Brexit or Brit-IN - Leave or Remain Debate

It looks like immigration is the biggest problem British people are complaining about. The problem exaggerated by the recent immigration due to Syrian war. British people are afraid that most of the immigrants eventually will end up in UK.  Given the situation and behaviour of French officials I can't blame them. They are normally turn the blind eye to refugees in Calais.

On the other hand people who emigrated to Britain half a century ago are blaming recent EU immigrants for job loses, house shortages and school places. That's also true.  Bangladeshi and Indian curry houses complain that recent changes to the law means it cost them more to bring chefs and other specific personnel from the relevant Asian countries. Minimum wage should be around 30,000 pounds to invite anyone with work permit and they say  they cannot afford to pay that much. They claim that they are forced to close their businesses. They want the laws to change specifically again for immigration purpose, so they can get cheap labour from India, Bangladesh and Pakistan. Most care home workers in UK are from African origin and from Asian countries. Prior to recent European migration most of the unskilled jobs in hospitals, hotels and catering industries were done by Asian and african migrants.

European migration from Poland, Romania, Bulgaria, Albania, kosovo  and other countries changed that. There were job losses among minority communities. These minority communities more or less concentrated in big cities.  Therefore earlier migrants from Asian and African countries want to support Brexit. They want their jobs back.

Then we have UKIP supporters, Nazi Pegida supporters and English Defence League supporters  who want to stop immigration altogether. They want to claim country back for white Majority.   I.e they don't like any migrants and that will include Asian and African migrants.  What they don't know is, as a result of the 2011 census the White British population was estimated 51,736,290 (81.9% of the UK total population). UK is a white majority country any way.

That's the hilarious situation here. These groups want to support  the Brexit for completely opposite reasons.


Then we have Boris Johnson and conservative right who want Britain to leave EU to claim back country's lost sovereignty allegedly.   I am sympathetic somewhat to their claim as Euro bureaucrats are not a very popular bunch these days. There are quite a few blunders committed by them and they are ignorant to the criticism.  For example roughly €114 million is spent every year to move the European Parliament between its Brussels and Strasbourg seats every month, according to a new assessment by the European Court of Auditors. It says here For decades, the European Parliament has been on the road once a month. "Between 3,000 and 4,000 people, among them roughly 800 MEPs, their assistants, employees and interpreters move 400 kilometres from Brussels to Strasbourg. Their workspaces are empty for 317 days per year."

Then there is accusation that Britain pays 350 million per week. Now that figure is wrong. Britain's actual payment is around £250 million.  Here are the figures.  UK's net contribution is £8.5 billion.  That is because of the rebate as well. Uk get 4.5 billion back from EU from Total Contribution of 12.9 Billion.

Another side who want Britain to leave Europe is Russia. Russians know very well that European ambition to admit  Ukraine and Moldova to Eu would be in disarray if Britain leaves.

 Germany's Angela Merkel's soft touch for Syrian and other refugees and her dealing with Turkish President Erdogan does not go down well with British public. There are worries that Merkel may do a backhanded deal to give millions of Turks free visas to enter Europe and Britain would be flooded.

I actually think there are problems but European migration is not bad for Britain. I can see that places like Walthamstow, Edmonton in London got a really good makeover after migrant numbers swelled. Businesses were booming. Most of the EU migrants are actually working rather than claiming benefits. Here are EU migrant numbers.

If UK political leaders can reduce EU bureaucracy and unnecessary spending, if they can avoid creating a European Bureaucratic state I don't see any good reason to leave.  To guide EU to better democratic institution UK should be in not OUT.

A reply I received from my wife Ines who is German national living in UK.

Just some thoughts From Ines:

1. This shows how the UK is protecting human rights of people who flee the war!

2. EU expansion since the 90s has filled job places or created more jobs - but also increased the average salary of Uk citizen :

If all European workforce will leave  - commonwealth workers will have to fill the places of qualified nurses, doctors, care staff!

3. Every EU country can interpreted the immigration laws to their own needs:

Germany introduced a new law - to allow immigrants from Syria to settle in places where population is at very low level - no overcrowding and housing issues in bid towns anymore, also integration and language courses are a must and any criminal offences leads to extradition - its up to the UK government to deal with their own issues!!!

4. English people are the least informed about EU (LSE Study) and media uses fear and anger instead of knowledge to convince people  - racially prejudices has risen steadily since 2001 and it will destroy this society!!!

https://www.theguardian.com/uk-news/2014/may/27/-sp-racism-on-rise-in-britain

http://www.theguardian.com/news/datablog/2015/nov/27/brits-least-knowledgeable-european-union-basic-questions

Which other lies do you need to convince you of your right choice??

