We have arrived at last at the final week of teaching for this term. The way the timetable has worked out, my last lecture before the break will be on Wednesday afternoon. Later that evening we have our staff Christmas party. I did one lecture this morning, by the end of which I had completed the syllabus for my Mechanics & Special Relativity Module. I have two more sessions with that class, tomorrow and Wednesday, which I will devote to some worked examples and revision for the examination which is on January 14th.
I’m sure the students are tired too, but at least they have the advantage of youth which probably endows them with more energy than I can summon at this point!
Two events over the weekend added to the general sense of exhaustion and made me feel even older. One was that a very dear friend whom I first met, when he was 19 and I was 29, just had his 50th birthday. I remember very well celebrating his 20th. For some reason I felt more comfortable when our ages began with the same digit, if only for a few months. Now he’s 50 and I’m 59…
The other thing that happened was that last night I watched the first episode of a three-part documentary series The Irish Civil War. I thought it was excellent and will definitely watch the other two programmes. The Irish Civil War, which was raging 100 years ago, was as brutal as it was tragic and the episode made uncomfortable viewing, not least because even a century later many of the scars are still painful.
The thought suddenly struck me watching the programme that I was born in 1963, just 40 years or so after the end of the Civil War and 20 years closer in time to that event than to today. Time passes.
Anyway, enough of that. I don’t have time to mope about feeling old. I’ve got some examples to work out for tomorrow’s lecture, including a problem on time dilation…
Now as we approach the last fortnight of term, I am nearing the end of both my modules, MP110 Mechanics 1 and Special Relativity and MP201 Vector Calculus and Fourier Series, and in each case am about to start the bit following the “and”…
In particular, having covered just about everything I need to do on Vector Calculus for MP201, tomorrow I start doing a block of lectures on Fourier Series. I have to wait until Monday to start doing Special Relativity with the first years.
As I have observed periodically, the two topics mentioned in the title of the module MP201 (Vector Calculs and Fourier Series) are not disconnected, but are linked via the heat equation, the solution of which led Joseph Fourier to devise his series in Mémoire sur la propagation de la chaleur dans les corps solides (1807), a truly remarkable work for its time that inspired so many subsequent developments.
Anyway I was looking for nice demonstrations of Fourier series to help my class get to grips with them when I remembered this little video recommended to me some time ago by esteemed Professor George Ellis. It’s a nice illustration of the principles of Fourier series, by which any periodic function can be decomposed into a series of sine and cosine functions.
This reminds me of a point I’ve made a few times in popular talks about astronomy. It’s a common view that Kepler’s laws of planetary motion according to which which the planets move in elliptical motion around the Sun, is a completely different formulation from the previous Ptolemaic system which involved epicycles and deferents and which is generally held to have been much more complicated.
The video demonstrates however that epicycles and deferents can be viewed as the elements used in the construction of a Fourier series. Since elliptical orbits are periodic, it is perfectly valid to present them in the form a Fourier series. Therefore, in a sense, there’s nothing so very wrong with epicycles. I admit, however, that a closed-form expression for such an orbit is considerably more compact and elegant than a Fourier representation, and also encapsulates a deeper level of physical understanding. What makes for a good physical theory is, in my view, largely a matter of economy: if two theories have equal predictive power, the one that takes less chalk to write it on a blackboard is the better one!
