“And” Time Draws Nigh

It’s November 30th 2020, which means we have just three teaching weeks to go until the end of term. I am currently teaching two modules: Mechanics 1 and Special Relativity for first-year students and  Vector Calculus and Fourier Series for second years. We’re now getting to the “and” bit in both modules.

I didn’t want to present the two topics mentioned in the title of the second year module as completely disconnected, so I decided to link them with a lecture in which I use the divergence theorem of vector calculus to derive 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.

That gives me an excuse to repost the following “remarkable” poem about Fourier by William Rowan Hamilton:

In the first-year module I will be spending most of this week talking about potentials and forces before starting special relativity next week, at the proper time.

This day and age we’re living in
Gives cause for apprehension
With speed and new invention
And things like fourth dimension
Yet we get a trifle weary
With Mr. Einstein’s theory
So we must get down to earth at times
Relax relieve the tension
And no matter what the progress
Or what may yet be proved
The simple facts of life are such
They cannot be removed

As time goes by, the other thing  drawing nigh is the loosening of Ireland’s current Level 5 Covid-19 restrictions which were imposed about six weeks ago though,  judging by the crowds drinking in Courthouse Square on Saturday night, a lot of folks have thrown the rules out the window already.

I think it’s a dangerous time. The daily cases are still hovering around the 250-300 mark and will undoubtedly start climbing even before Christmas itself:The chances of us getting back to anything normality during the early part of next year are exceedingly slim.

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Cosmological Non-Linearities as an Effective Fluid

We know our Universe is inhomogeneous, comprising regions of high density (galaxies and clusters of galaxies) as well as regions of much lower density (e.g. cosmic voids). Our standard cosmological models are based on exact solutions of Einstein’s equations of general relativity that assume homogeneity and isotropy. The general assumption is that if we confine ourselves to large enough scales the effect of the clumpiness of matter can either be disregarded or treated using perturbation theory. As far as we can tell, that approach works reasonably well but we know it must fail on smaller scales where the structure is in the non-linear regiome where it can’t be described accurately using perturbation theory because the fluctuations are so large.

From time to time I’ve idly wondered whether it might be possible to understand the effect of these non-linearities in general relativity by treating them as a kind of fluid with an energy-momentum tensor that acts as a correction to that of the perfect fluid form of the background cosmological model. This would have to be done via some sort of averaging so it would be an effective, coarse-grained description rather than an exact treatment. It is clear though that non-linearities would generate departures from the perfect fluid form, particularly resulting in off-diagonal terms in the energy-momentum tensor corresponding to anisotropic stresses (e.g. viscosity terms).

Anyway, a recent exchange on Twitter relating to a new paper that has just appeared revealed that far cleverer people than me had looked at this in quite a lot of detail a decade ago:

You can find the full paper here.

There are quite a lot of subtleties in this – how to do the spatial averaging, how to do the time-slicing, etc – which I don’t fully understand but at least I’m reassured that it isn’t a daft idea to try thinking of things this way!

P.S. The relativistic simulations reported in this paper could in principle be used to estimate the parameters mentioned in the abstract above, if that hasn’t been done before!

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John & Diego

The Guardian obituary of John Barrow (written by Michael Rowan-Robinson) has finally appeared in today’s print edition*, alongside that of footballer Diego Maradona who passed away yesterday.

As a lifelong football fan I think John would have been amused by the coincidence, especially because John’s first book (co-written with Joe Silk) was called The Left Hand of Creation:

*I don’t usually buy foreign newspapers, but I managed to find a copy of today’s Grauniad in Maynooth.

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Astrophysics & Cosmology Masterclass at Maynooth

Stealing the idea from our long-running Particle Physics Master Class (which sadly had to be cancelled this year for Covid-19 related reasons, but will resume in 2021), the Department of Theoretical Physics at Maynooth University has decided to launch a Masterclass in Astrophysics & Cosmology. The first one will be on January 14th 2021.

This 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, but 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 official poster and the programme:

I’ll be talking about cosmology early on, while John Regan will talk about black holes. After the coffee break one of our PhD 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 study!

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Job Opportunities in Quantum Information Processing in Maynooth

Gratuitous Graphic purporting to represent Quantum Information Processing

Regular readers of this blog may recall an announcement that the Department of Theoretical Physics scored a notable success, or rather Dr Professor Jiri Vala did, in securing funding as part of a project called Quantum Computing in Ireland: A Software Platform for Multiple Qubit Technologies. To be eligible for this kind of funding, projects must involve businesses and this particular project includes IBM Ireland Ltd, MasterCard Ireland, Rockley Photonics and Equal 1 Laboratories, the latter two being SMEs based in the Dublin area. The project also involves the Tyndall National Institute (Cork); University College Dublin; and Maynooth University. This is the first large collaboration in Ireland in this area.