Britons among least knowledgeable about European Union ... www.theguardian.com There is an ongoing argument about whether the UK government should launch an information campaign about the European Union before the in/out referendum on EU membership.

Racism on the rise in Britain | UK news | The Guardian www.theguardian.com The findings come as political leaders struggle to deal with the rise of the UK Independence party, which campaigned on an anti-immigrant, anti-EU platform and has ...

First Teacher's song

Your film was very impressive and I was very touched by the way you translated the simplicity of the life in Kazakhstan to the scenes in Nepal using Sri Lankan actors. I believe you have chosen the right people to represent the main parts and you touched upon everything what is important in life   - dejection, sadness, aggression, friendship, hope, love and using a wonderful scenery as a background. 

Although I felt that you tried to show the feeling of love between the two characters not as one which is develops out of admiration but instead as a love at first sight. Maybe this is the Sri Lankan way?!

I liked also the scene at the station when everyone understands that he reciprocates her love by letting her go   her own way and giving her the opportunity to live a fulfilled and self determined live. 

 
What I was missing though was the wonderful book ending to show the reconciliation with faith, when she, a successful lady, returned to the village and avoids shyly her first teacher and love - but decides to write the story and poignantly states her will to reconcile. (not only with her first love but also to apologize for taking credit - where credit was due to the ones who earned it - namely him - (I believe this could be an example to politicians and other people in Sri Lanka when they take credit for things accomplished by others.

I also felt that your character of the girl at 15  seemed to be portrait as a frail, vulnerable and weak  (overwhelming sobbing - which for me spoiled the last 20 min of the film) but in the book she is a much stronger willed girl, who was eager to learn and looking for her own freedom . Assuming that your  target audience consists of a mixture of young and old Sri Lankan people  - the character of the girl could have been a perfect example  for Sir Lankan women to overcome the male dominated society and to be able to find their own way in life!

I wish in your next movie you choose a story as beautiful as this one but also that you could bring about a modern context to it regarding relatable  issues among the people in the modern society (including Sri Lanka). Looking forward to your next movie!

I loved the way you used instead of the unfinished painting an unfinished piece of music script as a frame for the story - what a brilliant idea!

Ines baumann

(This is review about the Sinhala film Guru Githaya)

The Man who knew Infinity - A film about a mathematician

The brilliant performance by Jeremy Iron (who previously starred in the films 'Lolita' and 'Dead Ringers') and Dev Patel ('Slumdog Millionaire' and 'The Best Exotic Marigold Hotel') as Dr Hardy and Srinivasa Ramanujan in the film 'The Man Who Knew Infinity' delighted our whole family. I went to watch the film with my wife and daughters. One of my daughters is very artistic and other one is really good at maths. They both loved the film. I believe the film is very artistic, sensitive, very emotive and at the same time it gives you an idea about mystery of the mathematical world and mathematicians.

 I love maths and one of my other heroes of Indian origin is Dr Subrahmanyan Chandrasekhar, who found the Chandrasekhar limit (related to stars).
 Ramanujan's story fascinated me earlier on, perhaps because I did that Astrophysics course in Queens Mary. 'He could have gone on and solved the puzzles about 'Black Holes'' they said. 'How?' I asked.

On his deathbed, he mentioned 'theta functions' in a letter to Dr Hardy. Theta functions are supposed to be super -symmetric. Oh, I know, when we talk about supersymmetry, etc. something else comes to mind: 'string theory'.

A team of mathematicians later proved that theta functions indeed mimicked modular forms. They also found out that  expansion of mock modular forms helps physicists compute the entropy, or level of disorder, of black holes. Had Ramanujan lived to see that day, he would have added more functions.

He did not have any formal degree, but his brilliant mind produced amazing formulas of pure mathematics. One cannot call him anything other than a born genius. He thought Hindu goddess 'Namagiri' gave these formulas to him as her divine thoughts.

Ramanujan faced lot of hardship in India; he did not have a job in his earlier years. With his young wife and mother depending on him, Ramanujan needed the money to survive. He then found a job as a tax clerk. There was another clerk like that who also invented special theory of relativity later. But that genius, who turned out to be famous Albert Einstein, was more lucky than Ramanujan, because he lived in Europe.

After reading a letter Ramanujan sent to him, Dr Hardy invited Ramanujan to Cambridge, in England. Many of Dr Hardy's colleagues were against the idea. When Ramanujan was in England, he was not treated well. Racism arose, and there were many incidents due to Ramanujan's origins, but Dr Hardy and his friend Dr Littlewood trusted Ramanujan and his abilities. Dr Hardy pushed Ramanujan to produce the necessary proofs to his mathematical formulas and functions so he could publish them. Dr Hardy and Ramanujan were not similar in character and they did not share the same cultural background. Ramanujan was also a strict vegetarian and this led to the difficulty that he did not have enough nutritional food while World War 1 was raging across Europe.

