Picture Credit: Cian O’Regan
This image of February’s Full Moon (the “Snow Moon”) by Blackrock Castle Observatory in Cork is by Cian O’Regan. Prints of this and other beautiful images can be bought from his website here.
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The Moon and Blackrock Castle
Posted in Art, The Universe and Stuff with tags Cian O'Regan, photography on April 14, 2021 by telescoperTesting Cosmological Reciprocity
Posted in The Universe and Stuff with tags Cosmology, Etherington's Reciprocity Theorem, Hubble constant on April 13, 2021 by telescoperI have posted a few times about Etherington’s Reciprocity Theorem in cosmology, largely in connection with the Hubble constant tension – see, e.g., here.
The point is that if the Universe is described by a space-time with the Robertson-Walker Metric (which is the case if the Cosmological Principle applies in the framework of General Relativity) then angular diameter distances and luminosity distances can differ only by a factor of (1+z)2 where z is the redshift: DL=DA(1+z)2.
I’ve included here some slides from undergraduate course notes to add more detail to this if you’re interested:
The result DL=DA(1+z)2 is an example of Etherington’s Reciprocity Theorem and it does not depend on a particular energy-momentum tensor; the redshift of a source just depends on the scale factor when light is emitted and the scale factor when it is received, not how it evolves in between.
Etherington’s theorem requires light rays to be described by null geodesics which would not be the case if photons had mass, so introducing massive photons would violate the theorem. It also requires photon numbers to be conserved, so some mysterious way of making photons disappear might do the trick, so adding some exotic field that interacts with light in a peculiar way is another possibility, as is the possibility of having a space-time with torsion, i.e. a non-Riemannian space-time.
Another possibility you might think of is to abandon the Robertson-Walker metric. We know that the Universe is not exactly homogeneous and isotropic, so one could appeal to the gravitational lensing effect of lumpiness to provide a departure from the simple relationship given above. In fact a inhomogeneous cosmological model based on GR does not in itself violate Etherington’s theorem, but it means that the relation DL=DA(1+z)2 is no longer global. In such models there is no way of defining a global scale factor a(t) so the reciprocity relation applies only locally, in a different form for each source and observer. In order to test this idea one would have to have luminosity distances and angular diameter distances for each source. The most distant objects for which we have luminosity distance measures are supernovae, and we don’t usually have angular-diameter distances for them.
Anyway, these thoughts popped back into my head when I saw a new paper on the arXiv by Holanda et al, the abstract of which is here:
Here we have an example of a set of sources (galaxy clusters) for which we can estimate both luminosity and angular-diameter distances (the latter using gravitational lensing) and thus test the reciprocity relation (called the cosmic distance duality relation in the paper). The statistics aren’t great but the result is consistent with the standard theory, as are previous studies mentioned in the paper. So there’s no need yet to turn the Hubble tension into torsion!
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Posted in Biographical, Covid-19, Education, Maynooth on April 12, 2021 by telescoperAfter a few days off last week following the Easter Bank Holiday weekend it’s time to get back into the swing of things for the four weeks of teaching term that remain. It’s back to school today for all school students in Ireland too, so good luck to them on their first day in the classroom since Christmas!
As well as (remote) lectures the next four weeks will involve us getting our papers ready for the examination period which starts on 14th May this year. All our examinations will be remote online timed assessments (as indeed they were last year). I’ve been teaching three modules this Semester so have no fewer than six examinations to write: three main exams plus three repeat papers for the resit period in August. The decision has already been made to make all the repeat exams online so at least these will be of similar style to the original May versions.
Then it will be marking and Exam Boards and various other things heading into the summer break. Hopefully I will get some holiday this summer as I didn’t get any at all last year. On the other hand there’s a strong likelihood that Senior Management will think of something else for Heads of Department to do that will make this impossible.
What happens at the end of summer all depends on Covid-19 of course, and specifically how Ireland’s vaccination programme goes. My personal opinion is that we should continue with remote teaching until all staff and students have had their jabs, which is unlikely to be the case before September at the current rate, but you never know. The speed of vaccination shows signs of increasing though, so we might be able to do it.
Despite the more rapid progress with immunisation over the other side of the Irish Sea, UK university bosses are apparently complaining that they haven’t got a date for returning to campus. This surprises me as they run on roughly the same calendar as here in Ireland so there are only a few weeks of teaching left there too. Why bother to go back at such a late stage? Unless of course it’s so they can charge students for a full term’s accommodation…
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Grand National Takeaway
Posted in mathematics, Sport with tags Any Second Now, Grand National, Minella Times, Rachael Blackmore on April 11, 2021 by telescoper
Congratulations to Rachael Blackmore for becoming the first female jockey ever to ride the winner Minella Times of the Grand National yesterday. It was a good race for Ireland generally as the top five were all Irish horses.
