Nuclear Power – Converting Mass Into Energy?

One of the things that most people know about nuclear power is that it about turning mass into energy – E= mc2. Although this is not wrong it is extremely misleading.

First of all I am going to digress a bit. One of the things that makes Einsteins theory of relativity important is that it is universal. In fact one of the motivations of Einsteins work was that he wanted the laws of physics that are universal . Galileo worked out a system where the laws of physics were true irrespective of motion (although this turned out to only be true if the speed was small compared with the velocity of light). Newton worked out laws that were true on Earth and dictated the movement of planets. Einstein devised laws of physics where were true if the speed approached the speed of light with uniform motion – Special Relativity – and when they system is accelerating – General Relativity.

What E=mc2 tells us is that when there is an energy change there is always a mass change. It is not something that only happens in nuclear physics but also when there are other energy changes. For example there is a mass change when I stir a cup of tea or burn a piece of coal. However, in nuclear physics the energy changes are about a million time larger than chemical changes – e.g. burning a piece of coal (but see here why this is often misinterpreted). This means that the differing energy levels of different nuclei can actually be measured by their masses and this can be converted into differences in energies by using E=mc2.

Although the concept of  ‘turning mass into energy’  gives us a way of measuring the energy changes it tells us nothing of what is going on or calculating what those energy changes will be. To do this we need to understand the different energy levels of the nuclei and how those change during a nuclear reaction in a similar way that we can understand the energy changes during a chemical reaction by looking how the different energy levels of the electrons change.

I am not going to go into details here but will give a quick example.

238U undergoes alpha decay to 234Th:

U238

 If we look up the masses then we find

238U 238.05078
234Th 234.04360
alpha 4.00260

If we add the masses of the Thorium and Alpha particle we find that it is less than mass of the Uranium by 0.004577 atomic mass units. We can then use E=mc2 and calculate that the energy change is 4.264MeV. This is the energy of the alpha particle that is emitted (4.26975MeV) to quite a good approximation.

However, it tells us nothing about why the energy of the Uranium is unstable with respect to decay into a Thorium atom and an alpha particle.

The ‘unscientific’ approach to Radiation Risk

This post was going to be about the ICRP’s (International Committee on Radiological Protection) risk model. However, Dr Chris Busby has recently written1 an article for The Ecologist which covers some of what I was going to say. However, there are a few additional points I would like to make.

It is important to note that many of what are called ‘anti-nuclear’ arguments do not need this critique since they merely take the ICRP risk factors and apply them2. This gives about 5000 fatal cancers from Fukushima and more than 32,000 from Chernobyl.

To go onto the ‘unscientific’ way in which these risk model is applied it is important to understand something about the scientific method used. Since there are variables which can affect cancer risk in the real world understanding what is happening is a bit like detective work. There has been a murder and Colonel Mustard has been caught near the body with a bit of lead piping. So you think that he is the murderer. However, a little bit later a new bit of evidence appears. Professor Plum is found with a candlestick with the victims blood on it. There are several things that you can do with this new evidence:

  • ignore it
  • make it fit your original theory (Colonel Mustard must have given the candlestick to Professor Plum
  • rethink your original theory and think – maybe it was Professor Plum who is the murderer

Unfortunately many studies on the affects of radiation take the first two approaches rather than the last – they apply the risk factors from the Hiroshima and Nagasaki bombings, which as Dr Busby explains may be wrong1. If there is evidence that contradicts this – e.g.. more people are dying of cancer than you expect – then the evidence is either ignored or modified to fit the theory.

For example the number of people suffering ill health due to Chernobyl is greater than you would expect from the Hiroshima and Nagasaki data. Therefore there must be some other factor – they started smoking or started having promiscuous sex.

These are theoretical calculations based on the Hiroshima model that you say that if you have a certain radioactivity you know from Hiroshima that so and so many would die from it…

Hans Blix3

Similarly the leukaemia cluster near Sellafield was put down to various factors other than radiation since the radiation dose was ‘too small to create the affect’.

One of the things that prompted this post was a talk my Timothy Mousseau:

Again the evidence is ignored since it does not fit the theory.

Source Term

The evidence of more harm occurring than would be calculated from the Hiroshima and Nagasaki studies may not be solely or totally due to the calculated risk factors being wrong.