Yet this beautiful friendship with the renowned professor and self-taught genius blossomed, therefore helping the future of mathematics immensely. For example, there is the Ramanujan - Sato series, Ramanujan's PI formulas,  Continued Fraction and mock theta functions, to name a few. It is an interesting fellowship - Dr Hardy was an atheist while Ramanujan, a devout Hindu, thought his God spoke to him through his formulas. 

His brahmin origins prevented him going overseas for his further studies at first. Finally, his mother relented and with his wife's blessing as well, he set sail to England. His religious upbringing played a big part in his later life in England; it caused him to live more like a hermit, working hard on his amazing mathematical formulas.

He did not have good food during the First World War, as was previously mentioned. He did not ask much help from Dr Hardy, hiding his needs and his pain of not living with his beautiful, loving wife. His mother, on the other hand, hid letters meant for Ramanujan from her daughter-in-law. Ramanujan was soon diagnosed with tuberculosis and treated in England, but never recovered fully.

In his final days, Ramanujan was accepted as a 'Fellow of the Royal Society' (FRS), the second Indian to do so, and finally as a Fellow of the Trinity College. His work was stolen in Cambridge and he was harassed a lot, but he ignored those mishaps as a true gentleman.

He returned to his wife and mother, and within a year he died, leaving his young wife a widow. He was only 32 years old. I think England and Cambridge did not take care of him properly. His work on fractions was stolen and it was found by someone else in Wren Library at Trinity College, Cambridge in 1976.
These are now on Display at Cambridge.

The film does not reveal all of these incidents, but it does do a certain justice to this brilliant mathematical genius.

Sources:
1.  http://www.businessinsider.com/researchers-unlock-formula-mathematician-srinivasa-ramanujan-2012-12?IR=T
2. http://www.britannica.com/biography/Srinivasa-Ramanujan
3. http://ajitvadakayil.blogspot.co.uk/2011/11/fractal-mind-of-srinivasa-ramanujan.html
3. Picture from: http://www.famousscientists.org/srinivasa-ramanujan/

I had Syrian friends.

I had Syrian  friends when I studied in Soviet Union.  They were not refugees. They lived under Hasad Senior Hafez Al Asad. They could travel anywhere. Their women can drive cars and hold driving licenses. (Do you know a country that does not allow that ,  by any chance?) They could study including women (unlike Afghanistan I may say). Education was free (Including university education) . Muslims - Shia and Sunni, Christians of several denominations , some hindus lived side by side. No troubles. And then  his son came to power and nothing much changed. They had little bit of oil and some wealth. And some from the west  called him a dictator - Bashar Assad. He did not allow fundamentalists to take over the country.

Someone intervened we know who? Now Country is a mess and Syrian refugees are everywhere. There could well be terrorists among them we don't know. But before anyone posting any rubbish,  blame the people who created the crisis in the first place.

Assad may be a dictator. But we have seen worse.  Why we could not allow Syrian people to change their leader other  than impose it on them by some powerful country?

The Kobeningrad

I was reading news past few weeks and more and more drawn to the conflict and war in and around Kobane. Upto this far Islamic  fighters of ISIl had somewhat an easy ride. They attack some minority groups and won their lands. They have also said to be trading with captured female prisoners.
One of the minorities are Yazidis.
http://www.theguardian.com/world/2014/aug/07/who-yazidi-isis-iraq-religion-ethnicity-mountains

We were told by media that they (Islamic fighters)  have hunted the Yazidis people down and killed many. Captured Yazidi females to be sold or already have done so.

But Kobane is different. Kurdish population in this city started to fight back.  They did not gave up easily. They are fighting for their women and children. They are fighting for their livelihoods. Their city.  Most of all they are fighting for their freedom.

This reminds me of NaZi germany's troops approaching Stalingrad. The epic battle for Stalingrad claimed 2 million lives and after five months, one week and three days later Red Army of Soviet union won.
http://en.wikipedia.org/wiki/Battle_of_Stalingrad#Casualties

Battle for stalingrad fought in street corners, from the rooftops, from abasements, and face to face. There are films about this battle. For the Red Army and people for Stalingrad nowhere else to go. Order was not to  leave the stalingrad. Stayed they did.