The race was led for a long time by 80-1 outsider Jett who at one point was about 10 lengths clear of the field but you could see that about three fences from home the horse was very tired, fading badly over the final stages of the race to finish in eighth place.
At 11-1, Minella Times would have netted quite a few people a good return on their investment. I wasn’t so lucky but had a modest success. After studying the form carefully (i.e. sticking a pin in the list of runners), I settled on Any Second Now, also at 11-1, betting €25 each way. I was pleased yesterday to see the odds shortening to 15/2 at the start, which meant quite a lot of people were backing the same horse.
In the event Any Second Now finished 3rd which was a great result given that it was badly hampered by a faller (Double Shuffle) at the 12th fence. A thing like that is normally difficult to recover from but jockey Mark Walsh did well to get back in contention, though he was too far back and too tired to catch the winner, who ran a perfect race.
The Grand National is one race where I think an each-way bet is a sensible strategy. As a handicap with 40 runners (and a very tough race for which the probability of a horse not making it to the finish line is quite high) the odds are usually pretty long even on the favourite, and most bookies pay out for a place down to sixth. I bet €25 each way, which means €25 to win outright at 11-1 and €25 for a place at one-fifth the odds, i.e. 2.2 to 1. I lost the first €25 but won €55 on the place (plus the stake). My net result was therefore €50 staked for an €80, more than enough profit to pay for last night’s takeaway dinner.
The point is that if you want the place to cover the loss on the win the starting price has to be good. If the odds are N:1 they will only cover the loss if N/5 ≥1 with the equality meaning that you break even. In a race in which the odds are much shorter the place bet is usually not worth very much at all. In yesterday’s Grand National the favourite was 5-1.
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Posted in Cricket with tags County Championship, Glamorgan, Yorkshire on April 10, 2021 by telescoper
It’s Day 3 of Yorkshire versus Glamorgan at Headingley in the first round of this season’s County Championship matches.
Or it was because there won’t be any further play today owing to the inclement weather….
Glamorgan are actually doing well at 161 for 4 in their second innings after bowling out Yorkshire for 193 to establish a first innings lead of 137. That’s very good considering that they were 29 for 4 at one point. Currently 298 ahead with six wickets remaining, can they force a result tomorrow?
UPDATE: Glamorgan batted on for an hour on Sunday morning so both Clarke and Root could get hundreds, eventually declaring on 241-4 a leady of 378. Clarke and Root came together with the score on 29-4 so that was an unbroken partnership of 212 for the 5th wicket. Despite a wobble here and there, Yorkshire batted out the day and eventually a draw was agreed with their score on 223 for 4.
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Posted in The Universe and Stuff on April 10, 2021 by telescoperHere’s a discussion of the status of the latest measurements of (g-2) versus theory. This kind of problem is not confined to particle physics. It also happens in cosmology that we have problems making accurate predictions to compare with observations, especially when using galaxies to trace large-scale structure. There’s a lot of messy astrophysics to be accounted for.
Yesterday, Fermilab’s Muon g-2 experiment announced a new measurement of the magnetic moment of the muon, a number which describes how muons interact with magnetic fields. For what might seem like a small technical detail, physicists have been very excited about this measurement because it’s a small technical detail that the Standard Model seems to get wrong, making it a potential hint of new undiscovered particles. Quanta magazine has a great piece on the announcement, which explains more than I will here, but the upshot is that there are two different calculations on the market that attempt to predict the magnetic moment of the muon. One of them, using older methods, disagrees with the experiment. The other, with a new approach, agrees. The question then becomes, which calculation was wrong? And why?
What does it mean for a prediction to match an experimental result? The simple, wrong, answer is…
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Uniform at School?
Posted in Biographical, Education with tags Royal Grammar School Newcastle, School Uniforms, Schools on April 9, 2021 by telescoperI noticed a little news item this morning about school uniforms and thought I’d comment, because I think the author of the piece misses some important points.
I had to wear a uniform when I went to my secondary school, the Royal Grammar School in Newcastle upon Tyne. I got a place there under the Direct Grant system, after passing the 11+ examination. It was basically a private school but I won a scholarship and my parents didn’t have to pay anything, which was just as well as they would never have been able to afford the fees.
