this respect, the history of science, like the history of all civilization, has gone through cycles. Perhaps I can illustrate this with an actual example.

Seven hundred and sixty years ago,a young Scotsman left his native glens to travel south to Toledo in Spain. His name was Michael, his goal to live and work at the Arab Universities of Toledo and Cordova, where the greatest of Jewish scholars, Moses bin Maimoun, had taught a generation before.

Michael reached Toledo in 1217 AD. Once in Toledo, Michael formed the ambitious project of introducing Aristotle to Latin Europe, translating not from the original Greek, which he did not know, but from the Arabic translation then taught in Spain. From Toledo, Michael travelled to Sicily, to the Court of Emperor Frederick II.

Visiting the medical school at Salerno, chartered by Frederick in 1231, Michael met the Danish physician, Henrik Harpestraeng – later to be-come Court Physician of King Erik Plovpenning. Henrik had come to Salerno to compose his treatise on blood-letting and surgery. Henrik’s
sources were the medical canons of the great clinicians of Islam, Al-Razi and Avicenna, which only Michael the Scot could translate for him.

Toledo’s and Salerno’s schools, representing as they did the finest synthesis of Arabic, Greek, Latin and Hebrew scholarship, were some of the most memorable of international assays in scientific collaboration. To Toledo and Salerno came scholars not only from the rich countries of the East and the South, like Syria, Egypt, Iran and Afghanistan, but also from
developing lands of the West and the North like Scotland and Scandinavia. Then, as now, there were obstacles to this international scientific concourse, with an economic and intellectual disparity between different parts of the world. Men like Michael the Scot or Henrik Harpestraeng were singularities. They did not represent any flourishing schools of research in
their own countries. With all the best will in the world their teachers at
Toledo and Salerno doubted the wisdom and value of training them for
advanced scientific research. At least one of his masters counselled young
Michael the Scot to go back to clipping sheep and to the weaving of
woollen cloth.

In respect of this cycle of scientific disparity, perhaps I can be more quantitative. George Sarton, in his monumental five-volume History of Science chose to divide his story of achievement in sciences into ages, each age lasting half a century. With each half century he associated one central figure. Thus 450 BC – 400 BC Sarton calls the Age of Plato; this is followed by half centuries of Aristotle, of Euclid, of Archimedes and so on. From 600 AD to 650 AD is the Chinese half century of Hsiian Tsang, from 650 to 700 AD that of I-Ching, and then from 750 AD to 1100 AD – 350 years continuously – it is the unbroken succession of the Ages of Jabir,Khwarizmi, Razi, Masudi, Wafa, Biruni and Avicenna, and then Omar Khayam – Arabs, Turks, Afghans and Persians – men belonging to the culture of Islam. After 1100 appear the first Western names; Gerard of Cremona, Roger Bacon – but the honours are still shared with the names of Ibn-Rushd (Averroes), Moses Bin Maimoun, Tusi and Ibn-Nafi-the man who anticipated Harvey’s theory of circulation of blood. No Sarton has yet chronicled the history of scientific creativity among the pre-Spanish Mayas and Aztecs, with their invention of the zero, of the calendars of the ‘moon and Venus and of their diverse pharmacological discoveries, includ-
ing quinine, but the outline of the story is the same – one of undoubted superiority to the Western contemporary correlates.

After 1350, however, the developing world loses out except for the occasional flash of scientific work, like that of Ulugh Beg – the grandson of Timurlane, in Samarkand in 1400 AD; or of Maharaja Jai Singh of Jaipur in 1720 – who corrected the serious errors of the then Western tables of eclipses of the sun and the moon by as much as six minutes of arc. As it was, Jai Singh’s techniques were surpassed soon after with the development of the telescope in Europe. As a contemporary Indian chronicler wrote: “With him on the funeral pyre, expired also all science in the East.” And this brings us to this century when the cycle begun by Michael the Scot turns full circle, and it is we in the developing world who turn to the
Westwards for science. As Al-Kindi wrote 1100 years ago: “It is fitting then for us not to be ashamed to acknowledge and to assimilate it from whatever source it comes to us. For him who scales the truth there is nothing of higher value than truth itself; it never cheapens nor abases him.”

And by the way, do read the whole thing – if not for anything else atleast for the Pauli Stories 🙂

…The hut also contained Professor Villars of MIT, who was visiting Pauli the same day in Zurich. I gave him my paper. He returned the next day with a message from the Oracle;
“Give my regards to my friend Salam and tell him to think of something better”. This was discouraging, but I was compensated by Pauli’s excessive kindness a few months later, when Mrs. Wu’s, Lederman’s and Telegdi’s experiments were announced showing that left-right symmetry was indeed violated and ideas similar to mine about chiral symmetry were expressed independently by Landau and Lee and Yang. I received Pauli’s first somewhat apologetic letter on 24 January 1957.

