## How to Solve Physics Problems

Posted in Cute Problems, Education with tags , , , , , , on September 18, 2015 by telescoper

It’s Friday afternoon at the end of Induction Week here at the University of Sussex. By way of preparation for lectures proper – which start next Monday – I gave a lecture today to all the new students in Physics during which I gave some tips about how to tackle physics problems, not only in terms of how to solve them but also how to present the answer in an appropriate way.

I began with Richard Feynman’s formula (the geezer in the above picture) for solving physics problems:

1. Write down the problem.
2. Think very hard.

That may seem either arrogant or facetious, or just a bit of a joke, but that’s really just the middle bit. Feynman’s advice on points 1 and 3 is absolutely spot on and worth repeating many times to an audience of physics students.

I’m a throwback to an older style of school education when the approach to solving unseen mathematical or scientific problems was emphasized much more than it is now. Nowadays much more detailed instructions are given in School examinations than in my day, often to the extent that students  are only required to fill in blanks in a solution that has already been mapped out.

I find that many, particularly first-year, students struggle when confronted with a problem with nothing but a blank sheet of paper to write the solution on. The biggest problem we face in physics education, in my view, is not the lack of mathematical skill or background scientific knowledge needed to perform calculations, but a lack of experience of how to set the problem up in the first place and a consequent uncertainty about, or even fear of, how to start. I call this “blank paper syndrome”.

In this context, Feynman’s advice is the key to the first step of solving a problem. When I give tips to students I usually make the first step a bit more general, however. It’s important to read the question too. The key point is to write down the information given in the question and then try to think how it might be connected to the answer. To start with, define appropriate symbols and draw relevant diagrams. Also write down what you’re expected to prove or calculate and what physics might relate that to the information given.

The middle step is more difficult and often relies on flair or the ability to engage in lateral thinking, which some people do more easily than others, but that does not mean it can’t be nurtured.  The key part is to look at what you wrote down in the first step, and then apply your little grey cells to teasing out – with the aid of your physics knowledge – things that can lead you to the answer, perhaps via some intermediate quantities not given directly in the question. This is the part where some students get stuck and what one often finds is an impenetrable jumble of mathematical symbols  swirling around randomly on the page. The process of problem solving is not always linear. Sometimes it helps to work back a little from the answer you are expected to prove before you can return to the beginning and find a way forward.

Everyone gets stuck sometimes, but you can do yourself a big favour by at least putting some words in amongst the algebra to explain what it is you were attempting to do. That way, even if you get it wrong, you can be given some credit for having an idea of what direction you were thinking of travelling.

The last of Feynman’s steps  is also important. I lost count of the coursework attempts I marked this week in which the student got almost to the end, but didn’t finish with a clear statement of the answer to the question posed and just left a formula dangling.  Perhaps it’s because the students might have forgotten what they started out trying to do, but it seems very curious to me to get so far into a solution without making absolutely sure you score the points.  IHaving done all the hard work, you should learn to savour the finale in which you write “Therefore the answer is…” or “This proves the required result”. Scripts that don’t do this are like detective stories missing the last few pages in which the name of the murderer is finally revealed.

So, putting all these together, here are the three tips I gave to my undergraduate students this morning.

1. Read the question! Some students give solutions to problems other than that which is posed. Make sure you read the question carefully. A good habit to get into is first to translate everything given in the question into mathematical form and define any variables you need right at the outset. Also drawing a diagram helps a lot in visualizing the situation, especially helping to elucidate any relevant symmetries.
2. Remember to explain your reasoning when doing a mathematical solution. Sometimes it is very difficult to understand what students are trying to do from the maths alone, which makes it difficult to give partial credit if they are trying to the right thing but just make, e.g., a sign error.
3.  Finish your solution appropriately by stating the answer clearly (and, where relevant, in correct units). Do not let your solution fizzle out – make sure the marker knows you have reached the end and that you have done what was requested. In other words, finish with a flourish!

There are other tips I might add – such as checking answers by doing the numerical parts at least twice on your calculator and thinking about whether the order-of-magnitude of the answer is physically reasonable – but these are minor compared to the overall strategy.

