QED: the models behind quantum mechanics and classical mechanics.

This week – Thursday March 16 at 13.00 in C1-5 – a new series of QED lectures will begin.  The driving force behind the new QED program is the wish to understand the model behind quantum mechanics. This is a very successful model: it is assumed to represent the absolute truth of reality.  Realization of this wish will lead to a balance between mathematical theory and applications.  Theory and applications will be seen as two halves that strengthen each other.  In one direction, you will see how the theory helps in practice:  2X2 matrices, complex numbers, eigenvectors, eigenvalues, differentiation and integration will be used.  In the other direction, you will see how practical needs stimulate the development of theory. The first –formal - hour we will work on understanding, the second hour participants will work on and discuss  problems/puzzles from various topics.   

We aim for an understanding of three quantum `mysteries’. You might have read about these.

  1. Heisenberg uncertainty principle. There is a fundamental reason why it will never be possible to measure both position and velocity of an elementary particle as precise as you want. The limit to the precision is given by the constant of Planck.  This will be proved mathematically. A key role will be played by calculating the product of two matrices A and B in both orders: AB and BA.
  2. Wave or particle?  Elementary particles behave sometimes as a wave and sometimes as a particle. A dramatic illustration is given by the double-slit experiment.  A key role will be played by modelling elementary particles using vectors with complex numbers as entries.
  3. Entanglement. It can happen that two particles that are light years removed from each other are entangled. That means that if you make a change in one, then at the same moment the other one, very far away, changes.  This has potential applications to future quantum computers.  A key role will be played by the essential role of eigenvectors and eigenvalues in the model.

Our strategy is to attack quantum mechanics in block 5; then all participants will know about eigenvectors and eigenvalues from their course `Vector Calculus’. We will use block 4 to prepare for this by trying to understand the model behind classical mechanics.  Another successful model: it gives such a good approximation of the absolute truth of reality that it remains completely adequate for most everyday purposes.  The history of this model is a good illustration of how practical needs stimulate the development of theory.  All the theory that you have learned in your Analysis courses was developed by Newton in an attempt to discover the laws that govern the universe.  

It is recommended that you attend both hours, come weekly and try to solve some exercises/puzzles; then you will profit fully, but QED is as always free from any obligations!  For example, you do not need to attend always: I will try to make lectures as independent of each other as possible.

The only prerequisites for participation in QED are:  for block 4: that you have attended the course Analysis; for block 5: that you have attended moreover the courses Matrix Algebra and Vector Differentiation.  In particular, it is not necessary that you have attended QED in block 3.  Lecture notes will be provided after each lecture.

You are most welcome to attend some QED meetings! You can register for QED on SinOnline. Then you will find the lecture notes on Blackboard.

Jan Brinkhuis