 It is 1st December 2022, which means that it’s five years to the day since I started work at Maynooth University. So much has happened in that period it seems very much longer since I first arrived here. I’m very happy that I made the move here all those years ago. I won’t deny that the past five years have had their frustrations. The teaching and administrative workload, especially for the three years I was Head of Department, especially during the Covid-19 pandemic, has been very heavy and has made it difficult to be very active in research. Last year was a particularly tough year for the Department of Theoretical Physics, when we were forced to teach a whole year with only half the usual number of full-time teaching staff. It was very depressing not being able to deliver as a good a teaching experience as we wanted without the necessary resources. There never seems to be any shortage of funds for new senior management positions but not for the staff who actually perform the main function of a University. Fortunately our immediate staffing problem has passed and we now have our usual number of lecturers in place. I was entitled to take a sabbatical when I reached the end of my term as Head of Department, but I deferred it because I didn’t want to leave my colleagues short-staffed again before the ship was properly steadied. I will put in a request in January to take it in 2023/24. If anyone out there feels like playing host to an old cosmologist please let me know! On the bright side, I have great colleagues in the Department and the students are very engaged. There are few things in life more rewarding than teaching people who really want to learn. This year so far has been particularly enjoyable, if tiring because we have a large first year. I have also acquired two more PhD students and a Research Masters student. The thing I’m probably most proud of over the past five years is, with the huge help of staff at Maynooth University Library, getting the Open Journal of Astrophysics off the ground and attracting some excellent papers. We’re still growing, though perhaps not as quickly as I’d hoped. The pandemic had something to do with that. So, after a few years of hard and at times dispiriting slog, things are going pretty well. Meanwhile, in Brexit Britain, events have turned out exactly as I predicted, especially this: Brexit will also doom the National Health Service and the UK university system, and clear the way for the destruction of workers’ rights and environmental protection. The poor and the sick will suffer, while only the rich swindlers who bought the referendum result will prosper. The country in which I was born, and in which I have lived for the best part of 54 years, is no longer something of which I want to be a part. In other words I don’t regret for one minute my decision to leave Britain. Incidentally, five years is the term needed to qualify for Irish nationality by residence so if I had needed to I could now apply via that route. I noticed looking at the similar post I wrote on this day last year that academic colleagues in the UK were on strike on that day. They are still taking industrial action, and indeed were on strike yesterday. My biggest fear for the Irish Higher Education system is that it follows the “business model” of soulless teaching factories with courses delivered by demoralized staff on casual teaching contracts. Things are definitely going that way here and this trend must be resisted.
We have reached the end of Week 9 at Maynooth University, so there are now just three weeks to go until end of term. All of sudden the shops are filled with Christmas whatnots and thingies, and I’ve finally bowed to pressure and bought a ticket for this year’s Messiah.
As usual for this time of the year we have a pair of Open Days for undergraduate admissions. The first was today, Friday, and catered mainly for school trips whereas tomorrow’s (i.e. Saturday’s) is usually more parents with their offspring. During the pandemic these events have been online but we’re now having them on campus so that prospective students see the important features on campus in the flesh:
For the last few years, I’ve been the main person responsible for running the Theoretical Physics part of these Open Days but now that duty has passed on to the new Head of Department. It’s not that I disliked doing these events, it’s just that I think it’s better from now on to have a fresher face doing them. Today for me has therefore largely been a normal teaching day and I’m also able to have a lie-in tomorrow morning.
In past years, before the pandemic, some lectures have been cancelled to make way for Friday Open Day talks. That has included the Friday lecture of my 2nd year module on Vector Calculus which takes place in a room previously needed for admissions business on Open Days. Now, however, a new teaching building is available and many of the Open Day talks are in there so my lecture went ahead as planned. The room next door to mine was however used for the Open Day and a group of about ten schoolgirls, dressed in green blazers and plaid skirts in a manner highly reminiscent of the Derry Girls, almost came into my lecture by mistake.
I saw quite a few visitors around the campus this morning, and some came into the Science Building for a look around, but I don’t know how busy the day was in comparison to previous November events on campus. I don’t know how busy it will be tomorrow either, as I shall be putting my feet up at home.
Today wasn’t quite a normal day, however. I had lunch in Pugin Hall. I used to do that regularly before the pandemic but today was the first time I’ve been there since March 2020. Either Pugin Hall has been closed or I’ve been too busy to have anything other than a sandwich in my office.
