Sunday, 6 January 2013

I must be mad SM358 quantum mechanics

Well for better or worse I have decided to register for the quantum physics course. Ok technically I don't need it but I feel the OU would look more favourably on my application to do the quantum entanglement project in October if I have the course under my belt. It will be revision of one of my favourite subjects and also a chance to get a glimpse of the new stuff which has emerged since it was shown that quantum mechanics is incompatible with the Bell inequalities which forms the basis of quantum information theory.

As readers of this blog will know I tend to favour the minimalist interpretation in that the so called wave-function is essentially the complex sqaure root of a probability density function and not a real field in configuration space. It will be interesting to see what the official OU line is.  I hope it is more of the 'Shut up and calculate' rather than getting bogged down in interpretational issues. All a working physicist needs to apply quantum mechanics to model the world is

1) The Born rule namely the fact that the modulus squared of the wave function when suitably normalised gives rise to a probability density function.

2) An algorithm to convert classical Hamiltonians or lagrangians into quantum mechanical terms this is essentially converting momentum into a differential operator. For non- relativistic situations this leads to the Schrodinger equation, for relativistic situations it is depending on the spin of the particle involved either the Klein Gordan equation, The Dirac equation or for photons a quantised version of Maxwell's equations.

3) The eigenvalue - eigenstate rule for the wavefunction or probability state vector. Namely that the eigenvalues of the wavefunction or probability state vector is related to the energy levels of the system under consideration.

4) The most controversial aspect namely a rule for relating the time evolution of the wave-function of quantum mechanics which contains all the possiblities to the single outcome seen in measurement. The so called collapse of the wave-function. 

If you take the Born rule seriously then as the wavefunction is essentially statisitical this presents no problem in interpretation all that happens is that one of the many possiblities is realised, just as in classical probability theory one spin of the roulette wheel or throw of the dice realises one of the possibilities. There is nothing magical about this certainly we don't create the world by measurement.

On the other hand those interpretations such as many worlds or the Bohm interpretation (as currently formulated) have to postulate either the reality of the 3N+1 configuration space or the even more fantastical idea that a parallel universe is created every time a measurement is made. I prefer the simplest interpretation consistent with the facts and it seems to me seeing the wavefunction as the complex square root of a  probability density function is all one needs and dissolves much of the misguided debate about the real meaning of the wave-function.

 Anyway I'm looking forward to this as a preliminary to doing the entanglement project alongside Number theory and logic in October.


  1. I think you will love it.

    Kid in sweet shop? :-D

    I did see a recent journal paper that stated that the wave function, was actually a real wave, as shown by experiment. I think it was the Dutch in the Physics World publication this year; I'll try and dig it out.


  2. Well Daniel I know there are papers like that which emerge from time to time. But the problem with asserting that the wave-function is a real field in configuration space is that you are then commited to the existence of a 3N+1 dimensional space-time where N is the number of particles in the universe. That like parallel universes is a step to far for me to swallow.

    But yes I do feel like a kid in a sweet shop.

  3. I, too, have just signed for SM358 - but the February course starting in three weeks rather than next October.

    I need to empty my head now of the various QM books I've read, as they all seem to scatter in different directions when it comes to stating what's actually going on.

    I've gone from probability wave functions to holomorphic existence, to infinite parallel universes, and back.

    Looks very interesting though - QM, plus complex analysis = mind engaged and occupied, for me.

    I'm going to read back through my M343 probability notes as I go - would love to get some "intuition".

  4. Great just waiting on OUSBA to approve the funcing. Anyway I think and in my opinion quite rightly the emphasis on the course for the most part will be on learning how the mathematics of quantum mechanics works and the interpretational issues whilst there in the background will play a secondary role. It is quite remarkable that the formalism apart from the formal rules I've given above seems relatively independent of the interpretational issues.
    Dare say it wont be on the course fora though.