When there is a radiation exposure it is necessary to estimate the ‘source term’. i.e. how much radiation was released and how much the population was exposed to this radiation. This can be very difficult to estimate and different estimates can vary by several orders of magnitude.

Other Problems with Hiroshima and Nagasaki

There are several other problems with the Hiroshima and Nagasaki data which I am sure Dr Busby is aware of but is not in his article. The study was not started until five years after the bombings so some of the people more vulnerable to radiation affects would have already died and were not included in the study. There is also a problem with ‘missing doses’ in the studies4.

The evidence of risks greater than predicted by the Hiroshima and Nagasaki studies may or may not be criticised for the scientific methods and analysis used. However, they should not be rejected since they do not fit the ‘established theory’.


 

1 The ICRP’s radiation risk model is bogus science, The Ecologist, 2 October 2014 (http://www.theecologist.org/blogs_and_comments/commentators/2596275/the_icrps_radiation_risk_model_is_bogus_science.html)

2 New UNSCEAR Report on Fukushima: Collective Doses, Ian Fairlie, 2 April 2014 (http://www.ianfairlie.org/news/new-unscear-report-on-fukushima-collective-doses/)

3 The True Battle of Chernobyl (https://www.youtube.com/watch?v=mBAT13Bt9Ic) – this film is well worth watching if you have not seen it already.

4 Missing Doses in the Life Span Study of Japanese Atomic Bomb Survivor, David B. Richardson, Steve Wing, and Stephen R. Cole, American Journal of Epidemiology Advance Access published February 20, 2013 (http://aje.oxfordjournals.org/content/early/2013/02/20/aje.kws362.full.pdf)

 

 

A is for Atom

Here is a link to a 1992 programme by Adam Curtis called ‘A is for Atom’

http://www.bbc.co.uk/blogs/legacy/adamcurtis/2011/03/a_is_for_atom.html

What I found interesting was the interviews with some of the people involved in the very early days of the nuclear power industry including:

  • Alvin Weinberg, inventor of the PWR and BWR reactor
  • Glenn Seaborg, Chairman of the Atomic Energy Commission
  • Greg Minor, one of three engineers who resigned from General Electric because “nuclear power presented a profound threat to mankind”

The interviews start at about 23:40 if you want to skip the introduction to nuclear power at the beginning

 

“We discovered that our theoretical calculations didn’t have a strong correlation with reality.”

Robert Pollard, AEC Engineer

 

“In 1938, the year that Rutherford died their disappeared for ever the happy days of free scientific work which gave such delight in our youth. Science has lost her freedom. Science has become a productive force. She has become rich but she has become enslaved and veiled in secrecy. I do not know if Rutherford would continue to laugh and joke nowdays as he used to.”

Pyotr Kapitsa (Russian Nobel Prize winner

Human Rights, Worker Rights and the EU

In my previous post I noted a few things about the Human Rights Act and the European Convention on Human Rights. In this post I am going to talk a bit about what was left out of the European Convention and also the reason for some of the anti-EU sentiment in some political parties.

The European Convention Human Rights1 is based on the UN Universal Declaration on Human Rights2.

Many of ‘The Articles’  in the Universal Human Rights and the European Human Rights are very similar, however the ‘Universal Declaration’ contains some articles that the European Convention does not:

Article 23.
(1) Everyone has the right to work, to free choice of employment, to just and favourable conditions of work and to protection against unemployment.
(2) Everyone, without any discrimination, has the right to equal pay for equal work.
(3) Everyone who works has the right to just and favourable remuneration ensuring for himself and his family an existence worthy of human dignity, and supplemented, if necessary, by other means of social protection.
(4) Everyone has the right to form and to join trade unions for the protection of his interests.
Article 24.
Everyone has the right to rest and leisure, including reasonable limitation of working hours and periodic holidays with pay.
Article 25.
(1) Everyone has the right to a standard of living adequate for the health and well-being of himself and of his family, including food, clothing, housing and medical care and necessary social services, and the right to security in the event of unemployment, sickness, disability, widowhood, old age or other lack of livelihood in circumstances beyond his control.
(2) Motherhood and childhood are entitled to special care and assistance. All children, whether born in or out of wedlock, shall enjoy the same social protection.
Article 26.
(1) Everyone has the right to education. Education shall be free, at least in the elementary and fundamental stages. Elementary education shall be compulsory. Technical and professional education shall be made generally available and higher education shall be equally accessible to all on the basis of merit.
(2) Education shall be directed to the full development of the human personality and to the strengthening of respect for human rights and fundamental freedoms. It shall promote understanding, tolerance and friendship among all nations, racial or religious groups, and shall further the activities of the United Nations for the maintenance of peace.
(3) Parents have a prior right to choose the kind of education that shall be given to their children.

