Back to the day job, teaching Advanced Electromagnetism, I put up these two nice tutorial problems about the Lorentz transformation of Electric and Magnetic fields, as a prelude to doing the fully covariant formulation of the Maxwell equations. You might like to have a go at these exercises:
I was very sad to hear via the NASA website of the death, yesterday at the age of 94, of Professor Eugene N. Parker (known to all as “Gene”). He was best known for his work on solar magnetism and the solar wind, but he made important contributions across a wide range of astrophysics; he wrote an excellent book entitled Cosmical Magnetic Fields: Their Origin and Activity which I bought many years ago. Most recently NASA’s Parker Solar Probe was named in his honour.
I only met Gene Parker once, many years ago, and was a bit in awe of him because of his intellectual reputation but he came across as a very likeable and friendly man.
We have lost a giant in the field of astrophysics who leaves a huge legacy and will be greatly missed. I send my condolences to his family, friends and colleagues at the University of Chicago where he worked since 1955.
Rest in Peace, Professor Eugene N. Parker (1927-2022).
I was shocked to see just now the news that legendary Australian legspinner Shane Warne has passed away suddenly at the age of just 52. I always admired his bowling hugely no doubt partly because having tried to bowl leg-breaks myself I have some idea how difficult it is to do well! I thought as a tribute I would rehash a piece I posted about 12 years ago about the prodigious amount of spin Shane Warne was able to generate.
For those of you not so familiar with cricket here’s a clip of another prodigious spinner of the ball, Australia’s legend of legspin Shane Warne:
For beginners, the game of cricket is a bit similar to baseball (insofar as it’s a game involving a bat and a ball), but the “strike zone” in cricket is a physical object ( a “wicket” made of wooden stumps with bails balanced on the top) unlike the baseball equivalent, which exists only in the mind of the umpire. The batsman must prevent the ball hitting the wicket and also try to score runs if he can. In contrast to baseball, however, he doesn’t have to score; he can elect to play a purely defensive shot or even not play any short at all if he judges the ball is going to miss, which is what happened to the hapless batsman in the clip.
You will see that Warne imparts considerable spin on the ball, which has the effect of making it change direction when it bounces. The fact that the ball hits the playing surface before the batsman has a chance to play it introduces extra variables that you don’t see in baseball, such as the state of the pitch (which generally deteriorates over the five days of a Test match, especially in the “rough” where bowlers have been running in).
A spin bowler who causes the ball to deviate from right to left is called a legspin bowler, while one who makes it turn the other way is an offspin bowler. An orthodox legspinner generates most of the spin from a flick of the wrist while an offspinner mainly lets his fingers do the torquing.
Another difference that’s worth mentioning with respect to baseball is that the ball is bowled, i.e. the bowler’s arm is not supposed to bend during the delivery (although apparently that doesn’t apply if he’s from Sri Lanka). However, the bowler is allowed to take a run up, which will be quite short for a spin bowler, but long like a javelin thrower if it’s a fast bowler. Fast bowlers – who can bowl up to 95 mph (150 km/h) – don’t spin the ball to any degree but have other tricks up their sleeve I haven’t got time to go into here. A typical spin bowler delivers the ball at speeds ranging from 45 mph to 60 mph (70 km/hour to 100 km/hour).
The physical properties of a cricket ball are specified in the Laws of Cricket. It must be between 22.4 and 22.9 cm in circumference, i.e. 3.57 to 3.64 cm in radius and must weigh between 155.9g and 163g. It’s round, made of cork, and surrounded by a leather case with a stitched seam.
So now, after all that, I can give a back-of-the-envelope answer to the question I was wondering about on the way home. Looking at the video clip my initial impression was that the ball is deflected by an angle as large as a radian, but in fact the foreshortening effect of the camera is quite deceptive. In fact the ball deviates by less than a metre between pitching and hitting the stumps. There is a gap of about 1 metre between the popping crease (where the batsman stands) and the stumps – it looks much less from the camera angle shown – and the ball probably pitches at least 2 metres in front of the crease. I would guess therefore that it actually deflects by an angle less than twenty degrees or so.
What happens physically is that some of the rotational kinetic energy of the ball is converted into translational kinetic energy associated with a component of the velocity at right angles to the original direction of travel. In order for the deflection to be so large, the available rotational kinetic energy must be non-negligible compared to the original kinetic energy of the ball. Suppose the mass of the ball is 
Approximating the ball as a uniform sphere of mass 
or 
This estimate is obviously very rough because it ignores the direction of spin and the efficiency with the ball grips on the pitch – friction is obviously involved in the change of direction – but it gives a reasonable ballpark (or at least cricketground) estimate.
Of course if the bowler does the same thing every time it’s relatively easy for the batsman to allow for the spin. The best bowlers therefore vary the amount and angle of spin they impart on each ball. Most, in fact, have at least two qualitatively different types of ball but they disguise the differences in the act of delivery. Offspinners typically have an “arm ball” which doesn’t really spin but holds its line without appearing to be any different to their spinning delivery. Legspinners usually have a variety of alternative balls, including a topspinner and/or a flipper and/or a googly. The latter is a ball that comes out of the back of the hand and actually spins the opposite way to a legspinner while being produced with apparently the same action. It’s very hard to bowl a googly accurately, but it’s a deadly thing when done right.
