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.
There are now precisely four weeks to go until the end of teaching term at Maynooth University. Since the FIFA World Cup starts today it seems apt to borrow a sporting cliché and describe this as the final third. Miraculously, given that I’m having to fit 12 weeks of teaching into 11 week term for the first years, I’m almost on schedule with both my modules but I have this weekend come down with something which may affect the rest of term. I don’t think it’s Covid-19 – at least the antigen test I did yesterday was negative – but whatever it is I hope it doesn’t get worse. All the teaching staff in the Department of Theoretical Physics already have very heavy teaching loads already so we simply don’t have any spare staff to cover my lectures if I can’t deliver them. I don’t know what I’ll do in that case. I suppose I could recycle some of last year’s videos, or record some new ones from my sick bed. Let’s hope it doesn’t come to that. It may be just a cold.
Anyway, what was until last week an unusually mild autumn has turned into something much more wintry. The sudden cold snap has set off my arthritis, which is an additional complication on top of whatever bug I’ve got.
Evidence of the Berry Phase
Outside temperatures have plummeted so I have mobilized my bird feeders to take care of the feathered friends in the garden. Fortunately there is ready-made food at this time of the year in the form of berries on the Cotoneaster bushes. I watched a song thrush for about ten minutes tucking in yesterday. Pigeons like them too. The birds usually don’t strip all the berries so there’ll be food of that form for a while but some of the smaller birds can’t eat them so I’ve put out seed and peanuts too.
UPDATE: Monday 21st November. It appears it was just a cold, or something else very mild, as I felt much better this morning and went to work as normal.
As far as I know, there are no events planned at Maynooth to mark the occasion so for me it’s just a normal teaching day. I can nevertheless use the medium of this blog to wish all LGBTQ+ persons working in STEM subjects around the globe a very enjoyable day.
You can find out about events near you by checking here, looking for the hashtag #LGBTQSTEMDay on social media or by following the twitter account:
As next week is Science Week I thought I’d remind readers that as part of the festivities we are hosting a virtual Masterclass in Astrophysics & Cosmology in Maynoothon Wednesday 16th November 2022 .
You may remember that we have presented such events twice before. Last year’s event was a particularly 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!
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…
Not long ago I posted an item about the Summer Programme for Undergraduate Research (SPUR) at Maynooth University. This past summer I had two undergraduate students doing research projects with me funded under this scheme. They were both involved with making Monte Carlo simulations of galaxy clustering and using them to test various statistical analysis tools. The Department of Theoretical Physics actually had five students on three different projects, which is quite a lot for a small Department. The University as a whole had 57 SPUR students so we had almost ten percent of the total!
Well, earlier this week there was a Research Symposium at which all the summer’s research undergraduates presented posters on their work, with prizes being awarded for the best. I couldn’t attend the Symposium because of other commitments but I was delighted to find out that both my students won prizes – that’s two out of the five awarded. Here are the pictures of them being presented with their awards at the ceremony yesterday, flanked by the Vice-for Research and Innovation, Brian Donnellan and the President, Eeva Leinonen.
The Theoretical Physics Prize Winners, Pawel and Lisa
The awards ceremony was held in the foyer of the new TSI building yesterday afternoon, which wasn’t an ideal choice because the acoustic is very poor and lots of students were making their way to and from lectures. I didn’t hear a word of the speeches, actually. Nevertheless it was nice to see Pawel (top prize in the Science and Engineering category) and Lisa (audience choice prize winner) collect their awards. It was a pleasure to work with both of them this summer!
Incidentally, the SPUR students are paid for the projects, which last for (usually) six weeks but can be extended. I wish we could offer these projects to every student who wanted one, actually, but we just can’t afford to do that. I don’t agree with unpaid internships as these can only be taken up by students who have access to enough income to cover living expenses over the summer, so are discriminatory. We select students based on an application form and their academic performance.
Earlier today I found myself on the South Campus of Maynooth University where I encountered Maynooth University Library Cat looking not entirely gruntled. Behind bars like that I thought he looked like he was in the doghouse!
Anyway, this meeting reminded me of some important campus cat news from earlier in the week. On Tuesday afternoon I was just about to start my usual 3pm lecture on Vector Calculus and Fourier Series in Hall H on the North Campus. It was quite warm that day and all the windows on the side of the room (which is on the ground floor) were open. As soon as I started talking about line integrals I was interrupted by a plaintive mewing from outside which turned out to come from a small white cat who made its way outside to the rearmost window, climbed in and took a seat in the back row. It was quite disconcerting to see its little head looking at me, and its appearance put me right off my stride for a bit, but fortunately it didn’t ask any difficult questions and eventually dozed off.
I’ve never seen this cat before but apparently it has been hanging around near the Phoenix restaurant, where presumably it is being fed. It has no collar and, as far as I know, no name. We have recently experienced another visitation by rodents in the Science Building and wonder if it could be persuaded to investigate on our behalf?
So now we have a black cat on the South Campus and a white cat on the North Campus, polar opposites. Perhaps one is the anti-cat of the other? I do hope they don’t annihilate each other if they ever meet!
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!
Autumn is definitely here. It’s very nice to live in a tree-lined street but the consequence of that at this time of year is that there are leaves everywhere. They don’t call it “fall” for nothing. Actually I let the leaves lie until they compost down on the actual garden but unfortunately the side of my house is a bit of wind trap and they tend to accumulate there in large quantities. When they do start to break down it makes a slippery hazard for anyone visiting, especially if it rains.
So this lunchtime I cleared away most of the leaves from the path leading up to my front door, in which task I was joined by a little robin who was no doubt hoping I would disturb some bugs or at any rate something edible when I swept up the leaves. I’m not sure this is the same robin that came in my house earlier this year, but it wasn’t afraid to come very close.
Reading a little about robins I discovered that many don’t live to reach their first birthday, but those that do have a good chance of living quite a while longer. The record is 19 years! Today’s robin could be the same one I’ve seen before, but I can’t be certain.
That reminded me that it was about time to start putting the bird feeders out again so I went out and bought some seed and peanuts and fat balls, although I think I’ll keep those for when it’s a bit colder.
At some point soon I’ll have to get the ladders out and trim back the ivy which is once again reaching the top of the wall. That will have to wait a few days, though, as my garden refuse bin is now full and won’t be empty again until Wednesday.
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In the Dark 