Wednesday, 27 October 2010

Physics Projects 1 Big Bang

Outside of my OU work I have a number of physics projects I have been working on, on and off over the past 20 years or so. This post outlines my plan to fully understand the establishment of the big bang model in the late 1960's to early 1970's. When life was relatively simple and there was no dark matter, dark energy and only one universe to worry about. Open any book on cosmology, popular or otherwise and in the section entitled Big Bang Nuclear synthesis (BBN for short)  there will be a couple of graphs plotted showing the abundances of Helium and Hydrogen as they evolved in time from about 100th of a second to about 3 minutes after the big bang. Another graph will show the abundances of other light elements such as Lithium and Beylium. However what they will not tell you in any great detail is how these graph's were obtained. In those crucial moments the temperature of the universe (according to the story) was such that stable nuclei were able to be formed and in a few minutes all of the Hydrogen and Helium that we observe in the universe was created. The person who was able to synthesise his knowledge of both nuclear physics, statistical physics and  cosmology to give a coherent story which fits the facts was P J E Peebles ('Primordial Helium abundance and the Primordial Fireball II Astrophysical Journal 146 pp 545-552 1966). The significance, as readers of this blog will probably know, is that a number of cosmologists such as Fred Hoyle and Hermann Bondi had hoped that they could account for the Hydrogen and Helium abundances from Stellar explosions. Peebles calculation was what physicists//engineers refer to as a back of the envelope calculation and it wasn't long before more sophisticated calculations, based ironically on the codes that Hoyle had written to study stellar explosions were able to come up with more accurate predictions. This line of research culminated with the work of   Kawano in the early 1990's with a code written in FORTRAN (like all good scientific codes) which considers a staggering 88 basic nuclear reactions and is able to predict the abundances of all the light elements based on a knowledge of their reaction rates, a general relativistic cosmological model and relativistic statistical physics. Kawano's manual for the code he wrote is accessible from Fermi lab

and it is one of my long term ambitions to put all the pieces together in one place concentrating in detail on all the in's and out's of the calculation and culminating in my own code which is able to reproduce at least in rough outline the same results that Peeble's got. Now that I have a bit of spare time between courses I hope to be able to give this project a well deserved kick up the backside and rejuvenate it.    

The current status is as follows

1) A general overview based on a classical approximation.  (status Complete)  

   Some what bizarrely a good approximation to the results of Peeble's can be obtained on the basis of Newtonian Physics and classical statistical physics as enshrined in the Boltzmann distribution. I have summarised this work in a word document which provides a good overview hopefully understandable by anyone who has completed MS221 and possible S207. If people would like a copy please request one from my home e-mail

The core background to understand the calculation fully draws on three main topics 

                a) General Relativity and it's application to Cosmology in particular the Friedmann equations.

                b) Fermi's theory of the Weak Interaction and a calculation of the Nuclear Decay rate which is the  key parameter in the theory. One can always cheat by just quoting the experimental value, however one misses out on a key insight as to how particle physics and Cosmology combine together.

               c) Relativistic Statistical Physics

I've more or less completed some notes on neutron decay and I've got backgtound notes on General Relativity my aim over the next couple of months is to tidy these notes up and then make a start on relativistic statisitical physics. Statistical physics has never been one of my strong points when I was at Exeter a certain Dr Jones tried to teach our class it, but he taught it in an idiosyncratic manner to say the least and so I was always put off it. I hope to remedy this.

When all that is under my belt, I can start given the guidelines in Kawano's manual writing my own code.

So if I'm lucky this project should see completion in the next 2-3 years but I do have to stop procrastinating.

Sunday, 24 October 2010


Hi and welcome to this blog inspired by a number of my fellow Open University students such as Neil Anderson

 and Nilo de Rook.


I decided to create my own.

This blog will include my feelings about my Open University experiences but also a lot more. I've just finished my open university courses for this year these were:

                      MS211: Exploring Mathematics

                      A211:    Philosophy and the Human Situation

Earlier in this year I also did MST121 Using Mathematics.