I should mention that when I went to the RGS, in the 1970s, it was only for boys, but it is now for boys and girls.
Before actually starting at the RGS (in September 1974) we were sent a list of things that would be needed including various items of sports gear and, of course, the uniform. This included a distinctive blue* blazer with the school crest on the pocket. That was for the first two or three years. After that we got to wear a black/dark grey blazer which more closely resembled what other schools required and in the sixth form it was even more flexible, with many of the boys wearing a suit.
The list of things to be bought was quite long but we didn’t have to worry about the cost because we weren’t very well off and I qualified for vouchers from the Council to buy everything.
I was mightily relieved that I got to turn up for my first day at school in a new uniform because I didn’t have any good clothes – most of my normal clothes were hand-me-downs from my older brother. If I’d just worn my usual things it would have made be feel even more out of place than I did anyway, as all the posh kids would have been dressed much better than me. The uniform was a relief because it put everyone on the same footing – at least at a superficial level.
The big problem was that I had to travel every day on the bus from Benwell (a rough area, where I lived) to Jesmond (a posh area, where the RGS was and still is). The bright blue blazer was very conspicuous and I often got picked on by local kids while en route there or back. I remember getting spat on more than once. In the end I decided to wear a big coat over my uniform to avoid it being recognized, even on hot days.
The value of the uniform seemed to me that it was a leveller. It wasn’t really anything about expressing loyalty to the school, nor was it a means of imposing discipline and obedience, it just helped diminish the effect of parental wealth. In an environment in which social class was such a prominent factor it seemed to me that the uniform was a good thing. My friends from wealthier families disliked the uniform, usually for the same reason that I liked it.
I’m all in favour of updating the style of uniform to a more neutral, less gender-specific style – especially for coeducational schools – but I think as long as schools take in kids from a wide range of socioeconomic backgrounds then on balance they’re a good concept.
Anyway, you probably disagree so here’s a poll:
P.S. Our school had an exchange programme with a school in Germany – the Max Planck Gymnasium in Gelsenkirchen. When I was told the name I assumed the kids were all fantastic athletes, but then a teacher explained that the name came from the Greek word gymnos meaning “naked”. That minimal approach to a school uniform would never have taken on in Newcastle, on grounds of the weather among other reasons, but I learnt (to my disappointment) that it was only a metaphorical term anyway.
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Posted in Politics on April 8, 2021 by telescoper
Reaction to the announcement of a new measurement of (g-2)
Posted in Bad Statistics, The Universe and Stuff on April 7, 2021 by telescoper
Today’s announcement of a new measurement of the anomalous magnetic dipole moment – known to its friends as (g-2) of the muon – has been greeted with excitement by the scientific community, as it seems to provide evidence of a departure from the standard model of particle physics (by 4.2σ in frequentist parlance).
My own view is that the measurement of g-2, which seems to be a bit higher than theorists expected, can be straightforwardly reconciled with the predictions of the standard model of particle physics by simply adopting a slightly lower value for 2 in the theoretical calculations.
P.S. According to my own (unpublished) calculations, the value of g-2 ≈ 7.81 m s-2.
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Cosmology Talks: Dan Thomas on the first model-independent cosmological simulations of modified gravity
Posted in The Universe and Stuff with tags arXiv:2004.13051, arXiv:2103.05051, Cosmology, Cosmology Talks, Dan Thomas, modified gravity, Poisson's equation, Shaun Hotchkiss on April 7, 2021 by telescoperIt’s time I shared another one of those interesting cosmology talks on the Youtube channel curated by Shaun Hotchkiss. This channel features technical talks rather than popular expositions so it won’t be everyone’s cup of tea but for those seriously interested in cosmology at a research level they should prove interesting. This one was published just yesterday.
In the talk Dan Thomas discusses his recent work first creating a framework for describing modified gravity (i.e. extensions of general relativity) in a model-independent way on non-linear scales and then running N-body simulations in that framework. The framework involves finding a correspondence between large scale linear theory where everything is under control and small scale non-linear post-Newtonian dynamics. After a lot of care and rigour it boils down to a modified Poisson equation – on both large and small scales (in a particular gauge). The full generality of the modification to the Poisson equation allows, essentially, for a time and space dependent value for Newton’s constant. For most modified gravity models, the first level of deviation from general relativity can be parametrised in this way. This approach allows the method to use to constrain modified gravity using observations without needing to run a new simulation for every step of a Monte Carlo parameter fit.
P. S. A couple of papers to go with this talk can be found here and here.
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In the Dark 