So many of the articles in the ‘universal declaration’ about social rights are left out of the European Declaration. I would imagine that the David Cameron et al. would be even less enamoured with the declaration if these articles were included.

However, some of the rights mentioned are now being enacted by the European Union – for example the Working Time Directive.

If we look at the Conservative Party Manifesto3 we can see that one of the main things that the Conservatives want to do within the European Union is to scrap the working time directive. Workers in the UK should have ‘the right’ to work more than 48 hours per week and have ‘the right’ to have a reduced number of holidays. Despite the fact that the UK already have some of the longest working hours in Europe4.

The Conservatives and UKIP will talk about ‘democracy’ and ‘sovereignty’. However, if these were really issues that concerned them then they should be up in arms about the Transatlantic Trade and Investment Partnership5. Our democracy and sovereignty is being rapidly destroyed by increased powers of corporations6.

This post is not supporting or attacking the European Union. However, it is important to realise that anti-EU rhetoric from the Conservatives and UKIP is based on the perceived threat to company profits and the support of workers rights.


 

1 European Convention on Human Rights (http://www.echr.coe.int/documents/convention_eng.pdf)

2 The Universal Declaration on Human Rights, United Nations (http://www.un.org/en/documents/udhr/)

3 Conservative party European Election Manifesto 2014, (http://www.conservatives.com/~/media/Files/Downloadable%20Files/MANIFESTO%202014/Large%20Print%20Euro%20Manifesto_English.ashx)

4 Who works the longest hours in Europe?, The Guardian, December 2011 (http://www.theguardian.com/news/datablog/2011/dec/08/europe-working-hours)

5 This transatlantic trade deal is a full-frontal assault on democracy, George Monbiot, The Guardian, 4 November 2013 (http://www.theguardian.com/commentisfree/2013/nov/04/us-trade-deal-full-frontal-assault-on-democracy)

6 A mining company’s $300 million attack on El Salvador’s water, Ecologist, 5th October 2014 (http://www.theecologist.org/News/news_analysis/2562735/a_mining_companys_300_million_attack_on_el_salvadors_water.html)

David Cameron, Human Rights Act and Freedom Speech

In my last post I talked a bit about ‘humanitarian war’ . In this post I want to make a few points how this foreign policy often goes hand-in-hand with policy changes at home. One obvious example of this was the Reichstag Fire in Germany in 19331. Perceived, real threats or even, in the case of the Reichstag Fire possible ‘false flags’ can be used to create a crisis where civil liberties are curtailed.

UK Prime Minister, David Cameron recently said that he would like to scrap the Human Rights Act (HRA) and leave the European Convention on Human Rights (ECHR). However, the convention was brought in just to avoid the unsavoury consequences of the curtailment of civil liberties mentioned above.

It is important to correct the common misconception that the ECHR was something that was imposed on the UK by the European Union(EU). The convention is totally separate from the EU and was entered by the UK quite willingly. One of the reasons for the convention was to have basic human rights principles that were outside the control of any single state.

A lot of what has been said about the ECHR and HRA is misleading if not totally untrue. I will not go into this here since it has been covered well elsewhere2.

It is interesting that one of the main criticisms from David Cameron etc is that it limits what he can do. That is the purpose of the convention and it would be completely futile if it did not sometimes conflict with the wishes of the Executive. There must be a legal limit to avoid absolute power.

There may be cases in which application of the Human Rights Act seems to lead to what some may see as perverse rulings. This is not peculiar to the HRA but part of the legal system. The legal system is not perfect and is sometimes incoherent.