Stalingrad's embattled, hungry but  heroic soldiers:

What's happening in Kobane is in much simpler scale. Although as Nazis ISIS fighters have better weapons and more man power. They are trained. Most kurdish fighters are guerilla fighters with small weapons.  But we can see men and women fighting side by side with elders. It's heartening to see they are giving their all to stop the menacing advance. World waited and waited. Finally US and allies decided to aid their effort with air strikes.

Now I think battle is raging in street corners. Air strikes may not help much but psychological advance given to the ground resistance is enormous.

I hope for their children, for their womenfolk and for their city Kobane would not fall. So that they survived to tell the story of mini Stalingrad. The kobaningard.

Which hell are you going to end up?

I Was talking , rather arguing with four friends (Colleagues)  about religion. One is following Jehovah's witness, other one is a muslim, third one is a Catholic and fourth one is from some new age Christian sect. Each one claims their religion is the true one,  although catholic, Jehovah's witness and Christian New Age followers supposed to follow one god. The Jehovah's witness friend said his religion follows Bible to the letter and follows truest word of the god. Muslim friend disagreed and said his religion is the most truest and correct version as Christians changed stuff. Well Catholic guy believes he has the proper God and God mother etc. New Age Christian believes they are more open , don't do bad things, not aggressive, very high on morals etc. He in fact asked me where I get my morals. It seems he thinks I don't have any. I am the crappy , no morals etc upto no good atheist so I did not bother to go and teach morals to him.

Then I asked them this question. Just one. I asked the Jehovah's witness friend that, " do  they believe that if anyone don't follow his religion he/she would end up in hell.? Well he confirmed that yes they believe that way. So I told him weather according to his religion all other 4 colleagues (Catholic, Christian, Muslim and  I who is one time Buddhist but now half Buddhist) will end up in hell, in which he reluctantly agreed.

 I asked the same question from the Muslim friend. As a true believer he told us that all four other non believers will end up in hell by the grace of god. However I reminded him that he himself will be in Jehovah's witness friends hell.

Unfortunately for us our catholic friend confirmed that according to his religion / faith except him all other 4 people present will be in Catholic hell as we all are "non-believers".

I have to say our new age christian friend is bit more liberal. He was trying hard to explain perhaps hell is not that bad. It may be this earth, a bad place etc bla bla. But we will be in that hell nonetheless when we die.
Well some part of the world some Buddhists also believe others go to hell if you are a non believer and also commit some or other this and that sins.

Now think about this, after all of us die:

A buddhist, atheist, muslim, new age christian, Jehovah's witness guy will end up in ---------> Catholic hell.
An atheist, buddhist, New Age Christian, Catholic, Jehovah's witness guy will end up in ---------> Muslim hell.
An atheist, muslim, new age christian, Catholic, Jehovah's witness guy will end up in ---------> Buddhist hell.
An atheist, muslim, Buddhist, Catholic, Jehovah's witness guy will end up in ---------> new Age Christian's modified hell.

An atheist, muslim, Buddhist, Catholic, New Age Christian will end up in ---------> Jehovah's witness hell.

And also all of them believed they would go to heaven following their respective religious heavens that is.

So Muslim heaven is Buddhist, Catholic, Jehovah's witness, Christian hell. Catholic heaven is  muslim, Buddhist,  Jehovah's witness, Christian hell.
 Jehovah's witness heaven is everyone else's hell. etc etc.

All of us somehow end up in each others hell except if you are an atheist.

If you are an atheist:
A muslim, new age christian, Catholic, Buddhist will end up in ---------> no where as atheist's don't care about hells. We don't care where you guys will end up anyway.

What I can say: Choose wisely.

Laclau's Floating signifier, Gamow Peak and Intensity of Struggles

I was reading an article written in Sinhala language regarding political struggles. Some of the main points of the article were based on Ernesto Laclau's' floating signifiers. What Laclau is saying here is this. He is using a picture shown below for this explanation. In here he was trying to present the notion of 'empty signifier' at its purest.

 He took Tsarism (Ts) as an an example for a regime which was oppressive and it was separated by a political frontier from the demands of most sectors of society (D1, D2, D3 ,D4• • • etc.). Each demand is different to all the others in it's  articularity. This particularity is shown in the above diagram by the lower semicircle in the representation of each of them.  However they are all united in their common opposition to the Tsarist oppressive regime.

Laclau claims, this in turn leads to one of the demands stepping in and becoming the signifier of the whole chain - a tendentially empty signifier. He says that the whole model depends on the presence of the dichotomic frontier: without this, the equivalential relation would collapse and the identity of each demand would be

exhausted in its differential particularity. However when  the oppressive regime itself becoming hegemonic then the dichotomic frontier, without disappearing,

becoming blurred i.e trying to interrupt the equivalential chain of the

popular camp by an alternative equivalential chain, in which some of the

popular demands are articulated to entirely different links .