Following last week’s Maynooth Astrophysics and Cosmology Masterclass, a student asked (in the context of the Big Bang or a black hole) what a singularity is. I thought I’d share my response here in case anyone else was wondering. The following is what I wrote back to my correspondent:
–oo–
In general, a singularity is pathological mathematical situation wherein the value of a particular variable becomes infinite. To give a very simple example, consider the calculation of the Newtonian force due to gravity exerted by a massive body on a test particle at a distance r. This force is proportional to 1/r2,, so that if one tried to calculate the force for objects at zero separation (r=0), the result would be infinite.
Singularities are not always signs of serious mathematical problems. Sometimes they are simply caused by an inappropriate choice of coordinates. For example, something strange and akin to a singularity happens in the standard maps one finds in an atlas. These maps look quite sensible until one looks very near the poles. In a standard equatorial projection, the North Pole does not appear as a point, as it should, but is spread along straight line along the top of the map. But if you were to travel to the North Pole you would not see anything strange or catastrophic there. The singularity that causes this point to appear is an example of a coordinate singularity, and it can be transformed away by using a different projection.
More serious singularities occur with depressing regularity in solutions of the equations of general relativity. Some of these are coordinate singularities like the one discussed above and are not particularly serious. However, Einstein’s theory is special in that it predicts the existence of real singularities where real physical quantities (such as the matter density) become infinite. The curvature of space-time can also become infinite in certain situations.
Probably the most famous example of a singularity lies at the core of a black hole. This appears in the original Schwarzschild interior solution corresponding to an object with perfect spherical symmetry. For many years, physicists thought that the existence of a singularity of this kind was merely due to the special and rather artificial nature of the exactly spherical solution. However, a series of mathematical investigations, culminating in the singularity theorems of Penrose, showed no special symmetry is required and that singularities arise in the generic gravitational collapse problem.
As if to apologize for predicting these singularities in the first place, general relativity does its best to hide them from us. A Schwarzschild black hole is surrounded by an event horizon that effectively protects outside observers from the singularity itself. It seems likely that all singularities in general relativity are protected in this way, and so-called naked singularities are not thought to be physically realistic.
There is also a singularity at the very beginning in the standard Big Bang theory. This again is expected to be a real singularity where the temperature and density become infinite. In this respect the Big Bang can be thought of as a kind of time-reverse of the gravitational collapse that forms a black hole. As was the case with the Schwarzschild solution, many physicists thought that the initial cosmologcal singularity could be a consequence of the special symmetry required by the Cosmological Principle. But this is now known not to be the case. Hawking and Penrose generalized Penrose’s original black hole theorems to show that a singularity invariably exists in the past of an expanding Universe in which certain very general conditions apply.
So is it possible to avoid this singularity? And if so, how?
It is clear that the initial cosmological singularity might well just be a consequence of extrapolating deductions based on the classical ttheory of general relativity into a situation where this theory is no longer valid. Indeed, Einstein himself wrote:
The theory is based on a separation of the concepts of the gravitational field and matter. While this may be a valid approximation for weak fields, it may presumably be quite inadequate for very high densities of matter. One may not therefore assume the validity of the equations for very high densities and it is just possible that in a unified theory there would be no such singularity.
Einstein, A., 1950. The Meaning of Relativity, 3rd Edition, Princeton University Press.
We need new laws of physics to describe the behaviour of matter in the vicinity of the Big Bang, when the density and temperature are much higher than can be achieved in laboratory experiments. In particular, any theory of matter under such extreme conditions must take account of quantum effects on a cosmological scale. The name given to the theory of gravity that replaces general relativity at ultra-high energies by taking these effects into account is quantum gravity, but no such theory has yet been constructed.