More worrying is that David Cameron has spoken about clamping down on ‘non-violent’ protesters and limiting freedom of speech:


 

1 Reichstag fire, Wikipedia (http://en.wikipedia.org/wiki/Reichstag_fire)

2 Human Rights Act myths, Liberty (https://www.liberty-human-rights.org.uk/human-rights/what-are-human-rights/human-rights-act/human-rights-act-myths)

Iraq / Syria – Humanitarian War?

“There never has been a war yet which, if the facts had been put calmly before the ordinary folk, could not have been prevented … The common man, I think, is the great protection against war.”

Ernest Bevin

The aggressors in most wars claim that they are doing so on ‘humanitarian grounds’ from Hitler invasions of Czechoslovakia to Japans invasion of Manchuria and countless attempts by the British and other imperialist nations to bring ‘civilization and democracy’.

It is easy to understand why such wording is used to justify war. Many people feel the urge to do something when they hear about some of the atrocities that are occurring in the world. However, even if this was the true reason for the intervention (which it never is) it is often not as easy as sending over some troops of bombing a couple of pickup trucks.

One thing to remember is that we are constantly manipulated. Many atrocities are ignored by the media (sometimes because our government are actively supporting them) but suddenly a focus of media attention due to governments propaganda. Note that by propaganda I am not implying that what they say is factually incorrect – the best propaganda is not. However, we must ask ourselves why this issue is becoming prominent now and why pick this one from the hundreds of others.

Some of the problems that we are told we must ‘act on’ have been going on for years. For example the unrest in northern Iraq (see my previous post) was largely ignored by the media. Others are simply continually ignored. In Africa millions have died in the Democratic Republic of Congo1 with little media or political interest.

In the news today – well down the list and easy to miss if you do not look for it – is further details of what is happening in Libya2. The country whose people we were told to care so deeply about when the US and UK regimes wanted to topple Gaddafi are still suffering from the ‘humanitarian’ intervention.

Often these interventions make a bad situation worse as also happened during the war on Serbia3.

These wars often do work – Gaddafi and Saddam Hussein were toppled. However, they never met and were never meant to meet the ‘humanitarian’ aim of helping the people.

Hitting infrastructure in areas of  Iraq and Syria where there is a ISIS presence also affects the people in those areas. Not just through reprisals but loss of food and energy supplies. In wars it is often not the ‘collateral damage’ from bombs that kill innocent people. It is the ‘collateral damage’ from the lost of medical care, food and energy supplies and other infrastructure that kill innocent people.

My final point (for today anyway) is that what is the objective other than killing a few Jihadists. Who will take their place, how will the area be organised? If the aim is to put the control of the northern Sunni areas back into the hands of the regime in Baghdad whose treatment of them lead to the uprising in the first place, to leave the Sunni population open to further sectarian violence and retribution then you are going to have to drop a lot of bombs. If on the other hand you want the local population to reject ISIS (as they have done before) then bombing them is not going to help.

Again the long term humanitarian needs of the people we are told we are ‘saving’ have not been thought through – because they are not the real reason them bombs are falling.


1 Mortality in the Democratic Republic of Congo, Rescue International, International Rescue Committee, 2007 (http://www.rescue.org/sites/default/files/resource-file/2006-7_congoMortalitySurvey.pdf)

2 Libyan soldiers killed in Benghazi bombings and clashes, BBC, 3 October 2014 (http://www.bbc.co.uk/news/world-africa-29464748)

3 A Review of NATO’s War over Kosovo, Noam Chomsky, 2001 (http://www.chomsky.info/articles/200005–.htm)

Iraq / Syria background

It is disappointing that many comments on the current situation in Iraq and Syria, including many made by those in the ‘peace movement’ and ‘the left’ ignore the suffering of the people who live there. There is a lot of talk about did Assad gas his own people? is it part of the plan to weaken Iran, oil pipelines, who funds ISIS etc. It is important not to loose sight of what this should be about – people being terrorised by religious fanatics, people and essential infrastructure – food and energy supplies being bombed. While the ‘pawns’ in where the ‘game’ that is being currently played by the regimes in Syria, Iraq, UK, USA, Iran, Russia etc are on the sharp end of this we are also ‘pawns’. They use the ‘threat’ that they were instrumental in creating to try to get us to support actions that are nothing to do with ‘humanitarian intervention’ or stopping possible terrorist threats to the people of this country – it is about them furthering their own ends.

