## Friday, March 16, 2018

### Witten on Entanglement Properties of QFT - 2

(1) The ideas of entanglement and quantum information theory have invaded both quantum field theory and string theory and the developments are so extensive that even a long document of 70 pages is short to mention thes relevant issues.

So Witten refers us to the following review. This itself is 60 pages long.

[1] T. Nishioka, “Entanglement Entropy: Holography and Renormalization Group,” arXiv:1801.10352.

(2) The object in his notes is to collect the mathematical ideas that are relevant at a place and not to offer a review of the topic. The ideas are not easily available at a single place and hence we have to be thankful to him.

(3) He makes contact with older ideas of axiomatic and algebraic QFT. This is a topic that is obtuse because of its complexity as well as mathematical rigor. I was amongst those who used to think that we shall not need this kind of technology in future. Apparently I was wrong.

(4) Then we come to the Reech-Schlieder Theorem. It says that adjescent regions of QFT spacetime are entangled and the entanglement is ultraviolet divergent. This is true even without quantum gravity.

This is where the rub will lie. We though that entanglement is some quirk of black hole physics. We already have inconvenient things in QFT.

(5) The entanglement is not merely a property of the states but the algebras of observables itself.

(6) Witten's article aims at explaining these issues.

(7) Tomita-Takesaki Theory is a tool that helps us in those cases when entanglement is a property of the algebra of observables itself rather than the states.

(8) T3 is applicable in so many cases that Witten decides not to record all the references but describes an example in section 2.

(9) H. Araki's work too comes into focus in this regard.

(10) Then there is this talk about peeping behind the black hole horizon.

(11) Then we start seeing those typical terms that we see only in complex analysis - like monotonicity.

(12) That ends the preview of Section 2.

### Entanglement Properties of Quantum Field Theory

Entanglement is a fact of life.

You have milk, sugar and the juice of dried tea leaves entangles in your tea.

We are rarely interested in separating these entangled contents.

Indeed the process that would reverse the making of tea will not be that simple at all.

Clearly the same thing at quantum level will be even more tricky.

Advent of black holes, or rather their quantum mechanical studies, have brought the issue to the fore in a very dramatic and critical way.

People in condensed matter have been living with entanglement in the form of the density matrix for a long time.

Sometimes you do with less amount of information than can be gathered from the physical systems. That is density matrix for you. For many applications that is all that you need.

But then the question arises can we get more information? And how?

That is when we start worrying about quantum mechanics itself rather than its application in condensed matter physics.

Of course it is then natural to think that the more sophisticated form of quantum mechanics, the quantum field theory, will tell us more about these issues than the plain non-relativistic quantum mechanics.

Those who are in the game of quantum mechanics and quantum field theory also know that prodding quantum field theory for such matters will be different ball game altogether.

To compound the issue we need an approach to quantum field theory that is well known, or rather notorious, for its complexity - the axiomatic or constructive quantum field theory.

These are the issues that Edward Witten takes up in his latest posting on the arXiv on Pi day - March 14, 2018. It is called Notes on Some entanglement Properties of Quantum Field Theory. You need not rush to it immediately - it is 70 pages long.

It is preparatory and non-rigorous  document for the upcoming summer programme at the Institute of Advanced Studies at Princeton called Prospects in Theoretical Physics to be held in July 2018.

The original ideas are from different people like Borchers (163 pages),  Haag ( a book the Local Quantum Physics, 392 pages),  paper by Hollands and Sanders, called Entanglement Measures and Their Properties in Quantum Field Theory and finally another 161 pages long document by V.F.R. Jones called the van Neumann Algebras.

Witten's document has  seven Sections and an Appendix. After the Introduction the next Section is on the Reech-Schlieder Theorem. Witten is an excellent communicator, when he has the time to indulge in pedagogy, so even in case of daunting topics one can relax.

Section 3 is about Modular Operator and the Relative Entropy in Quantum field Theory. Section 4 is about Finite Dimensional Systems and Some Lessons.

Section 5 discusses a Fundamental Example while Section 6 is about Algebras with a Universal Divergence in the Entanglement Entropy.

The last section is about Factorized States and the Appendix about More Holomorphy.

## Wednesday, February 7, 2018

### Amid the hectic Indian conference season – the Hindustan Times Leadership Summit in December, the Raisina Dialogue in January, and now the Jaipur Literature Festival – it is worth asking ourselves a simple question. Are we witnessing the dawn or the demise of the public intellectual?

At one level, everyone with access to a smartphone and an active social media presence is a public intellectual today, or certainly acts like one. It has become easy to share one’s views with a large number of people on Facebook, Twitter, WhatsApp or any other social media platform.

Paradoxically, we also seem to be witnessing the global decline of public intellectualism, as politics becomes more rancorous, the media becomes more clickbait-driven, and academia retreats further into the ivory tower. Moreover, subject matter expertise has become more specialised and siloed, so that we are today less likely to have the archetypal man (or woman) of letters – a Bertrand Russell, John Maynard Keynes, Virginia Woolf, or Michel Foucault.

On Republic Day, I posed a question to friends on Facebook: Who are the five most important public intellectuals in India today? The inspiration was an article by Tufts University professor Daniel Drezner on his Washington Post blog, which was itself inspired by a tweet. Some of the responses I received were predictable. Former public servant and writer Gopalkrishna Gandhi and the historian Romila Thapar featured prominently. Economists such as Amartya Sen, Kaushik Basu, and Bibek Debroy, who are also fluid writers on a variety of subjects, made appearances. So did conservative writers and political figures like Arun Shourie and Swapan Dasgupta. There were some curious suggestions, including the widely-ridiculed if even more widely-read popular writer Chetan Bhagat.

Some absences were surprising. No one, for example, mentioned social theorist Ashis Nandy, who would perhaps have been foremost on people’s minds a couple of decades ago. I would also have expected influential figures such as economist Jean Drèze, environmentalist Sunita Narain, sociologist André Béteille, or Yogendra Yadav, Madhu Kishwar, or Mukul Kesavan to have made the cut for some people.

An assessment of an intellectual’s importance should not be conflated with concurrence or correspondence with one’s personal beliefs. Nor should it simply be correlated to influence or public profile. In this context, I would primarily equate importance with irreplaceability. Whose voices would be felt most by their absence? Obviously, there will be considerable disagreement even on this criterion, but these would be my humble suggestions:
1. Ramachandra Guha: Guha has written eloquently on history, politics, environmentalism, and cricket. No other writer is read as much by aspirants to the Indian civil services examination. Despite its many shortcomings, India After Gandhi still remains the go-to introduction to contemporary India. Until someone else can produce as broad and accessible a body of work, Guha would have to feature on any such list.
2. Pratap Bhanu Mehta: An institution-builder both at the Centre for Policy Research and now at Ashoka University, Mehta has become a household name from his regular newspaper columns. There is no aspect of public policy that has not been covered in his pieces in The Indian Express, and he has driven important work on public institutions. One may disagree with him on many accounts (and many on both the Right and Left certainly do), but few people today drive and shape the discourse on public affairs as much as he does.
3. Shashi Tharoor: If anyone puts the public in public intellectual in India, it is perhaps Tharoor, who writes faster than most of us read. Despite a political perch in the Lok Sabha, he finds time to pen a critique of the British Empire and a commentary on Hinduism, all while remaining a ubiquitous presence in the media, on the conference circuit, and at literary festivals. He is also an active presence on social media and commands some respect across the political aisle. His voice – and vocabulary – remain unique in India’s public sphere.
4. Ashok Malik: My inclusion in this list of Malik – who was appointed press secretary to the president of India in August – might appear the most surprising, but his is the most demonstrable case of importance by (temporary) absence. A journalist and columnist, Malik has written thoughtfully and critically on everything from the business of airlines and television, foreign policy and trade, and regionalism and high politics. Guha, Mehta and Tharoor often defy precise ideological pigeon-holing, but none could be said to be consistently conservative or Right-of-centre. The paucity of prominent Right-wing intellectuals despite having a notionally Right-wing government in power for the past four years in my mind necessitates Malik’s inclusion in such a list. He provides a lucid window into elements of politics, economics, and policy that most Indian intellectuals have long overlooked – and, unfortunately, continue to overlook.
5. Raghuram Rajan: At least one of the five should be an economist, and India has in fact produced its fair share of eminent economists (Jagdish Bhagwati, Arvind Panagariya, and Arvind Subramanian come to mind, in addition to Sen and Basu). A few years ago, Sen would have been the obvious candidate, as India’s only Nobel laureate in economics and writer of The Argumentative Indian, among other less scholarly and more popular works. However, Sen’s legacy has been tarnished somewhat of late, and based on his star power and outspokenness on a variety of issues, Rajan should probably take precedence in such a list today.

### Lack of diversity

A significant problem many might have with my list is that all five are elite-educated (Doon School, Oxford, St Stephens, La Martinière, and the Indian Institute of Technology) middle-aged males. Three of the five are based in New Delhi, none belong to religious minorities, and all write primarily in English. At least three of the five are ardent cricket fans. This lack of diversity is a fair criticism.