 The same democratic demands receive the structural pressure of rival hegemonic projects in such a case. This generates an autonomy of the popular signifiers different from the earlier ones and its meaning is indeterminate between alternative equivalential frontiers It is no longer that the particularism

of the demand becomes self-sufficient and independent of any equivalential articulation. Laclau call signifiers whose meaning is 'suspended' in that way 'floating signifiers'. Their operation is shown here in this diagram.

I am directly quoting from Laclau here. "As we can see, D1 is submitted to the structural pressure of two antagonistic equivalential chains represented by the dotted lines: the horizontal corresponds to the popular camp opposing Tsarism, as in the first diagram. The diagonal, however, establishes an equivalential link between D1 ' belonging to the popular camp, and two other demands that the latter would oppose as belonging to the camp of Tsarism. So we have two antagonistic ways of constituting the 'people' as a historical actor. The way in which the meaning of DI is going to be fixed will depend on the result of a hegemonic struggle. So the 'floating' dimension becomes most visible in periods of organic crisis, when the symbolic system needs to be radically recast. And, for that reason, that dimension has, as a necessary pattern, the unfixing of the relationship between the two semicircles in the representation of the demands: the upper semicircle is always the one that becomes autonomous in any floating, for it is in its equivalential virtualities that the representation of the (absent) fullness of society lies." - On populist Reason -Ernesto Laclau

Now what we can see is that even though Ernesto Laclau's approach here is correct for the struggles his diagrams do not consider the intensity of struggles. The struggles are not  the same if you consider the intensity of them. They have different intensities. They acted in different ways in different circumstances. Laclau takes example of Tsarism. If we consider the two definitive struggles from the same era, namely in 1905 and in 1917, each of these struggles has different intensities and one which managed better reached the turning point in 1917. (Please see the diagram below.)

Intensity of Struggles On X-Axis Time

In my opinion what is important is not that D1 is becoming floating signifier. Laclau's idea that floating signifier D1's meaning is going to be fixed by the result of a hegemonic struggle is to be understood differently. As the struggle intensifies the leading forces would act differently. There will be obvious two antagonistic forces will be evident. 

If we consider the evolution of the very early universe, primordial nucleosynthesis, star formation or planetary formation, evolutionary history of life we can see the chaotic way it works. We can find the formulas and mathematical equations to explain all these events, transactions, creations but the very fact is that they just happens with different intensity and amid the chaos of things. We only know how to explain them.

If we take a look at what happens inside the stars and nucleosyntheis in stars we find these.

http://quantumchecks.blogspot.co.uk/2014/05/quantum-tunnelling-and-gamow-energy.html

The point that interest me from the article above is this. The particle motion inside stars are very chaotic. They don't happen according to some god's plan or some other pre-determined fashion..  That's why we have to calculate Mean Free Path to find houd how these particles are interacting with each other.
"Mean Free Path- Identical particles travelling through a medium of targets travel different distances before interacting. The average distance they travel prior to reaction is called the mean free path l, and is a useful indicator of the condition of the target medium and the strength of the interaction. - Stellar Evolution and Nucleosynthesis" 

The struggles are happening the same way. We cannot say where and when the struggles will start and what problem or demand would create the particular struggle. We all know that there is this dialectical nature of the struggle between classes. We can  approximate the times and what the percentage of the masses participating in each struggle.  They happen in different intensity and a political entity  which learned the best way to manage the intensity can take the struggle through the potential barrier. (Barrier penetration).

 Let's think about what happened with  Euro Maidan in Ukraine. It started as a small protest against Yanukovych regime. (I am not taking any side here. That's not the idea) . But it was managed so cleverly by the (perhaps US/EU funding, perhaps from the oligarchs which were on their side) money they have received they could mobilise forces outside their reach by any means, propaganda money etc. The media war was managed so cleverly by leading western press and opinion in Europe was swayed protesters way. The intensity of the struggle went up by day when the killing started the struggle was at it's peak.  That was the turning point. We all know what happened after that.

The leftists parties should not intervene in every struggles for democracy. There are certain struggles by the capitalist leaning social democratic parties that leftist parties cannot participate. They can certainly support certain issues to save the democratic freedom and  other struggles which address cost of living, student fees etc. A leftist party should select the struggles they should just participate as a voice of support and select the struggles that they can manage and control separately. They have to use their time and energy to increase the intensity of the struggle and direct it towards abolishing the capitalist system.