And another thing is not to be discouraged if you find physics problems difficult. Never give up without a fight. It’s only by trying difficult things that you can improve your ability by learning from your mistakes. It’s not the job of a physics lecturer to make physics seem easy but to encourage you to believe that you can do things that are difficult.

To illustrate the advice I’ve given I used this problem, which I leave as an exercise to the reader. It is a slightly amended version the first physics problem I was set as tutorial work when I began my undergraduate studies way back in 1982. I think it illustrates very well the points I have made above, and it doesn’t require any complicated mathematics – not even calculus! See how you get on…

## The Renewed Threat to STEM

Posted in Education, Finance, Science Politics with tags , , , , , , on July 26, 2015 by telescoper

A couple of years ago, soon after taking over as Head of the School of Mathematical and Physical Sciences (MPS) at the University of Sussex, I wrote a blog post called The Threat to STEM from HEFCE’s Funding Policies about how the funding policies of the Higher Education Funding Council for England (HEFCE) were extremely biased against STEM disciplines. The main complaint I raised then was that the income per student for science subjects does not adequately reflect the huge expense of teaching these subjects compared to disciplines in the arts and humanities. The point is that universities now charge the same tuition fee for all subjects (usually £9K per annum) while the cost varies hugely across disciplines: science disciplines can cost as much as £16K per annum per student whereas arts subjects can cost as little as £6K. HEFCE makes a small gesture towards addressing this imbalance by providing an additional grant for “high cost” subjects, but that is only just over £1K per annum per student, not enough to make such courses financially viable on their own. And even that paltry contribution has been steadily dwindling.  In effect, fees paid by arts students are heavily subsidising the sciences across the Higher Education sector.

The situation was bad enough before last week’s announcement of an immediate £150M cut in HEFCE’s budget. Once again the axe has fallen hardest on STEM disciplines. Worst of all, a large part of the savings will be made retrospectively, i.e. by clawing back money that had already been allocated and which institutions had assumed in order to plan their budgets. To be fair, HEFCE had warned institutions that cuts were coming in 2015/16:

This means that any subsequent changes to the funding available to us from Government for 2015-16, or that we have assumed for 2016-17, are likely to affect the funding we are able to distribute to institutions in the 2015-16 academic year. This may include revising allocations after they have already been announced. Accordingly, institutions should plan their budgets prudently.

However, this warning does not mention the possibility of cuts to the current year (i.e. 2014-15). No amount of prudent planning of budgets will help when funding is taken away retrospectively, as it is now to the case. I should perhaps explain that funding allocations are made by HEFCE in a lagged fashion, based on actual student numbers, so that income for the academic year 2014-15 is received by institutions during 15/16. In fact my institution, in common with most others, operates a financial year that runs from August 1st to July 31st and I’ve just been through a lengthy process of setting the budget from August 1st 2015 onward; budgets are what I do most of the time these days, if I’m honest. I thought I had finished that job for the time being, but look:

In October 2015, we will notify institutions of changes to the adjusted 2014-15 teaching grants we announced in March 20158. These revised grant tables will incorporate the pro rata reduction of 2.4 per cent. This reduction, and any other changes for individual institutions to 2014-15 grant, will be implemented through our grant payments from November 2015. We do not intend to reissue 2014-15 grant tables to institutions before October 2015, but institutions will need to reflect any changes relating to 2014-15 in their accounts for that year (i.e. the current academic year). Any cash repayments due will be confirmed as part of the October announcements.

On top of this, any extra students recruited as as  result of the government scrapping student number controls won’t attract any support at all from HEFCE, so we wll only get the tuition fee.And the government says it wants the number of STEM students to increase? Someone tell me how that makes sense.

What a mess! It’s going to be back to the drawing board for me and my budget. And if a 2.4 per cent cut doesn’t sound much to you then you need to understand it in terms of how University budgets work. It is my job – as the budget holder for MPS – to ensure that the funding that comes in to my School is spent as efficiently and effectively on what the School is meant to do, i.e. teaching and research. To that end I have to match income and expenditure as closely as possible. It is emphatically not the job of the School to make a profit: the target I am given is to return a small surplus (actually 4 per cent of our turnover) to contribute to longer-term investments. I’ve set a budget that does this, but now I’ll have to wait until October to find out how much I have to find in terms of savings to absorb the grant cut. It’s exasperating when people keep moving the goalposts like this. One would almost think the government doesn’t care about the consequences of its decisions, as long as it satisfies its fixation with cuts.