While such potential criticism does not alter my submissions, it is only fair to highlight some of the emerging voices contributing in various ways to India’s intellectual discourse. Such a list can never do complete justice to every sector and viewpoint, but people like the prolific political theorist Madhav Khosla, the founder of the Takshashila Institution Nitin Pai, or the former banker and non-fiction writer Sanjeev Sanyal (currently principal economic advisor to the Finance Ministry) come immediately to mind.

There are also a very large number of women now shaping intellectual trends and undercurrents, among them writer and Financial Times columnist Nilanjana Roy, economist Gita Gopinath (currently an advisor to the chief minister of Kerala), president of the Centre for Policy Research Yamini Aiyar, lawyer Menaka Guruswamy, journalist and author Snigdha Poonam, and the economist (and my Brookings India colleague) Shamika Ravi.

We also have the phenomenon of non-Indians who comment intelligently and perceptively on several aspects of Indian public life, such as British biographer and historian Patrick French, Nepal-born political journalist Prashant Jha, and Washington-based Indian-American political analyst Milan Vaishnav. I am sure many others would come to mind upon further reflection.

Some of these names might make it to a list of most important public intellectuals in India in some years’ time. But even a superficial list of such emerging talent shows that while younger voices and women might soon feature more prominently in Indian public discourse, minorities, multilingual writers, and serious Right-of-centre thinkers remain under-represented. This remains something to remedy.

Dhruva Jaishankar is Fellow in Foreign Policy Studies at Brookings India.

### No Islamophobia There

(A Facebook friend posted a status with which this post begins. The comments too are appended. In fact at the moment the full post is not pasted below but the missing part is small.. I shall comment on the episode later on.)

Muslims really need to come out of their Islamophobiaphobia! Most otherwise seemingly secular folks will suddenly pull out their scimitars at the mention of criminality among ayatollahs. Suddenly all of Islam is under threat of destruction. The brain shuts down. No one will read links to information. Clues that show respectability of information sources, like back links, will be rejected. In effect, every evidence that shows anything negative about Islam, will be rejected out... See More

171 Parijat Misra, Jahanzeb Mashhadi and 169 others

Zohra Javed : We are all enclosed in our squares ... Kisi ke liye Modi kisi ke liye Khomeini kisi aur ke liye Zakir Naik ... And many many more ... So then stay enclosed ... And quiet too ... Don't shout against Modi and co if you cannot hear against The Khomeinis and The Saddams of the world !!!
Rulers are Rulers and they are all the same ... If a religious leader can influence political atmosphere in a country he is no religious leader

Pearly Gill : Zohra Javed....you shine like star on this thread💕

Zohra Javed : Bahot shukriya Pearly Gill ji and Shamim Kunju ji

I am grateful to my mentors ... Virtual though ... Dr Asghar Ali Engineer , Dev Saheb , Dr Badri Raina , Sahir Ludhianvi , The Dalai Lama ... Their writings have showed me the way forward

Makhan Singh : have u ever read the Quran, cover to cover? ya bas awein?

Rajiv Tyagi : Cover bhi koi padhne ki cheez hai kya? Phir bhi padhi. :)

Makhan Singh : sirf cover hi padh k chhor diya. it reflects in ur posts. 😊

Rajiv Tyagi : Cover ke baad baaki jahalat bhi ho sakta hai na? :)

Makhan Singh : wo to padhne k baad hi pata chalega. how can u decide without even reading?

i thot u r a rational person, but u hav disappointed me.

Rajiv Tyagi : No rational person engaged with religion... :)

Mohamed Ameenullah : Knowing or learning is not engaging.
deliberately wants to wipe out religions having no clue of what actually it is,this is no lesser than prejudiced religious people.
Disappointing to see the people whom i've believed to be secular turning into sanghis.

Makhan Singh : rational persons do not believe on hearsay. they put in some effort to find out the truth themselves.

wid each reply u r proving to be an ignorant sheep, simply following the herd, not a rational person. sorry to say tht.

Makhan Singh : u can read Quran to point out its mistakes n errors but u wont do it. coz u r afraid tht ur preconceived ideas abt Islam n Quran might get shattered.

Preet K S Bedi : Et tu, Brutus? What compelled u to see logic?

Rajiv Tyagi : I don't need to strive and strain to do that, Preet... :)

Yusuf Siddiqui : And you got the opportunity;Et tu ,Mr bedi?

Preet K S Bedi : Der aaye durust aaye. Islamophobia is an interesting catch-all condition. Let's see how long the infection lasts.

Preet K S Bedi : I don't need to make an effort. The world's fastest growing community (sic!) revels in victimhood 24x7. Gives me enough and more opportunities to tear into its humbug.

Umer Khan : U reminds me the late Indira Gandhi ji .Preet K S Bedi

Preet K S Bedi : That is bad news for me. Luckily I care a rats unwashed posterior about your certification so it's OK.

Yusuf Siddiqui : Preet K S Bedi If i may,your criticism to only one form of extremist looks fake when one wears religious extremism on his head to cheek to toe. Try Gillette 3 shaver,it works wonder,try different hairstyle,it's normal. Wish,you ain't in a rat race to wipe out other extremism to protect yours..get over wounded psyche of dhimmitude...it ain't real.

Yusuf Siddiqui : Sudarshan Udyavar I pity your miniscule intellect,ofcourse,wearing religious symbols including scull cap,tilak,choti,turban etc are meant to flaunt your faith and not fashion. Unless,it doesn't harm me or question others,it's fair but to question other one has to remove his. Simple.

Preet K S Bedi : Hahaha jaane do. When irrespective of gender u r castrated at a young age u can only think of Gillette blades! Btw Mohammed whose preaching Muslims garbaged literally the day he died, wore a headdress much like the turban. So did Abu Bakr Umar Othman and Ali. But it's OK they were Muslims. Unlike today's castrated cattle which carries Islamic names but garbages it's own.

Yusuf Siddiqui : A bit correction,not castrated but circumcised and that's custom not religion. I understand People who dwelled in Sand ,weared turban to protect themselves from Sun heat but i fail to see your reason/s ,sitting in AC rooms,driving in cool cars?

Preet K S Bedi : No no castrated. That's why the world's fastest growing community lacks the balls to even talk reform. And the three people who do all have fatwas against their name while thousands are raped and killed in the name of Allah and castrates remain silent. Castrated community. Both C's in caps.

Yusuf Siddiqui : Preet K S Bedi If my advice matters,i have suggestion,try Circumcision,you still have life..bet you won't repent.
I am all open for reforms but your start is quite poor..too rhetoric and i see your turban justification purely whataboutery. Any rational,i would hear,else we often hit each other.

Preet K S Bedi : Yes but the mullahs cut your balls. Pity u never even figured!

Yusuf Siddiqui : Ha Ha! I wonder ,why your intellectual arguments end with BALLS? It's cold storage for semens without which one can't breed . Hope,we aren't in a fight 'my balls are stronger than yours' you sounding funny!
1
Preet K S Bedi : Knowing the biology does not mean u have the balls.

Preet K S Bedi : As for breeding which is possibility only achievement the community has, if I were u I would check with the women.

Yusuf Siddiqui : My ball-logy instinct suggests,it's time to bid adieu,you have no further rational arguments left.
Wish to see you clean shaven and parted hair or jelled one..when we hit next time. 😊

Preet K S Bedi : May be the burqa and other instruments of misogyny including FGM r not as effective as u think

Yusuf Siddiqui : We can touch other subjects ,may be on some other day. You being too impatient,need solution in a single pckage...Ciao ! Ciao!

Preet K S Bedi : Really? The mass murderer Khomeini returned in 1979. 9×11 happened in 2001. Thousands have been kidnapped raped and killed since then both in internecine wars between shias and Sunnis since then. And continue to be killed. What had begun with Muslim Brotherhood has spawned into mujahidin, hizbul, al qaeda, boko, al shabaab, LeT, ISIS, Hamas, Hezbollah and dozens of others, each of which have killed and continue to kill by the day. And the world is expected to wait while the ghantadhari moderate Muslim acquires some balls and demand reform? Lolol. That it doesn't embarrass u is a miracle by itself. But so is the community of castrates.

Preeti Khaneja Kalra : Preet K S Bedi sharp & on fleek!

Danish Haroon : Rajiv tyagi, please teach your own community first that there is shambhu lal, karni sena, rss, bajrang dal,hindu yuva vahini, shiv sena, what the hell is this. You really don't know about islam, you just a google fact man run by zoinist ass holes. Nxt tym read quran in our mother tongue "hindi". Of you don't have inbox me, i will send you.

Omer Ghazi : Kaise kaise chutiya log hain...

Danish Haroon : Omer Ghazi, please indinetify chutiya is it me or admin. Lol

Faisal Saeed :  He is just another sanghi in garb of atheist

Sumeet Dutt Rishi : Funny! How quickly he became a sanghi and yet I never see a squeak when he tirades against sanghi’s!! I guess this liberal islamophobia is a real thing.

Adam A Khan :  He’s a sanghi atheist lol 😂

Faisal Saeed :  Funny how hidden sanghis when exposed react....