Thinking that Pauli’s spirit should by now be suitably crushed, I sent him two short notes I had written in the meantime. These contained suggestions to extend chiral symmetry to electrons and muons, assuming that their masses were a consequence of what has come to be known as dynamical spontaneous symmetry breaking. With chiral symmetry for electrons, muons and neutrinos, the only mesons that could mediate weak decays of the muons would have to carry spin one.

Reviving thus the notion of charged intermediate spin-one bosons, one could then postulate for these a type of gauge invariance which I called the “neutrino gauge”. Pauli’s reaction was swift and terrible. He wrote on 30th January 1957, then on 18 February and later on 11, 12 and 13 March: “I am reading (along the shores of Lake Zurich) in bright sunshine quietly your paper…”
“I am very much startled on the title of your paper ‘Universal Fermi interaction’ …For quite a while I have for myself the rule if a theoretician says universal it just means pure nonsense. This holds particularly in connection with the Fermi interaction, but otherwise too, and now you too, Brutus, my son, come with this word. …”….

Although he signed himself “With friendly regards”, Pauli had forgotten his
earlier penitence. He was clearly and rightly on the warpath.

… I must admit I was taken aback by Pauli’s fierce prejudice against
universalism – against what we would today call unification of basic forces –
but I did not take this too seriously. I felt this was a legacy of the exasperation
which Pauli had always felt at Einstein’s somewhat formalistic attempts at
unifying gravity with electromagnetism – forces which in Pauli’s phrase “cannot
be joined – for God hath rent them asunder”….

There is something more to Salam’s Legacy than Electroweak Unification. And of course, I’m thinking of the Abdus Salam International Centre for Theoretical Physics (ICTP) at Italy. And in a more subtle way, He also stands for a struggle – a struggle to provide the students from the third world(and in particular Pakistan) the joys of science…

To Quote Hoodboy

In interacting with Salam, I could see that two strong passions governed his life. Physics research occupied him intensely; his mind would lock onto a problem making him oblivious to all else. He would engage only the most challenging and difficult problems of the field, problems that only the greatest can dare try. The elegance of his solutions were startling, as for example in his brilliant creation of what are called superfields. Without this powerful mathematical concept, physicists would have a very hard time to progress beyond a certain point in grappling with the basic laws of nature.

Salam’s other passion was Pakistan. I have never been able to understand why he was so dedicated to the country of his birth given that he was virtually ostracised there, being an Ahmadi. I can remember that when the members of the physics department at Quaid-i-Azam University sought to invite him for a lecture after he received the Nobel Prize, the idea was vetoed when the student arm of a vociferous religio-political party threatened to use violence if he came to the campus. In spite of this and much more, Salam was never embittered and he never gave up trying to do whatever he could for his country.

So on this day, let us wish that hundreds of years hence, let nobody speak of him the way Salam spoke of Jai Singh – let nobody say “With him .. expired also all science in ” Pakistan .

“Life of a Star” – KITP Blackboard Lunch Monday, Nov 20 2006 

Am just listening/seeing one of the “Blackboard Lunches” from (Kavli Institute of Theoretical Physics) .

I’ve already linked to an absolutely great series of talks online at the KITP site. But, I suspect that that one post hasn’t done justice to KITP …

But, this week I came across another set of “Blackboard Lunches” which are great too.

Now, I am seeing this one – The Life of a Star.

The Life of a Star
Dr. Lars Bildsten, KITP

Using only chalk and one figure, I will derive the luminosity, lifetime, and major properties of all stars and explain why their ultimate fate (white dwarf, neutron star or black hole) depends on their mass. After this event, you should be able to explain it to your family and friends.

It’s a great talk (from the first two minutes I gather that even “geologists and string theorists” can understand it 😉 ).

Links on Nuclear Supersymmetry Wednesday, Nov 8 2006 

susy.jpg

Explanation of the image : In the words of its designer,

It has an apple in front of a mirror and the reflection is an orange. The idea being that fermions and bosons are as different as proverbial apples and oranges, yet supersymmetry (the mirror) relates them.

So why does this image have two mirrors at right angles and a total of four objects (one real, and three images)? Because it actually depicts a specific kind of supersymmetry that arises in nuclear physics. The symmetry relates the spectra of of four nuclei that differ by one in their number of protons or neutrons. If you like, there are two superymmetries at work; one changes the number of protons by 1, the other changes the number of neutrons by 1. Hence two mirrors.

Two of the elements related in this way are platinum and gold, which is why the orange in the mirror on the left is silvery, and the apple at the rear is golden….For completeness, here’s the caption that went with the image:

PROVERBIAL APPLES AND ORANGES are as different as the types of quantum particles called fermions and bosons. Just as an ordinary mirror cannot make an apple look like an orange, no ordinary symmetry in physics can transform a fermion into a boson, or vice versa. To do that trick requires supersymmetry, an extraordinary class of symmetries that may hold the key to a deep understanding of the universe. Experimenters have detected a nuclear version of supersymmetry that connects two isotopes of gold and two of platinum.