There are, however, ways of avoiding the initial singularity in classical general relativity without appealing to quantum effects. First, one can propose an equation of state for matter in the very early Universe that does not obey the conditions laid down by Hawking and Penrose. The most important of these conditions is called the strong energy condition: that r+3p/c2>0 where r is the matter density and p is the pressure. There are various ways in which this condition might indeed be violated. In particular, it is violated by a scalar field when its evolution is dominated by its vacuum energy, which is the condition necessary for driving inflationary Universe models into an accelerated expansion. The vacuum energy of the scalar field may be regarded as an effective cosmological constant; models in which the cosmological constant is included generally have a bounce rather than a singularity: running the clock back, the Universe reaches a minimum size and then expands again.
Whether the singularity is avoidable or not remains an open question, and the issue of whether we can describe the very earliest phases of the Big Bang, before the Planck time, will remain open at least until a complete theory of quantum gravity is constructed.
Today (and tomorrow) 70,000 members of the University and College Union at all 150 UK universities are on strike over over pay, working conditions and pensions.
Had I still been employed in the UK Higher Education system I would probably be standing on a picket line but I’m not, but at least I can send this message of solidarity to everyone who is!
So here we are then. The study break is over. Tomorrow we resume teaching. Six weeks of the semester gone. Another six to go. I didn’t do half the things I meant to do last week but at least I’m not behind with teaching things. I should be able to cover everything I need to cover in the second half without having to speed up too much. That’s the hope anyway.
Over the weekend I’ve been thinking a bit about my social media strategy, if you can call it that. It seems Elon Musk has realized that Twitter isn’t worth a fraction of what he paid for it, and is worth even less now that advertisers are fleeing, so has decided to recoup at least some of his losses by giving priority to anyone who wants to pay $8 a month so they can broadcast whatever they like withouyt moderation. The famous “blue tick” will no longer even mean a verified user, just someone willing to pay to shout at everyone else. Musk is also in the process of sacking about half his workforce.
I’m not going to pay anything to the Chief Twit and don’t like the way Twitter is going anyway so I’ve decided that I will indeed move to Mastodon, which I quite like, and where you can find me here. I don’t have a huge Twitter following so migrating to Mastodon is no big deal for me. I see many thousands I know on Twitter and many more I don’t are doing likewise.
Posts from this blog are automatically sent to Twitter and I won’t stop doing that, but I won’t be logging on there much except from time to time to block anyone I see who has a blue tick on their profile…
Anyway, in other news, the forthcoming week also sees me resume my feeble attempts to learn the Irish language, so it’s possible I may be boring you all with updates over the next few weeks and months. You have been warned.
Yesterday my Vector Calculus students gave me the above Hallowe’en gift, which was nice of them, although I did chastise them for missing the apostrophe. Of course Hallowe’en itself is not until Monday, but that is a Bank Holiday in Ireland and the rest of next week is Study Week so there are no lectures or tutorials.
Hallowe’en is, in pagan terminology, Samhain. This, a cross-quarter day – roughly halfway between the Autumnal Equinox and the Winter Solstice, represents the start of winter (“the dark half of the year“) in the Celtic calendar. Samhain is actually November 1st but in Celtic tradition the day begins and ends at sunset, so the celebrations begin on the evening of 31st.
Incidentally, Samhain is pronounced something like “sawin”. The h after the m denotes lenition of the consonant (which in older forms of Irish would have been denoted by a dot on top of the m) so when followed by a broad vowel the m is pronounced like the English “w”; when followed by a slender vowel or none “mh” is pronounced “v” or in other words like the German “w” (which makes it easier to remember). I only mention this because I will be resuming my Irish language education after the break with classes every week for the rest of the academic year. Hopefully I’ll make some progress.
This term has been very tiring so far. I have to teach a very big first-year class this year which meant adding another tutorial group. Although I stepped down as Head of Department at the end of August the powers that be delayed appointing a replacement until well into term which caused a lot of unnecessary stress for everyone. Once we got under way, though, everything has settled down reasonably well.