Iqbal Ahmad : the Qur'an talks about compassion, kindness and mercy, but most of the Muslims just talk about jihad, there's nothing better and advisable than mercy and compassion, but thanks to the mulla when we talk about Muslim there is always jihad somewhere in our mind

Satyajit Dash : Proud of you

Mohinder Bir Pal Singh : Such people are better known as manipulators! They are omnipresent in all religions! It's the blind faith in sermons that drive the followers haywire! Very well described Iqbal Ahmad sir!

Iqbal Ahmad : i assure you it's the mostly uneducated between who the hardline clergy have some influence, because the poor and uneducated can not research and find out what should be ideally followed, it's the same in neighboring nations of Pakistan and Bangladesh, where the middle and upper middle are largely secular and open minded, progressive

Arun P Mathew : Yes. A mdieval belief system will have aspects which are incompatible to modern life. If anyone says they cannot be criticised, that may not be agreeable to the rest. And yes,i have read the Quran and Hadiths to know this!

Yusuf Siddiqui : Ha Ha! Seen you being stung by Iran fans,same bunch of crusaders who often claim Iran as a peaceful and Sacred Nation It was quite humourous to see them defending Khomeni's extremism who killed lakhs of gullible followers.

Abhishek Singh:  Muslim bros, many of need to adopt a rational and secular outlook. u need to understand there is nothing absolute and everything keeps on changing with time except for truth, justice etc

Zohra Javed : Love the concluding sentence ... So true really ... :-D

Nadir Aslam : Rajiv Tyagi I remember reading this a few or many years back.But don't really know whose thinking it was or whose order it was.Whether it actually happened or it was only a rumor.My God is not going to send someone to heaven only because she was a virgin :) A virgin can go to hell for wrongs committed while even a non virgin can go to heaven if she was good.

Ashok Soni : Every Religion is a Political Party!

Sandeep Das : I'm much younger to you, Tyagi Sir, currently
we should not deviate from the Dushman.. Your point is right.. but I think we could debate it later..

Shariq MB : Right, Sandeep. And the Dushman is Communalism, prejudice, and hatred, which groups and certain individuals practice. Sadly, even well-meaning folks can fall into that trap and fan prejudice inadvertently because they failed to be judicious and believe everything as the Gospel of Truth. ;) 😂

Nishith Gupta : Dushman....hahaha...what a idiotic comment

Mobin Khaja : Agree

Shafi Patel : A belief system is different from many of its adherents,marketeers and exploiters. Atheism and agnosticism are no different in this respect.

Rajiv Joshi : If one is not sure about truth in their faith, then they are angry.If the faith petmits one to reason and discard what can not be justified and evolve then one is not scared of opposite views.

Manvendra Bhangui:  Just mugging your favourite 'Fairy Tale' by heart doesn't make one a scholar. None of these Ayatollahs were scholars and especially someone who orders assassination of a real scholar like Salman Rushdie.

Ashok R. Mundhada : Or actually murders Gauri Lankesh for that matter.

Kalyani Iyengar : You are no chicken definitely, forget a hen😜😜

Tushqa Manish Chawdhry : Bicharay religious people.. They are nothing but bahut buri tarah daray hue log. Arre bhai yeh he narak hae, marnay kae baad he narak sae chutkara milay ga 🤣

Shahid Anwar : Scratch a non believer and he will show his communal fangs.

Abhishek Tyagi : So long as people see you as a 'born' Hindu commenting on the Right wing Sanghis and Hinduism in general, you are a balanced secular, liberal person. The moment you comment on any other religion, people demand that you read their scriptures better to p...See More

Sankara Pillai : What a bhaktha you are!

Md Zishan Ahmed Kaif : Don't know why people are ashamed... Of things they do... The Quran talks about compassion, mercy kindness, humanity, but at the same time it ask to take action against unlawful activities... No need to come with interpretation that suits ur kind

Sachin Parashar : Dissolve all Religions and keep the Constitution OR keep One Religion and dissolve the Constitution. They can never go parallel.

Makhan Singh : Rajiv Tyagi ji it's time for u to take a sabbatical from FB. u seem to b fatigued. tht's why making absurd arguments.
To critique an omlette one definitely doesnt need to become a hen but only needs to eat the omlette. else, he/she doesn't hav any right to critique it.

Ashik Parvez Ahmed : Don’t judge a book by its cover. An intelligent person should read the Quran without any bias or prejudice.

Rafiq Lasne : Rajiv Tyagi sir... superbly said. (Y)

Khushnood Nizami : Is it a crime to be religious

Syed Aasim : देखना है, बहुत लंबा पोस्ट है

Mohd Arslan : I wonder why you have big constitutional book?? Instruction manuals?? And i am sure most of you don’t even read terms and conditions of most things and yet they are there. GET A LIFE!! And update your android!!😂😂

Preeti Khaneja Kalra : Kudos to you for saying that Rajiv tyagi! hope u understand how needful it is for our society that liberals like u with such an expansive following, come forth & raise such points!,,Not surprised by the resistance of your Muslim friends who are taking it in a sour note though!

Pearly Gill:  .......so funny ....every time you put up a post on Islam....all your wonderful,cheery followers/friends go for your jugular.
The double standards of these people is mind blowing.

Versailles Thomas : True! call out the assholes who are fucking it up instead of just isolating yourself from it and saying that's not us..The perpetrator is doing it with his clarity of the faith that he's following...

Faisal Saeed : He is just another sanghi in garb of an atheist

Sachin S : And CIA and zionists are behind this , right ? 😂😂

### T Jayaraman on CPI(M) Keeping a Distance from Congress

The roots of the rise of Hindutva lie in substantial measure in the nature of Congress rule and in particular the UPA governments of 2004 to 2014.
Many commentators, in the mainstream and on social media, have been urging the Left to align with the Congress in preparation for the parliamentary elections due next year. Several of them, who have been harping on the theme for some months now, turned harshly critical when the Communist Party of India (Marxist) recently announced that it was against electoral tie-ups in any form with the Congress.

A substantial part of such commentary emerges from sections who believe that the defeat of the Bharatiya Janata Party in 2019 is of such overriding importance that all other political considerations should be put aside. Alongside this view, such commentators also present increasingly extreme characterisations of the BJP, with any attempt to inject some sobriety or realism into such assessments being met with the charge of downplaying the danger that Hindutva represents..
Any strategy to deal with Hindutva must obviously begin from the acknowledgement of the basic point that the CPI(M) has always made – that the roots of its rise to the current state lie in substantial measure in the nature of Congress rule and in particular the UPA governments of 2004 to 2014. It was the determined pursuit of neoliberal policies by the Congress (and state governments of the non-Left variety) that had alienated the people, with little improvement in their general well-being on a mass scale – a failure that Hindutva seized, promising development.

Further, given the hold that Hindutva has obtained on Indian society as a whole, across various spheres of national life, mere electoral defeat is hardly the key to halting its advance. Without mass mobilisation on issues that affect the people and without winning a substantial section of the people away from Hindutva ideology, through mass movements for secular and democratic advance, banking on electoral arithmetic alone is likely to be of little use and indeed diversionary. Such mobilisation cannot have unity with the Congress party as its basis, when the alienation of the people at large from it has formed part of the very basis of the rise of Hindutva.

Events of the last two years lend substantial weight to this understanding – one has only to recall the collapse of the Nitish Kumar-led mahagatbandhan experiment that was much touted at the time of its victory (and the Left excoriated for its non-participation in this alliance) and the failure of the Akhilesh Yadav-Rahul Gandhi led combine in the Uttar Pradesh elections, returning the BJP to power in a virulent avatar in a state where it had not succeeded for almost 15 years. In retrospect, it is clear that even the defeat that Hindutva forces suffered in the 2004 elections was merely a temporary setback, from which they emerged to victory, considerably strengthened, in 2014, led by none other than Narendra Modi, the figure who represented the nadir of the earlier spell of Hindutva rule.,

On the other hand, from the large-scale mobilisations of farmers in the agitations of Maharashtra, Rajasthan and Madhya Pradesh and the workers’ rally in Delhi, to the prompt condemnation by incensed scientists against the obscurantist remarks of the minister of state for education on teaching evolution, from the mobilisation at Una to the protests at Bhima Koregaon and their aftermath, and the long-drawn student agitations in a number of leading universities – all of these speak to the scope for mobilisation against Hindutva. To convert the energies and advances of such movements into lasting political capital is undoubtedly the challenge.
But why does the enthusiasm for Left-Congress unity override this logic even among some on the Left and in sections otherwise well-disposed to the CPI(M)? Ever since independence, it has been a persistent illusion among a section of progressive opinion that the Congress is in fact a viable vehicle for the project of secular and democratic nation-building. Since the Congress has been the dominant political formation for the better part of post-independence India, even after the communal danger became significant, it is tempting to attribute all forward movement in any sphere of national life to the leadership of the Congress.
Unfortunately what this one-sided view misses is the responsibility of the Congress for all that has not been achieved, and that the Congress had presided over the pursuit of a path of development that had fundamental contradictions, leading to the all-round crisis that began enveloping the Indian state at the beginning of the 1990s.