ISIS needs to threat of western intervention in the area to maintain their support as much as the regimes in US/UK need ISIS to further their goals in the area.

Having said all of that it is important to look ‘behind the scenes’ at some of the things that have happened so I would just like to make a few points.

North West Iraq

Since the invasion of Iraq in 2003 and the Shia dominated government there has been continued unrest in many Sunni areas where people feel that they have been politically and economically disadvantaged. The unrest led to the setting up of special units within the Iraqi police which carried out torture and death squad activities similar to counter insurgency activities used in El Salvador. The units where equipped and advised by the US1.

ISIS which was then just ‘Al-Qaeda in Iraq’ began to get involved in the Sunni rebellion. However, the some local Sunni fighters disapproved of the ‘foreign fighters’ hardline attitudes and tactic. This led to the formation of the ‘Sunni Awakening Movement’ (also know as the ‘Anbar’s Awakening’, ‘Sons of Iraq’…) who stopped their campaign against the coalition forces and fought against Al-Qaeda in Iraq eventually pushing them out of Iraq and into Syria. The Awakening Movement was armed and funded by the US Military. They made a significant contribution to the 90% drop in the sectarian violence in the area. It was planned to integrate these forces into the Iraqi Military, however this never happened2,3. Some of the Awakening leaders where later imprisoned or executed4.

Unrest in Sunni area increased in late 2012 and a protest camp was set up in  “Pride and Dignity Square” in Ramadi.  The protest quickly spread to other Sunni provinces. Near a protest site in Huwija a soldier was shot. The camp was encircled by the army for several days before a SWAT team moved in to clear the site and 44 protestors were killed5.

Several groups were involved in the protests – including former Awakening Movement members, Baathists and also ISIS supporters. However, many Sunni leaders and the Anbar Tribal Council supported the Iraqi government’s military action against ISIS. However, president Maliki accused the protest camps of being ISIS headquarters. Several raids against people seen as the ‘protest leaders’ were made, martial law was imposed and the protest camp in Ramadi was bulldozed. In response armed groups confronted the curfew by force5.

The tribal leaders who only a few weeks previous had supported military action against ISIS now worked with ISIS to fend off what they saw as the government attacks on the Sunnis.

Syria

The relationship between the  Baathist regime in Syria is complex6.  The Syrian regime was aware that following the invasion of Iraq in 2003 there were people in the US who had Syria next on the list7. The Syrian regime therefore actively supported jihadists  entering Iraq to fight the occupation forces8. As with many other governments the Syrians were not adverse to supporting the Jihadists as long as they were causing problems in another country.

Inspired by the ‘Arab Spring’ in 2011 a civil uprising occurred in Syria which was brutally repressed by the Syrian regime. This allowed ISIS to regroup in the west of Syria where they later re-expanded back into Iraq.

Although the media talk about ISIS controlled areas it is important to look at this in context – first of all have a look at a population density map of the relavant parts of Syria and Iraq – they ‘control’ a lot of nothing. As made clear above they are not working in a vacuum and large parts of Iraq are controlled by local Sunnis with some ISIS presence.

What ISIS do provide is some connection between the various areas which are controlled by local militia. They also provide medical facilities and distribute food – something that wins support for other groups such as Hamas and Hezbollah.


1  From El Salvador to Iraq: Washington’s man behind brutal police squads, The Independent 2013 (http://www.theguardian.com/world/2013/mar/06/el-salvador-iraq-police-squads-washington)

2 Make or Break: Iraq’s Sunnis and the State, International Crisis Group, August 2013 (http://www.crisisgroup.org/en/regions/middle-east-north-africa/iraq-iran-gulf/iraq/144-make-or-break-iraq-s-sunnis-and-the-state.aspx?utm_source=iraq-report&utm_medium=1&utm_campaign=mremail)

3 Who’s to blame for Iraq crisis, CNN, 12 June 2014 (http://edition.cnn.com/2014/06/12/opinion/pregent-harvey-northern-iraq-collapse/?c=&page=0)

4 Iraq Sentences Sunni Leader to Death, The New York Times, November 2009 (http://www.nytimes.com/2009/11/20/world/middleeast/20iraq.html?_r=0)