And it’s not only teaching that is going to suffer. Another big slice of savings (£52M) is coming from scrapping the so-called “transitional relief” for STEM departments who lost out as a result of the last Research Excellence Framework. This again is a policy that singles out STEM disciplines for cuts. You can find the previous allocations of transitional relief in an excel spreadsheet here. The cash cuts are largest in large universities with big activities in STEM disciplines – e.g. Imperial College will lose £10.9M previous allocated, UCL about £4.3M, and Cambridge about £4M. These are quite wealthy institutions of course, and they will no doubt cope, but that doesn’t make it any more acceptable for HEFCE to break a promise.

This cut in fact won’t alter my School’s budget either. Although we were disappointed with the REF outcome in terms of league table position, we actually increased our QR income. As an institution the University of Sussex only attracted £237,174 in transitional relief so this cut is small potatoes for us, but that doesn’t make this clawback any more palatable from the point of view of the general state of health of STEM disciplines in the United Kingdom.

These cuts are also directly contrary to the claim that the UK research budget is “ring-fenced”. It clearly isn’t, and with a Comprehensive Spending Review coming up many of us are nervous that these cuts are just a foretaste of much worse things to come. Research Councils are being asked to come up with plans based on a 40% cut in cash.

Be afraid. Be very afraid.

## Taking Notes…

Posted in Education with tags , , , , on November 6, 2012 by telescoper

As if this week wasn’t busy enough, I’ve just received back the student questionnaires for my second-year module The Physics of Fields and Flows (which includes some theoretical physics techniques, such as vector calculus and Fourier methods, together with applications to fluid flow, electromagnetism and a few other things). I’ve only just taken up this module this year and was planning to prepare it over the summer, but circumstances rather intervened and I’ve had to put together more-or-less on the fly. I was, therefore, not inconsiderably apprehensive about the reaction I’d get from the students.

Fortunately most of the comments were fairly positive, although there were some very useful constructive criticisms, which I’ll definitely take into account for the rest of the term.

However, one recurring comment was that I write too fast on the whiteboard. In fact I go far more slowly than the lecturers I had at University. That brings me back to an old post I did some time ago about  lecture notes.

I won’t repeat the entire content of my earlier discussion, but one of the main points I made in that was about how inefficient many students are at taking notes during lectures, so much so that the effort of copying things onto paper must surely prevent them absorbing the intellectual content of the lecture.

I dealt with this problem when I was an undergraduate by learning to write very quickly without looking at the paper as I did so. That way I didn’t waste time moving my head to and fro between paper and screen or blackboard. Of course, the notes I produced using this method weren’t exactly aesthetically pleasing, but my handwriting is awful at the best of times so that didn’t make much difference to me. I always wrote my notes up more neatly after the lecture anyway. But the great advantage was that I could write down everything in real time without this interfering with my ability to listen to what the lecturer was saying.

An alternative to this approach is to learn shorthand, or invent your own form of abbreviated language. This approach is, however, unlikely to help you take down mathematical equations quickly.

My experience nowadays is that students simply aren’t used to taking notes like this – I suppose because they get given so many powerpoint presentations or other kinds of handout –  so they struggle to cope with the old-fashioned chalk-and-talk style of teaching that some lecturers still prefer. That’s probably because they get much less practice at school than my generation. Most of my school education was done via the blackboard..

Nowadays,  most lecturers use more “modern” methods than this. Many lecturers using powerpoint, and often they give copies of the slides to students. Others give out complete sets of printed notes before, during, or after lectures. That’s all very well, I think, but what are the students supposed to be doing during the lecture if you do that? Listen, of course, but if there is to be a long-term benefit they should take notes too.

Even if I hand out copies of slides or other notes, I always encourage my students to make their own independent set of notes, as complete as possible. I don’t mean copying down what they see on the screen and what they may have on paper already, but trying to write down what I say as I say it. I don’t think many take that advice, which means much of the spoken illustrations and explanations I give don’t find their way into any long term record of the lecture.

And if the lecturer just reads out the printed notes, adding nothing by way of illustration or explanation, then the audience is bound to get bored very quickly.