Even after the sharp, rightward shift in economic policy, the illusion has persisted that if not the Congress, other parliamentary coalitions could be the vehicle for a radical movement forward, with the Congress, even if reluctantly, being somehow forced to join. This has been further sustained by the fact that the two responses of the Indian state to the crises of the 1990s, economic reform on the one hand and the push to abandon the secular ideal on the other, have been led by two different parties, the Congress and the BJP respectively.
In reality, this has not stopped the latter from embracing economic reform when in power (however critical they may have been in opposition) and the former from discreetly avoiding head-on engagement with the anti-secular agenda. Both of course have come together in lining up to become a camp follower of the US in foreign policy.

Unfortunately though, if in an earlier era a section of progressive opinion was seduced by the slogan of Congress socialism, it is now seduced by the slogan of Congress secularism, ignoring the reality that it is the whole gamut of Congress policies that have paved the way for the rise of Hindutva. The dithering and inaction of the P.V. Narasimha Rao government on the eve of the Babri Masjid demolition and the UPA’s refusal in 2004 to heed Harkishen Singh Surjeet’s (then CPI(M) general secretary) call to “detoxify” the government of RSS influence are two outstanding examples of the compromising stance of the Congress on secularism.

The record of the CPI(M) shows that it chose, since its formation, a completely different course. In an earlier era, in the 1960s and 70s, it stood out in its refusal to tail the Congress, holding it responsible, as the key representative of India’s ruling elite, for the condition of the masses. It led a rising wave of resistance and opposition to Congress rule across the country wherever its strength allowed, leveraging in some areas the effect of other currents of opposition, even while being critical of their shortcomings.

Within ten years, with the Emergency, the correctness of its assessment was amply demonstrated. The party emerging in the post-Emergency era with substantial gains in its strength and mass following, in striking contrast to the diminution of the strength of the Communist Party of India. In the subsequent years, one of the testing periods was that of the V.P. Singh-led National Front government, to which the CPI(M) provided outside support, with the BJP providing another supportive crutch to him.

Critics of the party’s current position would do well to go back to its public, and frankly self-critical, analysis of its political tactics over the last 25 years adopted at its Visakhapatnam congress. This analysis highlighted the fact that the pursuit of electoral alliances, however fruitful in the short term, had led to distraction from the key issue of building the independent strength of the Left and democratic movement, without whose significant presence no stable political shift away from Hindutva could be consolidated.

The CPI(M)’s latest decision has followed this understanding, even if, as is well known, there have been strains earlier in implementing this line in the Bengal assembly elections. Critics would do well to give credit to the fact that the CPI(M)’s view arises from a well-argued and well-debated understanding, with an objective view of ground realities and not falling for illusions of grandeur. It certainly is not the product of mere inner-party factionalism or the product of seeking some opportunistic, short-term gains as innuendos in the media have made out.

There can be no short-cut to fighting Hindutva. We are in for the long-haul and it will be a grim fight indeed. But panic-stricken and hasty assessments and the search for quickfire solutions through hasty electoral alliances have not worked for the last 25 years. They are unlikely to do so in the future too.

T. Jayaraman teaches and undertakes research in climate change, sustainable development and science policy at TISS.. The views expressed here are personal.

Source : The Wire

## Wednesday, January 31, 2018

### Riemann-Roch Theorem Redux

Riemann-Roch theorem is a mathematical assertion. It occurs in different branches suited to the occasion. Originally it is in complex analysis. There is a version for the surfaces. The version for algebraic varieties was given by Hirzebruch. The algebraic geometry version was given by Grothendiek. The version for higher genus is by Faltings. The investigations in Algebraic topology are associated with the names of Atiyah, Singer and Patodi. In Physics investigations by Edward Witten have very fundamental implications.

In this note we would like to demystify some of the aura associated with this fundamental and deep result in a plain language to the extent possible with our capabilities. We shall take up the topic from the point of view of the above mentioned different contexts and go through them.

(Developing article)

# Amy Morin

For more than a decade in my work as a psychotherapist, I helped clients identify their existing talents, skills and support systems. Then we’d figure out how to address their struggles by expanding on their existing strengths. For much of my career, I felt like this positive plan of attack was an effective way to help people overcome adversity.

But when I experienced tragedy firsthand, I began to rethink this optimistic method. In 2003 my mother died unexpectedly. Then two days before the third anniversary of her death, my 26-year-old husband suffered a fatal heart attack. Seven years later, I lost my father-in-law.
Throughout my grief, I realized that focusing on my strengths—and ignoring my weaknesses—had serious limitations. If I wanted to emerge from that painful period stronger than before, I needed to pay close attention to the bad habits that held me back. Letting myself feel like a victim, complaining about my circumstances and distracting myself from the pain might help me feel better in the short term but would only cause more problems over the long term.
My hardships taught me that it only takes one or two bad habits—no matter how minor they might seem—to stall progress.
Reaching your greatest potential doesn’t require you to work harder by adding desirable habits to your already busy life. Instead you can work smarter by eliminating the routines that erode effectiveness and siphon off mental strength. Here are the 13 things mentally strong people don’t do:

## 1. Waste time feeling sorry for themselves.

It’s futile to wallow in your problems, exaggerate your misfortune and keep score of how many hardships you’ve endured. Whether you’re struggling to pay your bills or experiencing a serious health problem, throwing a pity party only makes things worse. Self-pity keeps you focused on the problem and prevents you from developing a solution.
Hardship and sorrow are inevitable, but feeling sorry for yourself is a choice. Even when you can’t solve the problem, you can choose to control your attitude. Find three things to be grateful for every day to keep self-pity at bay.

## 2. Give away their power.

You can’t feel like a victim and be mentally strong; that’s impossible. If your thoughts send you into victim mode—My sister-in-law drives me crazy or My boss makes me feel bad about myself—you give others power over you. No one has power over the way you think, feel or behave.
Changing your daily vocabulary is one way to recognize that the choices you make are yours. Rather than saying, “I have to work late today,” edit that sentiment to “I’m choosing to stay late.” There may be consequences if you don’t work late, but it’s still a choice. Empowering yourself is an essential component to creating the kind of life you want.

## 3. Shy away from change.

If you worry that change will make things worse, you’ll stay stuck in your old ways. The world is changing, and your success depends on your ability to adapt. The more you practice tolerating distress from various sources—perhaps taking a new job or leaving an unhealthy relationship—the more confident you’ll become in your ability to adapt and create positive change in yourself.

## 4. Squander energy on things they can’t control.

Complaining, worrying and wishful thinking don’t solve problems; they only waste your energy. But if you invest that same energy in the things you can control, you’ll be much better prepared for whatever life throws your way.
Pay attention to the times when you’re tempted to worry about things you can’t control—such as the choices other people make or how your competitor behaves—and devote that energy to something more productive, such as finishing a project at work or home or helping a friend with hers. Accept situations that are beyond your control and focus on influencing, rather than controlling, people around you.

## 5. Worry about pleasing everyone.

Whether you’re nervous that your father-in-law will criticize your latest endeavor or you attend an event you’d rather skip to avoid a guilt trip from your mother, trying to make other people happy drains your mental strength and causes you to lose sight of your goals.
Making choices that disappoint or upset others takes courage, but living an authentic life requires you to act according to your values. Write down your top five values and focus your energy on staying true to them, even when your choices aren’t met with favor.

## 6. Fear taking risks.

If something seems scary, you might not take the risk, even a small one. On the contrary, if you’re excited about a new opportunity, you may overlook a giant risk and forge ahead. Emotions cloud your judgment and interfere with your ability to accurately calculate risk. You can’t become extraordinary without taking chances, but a successful outcome depends on your ability to take the right risks. Acknowledge how you’re feeling about a certain risk and recognize how your emotions influence your thoughts. Create a list of the pros and cons of taking the risk to help you make a decision based on a balance of emotion and logic.

## 7. Dwell on the past.

While learning from the past helps you build mental strength, ruminating is harmful. Constantly questioning your past choices or romanticizing about the good ol’ days keeps you from both enjoying the present and making the future as good as it can be.
Make peace with the past. Sometimes doing so will involve forgiving someone who hurt you, and other times, moving forward means letting go of regret. Rather than reliving your past, work through the painful emotions that keep you stuck.

## 8. Repeat their mistakes.

Whether you felt embarrassed when you gave the wrong answer in class or you were scolded for messing up, you may have learned from a young age that mistakes are bad. So you may hide or excuse your mistakes to bury the shame associated with them, and doing so will prevent you from learning from them.
Whether you gained back the weight that you worked hard to lose or you forgot an important deadline, view each misstep as an opportunity for growth. Set aside your pride and humbly evaluate why you goofed up. Use that knowledge to move forward better than before.

## 9. Resent other people’s successes.

Watching a co-worker receive a promotion, hearing a friend talk about her latest achievement or seeing a family member buy a car you can’t afford can stir up feelings of envy. But jealousy shifts the focus from your efforts and interferes with your ability to reach your goals.
Write down your definition of success. When you’re secure in that definition, you’ll stop resenting others for attaining their goals, and you’ll stay committed to reaching yours. Recognize that when other people reach their goals, their accomplishments don’t minimize your achievements.