Therefore I think it is necessary for a party to have intelligence gathering and analysis unit purely to collect and analyse data on struggles happening in any particular country of their concern. Then they should advice politburo of the party to take necessary action. Through out any struggle this process should carry on and they should maintain the link between each struggles themselves and with the party. They would then easily recognise turning point of any major struggle.

Will New Russia is turning back to socialism? Victory Parade of 9th of May

The victory parade in Moscow on 9th of May is somewhat a chilling reminder of old soviet days. The parade comes after  the annexation of Crimea. 

Ok, we all know what Nikita Khrushchev did. After all he is the man who took out his shoe in UN while addressing the general assembly. He handed Crimea to Ukraine and after Putin's annexation of Crimea back to Russia,  Russian National pride is all time high.

 However this parade was quite similar to those conducted in the former USSR, which I used to watch since 1984. I was somewhat perplexed by this flag shown below behind the military vehicles.  It has hammer and sickle in it. And not only that. Flag on the left has CCCP printed on it, which is  USSR in Russian.

 Most interesting thing is the words used by the generals and soldiers. 

The Commanding General addressed the soldiers as comrade soldiers. Then the soldiers replied to him calling him "thovarish genaral" in Russian meaning comrade general. 

Then the General reported to Defence minister the readiness of the troops to the possession.  He addressed the minister as comrade minister and minister replied to him addressing as comrade general. 

Most intriguing part is that the minister addressed the  president putin as comrade Vladimir Putin and not as his excellency the president. 

Then Putin addressed the soldiers as  comrade soldiers. Is this normal? Or is it that Russia is firmly heading back to Soviet system with some sort of a mixed capitalist system like in China. In that case this day will be a memorable one. 

---ajith Dharmakeerthi 

Quantum tunnelling and Gamow Energy

Quantum tunnelling:

Quantum tunnelling also known as the barrier penetration, is the key to the occurrence of fusion reactions in stars. If the particle's total energy is less than the potential energy of some barrier it cannot pass that barrier. Think about throwing a ball over a wall. Unless there is sufficient kinetic energy to attain a height greater than the wall, there is no way the ball will reach the other side. Kinetic energy of the ball, once transformed to gravitational potential energy should exceed the gravitational potential energy of the wall.
However this restriction does not apply to quantum mechanics. We have to consider the wave properties of the particle in quantum mechanics. The amplitude of particle's wave function goes to zero only for an infinitely high barrier although the wave function associated with a particle is attenuated by a potential barrier.

As we know that the finite potential barriers exist in reality, the wave function inside and beyond the barrier is non-zero. Hence the position probability density is also non-zero. (position probability density).  Therefore there is a small but non-zero probability that a particle will make its way through a barrier, in such a case and even though that may appear impenetrable or insurmountable in normal circumstances. If we think about the ball again, if a ball and the wall were small enough for quantum properties to dominate over the classical scenario, it would be possible for a ball to reach the other side. That is even if it did not have enough kinetic energy to overcome the gravitational potential energy at the wall's top. This seems strange but this is precisely what happens during collisions of nuclei.

For the nucleus to be stable, the nucleons in a nucleus sit in a potential well surrounded by a Coulomb potential barrier of finite height and width. There is a non-zero probability of a particle with energy less than the height of the barrier would make its way from outside the barrier to inside due to barrier penetration to reach the nucleus.

The Gamow energy

The  barrier potentials do vary with separation, i.e. V is a function of r. For the Coulomb barrier, the penetration probability may be expressed in terms of the particle energy E, and the Gamow energy EG which depends on the atomic number of the interacting nuclei, and hence the size of the Coulomb barrier:

Therefor Gamow Energy:

where α is the fine structure constant ≈ 1/137.0.  and and C is Speed of light.
The rate of nuclear fusion therefore depends on the penetration probability of the Coulomb barrier. This penetration probability in turn is described by its Gamow energy.
A higher EG reduces the probability that the barrier will be penetrated. The Gamow energy measures the strength of the Coulomb repulsion, which determines the height of the Coulomb barrier.

The Gamow energy is named for George Gamow (1904–1968), a Russian physicist and cosmologist who escaped to the USA in 1934. His paper ‘The origin of chemical elements’ (1948) by Alpher, Bethe & Gamow attempted to explain much of astrophysical nucleosynthesis in the big bang and also predicted the existence of the cosmic microwave background radiation.

The Gamow Peak: 

The fusion probability as a function of energy for nuclei.  The energy at which the fusion rate is a maximum is called the Gamow peak. The region on either side of the peak in which the fusion probability is significant is called the Gamow window.