My argument, then, is that regardless of what technology the lecturer uses, whether he/she gives out printed notes or not, then if the students can’t take notes accurately and efficiently then lecturing is a complete waste of time. In fact for the module I’m doing now I don’t hand out lecture notes at all during the lectures, although I do post lecture summaries and answers to the exercises online after they’ve been done.

I like lecturing, because I like talking about physics and astronomy, but as I’ve got older I’ve become less convinced that lectures play a useful role in actually teaching anything. I think we should use lectures more sparingly, relying more on problem-based learning to instil proper understanding. When we do give lectures, they should focus much more on stimulating interest by being entertaining and thought-provoking. They should not be for the routine transmission of information, which is far too often the default.

I’m not saying we should scrap lectures altogether. At the very least they have the advantage of giving the students a shared experience, which is good for networking and building a group identity. Some students probably get a lot out of lectures anyway, perhaps more than I did when I was their age. But different people benefit from different styles of teaching, so we need to move away from lecturing as the default option.

I don’t think I ever learned very much about physics from lectures, but I’m nevertheless glad I learned out how to take notes the way I did because I find it useful in all kinds of situations. Effective note-taking is definitely a transferable skill, but it’s also a dying art.

## Three Tips for Solving Physics Problems

Posted in Cute Problems, Education with tags , , , , , on November 2, 2012 by telescoper

I spent quite some time this morning going over some coursework problems with my second-year Physics class. It’s quite a big course – about 100 students take it – but I mark all the coursework myself so as to get a picture of what  the students are finding easy and what difficult. After returning the marked scripts I then go through general matters arising with them, as well as making the solutions available on our on-line system called Learning Central.

Anyway, this morning I decided to devote quite a bit of time to some tips about how to tackle physics problems, not only in terms of how to solve them but also how to present the answer in an appropriate way.

I began with the Feynman algorithm for solving physics problems:

1. Write down the problem.
2. Think very hard.

That may seem either arrogant or facetious, or just a bit of a joke, but that’s really just the middle bit. Feynman’s advice on points 1 and 3 is absolutely spot on and worth repeating many times to an audience of physics students.

I’m a throwback to an older style of school education when the approach to solving unseen mathematical or scientific problems was emphasized much more than it is now. Nowadays much more detailed instructions are given in School examinations than in my day, often to the extent that students  are only required to fill in blanks in a solution that has already been mapped out.

I find that many, particularly first-year, students struggle when confronted with a problem with nothing but a blank sheet of paper to write the solution on. The biggest problem we face in physics education, in my view, is not the lack of mathematical skill or background scientific knowledge needed to perform calculations, but a lack of experience of how to set the problem up in the first place and a consequent uncertainty about, or even fear of, how to start. I call this “blank paper syndrome”.

In this context, Feynman’s advice is the key to the first step of solving a problem. When I give tips to students I usually make the first step a bit more general, however. It’s important to read the question too.

The middle step is more difficult and often relies on flair or the ability to engage in lateral thinking, which some people do more easily than others, but that does not mean it can’t be nurtured.  The key part is to look at what you wrote down in the first step, and then apply your little grey cells to teasing out – with the aid of your physics knowledge – things that can lead you to the answer, perhaps via some intermediate quantities not given directly in the question. This is the part where some students get stuck and what one often finds is an impenetrable jumble of mathematical symbols  swirling around randomly on the page.

Everyone gets stuck sometimes, but you can do yourself a big favour by at least putting some words in amongst the algebra to explain what it is you were attempting to do. That way, even if you get it wrong, you can be given some credit for having an idea of what direction you were thinking of travelling.

The last of Feynman’s steps  is also important. I lost count of the coursework attempts I marked this week in which the student got almost to the end, but didn’t finish with a clear statement of the answer to the question posed and just left a formula dangling.  Perhaps it’s because the students might have forgotten what they started out trying to do, but it seems very curious to me to get so far into a solution without making absolutely sure you score the points.  IHaving done all the hard work, you should learn to savour the finale in which you write “Therefore the answer is…” or “This proves the required result”. Scripts that don’t do this are like detective stories missing the last few pages in which the name of the murderer is finally revealed.

So, putting all these together, here are the three tips I gave to my undergraduate students this morning.

