Sunday, 24 February 2013

Odds and Sods

This is more of a general catch up post rather than anything specific.

Current Status of A224

I've just finished my 4th TMA for my music course. Not much to say really it involved analysing an Allegro for String Quartet and a Scherzo and Trio for piano. Musical analysis in many ways is a bit like going through a mathematical proof. The main thing to look for are the Key changes and how they are implemented for simple pieces this is quite straightforward as one simply moves from the Tonic Key to the Dominant in the first half and then back again. Or if it is a minor key one usually ends up in the relative major. For more complicated pieces where there is a transition passage exploring many keys the key changes almost on a bar by bar basis and it can be quite tricky to work out what is going on. I think whilst I got the major key changes I fudged the transition keys. Other things to look out for are contrasts in the melody and texture of the piece. Unlike TMA02 at least we had the scores and so didn't have to rely on purely aural effects. So this is in hand but can be quite time consuming.

Piano Playing

Well last January a colleague of mine at work has lent me his sons Yamaha Clavinova and I've got used to playing it. It's important to get something which feels like a real piano. Keyboards just don't hack it. I can play more or less all the scales for Grades 1 and 2 and the Arpeggios and broken chords. I wish I could say the same for the pieces though I'm struggling with the Grade 1 book of pieces although as I practice more I'm stumbling less I guess it's just a matter of time really. My plan is after June when the music course has finished to start getting lessons and hopefully be fit to do at least grade 1 in November maybe even grade 1 and 2. We'll see. My practice routine most days is to go through the scales in the morning before work and play the pieces a couple of times. Then in the evening if I have time spend 15 minutes per piece. I think my practice is skewed more to scales but as they form the building blocks It's best to concentrate on those first.

Fluids I really need to spend the next week polishing off the second TMA more next week

Quantum Mechanics   I have done the first two assignments ICMA's as they are called, I got above 80% for both so decided to leave it at that. They don't really count I need to do the first proper TMA by the end of March so have plenty of time. On a related note I just invested in what would be the first text book account of the Many Worlds interpretation that isn't just popular science

Not that I'm convinced but it's useful to have as a definitive account so one knows what one is arguing about. I have written the first review of it on Amazon.

I also took time out to see Lincoln and Master Django. Lincoln is an absolutely brilliant film and I hope it gets the Oscars. I hadn't realised that after the Emancipation proclamation Lincoln struggled to get the bill through the house of representatives. Sounds as if things haven't changed much Obama seems to have similar problems. The film shows just how much compromise and dirty deals are needed to get any progressive legislation through. The best part as far as I was concerned was that of Thaddeus Stephens played by Timothy Lee Jones. I hope he gets a best supporting actor role. I've ordered the book on which the film was based apparently it was one of President Obama's favourite books

Also a book I read about 15 years ago on the American Civil War by McPherson

Master Django Unchained is also in it's way a good film quite a contrast to Lincoln really brutal in parts and doesn't flinch about the racism of the Southern States. Tarantino injects some humour especially in a scene where the Ku Klux Clan start complaining that they can't see through the badly cut holes in their pillow sheets. Whilst Lincoln is more my type of film this is still definitely worth watching if only to bring home just how brutally slaves were treated in the South during that period. Again the supporting role played by Christopher Waltz (the baddie from Inglorious basterds) was very good.

So that about wraps it up for this time Next post will be on the second TMA for Fluids.

Saturday, 9 February 2013

SM358 Quantum Mechanics First Impressions

I have started SM358 and here is a quick first impression of the course it seems to cover the basics pretty well there are three units

1) Wave Mechanics, this sets the background to the development of Schrodinger's equation and solves it for simple problems such as the square well potential, transmission and reflection at a barrier and the simple harmonic oscillator which it solves by annhilation and creation operators as well as giving a brief overview of the solution by series using Hermite's polynomials. As this is a physics course, not one addressed to mathematicians, then it does tend to skip over some mathematical details. Certainly one is not likley to be asked to solve Schrodinger's equation in parabolic coordinates or solve many complicated problems. For that one would need a course based on a book such as Landau and Lifshitz volume 3

If I get time as a tour de-force I would love to work through the solution of Schrodinger's equation for parabolic coordinates for both the bound state problem and the scattering problem which for the coulomb potential is exact even if it does involve functions which go by the ridiculous name of the Confluent Hypergeometric Function.