Ref: Stellar Evolution and Nucleosynthesis - Sean G Ryan, Andrew J Norton

Predicting the Abundances and Successes of the Standard Model

Predicting the Abundances: 
There are a few complications predicting the abundances. One of the complications is tracking the abundances of few dif ferent nuclei instead of just a single element hydrogen. Next problem is that neutrons are unstable when not in a nucleus. They have a half-life of about 11 minutes. Third, several light nuclei end products have very small binding energies, therefore delaying the freeze-out.

BBN has it's own shortcomings earlier on like not being able to produce the observed abundances of all of the element isotopes, primarily due to the unstable nuclei with atomic number A = 5 and A = 8. Therefore as Burbidge et al. (1957) correctly noted stellar nucleosynthesis caught attention of the astrophysicists. If we assumes that 4He is entirely of stellar origin, then we should be able to find places in the universe in which the 4He mass fraction 25% . The data for 4He ( The helium(Y) vs oxygen (O=H) abundances in extragalactic HII regions emphasized
the lack of low 4He regions. [ref: Olive (1999)] shows the fact that no such region with low 4He has been observed and that leads to a conclusion that BBN nucleosynthesis is responsible for 4He abundance and should be part of any cosmological model.

The element abundances depend on the number of baryons per photon, or on or  .
 Big Bang nucleosyntheis therefore makes very clear predictions for the
primordial abundances of elements created in the first half hour of the Universe's
existence. These predictions can be tested, and the overall level of agreement with
observations is one of the many successes of the Big Bang model. However, the
tricky part of the experiment is to determine primordial abundance of baryonic
matter that has remained in its primordial condition for the ~ 13.7 billion years
since the nucleosyntheis epoch.

Burles et al. (1999b) noted that, the predicted abundances of the light elements

 have been used to test the consistency of the hot big bang model at very early times (t ~0.01200sec). Fields et al. (1996) pointed out that the abundances of 4He and 7Li alone are su cient to probe and test the theory

and determine the single remaining parameter in the standard model, the baryon to
photon ratio.

Successes of the Standard Model

The assumptions that the standard model is based on are the laws of physics, which have been verifi ed at the present time by experiments, are also valid in the early universe. The cosmological principle described above holds. The temperature at early time t1 is greater than and contents of the universe are in thermal equilibrium.

It is suggested that (t1) is very close to 1. A baryon asymmetry is consistent with
observed radiation density.  It is assumed also that the initial density fluctuations gave rise to later formation of structures. The standard cosmology model nonetheless achieved success.

Close connections have been developed between theory and observations for Standard Big Bang Nucleosynthesis (SBBN), and observations are more and more reliable now. The BBN model leads to a deeper understanding of the creation of primordial elements and the predictions of the CMB. The most important of all is predicting abundances of   and explaining it through a single free parameter  .  The value of baryon density    agrees with other estimated values. Astrophysicists up to now used SBBN predictions and measured abundances to successfully estimate best values for cosmological parameters of baryon density  and baryon to photon ratio   . Generally one uses the low D/H ratio as the decent estimator for find for the baryon density. The next chapter will show that, the observed abundances of elements D, 4He and 7Li are close to the primordial abundances predicted by SBBN.

References:
1.E. M. Burbidge, G. R. Burbidge, W. A. Fowler, and F. Hoyle. Synthesis of
the elements in stars. Rev. Mod. Phys., 29:547{650, Oct 1957. doi: 10.1103/
RevModPhys.29.547. URL http://link.aps.org/doi/10.1103/RevModPhys.
29.547.
2. S. Burles, K. M. Nollett, J. W. Truran, and M. S. Turner. Sharpening the predictions of big-bang nucleosynthesis. Physical Review Letters, 82:4176{4179, May 1999b. doi: 10.1103/PhysRevLett.82.4176.
3. B. D. Fields, K. Kainulainen, K. A. Olive, and D. Thomas. Model independent
predictions of big bang nucleosynthesis from ^4He and ^7Li: consistency and
implications. New A, 1:77{96, July 1996. doi: 10.1016/S1384-1076(96)00007-3.

BBN - Reactions Explained

Deuterium bottleneck - At high temperatures and densities, according to Hawley and Holcomb (1997) neutrons and protons can fuse directly to form deuterium (also called heavy hydrogen) nuclei, or deuterons.

Deuterium is the isotope of hydrogen, and it contains one proton and one neutron

in its nucleus. The reaction that formed the deuterium is shown here is on of the first reactions

of key fusion reactions . The in this reaction represents a photon.This reaction liberates the binding energy (energy equal to the energy liberated when a nucleus is created from other nucleons or nuclei -Wikipedia)  of the deuterium nucleus in the form of photon. Deuterium then fuses with a proton or another deuterium as in here shown in the second reaction, 

 to form the helium nucleus 3He or as shown in below 3rd reaction, 

fuses with neutron to create a tritium 3H. As shown in following reaction 4 

 both these nuclei (3He and 3H) then react with additional particles, 3He with a neutron or a deuteron, and the tritium with a proton or a deuteron, to form 4He. This is the most common isotope in the universe and almost all helium in the universe was created in this nucleosynthesis epoch, shortly after the big bang.