1. Read the question! Some solutions were to problems other than that which was posed. Make sure you read the question carefully. A good habit to get into is first to translate everything given in the question into mathematical form and define any variables you need right at the outset. Also drawing a diagram helps a lot in visualizing the situation, especially helping to elucidate any relevant symmetries.
2. Remember to explain your reasoning when doing a mathematical solution. Sometimes it is very difficult to understand what you’re trying to do from the maths alone, which makes it difficult to give partial credit if you are trying to the right thing but just make, e.g., a sign error.
3.  Finish your solution appropriately by stating the answer clearly (and, where relevant, in correct units). Do not let your solution fizzle out – make sure the marker knows you have reached the end and that you have done what was requested.

There are other tips I might add – such as checking answers by doing the numerical parts at least twice on your calculator and thinking about whether the order-of-magnitude of the answer is physically reasonable – but these are minor compared to the overall strategy.

And another thing is not to be discouraged if you find physics problems difficult. Never give up without a fight. It’s only by trying difficult things that you can improve your ability by learning from your mistakes. It’s not the job of a physics lecturer to make physics seem easy but to encourage you to believe that you can do things that are difficult.

So anyway that’s my bit of “reflective practice” for the day. I’m sure there’ll be other folk reading this who have other tips for solving mathematical and scientific problems, in which case feel free to add them through the comments box.

Posted in Biographical, Education, The Universe and Stuff with tags , , , , , on July 14, 2012 by telescoper

I sneaked into the department this morning to pick up some things from the office and leave some other things that I’ve finished with. I went quite early, to avoid the Saturday crowds there and back.

One of the things I found in my pigeonhole was a packet of student questionnaires about the third-year module Nuclear and Particle Physics for which I was responsible. It seems like a decade since I finished teaching it and marked the exams, but it can only be a couple of months. I was dreading reading the responses this time because I know I struggled a bit with this module, partly because it’s the first time I taught the Nuclear Physics part and partly for other reasons I won’t go into.

In fact the students were very kind and gave me quite good reviews; the only score that let me down really was that they thought the material was rather difficult. I’m not really surprised by that, because I think it is. However, as I’ve said before, I don’t think it’s a physics lecturer’s job to pretend that the subject  is easy; it is  a lecturer’s job to try to convince students that they can do things that are difficult. I don’t mean making  things difficult just for the sake of it, but trying to get the message across that a brain is made for thinking with and figuring difficult things out can be intensely rewarding.

The main criticism that students wrote in the space provided for their own comments was that they didn’t like the fact that I used powerpoint for some lectures. Actually, I don’t like using powerpoint for lectures either, but unfortunately I had no choice on some occasions. First I had a rather large class (85 students) and one of the rooms I had to use had a very small whiteboard; I was worried about its visibility from the back and the need to keep cleaning it every five minutes. Also in that room the projector screen covers the same area as the whiteboard, so it’s a pain to keep changing between powerpoint and whiteboard. Anyway, it’s a fair criticism. I’ll try to work out a better way of doing it next year.

To be perfectly honest I don’t like whiteboards much either. Call me old-fashioned, but  chalkboards are much better. Received wisdom, however, is that we have to have whiteboards, with all the ludicrous cost and environmental unfriendliness of the accompanying dry-wipe marker pens. But I digress.

Anyway, next Wednesday afternoon will see our graduation ceremony. Graduation day always reminds me of something somebody told me years ago when I attended my first one, at Queen Mary (and Westfield College, as it was then).  The essence of the comment was that what you have to remember as a lecturer is that when the students do well it’s their achievement; but when they don’t it’s your fault. Life’s like that, it’s never as symmetrical as particle physics.

Many of the students who took  Nuclear and Particle Physics will be graduating on Wednesday. I’m distraught that I won’t be able to go myself; this will be the first ceremony I’ve missed since I moved here five years ago.  If any of the graduating Physics class from Cardiff University happens to read this, I really hope you have a great day on Wednesday. I wish I could be there to shake your hand and wish you a very fond goodbye, but sadly that’s just not possible on this occasion.