5 Maliki’s Anbar Blunder, Foreign Policy, 15 January 2014 (http://mideastafrica.foreignpolicy.com/posts/2014/01/15/maliki_s_anbar_blunder)

6 Suspects into Collaborators, Peter Neumann, London Review of Books, 15 April 2014 (http://www.lrb.co.uk/v36/n07/peter-neumann/suspects-into-collaborators)

7 General Wesley Clark (https://www.youtube.com/watch?v=9RC1Mepk_Sw)

8 Syria Condemns Unprecedented US Cross-Border Strike, CNS News, 26 October 2008 (https://cnsnews.com/news/article/syria-condemns-unprecedented-us-cross-border-strike)

 

Putting Thugs In Control

From the media and the announcements of various politicians it is easy to see large areas of Syria and Iraq as being populated only by psychopathic Islamic fundamentalists. However, most of the people there are merely trying to live their lives as best as possible under very difficult circumstances. They want to be able to feed themselves and their families, to be able to get medical care for their children if they become sick.

Most places I have lived have one or two well known gang/families who are the local ‘heavies’. What would the result be if some of them were funded and armed to ‘keep the peace’. Do you think that this would be a good idea? Alternatively do you think that they would use these resources for extortion, corruption and settling disputes with rivals? Put this into a context of existing religious tensions – for example arming Protestant gangs in Northern Ireland – then perhaps this idea becomes even worse. What state do you think that the country would be in after 30 years of this rule by armed gangs as has happened in Afghanistan.

The western forces have been arming, funding and supporting paedophiles, rapists and murders in Afghanistan1,2. The have supported murder squads in Iraq in a similar fashion in which they have done in other places such as El Salvador3.

In Syria they have been supporting Islamic fundamentalists including Al Qaeda who bring “discipline, religious fervor, battle experience from Iraq, funding from Sunni sympathizers in the Gulf, and most importantly, deadly results. In short, the FSA [Free Syrian Army] needs al-Qaeda now.”  This was not something that they did not know at the time but  “The unspoken political calculation among policymakers is to get rid of Assad first—weakening Iran’s position in the region—and then deal with al-Qaeda later.”4

Even now with US lead airstrikes against the Islamic State there is no let up in the ‘more important’ goal of removing Assad. Our governments will continue to support the ‘moderates’ .

goodbad

It is true that some of the local population in Northern Iraq support the Islamic State over the Iraqi government and that some people in Afghanistan support the Taliban over the Afghan government. A lot of what we hear about ISIL and the Taliban is undoubtedly correct so how bad does the governments that we put into power and continue to support in Afghanistan and Iraq have to be that people prefer to live under the Taliban/ISIS.

It could be argued that the general population in areas controlled by ISIL and the Taliban should have risen up against such oppression.  Perhaps the general population in this country should rise up against our politicians who are complicit in atrocities.


1 Afghanistan’s US-Backed Child-Raping Police, Counterpunch, July 30, 2009, (http://www.counterpunch.org/2009/07/30/afghanistan-s-us-backed-child-raping-police/)

2 Exit Afghanistan,aAVPRO/Tegenlicht documentary by Mariusz Pilis and Olaf Oudheusden  (https://www.youtube.com/watch?v=Wo-R_Yp2py0)

3 From El Salvador to Iraq: Washington’s man behind brutal police squads, The Guardian, 6 March 2013 (http://www.theguardian.com/world/2013/mar/06/el-salvador-iraq-police-squads-washington)

4 Al-Qaeda’s Specter in Syria, Council on Foreign Relations, August 2012 (http://www.cfr.org/syria/al-qaedas-specter-syria/p28782)

Learning The Lessons Of The Titanic

In a recent news article1 about the evacuation zone around Sizewell nuclear power plant Jeremy Western, director of special projects and nuclear new build for EDF, said that the zone was so small because the likelihood of an accident was “exceedingly unlikely”.

This is rather like saying that an ocean liner does not need a full compliment of lifeboats because the chances of it sinking are “exceedingly unlikely”.

The accident at Fukushima has shown that the aim of emergency planning should be to be prepared for events that are not ”reasonably foreseeable”. What should be learnt from Fukushima is that we have ‘consideration of an extreme accident’ which could be caused by events that are beyond the design of the power plant. It is clear from Chernobyl and Fukushima that such events, even if they are “exceedingly unlikely” would require an evacuation zone of at least 20Km.