## 10. Give up after their first failure.

Some people avoid failure at all costs because it unravels their sense of self-worth. Not trying at all or giving up after your first attempt will prevent you from reaching your potential. Almost every story about a wildly successful person starts with tales of repeated failure (consider Thomas Edison’s thousands of failures before he invented a viable lightbulb, for instance).
Face your fear of defeat head-on by stretching yourself to your limits. Even when you feel embarrassed, rejected or ashamed, hold your head high and refuse to let lack of success define you as a person. Focus on improving your skills and be willing to try again after you fail.

## 11. Fear “alone time.”

Solitude can sometimes feel unproductive; for some people, the thought of being alone with their thoughts is downright scary. Most people avoid silence by filling their days with a flurry of activity and background noise.
Alone time, however, is an essential component to building mental strength. Carve out at least 10 minutes each day to gather your thoughts without the distractions of the world. Use the time to reflect on your progress and create goals for the future.

## 12. Feel the world owes them something.

We like to think that if we put in enough hard work or tough it out through bad times, then we deserve success. But waiting for the world to give you what you think you’re owed isn’t a productive life strategy.
Take notice of times when you feel as though you deserve something better. Intentionally focus on all that you have to give rather than what you think you deserve. Regardless of whether you think you’ve been dealt a fair hand in life, you have gifts to share with others.

## 13. Expect immediate results.

Self-growth develops slowly. Whether you’re trying to shed your procrastination tendencies or improve your marriage, expecting instant results will lead to disappointment. Think of your efforts as a marathon, not a sprint. View bumps in the road as minor setbacks rather than as total roadblocks.
You’ll need all the mental strength you can muster at some point in your life, whether it’s the loss of a loved one, a financial hardship or a major health problem. Mental strength will give you the resilience to push through the challenges.
And the great news is that everyone can strengthen his or her mental muscle. Practice being your own mental strength coach. Pay attention to areas in which you’re doing well and figure out where you need improvement. Create opportunities for growth and then challenge yourself to become a little better today than you were yesterday.

Source : Success

## Thursday, December 14, 2017

### Engineer Saleem Pirzada Passed Away - 2

Personally I was in a state of hiatus with him. My attitude has been to understand the causes behind the present state of Muslims in India while he was a man of action who was fast running out of time.

I used to sit in the party office for long hours and there used to be a series of visitors with a broad band of age spectrum. Young university boys saw a mentor in him while senior people saw in him an old comrade of those glorious gone by years when they were out there to change the history or recreate it.

To remain close to the unpleasant reality let us record that the youth was not crowding around him and the old company even in its prime did not perform mind bending fete. Saleem Pirzada will go into the footnote of history unsung for destiny decided that he will be the brick that disappears into the foundation of an edifice that gathers only lack of acknowledgement and no share in the grandeur. He is like the supplication that is so delicate that the angels hide it most carefully in their wings so as to protect it from all worldly fame, fortune and glory.

Indeed he would not get credit even to the level that came to the stalwarts of Babri Masjid protection movement - another lost cause from recent Muslim history in India. When I was exploring the life and events of Dr Zakir Hussain a senior friend remarked that it was not substantial. There lies the tragedy of significant Muslim figures of independent India. Saleem Pirzada is destined to get less share in achievements.

This brings us to the question then - what makes some of us so sentimental and emotional about him. He was not a family man - marriage he sacrificed for the sake of his mission. He certainly was a man of friends but this aspect never overwhelmed his vision or made any significant encroachment on his ideals. Mentor he was but only to those who came along and the fact remains that very few did so. Busy he kept himself throughout his life but every single possible outcome that could go into making a glorious bio-data went into the black hole called Muslim Politics of Independent India.

He was a Pathan of Khanqah, Muslim Monastery, lineage but the family has not visible inclination to that angle. Having lost his father at the tender age of six he was brought up by his mother and strangely had a father figure attitude towards so many of his juniors. He was very proud of several martyrs for freedom from his locality.

Arriving in Aligarh he soon got the hand of students politics that is what became the high point of his life and career. The story picks up in late sixties and through seventies of twentieth century. This was global high of students movements in the world. Even in the US they have not understood the phenomenon till today. Main cause might be the Marxist influence and global ideological awakening but ideologically he was placed against it - his ideology was Sir Syed, from beginning till end.

Just like their socialist, communist, Marxist counter parts Lovey and company too honed their political analysis on the road side tea stalls around the AMU campus. In independent India the academic political discourse has been usurped by the leftist intelligentsia rather completely but looking at the documentary evidence in terms of books and recorded speeches and published articles one comes to unmistakable conclusion that these people not only had a Muslim narrative but their oratorical prowess was even better and far superior to that of the left and indeed the demagoguery of AB Vajpayee. Javed Habib, Lovey Pirzada, Ali Amir, Ariful Islam and many more could be counted in this genre.

As mentioned above this spark of intellectual revival of Islam or political underpinnings of Muslims has not reached yet its maturity. The main subterfuge happened due to partition. Sir Syed and his close friends were worried about the fate of Muslims in independent India. The question that exercised the minds of these old men was whether Muslims will end up being like second class citizen and subjugated minority. They worked to obviate such an eventuality.

Mahatma Gandhi and Jawaharlal Nehru were of the opinion that the majority community in her magnanimity would take good care of the interests of all the minorities including the Muslims.

Muslim leaders like Maulana Azad and the Muslims belonging to Jamiat-e-Ulema-e-Hind (Muslim Religious Scholars Assembly) bought this theory and assurance. This view came to be known as the one nation theory.

The other point of view was the so called two nation theory and it was pursued by the Muslim League in pre-independence India. They pursued the course where they wanted constitutional guarantee that minorities, Muslims in particular, will not end up in a position of subjugation. Just before independence such a mechanism was indeed worked out by the British - the people who were still in charge of the situation.

This cabinet Mission Plan was the one that was inexplicably torpedoed by Pandit Nehru. The immediate consequence was that the leader of Muslim league MA Jinnah flew off the handle and abandoned the path of reconciliation with Congress. They also abandoned Dr Muhammed Iqbal's idea of autonomous administration of Muslim majority areas in North-East part of India. In the 1940  Lahore session of Muslim League a one paragraph proposal for Pakistan was moved in and passed. Seven years later India was partitioned and the bill of partition came to the Muslims of India.

British in their hurry to leave India failed in a department that was supposed to be their strongest forte - administration. Lord Mountbatten, the then Viceroy, forgot to post even a policeman on the now India-Pakistan border during the population transfer. Muslim-Sikh riots ensued and countless innocent lives perished.

The League was a very strong force amongst Muslims but by no means the only voice. People like Maulana Azad and Hussain Ahmed Madani and a long list of many others were very much pro-India and against the partition but even in secular sections shadow of partition has clouded the sky for Muslims. Organizations like RSS always held the view that once Pakistan came into existence what are Muslims doing in India but today the circle of people possessing such views has become much wider.

This is the legacy with which people like Lovey Pirzada had to operate. Democracy has this inherent instability that it might turn into majoritarianism and that is what has happened in India today. Saleem Pirzada was amongst those brave souls who who chose to work in opposition to this tide knowing fully well that this was an uphill task to say the least. Even naive political opinion holders consider it silly to take the stand that Lovey took.

He took the side of truth and justice in a situation where it was not only politically unwise but plain dangerous as the events of last three years have made amply clear. On December 10, 2017 he posted a status on Facebook where it starkly says that the count of Muslim skilled in last three and half years has been already 39 and be prepared to keep counting. This was perhaps minutes before his massive cardiac attack and hours before his demise.

When you work against such monumental odds the the fair deal would be that your small achievements should be counted as big. What were these achievements? Let us get to these in the next part.

## Wednesday, December 13, 2017

### Engineer Saleem Pirzada Passed Away

Lovey Bhai, engineer Saleem Pirzada, National President of Parcham Party of India expired in the night between December 12 and 13, 2017 in Apollo Hospital, Delhi. He was referred to that place from our own Hospital of the JN Medical College at AMU via Sir Ganga Ram Hospital following a massive heart attack that left him in a state of paralysis.

But these are dry and mundane details about the sad demise of a political personality of the level of a statesman. Urdu speakers use very expressive words and couplets for departed people and since not all of the departed souls deserve such high assessment these words are mostly lost in their worth. This time all of the seemed so appropriate.

In this view due leverage should be given to the fact that I felt so impressed by his genuineness that objectivity might slip out of my words but I assure all that I am striving not to allow that.

So here we list some of the Urdu expressions first that have been just used for late engineer Saleem Pirzada.

Hazaron saal nargis apni be noori pe roti hai,
Bari mushkil se hota hai chaman main deedawar paida..

Nargis (flower) cries for a millennium at her lack luster life
After mighty hurdles a connoisseur of beauty is born in garden

Muslim community the world over is easily one and half a billion strong. Yet they are in a state of shambles in the world today. I would count him amongst those rare souls who worked selflessly for whole life with every possible sacrifice barring life. the fete is all the more awesome owing to the fact that success could never have come in his lifetime. It need monumental courage and fortitude, patience and utter and complete lack of selfish motives to make that kind of commitment.