## Failed Physics Teaching Analogies

Posted in Education, The Universe and Stuff with tags , , , , , , , on March 18, 2012 by telescoper

Last week I deputized for a colleague who was skiving off away at an important meeting so, for the first time ever in my current job, I actually got to give a proper lecture on cosmology. As the only out-and-out specialist in cosmology research in the School of Physics and Astronomy at Cardiff, I’ve always thought it a bit strange that I’ve never been asked to teach this subject to undergraduates, but there you are. Ours not to reason why, etc. Anyway, the lecture I gave was about the cosmic microwave background, and since I have taught cosmology elsewhere in the past it was quite easy to cobble something together.

As a lecturer you find, over the years, that various analogies come to mind that you think will help students understand the physical concepts underpinning what’s going on, and that you hope will complement the way they are developed in a more mathematical language. Sometimes these seem to work well during the lecture, but only afterwards do you find out they didn’t really serve their intended purpose. Sadly it also  sometimes turns out that they can also confuse rather than enlighten…

For instance, the two key ideas behind the production of the cosmic microwave background are recombination and the consequent decoupling of matter and radiation. In the early stages of the Big Bang there was a hot plasma consisting mainly of protons and electrons in an intense radiation field. Since it  was extremely hot back then  the plasma was more-or-less  fully ionized, which is to say that the equilibrium for the formation of neutral hydrogen atoms via

$p+e^{-} \rightarrow H+ \gamma$

lay firmly to the left hand side. The free electrons scatter radiation very efficiently via Compton  scattering

$\gamma +e^{-} \rightarrow \gamma + e^{-}$

thus establishing thermal equilibrium between the matter and the radiation field. In effect, the plasma is opaque so that the radiation field acquires an accurate black-body spectrum (as observed). As long as the rate of collisions between electrons and photons remains large the radiation temperature adjusts to that of the matter and equilibrium is preserved because matter and radiation are in good thermal contact.

Eventually, however, the temperature falls to a point at which electrons begin to bind with protons to form hydrogen atoms. When this happens the efficiency of scattering falls dramatically and as a consequence the matter and radiation temperatures are no longer coupled together, i.e. decoupling occurs; collisions can longer keep everything in thermal equilibrium. The matter in the Universe then becomes transparent, and the radiation field propagates freely as a kind of relic of the time that it was last in thermal equilibrium. We see that radiation now, heavily redshifted, as the cosmic microwave background.

So far, so good, but I’ve always thought that everyday analogies are useful to explain physics like this so I thought of the following. When people are young and energetic, they interact very effectively with everyone around them and that process allows them to keep in touch with all the latest trends in clothing, music, books, and so on. As you get older you don’t get about so much , and may even get married (which is just like recombination, in that it dramatically  reduces your cross-section for interaction with the outside world). Changing trends begin to pass you buy and eventually you become a relic, surrounded by records and books you acquired in the past when you were less introverted, and wearing clothes that went out of fashion years ago.

I’ve used this analogy in the past and students generally find it quite amusing even if it has modest explanatory value. I wasn’t best pleased, however, when a few years ago I set an examination question which asked the students to explain the processes of recombination and decoupling. One answer said “Decoupling explains Prof. Coles’ terrible fashion sense”. Grrr.

An even worse example happened when I was teaching particle physics some time ago. I had to explain neutrino oscillations, a process in which neutrinos (which have three distinct flavour states, associated with the electron, mu and tau leptons) can change flavour as they propagate. It’s quite a weird thing to spring on students who previously thought that lepton number was always conserved so I decided to start with an analogy based on more familiar physics.

A charged fermion such as an electron (or in fact anything that has a magnetic moment, which would include, e.g. the neutron)  has spin and, according to standard quantum mechanics, the component of this in any direction can  can be described in terms of two basis states, say $|\uparrow>$ and $|\downarrow>$ for spin in the $z$ direction. In general, however, the spin state will be a superposition of these, e.g.

$\frac{1}{\sqrt{2}} \left( |\uparrow> + |\downarrow>\right)$

In this example, as long as the particle is travelling through empty space, the probability of finding it with spin “up” is  50%, as is the probability of finding it in the spin “down” state. Once a measurement is made, the state collapses into a definite “up” or “down” wherein it remains until something else is done to it.