One thing I was a bit worried about this term was that the resumption of in-person teaching would lead to a surge in Covid-19 cases, not only in Maynooth but across the country. However there isn’t any evidence of significant increases in the latest figures (updated weekly nowadays, on Wednesdays):
Some students have come down with Covid-19 of course but not in the numbers I had feared. Also despite accommodation shortages and other difficulties, attendance at lectures and tutorials has so far held up well.
I like having the study break. I’ve never previously worked at an institution that has such a thing, but I think 12 weeks of non-stop teaching would be extremely exhausting. Anyway, after the break we have a further six weeks of teaching until December 16th, which is the official end of term, but for now I have Monday off completely and the rest of the week without teaching duties. That’s not to say I’ll be on holiday though. I have a number of tasks to catch up on, including setting examination papers for January…
Regular readers of the blog – both of them – may remember that we have twice previously presented a Masterclass in Astrophysics & Cosmology in Maynooth. Well, owing to popular demand, we’ve decided to do a re-run of the event on Wednesday 16th November 2022 during this year’s Science Week. Last year’s event was a big success, with over a hundred schools joining in, with probably over a thousand young people listening and asking questions.
Like last year’s event this year’s will be a half-day virtual event via Zoom. It’s meant for school students in their 5th or 6th year of the Irish system. There might be a few of them or their teachers who see this blog so I thought I’d share the news here. You can find more information, including instructions on how to book a place, here.
Here is the flyer for the event:
I’ll be talking about cosmology early on, and John Regan will talk about black holes later on. After the coffee break one of our students will talk about why they wanted to study astrophysics. Then I’ll say something about our degree programmes for those students who might be interested in studying astrophysics and/or cosmology as part of a science course. We’ll finish with questions either about the science or the studying!
Here is a more detailed programme:
Fortunately this year I don’t need to dash away at noon to do a lecture!
A couple of articles appeared recently that I encourage people to read who are studying physics, or interested in studying physics.
The first article by Carl Wieman is from Physics Today and is entitled How to become a successful physicist. It is aimed at graduate students, though most of what it says is relevant to those at an earlier stage of their studies. Here’s an excerpt from near the beginning:
The primary characteristic of a successful physicist is being a good problem solver.
The article goes on to say some very interesting and instructive things, and is well worth reading in its entirety. There are one or two things that I don’t agree with though. One is the statement that…
…textbook problems provide all the information needed and have a single well-defined path to a solution.
That’s true of many problems at an elementary level, but problems at undergraduate or graduate level often have more than one way of finding the solution. That’s certainly true of many that I set as assignments. Indeed, sometimes the students come up with better ways of approaching them than I did! The important difference between textbook and research problems is that you know the textbook problems have a solution. Research is scarier because you don’t know at the outset that an answer can be found!
The second article, by Ethan Siegel, is called The secret to becoming an excellent physicist. Here is a quote from that, revealing the “secret”:
It’s simplicity itself: you become good at physics by solving physics problems. That’s it: that’s the secret. If you want to become competent at physics, you will solve physics problems in the area you wish to learn.
I hope you get the message. It’s not about rote-learning facts and formulae. The brain is much more than a memory device. It’s all about problem-solving. The ability to do that effectively can only be learned through practice.
I’m currently teaching two modules on Mathematical Physics and I devote most of the time in lectures for both of them to doing worked examples rather than proving theorems or presenting facts, theorems, derivations, formulae, etc to learn. I spend quite a lot of time in lectures giving students things to work out, which makes classes more interactive, but students also have tutorials built around problem-solving tasks to complement this.
I’d add one piece of advice. If you really want to develop as a physicist, don’t just solve a lot of easy problems; challenge yourself by tackling difficult ones too. Don’t be afraid to get “stuck” or make a mistake, as those are both necessary parts of the learning process. Above all, develop the confidence in your ability to take on a problem and back yourself to solve it and don’t be deterred if the answer doesn’t come quickly!
The views presented here are personal and not necessarily those of my employer (or anyone else for that matter).
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In the Dark 