We can fi nd that the equilibrium Hydrogen density is proportional to exp(B/kT) where B = 13:6eV is the binding energy of the hydrogen atom. The most strongly bound light nucleus is 4He, with binding energy B4 =28:5MeV . So most of the nucleons end up as Helium in equilibrium and that's why we should have Helium abundances now. As the universe cooled down and expanded di fferent nuclear reactions froze out, leaving the relic abundances of the stable nuclei.

Key Fusion Reactions:

Below are the Key fusion reactions of Big Bang nucleosynthesis taken from lecture

from Steven Weinberg:

4He is a very stable nuclei with close to 28MeV binding energy. However, a nuclei with atomic number A = 5 is unstable. Therefore the further fusion is rare with lower binding energies. However this would be overcome and the production of 7Li will proceeds through. These further reactions with Li production are shown here:

The weak interaction rates responsible for n - p equilibrium freeze -out at 

T ~0:8MeV . The neutron to proton ratio at this is about 1/6. However when taking

into account the fact that free neutron decays prior to deuterium formation, this

ratio drops to n/p ~ 1/7. Then the 4He mass fraction is  ~ 0:25.

Reference:

1. J. Hawley and K. Holcomb. Foundations of Modern Cosmology. Oxford University Press, USA, 1997. ISBN 9780195104974. URL http://books.google.co.uk/

books?id=eBFawfP8ak8C.

2.http://star-www.st-and.ac.uk/ kdh1/cos/cos17.pdf

3 http://en.wikipedia.org/wiki/Steven Weinberg

Big Bang Nucleosynthesis (BBN) -Historical background

Historical background: The early universe behaved like a nuclear explosion or like a fusion bomb, creating the temperatures required for the creation of light elements. After that first minute with the temperature close to perhaps a billion kelvins nuclear reactions started. Approximately 180 seconds after the big bang, the temperature of the universe was  according to Hawley and Holcomb (1997). The content of the Universe consisted of a dilute gas of free streaming neutrinos , photons ,
 electron positron pairs
 and trace amount of nucleons(the protons and neutrons) as noted by Boesgaard and Steigman (1985). The temperature and densities were still very high, but dropped sufficiently so that the nuclei of atom could remain stable. The creation of atomic nuclei through nuclear reactions called nucleosinthesis, thought to be commenced at this point. Hence, this period in the big bang is known as the nucleosynthesis epoch. Olive (1999) noted that Big Bang Nucleosunthesis (BBN) is the theory explaining the origins of the light elements D;3 He;4 He and 7Li and their primordial abundances. Ellis (2011) commented that, the theoretical framework for BBN is based on Friedmann-Lemaitre-Robertson-Walker cosmology and a network of nuclear reactions.

BBN requires temperatures greater than 100keV and corresponds to time scales less than 200 seconds. It was necessary to achieve a density n  . The current density of visible matter is

 and we can estimate  the current temperature of the universe as  ~ 10K. 

In the early Universe at temperatures T < or ~ to 1MeV , conditions for the synthesis of the light elements were attained. Weak interactions were in equilibrium at higher temperatures. The following processes fix the ratio of number densities of neutrons to protons. 

(a neutron plus a positive electron (positron)  create  a proton and an anti-nuetrino and vice-versa, a neutron plus a nuetrino create a proton and electron,  from a  nuetron  a proton, electron and antinuerino is fixed).

The ratio of neutrons to protons at equilibrium at temperature T is given by a Boltzman factor: 

where Nn and Np are number densities of neutrons and protons, delta m

 is the neutron proton mass difference,1.3 MeV. Olive (1999) notes that, when the temperature  the ratio of neutron to proton was

.

Reference: 

1. K. A. Olive. Primordial big bang nucleosynthesis. ArXiv Astrophysics e-prints, Jan. 1999. URL http://arxiv.org/abs/astro-ph/9901231.

2. A. M. Boesgaard and G. Steigman. Big bang nucleosynthesis - theories and observations. ARA&A, 23:319{378, 1985. doi: 10.1146/annurev.aa.23.090185.001535.

3. G. F. R. Ellis. Inhomogeneity eff ects in cosmology. Classical and Quantum Gravity, 28(16):164001, Aug. 2011. doi: 10.1088/0264-9381/28/16/164001.