If, on the other hand, the particle  is travelling through a region where there is a  magnetic field the “spin-up” and “spin-down” states can acquire different energies owing to the interaction between the spin and the magnetic field. This is important because it means the bits of the wave function describing the up and down states evolve at different rates, and this  has measurable consequences: measurements made at different positions yield different probabilities of finding the spin pointing in different directions. In effect, the spin vector of the  particle performs  a sort of oscillation, similar to the classical phenomenon called  precession.

The mathematical description of neutrino oscillations is very similar to this, except it’s not the spin part of the wavefunction being affected by an external field that breaks the symmetry between “up” and “down”. Instead the flavour part of the wavefunction is “precessing” because the flavour states don’t coincide with the eigenstates of the Hamiltonian that describes the neutrinos’ evolution. However, it does require that different neutrino types have intrinsically different energies  (which, in turn, means that the neutrinos must have different masses), in quite  a similar way similar to the spin-precession example.

Although this isn’t a perfect analogy I thought it was a good way of getting across the basic idea. Unfortunately, however, when I subsequently asked an examination question about neutrino oscillations I got a significant number of answers that said “neutrino oscillations happen when a neutrino travels through a magnetic field….”. Sigh. Neutrinos don’t interact with  magnetic fields, you see…

Anyhow, I’m sure there’s more than one reader out there who has had a similar experience with an analogy that wasn’t perhaps as instructive as hoped. Feel free to share through the comments box…

## To Edinburgh and Back

Posted in Biographical, Education with tags , , , on November 10, 2011 by telescoper

I’m back home now after a trip to and from the fine city of Edinburgh which, in case you weren’t aware, is known to the locals as Auld Reekie. I wonder if there’s a local internet guide called Reekipedia?

The excuse for this trip was an invitation to take part in an exercise called a Teaching Programme Review in the School of Physics & Astronomy at the University of Edinburgh. The TPR is an exercise that looks at the courses on offer in the department, how they are taught, as well as the technical and administrative arrangements to back it all up. The Panel involved people from other departments inside the University and a couple of external advisers (both physicists), of which I was one. The Panel will be writing a detailed report on our findings which I hope will turn out to be useful, but it definitely wouldn’t be appropriate to comment on the details here.

What I will say here is that, although it was a very intense and busy few days, including face-to-face meetings with all kinds of academic and support staff, as well as current students, it was extremely interesting. As well as hopefully providing some input and suggestions to the TPR, it was also a chance for me to see the inner workings of another department and pick up a few ideas for the way we teach Physics courses in Cardiff.

One of the striking things about this visit was how similar are many of the problems facing Edinburgh to those we encounter in Cardiff. Another is how easy it is to recognize kindred spirits. It may not always be obvious to the students, but physicists are passionate about their subject, not only in terms of their research but also in terms of nurturing the talents of the students in their care. In the Brave New World of Higher Education we’re all supposed to see universities as businesses, competing ruthlessly in an unforgiving marketplace. In fact, most of us at the real business end of the university system (i.e. teaching and research as opposed to PR and marketing) see our competitors more as colleagues than as rivals. Long may that continue, in my opinion.

During the visit I was taken on a tour of the excellent facilities available at Edinburgh, including some really snazzy and impressive “teaching studios” the like of which I’d never seen before. I’d really love to have a go at teaching in one of those some day, as they offer a different style of education which I’m sure complements the more traditional lecture format. The students seem to like them a lot, which is the most important thing.

However, I have to say that the thing that I was most jealous about was the fact that most of their teaching rooms still have blackboards. Ours have all been replaced with horrible whiteboards that require expensive markers and are far less visible to a big audience. “Chalk and talk” is a tried and tested method and when it’s done well I still think it’s a very effective one. I’m all for innovation in teaching, but some traditional methods are actually pretty good!

Anyway, I’d like to thank everyone from Auld Reekie University for hosting this visit. It was hard work, but thoroughly enjoyable. If anyone from Edinburgh reads this I hope they will pass on my thanks to all the staff and students there for making it such a rewarding occasion! I’m just sorry I didn’t have the chance to see a bit more of the city, but the schedule was just too hectic.

What I did enjoy was staying in a nice hotel for 3 days that offered a truly splendid cooked breakfast in the mornings. I hadn’t started the day with kippers for a very long time! Might need to go on a diet for a few days though….