 I have an MSc in Theoretical Physics focusing on particle physics for which I did the exams in 1979 - 80 and completed the disseration in 1984. I also have a BSc in the same subject which I got from Exeter in 1978. Since then I have acquired a postgraduate certificate in Further Education and a diploma in Optoelectronics from Heriot Watt University Edinburgh. I have also had two postgraduate research associateships one in Theoretical Chemistry at Bristol university where I spent an admittedly frustrating year trying to get a code to model the photodissociation of molecules working and one in image processing at Heriot Watt university where I did a comparative study of three image processing techniques. Since 1990 I have worked in the antenna departments of GEC Marconi Chelmsford and since 1994 I have been working in Edinburgh again in the antenna department of a company which has changed its name from GEC to BAE Systems and is now called SELEX - Galileo. Despite all these changes my job has essentially remained the same which is to model the effects of the nose of an aircraft (the radome) on the radiation pattern of the antenna and investigate the effects of the radome on clutter. This involves quite intensive computational electromagnetics.

Despite the switch to Applied Physics since the mid eighties I have retained my interest in pure physics and I was most happiest when doing my part time MSc at Southampton. There I was introduced to the exciting world of particle physics and the main tools that physicists use to investigate this subject namely relativistic quantum field theory and symmetries based on Lie Group theory. I came just as the Standard model of particle physics was being finalised. I think that this is probably the greatest intellectual achievement of the last quarter of the 20th Century. I also think that given the lack of data, extensions to the Standard model of physics such as superstrings M theory and so forth whilst interesting mathematics can only be speculation. I have at present no desire to pursue these topics as I really don't think they will lead anywhere. In the words of Dirac/Pauli because they can't be tested they are not even wrong. One of my aims to be discussed further in other posts is to get to the stage where I can do what are called radiative corrections to processes  from the Standard Model to model the scattering  of such reactions  as electron neutrino scattering,  electron positron annhilation or investigate the predicted properties of the Higgs boson. 

My aim as far as my Open University studies are concerned is to get the MSc in mathematics  concentrating on the pure side. Mainly because modern physics uses a lot of pure maths concepts such as functional analysis, group theory and differential geometry for which the average theoretical physicist is ill prepared. Indeed, despite the fact that I can solve Maxwell's equations, apply quantum mechanics to solve problems in scattering theory and atomic and molecular spectroscopy, apply General Relativity to investigate the properties of stars and cosmological models and so forth. There are two significant books in the foundations of physics which I've had for thirty years which may have been written by people from a different planet and it is my long term ambition to study these.

These are 

1) Hawking and Ellis 'The Large Scale structure of space time' 
This book was the first coherent account of the singularity theorems of classical General Relativity showing that apparent singularities which occur in say the Schwarzschild solution or the Big Bang model were not accidents of the coordinate system but inherent in the basic equations of General Relativity. The background needed to understand this is topology and co-ordinate free differential geometry.

2) Von Neumann "The Mathematical Foundations of Quantum Mechanics" 
This book showed that the underlying mathematical structure of quantum mechanics was that of a complex Hilbert Space. To understand this the mathematical background needed is a grasp of real analysis, complex analysis, Linear analysis, and last but not least Functional analysis. 

Unfortunately the mathematical background of the average theoretical physicist is not adequate to this especially in the fields of analysis . Hence the Open University maths courses. Next year I embark on

         M208 Introduction to Pure Maths

And taking a bit of a risk as it presumes a knowledge of real analysis got from M208.

        M337 Complex Analysis

Which will hopefully get me the understanding in real and complex analysis I need to move forward. It might be considered risky to do M337 in the same year as M208. However I want to embark on the MSc by 2013 and the M337 course is only available in Odd years. I don't feel so bad as the analysis part of M208 is covered by David Brannan's book  'Introduction to Mathematical Analysis' which I've been reading since August and am about 1/2 way through hope to finish it by Christmas. I also have copies of the course material for M208 and M337 from the wonderful university bookshop which enables people who have done OU courses to sell their course material to other people.

Of course the course you want might not be immediately available however just keep looking.

So at the risk of hubris I'm reasonably confident of getting through the material for these courses next year and with a reasonable grade. I'm aiming for grade 2 i.e a combination of > 70% in both the continuous assessment and the final exam. This is sufficient to get onto the MSc and means that I don't put so much pressure on myself I know some people on MS221 seemed to put great pressure on themselves to get distincition (i.e > 85% for the exam and continuous assessment ). I'll explain the OU marking system which seems rather unfair these days as someone could get > 85: for their continuous assessment but have a bad exam and so only end up with a grade 4 or even fail). 

Anyway I think this is enough for this initial post. I'll put a number of posts explaining the background to my other interests over the next week or two, outlining my thoughts on other Open Uninversity courses and the other major part of my intellectual journey to understand philosophy. Hope you enjoy this

Best wishes Chris