Now to the actual post. Sometime ago, I was collecting links on nuclear supersymmetry(explanation below) for Adish and I came across some really good articles on the subject worth posting here.

Note that this supersymmetry is different from the one which can occur in particle physics. Whereas supersymmetry in particle physics is still just a hypothesis waiting to be confirmed/disproved , there are occurences of supersymmetry in nuclear physics which seem to have stronger evidences to its favour.

You can start off by looking at these two news articles(written at a popular level) which report evidences for nuclear supersymmetry

Supersymmetry stands the test
Evidence for supersymmetry found

These were inspired by the PRL paper- Evidence for the Existence of Supersymmetry in Atomic Nuclei by Metz.,et al (subscription required)

Another good article written at a popular level is an article from Scientific american titled Uncovering Supersymmetry. Just to nudge you into reading this, I’ll give some excerpts out of it

Supersymmetry is a remarkable symmetry. In elementary particle physics, it interchanges particles of completely dissimilar types—the kind called fermions (such as electrons, protons and neutrons), which make up the material world, and those called bosons (such as photons), which generate the forces of nature. Fermions are inherently the individualists and loners of the quantum particle world: no two fermions ever occupy the same quantum state. Their aversion to close company is strong enough to hold up a neutron star against collapse even when the crushing weight of gravity has overcome every other force of nature. Bosons, in contrast, are convivial copycats and readily gather in identical states. Every boson in a particular state encourages more of its species to emulate it. Under the right conditions, bosons form regimented armies of clones, such as the photons in a laser beam or the atoms in superfluid helium 4.

Yet somehow in the mirror of supersymmetry, standoffish fermions look magically like sociable bosons, and vice versa….

At least that’s the theory. Elementary particle theorists have studied
supersymmetry intensively since its invention in the 1970s, and many
believe it holds the key to the next major advance in our understanding
of the fundamental particles and forces. Experimenters, however, have
searched at their highest-energy colliders for particles predicted by
supersymmetry, so far to no avail.

In the 1980s nuclear theorists proposed that superviolent collisions were
not necessarily the only way to see supersymmetry; they predicted that
a different form of supersymmetry could exist in certain atomic nuclei.
Here, too, the symmetry relates what in physics are quite dissimilar objects: nuclei with even numbers of protons and neutrons and those with odd numbers.(This again involves fermions and bosons, because a composite particle made of an odd number of fermions is itself a fermion, whereas an even number produces a boson.)….

The atomic nucleus is a fascinating quantum system holding many secrets. Its study over the decades has been a continuous source of unexpected observations. Theorists must use many tools to understand all the facets of the very complicated physics of nuclei. The new result adds supersymmetry to the toolkit and it shows that supersymmetry is not just a mathematical curiosity but exists in the world.

Nuclear physics research also provides tools needed to understand other quantum systems that have general features similar to nuclei— the so-called finite many-body systems, containing anything from a few particles to hundreds of them. Experimental methods now allow the study of such objects built from small numbers of atoms or molecules. Supersymmetry might also be important to those fields of physics…

Do read the whole article !

Endnote : For people who are not satisfied with popular articles, I will provide below some more technical articles that I came across. Note that I’ven’t read/understood any of these completely 🙂


An Introduction to Nuclear Supersymmetry: a Unification Scheme for Nuclei

Dynamic symmetries and supersymmetries in nuclear physics(RMP article – subscription required)

Dynamical symmetries in the structure of nuclei

A good (but, unfortunately old) review on interacting boson model – The interacting boson model of nuclear structure

Geometry and Topology for Physicists Thursday, Oct 26 2006 

Previous post reminded me of one link I wanted to post earlier but somehow forgot:

Geometry and Topology for Physicists

I think these are quite a gem.
As the webpage says: “No particular mathematics background is required beyond that usually expected of graduate students in physics (linear algebra, complex analysis, etc), but it will help if you have some familiarity with mathematical notation and ways of thinking”.

Books by Sternberg Wednesday, Oct 25 2006 

Prereq. : Varies. But, I guess some amount of “math-maturity” and interest can take one far. 😉

Link : http://www.math.harvard.edu/~shlomo/

Some good mathematical books written by sternberg. The books available are

* Theory of Functions of real variable (2 Meg PDF)
* Advanced Calculus (58 Meg PDF)
* Dynamical systems (1 Meg PDF)
* Lie Algebras (900 K PDF)
* Geometric Asymptotics (AMS Books online)
* Semiriemannian Geometry (1 Meg PDF)

And over here, you can see a list with names of many math books.

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