Above Urdu couplet is by Dr Sir Muhammed Iqbal, himself an epitome of the same ideals. This couplet is mostly lost on those for whom it is so often applied. Not in case of Allama Iqbal and not in case of Saleem alias Lovey Pirzada.

Nazar Abbas wrote :

Bade ghaur se sun raha tha zamana
Humein so gaye dastan kehte kehte

The world was listening rather attentively
It was me who slept while narrating the tale

Indeed he was telling a tale that was worth listening. Islam is the tale of real purpose of life as ordained by God. Muslim community is the flag bearer of that mission. This is the faith of Muslims. But Lovey did not pursue that angle. His mission was mission of Sir Syed Ahmed Khan. It is also called Aligarh Movement. in a nut-shell it can be summarized as follows : To empower Muslims of modern education so that they can take their rightful place in the scheme of things Indian.

This is the tale that was left incomplete by his departure from amongst us. The moment you utter the word Muslim you are very likely to be termed communal in a partisan sense in our country today. That this is not the case was the onerous task he had assigned himself, the task of the proportions of cleaning the fables Augean Stables.

Importance of Nehru's sabotage of the Cabinet Mission Plan, a dry bit from the history of the freedom movement of India, became significant to my mind only after those excruciatingly long discussions that I had with him for years. If a person like me takes that much of time then communicating the same to the country as a whole is task that is next to impossible and that brings the tragedy of being Lovey Pirzada into perspective.

If I allow his life to be cast as a tragedy. My intentions are absolutely otherwise. It is exceedingly difficult to adjust with the most inconvenient reality that he took upon himself a problem that could not have been solved in a single life time. So many people will think of it as a foolish choice. Not me. It was a tough, gutsy and extremely courageous choice. I salute the man.

He was not a flawless man. Who amongst us is? I am not the one to indulge in fault finding in a departed soul. let alone a friend and well wisher like Lovey. Indeed I might add that anyone trying to indulge in this activity will not get much benefit but indeed will be depriving himself of enormous felicity. That was the level of his purity of intentions. In Islamic languages we have word for that Ikhlas.

And that is why the pain of his departure is so excessive. that is why it was so difficult to console two students today in his burial - both of these are absolutely firebrand and feisty activists.

Personally I have no aptitude for students politics. I never had in my student days and nor I am satisfied at the present political exercise in students community. This inevitably brings me in a state of considerable difference of opinion with the departed leader but I am not going to allow that to come in my way while making my observations about him.

Fervour of any political inclination has a fire in it. The heat of this fire varies in degrees. The temperature in case of Lovey was extraordinarily high.

That worldly success could not have come his way and that it did not come his way I have already alluded to. I have also told what makes him monumentally important - his taking up the impossible task in the face of almost certain lack of possible success.

This lack of visible success certainly had its due toll on his health and I am sure he was aware of it - a sacrifice is a sacrifice only when you know the upcoming loss. Ultimately it took his life. This should not be interpreted in any morbid sense - in Islam it is glorious and glorious it was. he never couched his sentiments in religious, Islamic, language. His disposition was not at all communal. This is a fact that will need enormous amount of work to delineate for he used the terminology of political interests of Muslims.

He certainly had regrets for Muslims of India not listening to him and not taking up his call. But then why do I say that the world was listening attentively?

Answer to this question is same as to the question regarding  whether Muslims are aware of their miserable lot in present India. They are of course aware and completely so.

My personal view is that the lacuna in Lovey Pirzada's plan was not his lack of personal commitment on his part but lack of ideological clarification on part of academia - Muslim or secular.

The ideologues who supplied him ideology did little better than telling him - improve the political lot of Muslims of India. that simply does not help. The proposal has to be viable. No academician supplied him that.

In a milieu where talk of the secular interests of Muslims of India ended up in the partition of the country refinement of the same issue for the Muslims who consciously opted to remain in India at the time of the partition was very tricky issue and it remains so till now. problem did not reside in Lovey Pirzada's efforts but in the tools handed over to him by the academia.

I persistently assured him of the rightness of his mission and choice and tried my level best to convince about my point of view but my consolations did not bring any solace to him. This again should not be taken in any negative sense. He was a committed man and he left this world in that state.

Let us not forget that Javed Habib, another product of AMU Students Union, too left this world with the gigantic burden of destruction of Babri Masjid on his conscience.

## Thursday, November 30, 2017

### On Witten Index

This is in the context of the Riemann-Roch Theorem.We begin with its connection with Physics for the theorem will be most clear to Physics oriented people in this context only. The connection is in the context of a concept in theoretical Particle Physics. This is the concept of supersymmetry.

This story begins in the paper

E. Witten, Constraints on Supersymmetry Breaking, Nucl. Phys. B202 (1982) 253.

As per the INSPIRE HEP database this article has been cited by 1539 papers. This means, among other things, that one can not track anymore the diverse ideas that have used this paper.  This papers is about non-perturbative constraints on supersymmetry breaking.

In this paper, by a monumental survey of known supersymmetry models, Edward Witten came to conclusion that dynamical supersymmetry breaking does occur in anyone of these models. This survey is impressive both by techniques employed and the length, breadth and comprehensiveness of the models surveyed. because of this the negative result is rather discouraging.

In summary it means that once you have supersymmetry then you can not break it. This is a disaster when it comes to applications of the beautiful concept of supersymmetry to real Physics. Supersymmetry is the symmetry between fermions and bosons.

Our best theory of Particle Physics is the Standard Model. It has both fermions and bosons. But it has no supersymmetry. Clearly at the practical level, empirical level, in real life, at the experimental level supersymmetry is broken.

In fact the latest searches for supersymmetry at the Large Hadron Collider of CERN in Geneva very extensive experimental survey has yielded so far absolutely no evidence for supersymmetry.

Anyway even if supersymmetry is found the fact will remain that at energies that are available up till now there the world of Particle Physics is not supersymmetric and that means it, supersymmetry, is broken.

This should give us a perspective on the puzzle that we face today about supersymmetry. Experimentally supersymmetry is not found and hence it must be broken while theoretically we do not know even a single model where it is dynamically broken.

One may inquire here in what way dynamical breaking is different from just breaking. The hint in this subtlety of expression is the following. Explicit breaking of supersymmetry means that we begin with such a Lagrangian for Physics that has terms that break supersymmetry. These terms, be definition, do not possess supersymmetry. They are not invariant under supersymmetry transformations. In this case we are starting with a theory that simply does not possess supersymmetry. This is the case of explicit supersymmetry breaking.

Dynamical supersymmetry breaking is more interesting. Here we begin with a Lagrangian, hence a theory, that has supersymmetry to begin with. Then after dynamical effects set in, when dynamics shows its effects, then we end up in a theory that breaks supersymmetry. This process of supersymmetry breaking is more elegant and physically more attractive and acceptable.

Finally we must also explain the meaning of word perturbative. This is a technical term from quantum mechanics and is applicable to every application that uses quantum mechanics. Exactly solvable problems in quantum mechanics are very few. Free particle, particle in a box, particle hitting a potential barrier, particle facing a potential step or a finite potential well, particle in an infinite vertical potential well, particle in harmonic oscillator potential and hydrogen atom problem are practically the exhaustive set of exactly solvable problems.

For every other problem of Physics that uses quantum mechanics we must use some approximation method to get the useful and practical information. Amongst these approximation methods perturbation theory is the most effective and useful technique. This method gives a series expansion for physical quantities like energy.

This series is mostly infinite and this method can not always be applied. It is only applicable when the given problem is close to some exactly solvable problem. By Closeness we mean that the Hamiltonian or the Lagrangian of the theory differs by a term, which we call the perturbation, that is small in some sense. This sense of smallness is not difficult to understand. For example in case of energies the corrections engendered by the new term, the perturbation, should be small as compared to the energy in case of exactly solvable problem.

This much is very well known to every one who has learned basics of quantum mechanics. The perturbation Hamiltonian or Lagrangian in most cases is the interaction term and contains a constant that gives the strength of the interaction and it is called the coupling constant. When the coupling constant is small then the perturbation theory is useful because perturbation series is convergent and hence useful. This is called the perturbative regime or the weak coupling regime or the weak coupling limit.

The other case is of strong coupling and hence of large interaction and in this case perturbation theory is not useful because perturbation series is not convergent. In this case perturbation theory has failed and we can not use it. In such cases we must use other methods to get useful information about the physical system. The unimaginative collective name for such methods is non-perturbative methods.

Apart from this distinction of weak and strong couplings and corresponding respective perturbative and non-perturbative regimes there is another distinct division of physical regimes of quantum field theories. These are the regimes of low and high energies.

These two classifications get entangled with each other because of the following considerations. In quantum field theories, theories that we use to describe Particle Physics, couplings change with changing energies. This means that the perturbation term in the Lagrangian or the Hamiltonian changes with changing energy. In other words the coupling constants are not constants but become the parameters that change (with energy).