Still fair enough for the type of course this is meant to be. On a slightly down side it does push the standard line that particles in set ups as the two slit experiment must be travelling down two slits at once and treats wave function collapse as a physical process (although as is usual the mechanism is never given). No mention is made of the epistemic view of the wave function that the wave function is a mathematical representation of the probabilities associated with  a quantum system and that when an event occurs one of the possibilites is realised thats all.

2) Quantum Mechanics and It's interpretation. This gives a good overview of the Dirac Formalism and it's application to angular momentum and spin.  However it stops short of Clebsch Gordan coefficients which describe the coupling of many particles.

It then goes on to discuss the violation of the Bell inequalities and how they rule out local hidden variable theories. However they don't seem to accept that there are interpretations such as Bohm's theory which get round the problem by invoking Non-local Hidden variables or even the many worlds theory I would have thought some mention of these alternative views might have been mentioned. Conversely the text seems to want to have it's cake and eat it. Having dismissed the hidden variable point of view it still maintains that non-locality is an essential feature of quantum mechanics but the alternatives are Non local hidden variable theories (or realist theories) or local non hidden variable theories or non realist theories.

To expand slightly for pairs of properties subject to the uncertainty principle such as spin components or postion and momentum it is impossible to assign definite values to each pair of values. Thus these are undetermined or cannot be measured simultaneously. This introduces a degree of Non realism into the debate and those who don't subscribe to Hidden variable theories claim that the uncertainty principle is fundamental and precludes any hidden variable for these pairs of propeties. However it must be stressed that not all properties of quantum systems are subject to the uncertainty principle these include charge mass and intrinsic spin. So rejection of Hidden variables or realism vis a vis pairs of properties subject to the uncertainty principle is not the same as rejection of  realism per se.

Bell showed that the combination of locality and Hidden variables vis a vis pairs of properties subject to the uncertainty principle was in contradiction with the predictions of quantum mechanics but if you reject Hidden variables as the course text does you are not commited to non locality it is perfectly acceptable to have non realistic local theories. However the course text speaks about signals between two particles travelling faster than the speed of light. Oh really what is the mechanism for this. Anyway despite this caveat it gives a reasonable over-view of the mathematics involved. It then goes on in the final chapter to discuss applications of entanglement to cryptography and so called tele-portation.

The final book Quantum mechanics of matter, discusses some of the standard applications of quantum mechanics to the hydrogen atom, molecule, solid state and lasers. Again the maths is a bit sketchy enough is given for those dedicated to fill in the gaps but the emphasis seems to be on using the wave functions to predict various quantites rather than the derivations of the wave functions themselves.  Given the limitations this is a reasonable overview, but the subjects touched are far deeper and this can only provide an brief sketch of the applications of quantum mechanics.

In general this promises to be quite a good course, however it is a shame that this is the only course on quantum physics that the OU offers. There should be follow up courses on the applications of Group theory to quantum mechanics, A course on statistical physics, A course on Solid state physics, a course on quantum optics, quantum information theory and computing,  quantum scattering theory and ideally a course on particle and nuclear physics. I doubt this will ever happen and so people who do this course will be left wanting more. Unfortunately there seems to be a dire lack of on line courses offering this so one is left to ones own devices.

As a final point the method of assessment for physics courses seems different to that for maths courses in that there are 6 so called ICMAs (Interactive Computer Marked assignments) which you can have as many attempts as you like and 4 TMA's   But none of these count towards your final assessment provided you get an average of 30% or more. This means that far more emphasis is placed on the exam so I need to refine my exam technique in order to be sure of a good grade.

As a footnote I managed to catch a lecture given by the ubiquitous Brian Cox on quantum mechanics given to celebreties. On the whole quite a good overview, but one thing slightly puzzled me he made the claim that the Pauli Exclusion principle applied to all electrons in the universe so that when one electron changed it's energy all the other electrons in the universe did so as well. I find this a bit bizarre surely one can speak of isolated systems so that the energy levels of a hydrogen atom in Manchester will be the same as the energy levels of a hydrogen atom in Edinburgh. If they were not then how would spectroscopy work. So I confess to not understanding the claim if anyone knows of a reference then I would be grateful