The nuclear industry constantly tell us that we should trust them and that they know what they are doing. How are we meant to do this if they have not learnt the lessons, not just from Fukushima but from the Titanic.


1 Sizewell: Accident evacuation zone ‘ridiculously small’, say campaigners, EADT, September 13, 2014 (http://www.eadt.co.uk/news/sizewell_accident_evacuation_zone_ridiculously_small_say_campaigners_1_3767935)

Black Holes – Classical Theory

This is just a short discussion about black holes which does not use any of Einsteins complicated field equations and relies (mainly) on school level physics with a few digressions on the way.

Escape Velocity

First of all I am going to discuss the ‘escape velocity’ – the speed that we would need to throw an object so as it escapes the Earth’s gravitational pull. To do so the kinetic of the object must be greater than the energy needed to go from the Earth’s surface to outer space (infinity).

Kinetic energy is given by

gr1

where m1 is the mass of the object and v is its velocity.

Newtons tells us that the force of gravity is given by

gr10

where G is Newtons gravitational constant and m1 and m2 are two masses separated by a distance r. The energy needed (again from Newton) is the force times distance. However, since the force on out mass changes with distance we cannot just multiply by the distance.

Inverse Square Laws – digression

Just a quick diversion into the reasons for inverse square laws. It is not that the ‘force gets weaker’ – it is just spread over a larger area as you move away from the Earth. The area it is spread over is the area of the sphere distance r from the Earth i.e 4πr2. This is explicit in the usual formula for the electrostatic force between two charges q1 and q2:

gr15

In Newtons gravitational equation the 4π is incorporated into Newston’s constant G.

Back to Escape Velocities

If we do a bit of calculus we find that the actual energy need to move a mass m1 from a distance r0 from mass m2 is given by1:

gr11

To escape the Earth’s gravitational pull this must equal the kinetic energy therefore:

gr5

cancelling the mass of our object – m1rearranging we can find the escape velocity:

gr6

We now can bring in some real numbers

Mass of Earth 5.97×1024 Kg
Gravitational Constant 6.67×10-11 N·(m/kg)2
Speed of light 2.999×108  m/s
Radius of Earth 6.371×106 m

putting these figures into the formula above gives the escape velocity for the Earth as 11,185 m/s (11.2Km/s).

The Sun’s Gravity – digression

This figure is much, much smaller than would actually be needed since the object would have to escape the gravitational pull of the Sun which is much larger. If it is so large then why do we not feel it on Earth? The reason is that we do and we are actually in free fall towards the Sun. However, since the Earth is also moving it continually misses – i.e. the Earth is in orbit.

Black Holes

Now if we keep the mass of the Earth the same but decrease its radius do we get to a point where the escape velocity is greater than the speed of light? That would mean that not even light could escape the gravitational pull – i.e. we would have a black hole.

If we go back a few steps and replace our escape velocity v by the speed of light c then we have:

gr7

We can now rearrange to find the radius r where this will happen

gr16

If we plug in some numbers again then we find that if the mass of the Earth was concentrated in a sphere of radius 0.0088m (8.8mm) then it would be so dense that light could not escape – i.e. it would be a black hole.

If we consider a body the mass of the Sun, 1.989 x 1030 Kg, then the radius is 2.95Km.

Although this simple classical analysis does not capture all the intricacies of black holes the radius calculated agrees well with those calculated by Swarzschild using Einsteins field equations.

If you want to play about with the numbers then my spreadsheet is here.


 1 If you don’t mind a bit of calculus then energy is given by

gr2

putting in Newtons gravitational force expression we get

gr3

evaluating this integral gives

gr11

While we are here we can also work out the kinetic energy. If we consider motion in the x direction and using F = ma then the energy becomes

gr12

we can now change the integration variable since we know that

gr13

this gives

gr14

Notice that we have an integration constant. We now know from Einstein that this is mc2. What most people know about Einsteins special theory of relativity (E=mc2) is in fact not relativitistic – it has always been hidden there, however Einstein also gives more terms in the expression of kinetic energy alongside E = mc2 + 1/2mv2