This is the case of running coupling constants. A constant is not supposed to change but in case of field theory that is what is an inevitable conclusion. This oxymoron expression, this contradiction in terms, is a very profound and fundamental one. This observation bears the same depth of insight as the first time realization of wave particle duality or uncertainty relations. Unfortunately the wave-particle duality and the uncertainty principle are common knowledge but running of coupling constant is not. The reason is not difficult to understand. quantum field theory is removed from our experience in quantum mechanics by one further level along the same line where quantum mechanics is removed from our classical experience.

Now let is once again summarize what we have discussed above. We would like to talk about the Riemann-Roch Theorem and we have began with its connection with Physics and this connection is through Witten Index that was defined in above cited paper.

To investigate theoretical models that begin with supersymmetry but ultimately break it Witten needed tools to analyze the models of supersymmetry available. In Section 2 of above cited paper he defined the now famous Witten Index. Symbolically he defined it as the operator in which the number minus one is raised to the power F. This is a notation for $\exp(2i\pi J_z)$. This later operator gives plus one eigenvalue for a bosonic state and minus one for a fermionic state.

This might look terribly abstract, obtuse and opaque - just to begin with. Luckily Witten is at his pedagogical best in this Section, as well as the whole paper itself. In this Section he has also exhibits his hallmark simplicity of the genius in statements like - "Supersymmetry breaking just means that the ground-state energy is positive".

By a very simple argument we can show that states with non-zero energy are paired by the action of the supersymmetry generator Q. One implication of this is that at the level of excited states we shall never have supersymmetry breaking - fermionic and bosonic states are paired.

In case of zero energy states this pairing is absent. Thus at zero energy there can be an arbitrary number of bosonic states and another arbitrary number of fermionic states.

As the parameters of the theory, masses and couplings, are varied fermionic and bosonic states might jump up from the zero energy to non-zero or vice-a-versa. In this process the difference between the number of bosonic and fermionic states at the zero energy will remain constant because the states jump up or down in pairs to maintain pairing at non-zero energies.

Clearly the difference of bosonic and fermionic states of zero energy is parameter independent and hence it can be calculated in most convenient limit for us to do calculations.

If this difference is non-zero then there is at least one bosonic or fermionic zero energy state. In this case supersymmetry is unbroken.

# A Fight for the Soul of Science

String theory, the multiverse and other ideas of modern physics are potentially untestable. At a historic meeting in Munich, scientists and philosophers asked: should we trust them anyway?
Physicists typically think they “need philosophers and historians of science like birds need ornithologists,” the Nobel laureate David Gross told a roomful of philosophers, historians and physicists last week in Munich, Germany, paraphrasing Richard Feynman.
But desperate times call for desperate measures.
Fundamental physics faces a problem, Gross explained — one dire enough to call for outsiders’ perspectives. “I’m not sure that we don’t need each other at this point in time,” he said.

The crisis, as Ellis and Silk tell it, is the wildly speculative nature of modern physics theories, which they say reflects a dangerous departure from the scientific method. Many of today’s theorists — chief among them the proponents of string theory and the multiverse hypothesis — appear convinced of their ideas on the grounds that they are beautiful or logically compelling, despite the impossibility of testing them. Ellis and Silk accused these theorists of “moving the goalposts” of science and blurring the line between physics and pseudoscience. “The imprimatur of science should be awarded only to a theory that is testable,” Ellis and Silk wrote, thereby disqualifying most of the leading theories of the past 40 years. “Only then can we defend science from attack.”
They were reacting, in part, to the controversial ideas of Richard Dawid, an Austrian philosopher whose 2013 book String Theory and the Scientific Method identified three kinds of “non-empirical” evidence that Dawid says can help build trust in scientific theories absent empirical data. Dawid, a researcher at LMU Munich, answered Ellis and Silk’s battle cry and assembled far-flung scholars anchoring all sides of the argument for the high-profile event last week.
Gross, a supporter of string theory who won the 2004 Nobel Prize in physics for his work on the force that glues atoms together, kicked off the workshop by asserting that the problem lies not with physicists but with a “fact of nature” — one that we have been approaching inevitably for four centuries.
The dogged pursuit of a fundamental theory governing all forces of nature requires physicists to inspect the universe more and more closely — to examine, for instance, the atoms within matter, the protons and neutrons within those atoms, and the quarks within those protons and neutrons. But this zooming in demands evermore energy, and the difficulty and cost of building new machines increases exponentially relative to the energy requirement, Gross said. “It hasn’t been a problem so much for the last 400 years, where we’ve gone from centimeters to millionths of a millionth of a millionth of a centimeter” — the current resolving power of the Large Hadron Collider (LHC) in Switzerland, he said. “We’ve gone very far, but this energy-squared is killing us.”
As we approach the practical limits of our ability to probe nature’s underlying principles, the minds of theorists have wandered far beyond the tiniest observable distances and highest possible energies. Strong clues indicate that the truly fundamental constituents of the universe lie at a distance scale 10 million billion times smaller than the resolving power of the LHC. This is the domain of nature that string theory, a candidate “theory of everything,” attempts to describe. But it’s a domain that no one has the faintest idea how to access.
The problem also hampers physicists’ quest to understand the universe on a cosmic scale: No telescope will ever manage to peer past our universe’s cosmic horizon and glimpse the other universes posited by the multiverse hypothesis. Yet modern theories of cosmology lead logically to the possibility that our universe is just one of many.
Whether the fault lies with theorists for getting carried away, or with nature, for burying its best secrets, the conclusion is the same: Theory has detached itself from experiment. The objects of theoretical speculation are now too far away, too small, too energetic or too far in the past to reach or rule out with our earthly instruments. So, what is to be done? As Ellis and Silk wrote, “Physicists, philosophers and other scientists should hammer out a new narrative for the scientific method that can deal with the scope of modern physics.”
“The issue in confronting the next step,” said Gross, “is not one of ideology but strategy: What is the most useful way of doing science?”
Over three mild winter days, scholars grappled with the meaning of theory, confirmation and truth; how science works; and whether, in this day and age, philosophy should guide research in physics or the other way around. Over the course of these pressing yet timeless discussions, a degree of consensus took shape.

## Rules of the Game

Throughout history, the rules of science have been written on the fly, only to be revised to fit evolving circumstances. The ancients believed they could reason their way toward scientific truth. Then, in the 17th century, Isaac Newton ignited modern science by breaking with this “rationalist” philosophy, adopting instead the “empiricist” view that scientific knowledge derives only from empirical observation. In other words, a theory must be proved experimentally to enter the book of knowledge.
But what requirements must an untested theory meet to be considered scientific? Theorists guide the scientific enterprise by dreaming up the ideas to be put to the test and then interpreting the experimental results; what keeps theorists within the bounds of science?
Today, most physicists judge the soundness of a theory by using the Austrian-British philosopher Karl Popper’s rule of thumb. In the 1930s, Popper drew a line between science and nonscience in comparing the work of Albert Einstein with that of Sigmund Freud. Einstein’s theory of general relativity, which cast the force of gravity as curves in space and time, made risky predictions — ones that, if they hadn’t succeeded so brilliantly, would have failed miserably, falsifying the theory. But Freudian psychoanalysis was slippery: Any fault of your mother’s could be worked into your diagnosis. The theory wasn’t falsifiable, and so, Popper decided, it wasn’t science.
Critics accuse string theory and the multiverse hypothesis, as well as cosmic inflation — the leading theory of how the universe began — of falling on the wrong side of Popper’s line of demarcation. To borrow the title of the Columbia University physicist Peter Woit’s 2006 book on string theory, these ideas are “not even wrong,” say critics. In their editorial, Ellis and Silk invoked the spirit of Popper: “A theory must be falsifiable to be scientific.”
But, as many in Munich were surprised to learn, falsificationism is no longer the reigning philosophy of science. Massimo Pigliucci, a philosopher at the Graduate Center of the City University of New York, pointed out that falsifiability is woefully inadequate as a separator of science and nonscience, as Popper himself recognized. Astrology, for instance, is falsifiable — indeed, it has been falsified ad nauseam — and yet it isn’t science. Physicists’ preoccupation with Popper “is really something that needs to stop,” Pigliucci said. “We need to talk about current philosophy of science. We don’t talk about something that was current 50 years ago.”
Nowadays, as several philosophers at the workshop said, Popperian falsificationism has been supplanted by Bayesian confirmation theory, or Bayesianism, a modern framework based on the 18th-century probability theory of the English statistician and minister Thomas Bayes. Bayesianism allows for the fact that modern scientific theories typically make claims far beyond what can be directly observed — no one has ever seen an atom — and so today’s theories often resist a falsified-unfalsified dichotomy. Instead, trust in a theory often falls somewhere along a continuum, sliding up or down between 0 and 100 percent as new information becomes available. “The Bayesian framework is much more flexible” than Popper’s theory, said Stephan Hartmann, a Bayesian philosopher at LMU. “It also connects nicely to the psychology of reasoning.”
Gross concurred, saying that, upon learning about Bayesian confirmation theory from Dawid’s book, he felt “somewhat like the Molière character who said, ‘Oh my God, I’ve been talking prose all my life!’”
Another advantage of Bayesianism, Hartmann said, is that it is enabling philosophers like Dawid to figure out “how this non-empirical evidence fits in, or can be fit in.”