Well, now that the funds have actually arrived, I  thought I’d use the medium of this blog to pass on the information that the Department of Theoretical Physics at Maynooth University is looking two appoint not one but two theoretical physicists as postdoctoral researchers to work on this project.

The first position (for which you can find further details here) is  to work on modelling and simulations of quantum photonic systems for quantum information processing.

The second position (further details here) is to work on the evelopment of compilers, quantum control protocols and algorithms for quantum information processing in quantum photonic systems.

The deadline for both positions is Sunday 6th December 2020, so there’s not much time to apply!

Please feel free to pass this on to anyone you think may be interested!

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Dreams, Planes and Automobiles

I’ve blogged before about the strange dreams that I’ve been having during this time of Covid-19 lockdowns, but last night I had a doozy. I’ve recently been doing some examples of Newtonian Mechanics problems for my first-year class: blocks sliding up and down planes attached by pulleys to other blocks by inextensible strings; you know the sort of thing.

Anyway, last night I had a dream in which I was giving a lecture about cars going up and down hills taking particular account of the effects of friction and air resistance. The lecture was in front of a camera and using a portable blackboard and chalk, but all that was set up outside in the middle of a main road with traffic whizzing along either side and in the presence of a strong gusty wind. I had to keep stopping to pick up my notes which had blown away, dodging cars as I went.

It would undoubtedly make for much more exciting lectures if I recorded them in such a situation, but I think I’d be contravening traffic regulations by setting up in the middle of the Straffan Road. On the other hand, I could buy myself a green screen and add all that digitally in post-production…

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The End of Arecibo

I’ve just heard the news that the famous (and indeed iconic) radio telescope in Puerto Rico known as the Arecibo Observatory is to be decommissioned. The facility was badly damaged by Hurricane Maria in 2017 and it was feared it might close then, but it was saved when an agreement was reached whereby a Consortium led by the University of Central Florida took over its operations.

Unfortunately, in August 2020 an auxiliary cable broke in August and tore a 30-metre diameter hole in the reflector dish and damaged the dome above it. Then, earlier this month, one of the telescope’s main steel cables snapped, causing further damage. It has now been decided that it will be too dangerous and too expensive to repair the telescope. It is to be decommissioned and then dismantled entirely. Presumably the site will be returned to the state it was in before the telescope was built.

This will be sad news for the people who work at Arecibo Observatory and for the local economy in Puerto Rico not to mention the many astronomers who have used the facility over the years. For a time it was the largest radio telescope in the world, its 1000ft diameter dish enabling it to achieve a resolution of about 3.5 arc minutes at 21cm. Even before the Hurricane struck, however, Arecibo had been struggling to find the funds necessary to maintain its operations. Now, almost 60 years after it was built, that struggle is over.

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A Remnant Problem

 

I haven’t posted any physics problems for a while so here’s  a quickie involving dimensional analysis. You have to assume that the supernova remnant mentioned in the question is roughly spherical, like the one shown above (SNR 0500-67.5):

As usual, answers and comments through the box below please!

Click on the `continue reading’ thing if you would like to see my worked solution:

Newton’s Laws in Words

I’ve been teaching my first-year Mathematical Physics students about Newton’s Laws of Motion so decided to record this little video as an aside discussing the history terminology and use of language.

Unfortunately the only microphone I have is the one built into my laptop and it tends to suffer sometimes from a crackle caused (I think) by the fan inside the machine interfering with the mike. I guess the noise appears when the CPU is working hard causing the machine to heat up so the fan works harder. The sound on video recordings I make this low budget way do break up from time to time, which is rather irritating. Obviously I need to buy an external microphone and when I do I might record this again but in the meantime you’ll just have to put up with it breaking up a couple of times!

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Memories of Philae

It seems that today is the sixth anniversary of the day (November 12th 2014) that the probe Philae, having detached from its parent spacecraft Rosetta, and subsequently landed successfully (ish) on the Comet 67P/Churyumov-Gerasimenko.

I didn’t realise it was so long ago, but who could forget the feeling of intense excitement we felt on that day as Philae approached its objective?

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