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Vacation project 2006

I have produced some novel research results based upon space time manifolds that are not time orientable (time can go backwards after some journeys). The results show links to electric charges, spin half and quantum theory. The results are hard to visualise, which limits communication. The aim of this project is to illustrate these peculiar results using computer graphics and animations. It has the option to start with simpler results on manifolds that are not space orientable. If very successful there are new areas to extent the research to.

 

The project will give the student exposure to and appreciation of advanced theoretical physics, particularly linking mathematics they are familiar with to fascinating counter examples.

 

Using software for depicting the vector fields and constructing the animations is a transferable skill, valuable for research and in industry. Grappling with the difficult new concepts will give a real feel for research.

 

The project is suitable for a first class Maths/Phys student only.

 

The student will work in collaboration with the supervisor and will interact with the other vacation students working in the department – expected to number about 12.

 

Project Plan

 

  1. Familiarisation with the software (probably Mathematica) to create animations
  2. Illustrate non-orientability of a mobius strip, also show that it is not co-orientable, that the centre circle is orientable but no co-orientable
  3. Use the Mobius strip as an example of a 1+1D spacetime that is not time orientable
  4. Illustrate Gauss and Stoke's theorem. Particularly with reference to Electromagnetism.
  5. Show counter examples to the theorems when the manifold is not compact, or not orientable or co-orientable.
  6. illustrate apparent electric charge from source free equations
  7. Illustrate rotation vector fields on a manifold.
  8. Illustrate Spin half rotation properties of box in a box etc.
  9. Show manifolds that do not admit rotation vector fields
  10. Illustrate a physical rotation (parameterised by a time coordinate)
  11. show the counter examples on manifolds that are not time orientable
  12. Try to understand particle interchange on non-time orientable manifolds - is there a link to boson and fermion statistics.

 The work will probably use Mathematica and the results should all be published on the web and may be turned into short PR releases inconjuction with research TV