## Another Kind of Evidence

Dawid, who is 49, mild-mannered and smiley with floppy brown hair, started his career as a theoretical physicist. In the late 1990s, during a stint at the University of California, Berkeley, a hub of string-theory research, Dawid became fascinated by how confident many string theorists seemed to be that they were on the right track, despite string theory’s complete lack of empirical support. “Why do they trust the theory?” he recalls wondering. “Do they have different ways of thinking about it than the canonical understanding?”
String theory says that elementary particles have dimensionality when viewed close-up, appearing as wiggling loops (or “strings”) and membranes at nature’s highest zoom level. According to the theory, extra dimensions also materialize in the fabric of space itself. The different vibrational modes of the strings in this higher-dimensional space give rise to the spectrum of particles that make up the observable world. In particular, one of the vibrational modes fits the profile of the “graviton” — the hypothetical particle associated with the force of gravity. Thus, string theory unifies gravity, now described by Einstein’s theory of general relativity, with the rest of particle physics.
Laetitia Vancon for Quanta Magazine
Video: Richard Dawid, a physicist-turned-philosopher at Ludwig Maximilian University in Munich.
However string theory, which has its roots in ideas developed in the late 1960s, has made no testable predictions about the observable universe. To understand why so many researchers trust it anyway, Dawid signed up for some classes in philosophy of science, and upon discovering how little study had been devoted to the phenomenon, he switched fields.
In the early 2000s, he identified three non-empirical arguments that generate trust in string theory among its proponents. First, there appears to be only one version of string theory capable of achieving unification in a consistent way (though it has many different mathematical representations); furthermore, no other “theory of everything” capable of unifying all the fundamental forces has been found, despite immense effort. (A rival approach called loop quantum gravity describes gravity at the quantum scale, but makes no attempt to unify it with the other forces.) This “no-alternatives” argument, colloquially known as “string theory is the only game in town,” boosts theorists’ confidence that few or no other possible unifications of the four fundamental forces exist, making it more likely that string theory is the right approach.
Second, string theory grew out of the Standard Model — the accepted, empirically validated theory incorporating all known fundamental particles and forces (apart from gravity) in a single mathematical structure — and the Standard Model also had no alternatives during its formative years. This “meta-inductive” argument, as Dawid calls it, buttresses the no-alternatives argument by showing that it has worked before in similar contexts, countering the possibility that physicists simply aren’t clever enough to find the alternatives that exist.
Emily Fuhrman for Quanta Magazine, with text by Natalie Wolchover and art direction by Olena Shmahalo.
The third non-empirical argument is that string theory has unexpectedly delivered explanations for several other theoretical problems aside from the unification problem it was intended to address. The staunch string theorist Joe Polchinski of the University of California, Santa Barbara, presented several examples of these “unexpected explanatory interconnections,” as Dawid has termed them, in a paper read in Munich in his absence. String theory explains the entropy of black holes, for example, and, in a surprising discovery that has caused a surge of research in the past 15 years, is mathematically translatable into a theory of particles, such as the theory describing the nuclei of atoms.
Polchinski concludes that, considering how far away we are from the exceptionally fine grain of nature’s fundamental distance scale, we should count ourselves lucky: “String theory exists, and we have found it.” (Polchinski also used Dawid’s non-empirical arguments to calculate the Bayesian odds that the multiverse exists as 94 percent — a value that has been ridiculed by the Internet’s vocal multiverse critics.)
One concern with including non-empirical arguments in Bayesian confirmation theory, Dawid acknowledged in his talk, is “that it opens the floodgates to abandoning all scientific principles.” One can come up with all kinds of non-empirical virtues when arguing in favor of a pet idea. “Clearly the risk is there, and clearly one has to be careful about this kind of reasoning,” Dawid said. “But acknowledging that non-empirical confirmation is part of science, and has been part of science for quite some time, provides a better basis for having that discussion than pretending that it wasn’t there, and only implicitly using it, and then saying I haven’t done it. Once it’s out in the open, one can discuss the pros and cons of those arguments within a specific context.”

## The Munich Debate

The trash heap of history is littered with beautiful theories. The Danish historian of cosmology Helge Kragh, who detailed a number of these failures in his 2011 book, Higher Speculations, spoke in Munich about the 19th-century vortex theory of atoms. This “Victorian theory of everything,” developed by the Scots Peter Tait and Lord Kelvin, postulated that atoms are microscopic vortexes in the ether, the fluid medium that was believed at the time to fill space. Hydrogen, oxygen and all other atoms were, deep down, just different types of vortical knots. At first, the theory “seemed to be highly promising,” Kragh said. “People were fascinated by the richness of the mathematics, which could keep mathematicians busy for centuries, as was said at the time.” Alas, atoms are not vortexes, the ether does not exist, and theoretical beauty is not always truth. Except sometimes it is. Rationalism guided Einstein toward his theory of relativity, which he believed in wholeheartedly on rational grounds before it was ever tested. “I hold it true that pure thought can grasp reality, as the ancients dreamed,” Einstein said in 1933, years after his theory had been confirmed by observations of starlight bending around the sun.
The question for the philosophers is: Without experiments, is there any way to distinguish between the non-empirical virtues of vortex theory and those of Einstein’s theory? Can we ever really trust a theory on non-empirical grounds?
In discussions on the third afternoon of the workshop, the LMU philosopher Radin Dardashti asserted that Dawid’s philosophy specifically aims to pinpoint which non-empirical arguments should carry weight, allowing scientists to “make an assessment that is not based on simplicity, which is not based on beauty.” Dawidian assessment is meant to be more objective than these measures, Dardashti explained — and more revealing of a theory’s true promise.
Gross said Dawid has “described beautifully” the strategies physicists use “to gain confidence in a speculation, a new idea, a new theory.”
“You mean confidence that it’s true?” asked Peter Achinstein, an 80-year-old philosopher and historian of science at Johns Hopkins University. “Confidence that it’s useful? confidence that …”
“Let’s give an operational definition of confidence: I will continue to work on it,” Gross said.
“That’s pretty low,” Achinstein said.
“Not for science,” Gross said. “That’s the question that matters.”
Kragh pointed out that even Popper saw value in the kind of thinking that motivates string theorists today. Popper called speculation that did not yield testable predictions “metaphysics,” but he considered such activity worthwhile, since it might become testable in the future. This was true of atomic theory, which many 19th-century physicists feared would never be empirically confirmed. “Popper was not a naive Popperian,” Kragh said. “If a theory is not falsifiable,” Kragh said, channeling Popper, “it should not be given up. We have to wait.”
But several workshop participants raised qualms about Bayesian confirmation theory, and about Dawid’s non-empirical arguments in particular.
Carlo Rovelli, a proponent of loop quantum gravity (string theory’s rival) who is based at Aix-Marseille University in France, objected that Bayesian confirmation theory does not allow for an important distinction that exists in science between theories that scientists are certain about and those that are still being tested. The Bayesian “confirmation” that atoms exist is essentially 100 percent, as a result of countless experiments. But Rovelli says that the degree of confirmation of atomic theory shouldn’t even be measured in the same units as that of string theory. String theory is not, say, 10 percent as confirmed as atomic theory; the two have different statuses entirely. “The problem with Dawid’s ‘non-empirical confirmation’ is that it muddles the point,” Rovelli said. “And of course some string theorists are happy of muddling it this way, because they can then say that string theory is ‘confirmed,’ equivocating.”
The German physicist Sabine Hossenfelder, in her talk, argued that progress in fundamental physics very often comes from abandoning cherished prejudices (such as, perhaps, the assumption that the forces of nature must be unified). Echoing this point, Rovelli said “Dawid’s idea of non-empirical confirmation [forms] an obstacle to this possibility of progress, because it bases our credence on our own previous credences.” It “takes away one of the tools — maybe the soul itself — of scientific thinking,” he continued, “which is ‘do not trust your own thinking.’”
The Munich proceedings will be compiled and published, probably as a book, in 2017. As for what was accomplished, one important outcome, according to Ellis, was an acknowledgment by participating string theorists that the theory is not “confirmed” in the sense of being verified. “David Gross made his position clear: Dawid’s criteria are good for justifying working on the theory, not for saying the theory is validated in a non-empirical way,” Ellis wrote in an email. “That seems to me a good position — and explicitly stating that is progress.”
In considering how theorists should proceed, many attendees expressed the view that work on string theory and other as-yet-untestable ideas should continue. “Keep speculating,” Achinstein wrote in an email after the workshop, but “give your motivation for speculating, give your explanations, but admit that they are only possible explanations.”
“Maybe someday things will change,” Achinstein added, “and the speculations will become testable; and maybe not, maybe never.” We may never know for sure the way the universe works at all distances and all times, “but perhaps you can narrow the live possibilities to just a few,” he said. “I think that would be some progress.”