Another thing also worth mentioning is that the rotation of the cricket ball also causes a deviation of its flightpath through the air, by virtue of the Magnus effect. This causes the ball to curve in the air in the opposite direction to which it is going to deviate on bouncing, i.e. it would drift into a right-handed batsman before breaking away from him off the pitch. You can see a considerable amount of such movement in the video clip, away from the left-hander in the air and then back into him off the pitch. Nature clearly likes to make things tough for batsmen!
With a number of secret weapons in his armoury the spin bowler can be a formidable opponent, a fact that has apparently been known to poets, philosophers and astronomers for the best part of a thousand years:
The Ball no Question makes of Ayes and Noes,
But Right or Left, as strikes the Player goes;
And he that toss’d Thee down into the Field,
He knows about it all — He knows — HE knows!
The Rubaiyat of Omar Khayyam [50]
You can’t spend over 30 years working in theoretical physics without encountering Russian physicists and mathematicians. Over the years I’ve got to know a few quite well, through collaborations and discussions, and others by acquaintance. It occurred to me this morning that many of them might get caught up in the widespread condemnation of the Putin regime’s invasion of Ukraine. I don’t know any Russians (physicists or anything else) who support Putin or his oligarchs. I’m not saying that there are no such people, just that I don’t know any.
I think it’s important to say that my comments yesterday were not aimed at the many Russians around the world – including Russia itself – who want no part of the war and are horrified by the actions taken by the Russian leader.
As if to prove my point, there is an open letter from Russian scientists and science writers (in Russian here) which is already attracted a great many signatures.
On a related note this news, of Russian agency Roscosmos suspending all flights of the Soyuz spacecraft from the ESA launch facility in Kourou and withdrawing all Russian personnel from the site, seems to confirm what I thought yesterday, that the launch of Euclid will be postponed indefinitely. The alternative launcher, Ariane 6, has not yet had its first flight and at least two successful launches are required before it can be established as the vehicle for Euclid. On top of that the Euclid spacecraft itself will be need to be modified for the different vehicle. Details are yet to be confirmed, but it seems a lengthy delay is likely.
We’ve had three major storms over the past week (Dudley, Eunice and Franklin). Today I was reminded that precisely five years ago today I was trying to make it from Cardiff to Lincoln to give a lecture, so I thought I’d reblog the post I wrote at the time. It took me nearly all day and I was an hour late, but, you know, the show must go on and so it did.
There’s obviously a thing about February and storms!
What a day!
This morning I set out from Cardiff to travel here to Lincoln for mypublic lecture. I took the9.45 train via Birmingham which, after a change of trains in Nottingham, should have got me into Lincoln at 14.23, with plenty of time to have a look around and chat to people before the scheduled start of my talk at 18.00 hours.
That was the plan, but it omitted an important factor:Storm Doris.Fallen trees, broken down trains and general disorganisation meant that it took ninehours to get to Lincoln, even including getting a taxi from Nottingham because I missed my connection.
The strangest thing was that I never actually saw any particularly bad weather. In fact there was quite a lot of sunshine en route. All the chaos was caused elsewhere, apparently.
Anyway I finally turned up almost an hour late for my talk…
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Catching up on some literature on the inestimable arXiv I came across this paper by Obinna Umeh which I haven’t gone through in detail but which looks very interesting:
How does a smooth cosmic distance ladder emerge from observations made from a single location in a lumpy Universe? Distances to the Type Ia supernova (SN1A) in the Hubble flow are anchored on local distance measurements to sources that are very nearby. We described how this configuration could be built in a perturbed universe where lumpiness is described as small perturbations on top of a flat Friedmann-Lemaıtre Robertson-Walker (FLRW) spacetime. We show that there is a non-negligible modification (about 11%) to the background FLRW area distance due to the presence of inhomogeneities in the immediate neighbourhood of an observer. We find that the modification is sourced by the electric part of the Weyl tensor indicating a tidal deformation of the local spacetime of the observer. We show in detail how it could impact the calibration of the SN1A absolute magnitude in the Hubble flow. We show that it resolves the SN1A absolute magnitude and Hubble tensions simultaneously without the need for early or late dark energy.
The area distance here is what I usually call the angular-diameter distance; when one thinks of supernova measurements one usually thinks of the luminosity distance but these are related through the reciprocity relation discussed here which applies to each source regardless of whether the metric is of FLRW form or not. For a general discussion of cosmological distances see here.
It’s time yet again to announce a new publication in the Open Journal of Astrophysics! This one is the 3rd paper in Volume 5 (2022) and the 51st in all. We actually published this on Friday, byt I’ve only just got around to announcing it here now.
The latest publication is entitled Differentiable Predictions for Large Scale Structure with SHAMNet and is written by Andrew Hearin, Nesar Ramachandra and Matthew R. Becker of the Argonne National Laboratory and Joseph DeRose of the Lawrence Berkeley Laboratory (both institutions being in the USA).
Here is a screen grab of the overlay which includes the abstract:
You can click on the image to make it larger should you wish to do so. You can find the arXiv version of the paper here. This paper is in our popular Cosmology and Non-galactic Astrophysics section.
P. S. Here’s a bit of feedback from the author of this paper about the referees:
They reviewed the paper in conscientious detail, and every comment was thoughtful. We feel that our paper has materially improved in clarity as a result of their critique.”
There’s a paper recently published in Nature Astronomy by Moreno et al, which you can find on the arXiv here. The title is Galaxies lacking dark matter produced by close encounters in a cosmological simulation and the abstract is here:
The standard cold dark matter plus cosmological constant model predicts that galaxies form within dark-matter haloes, and that low-mass galaxies are more dark-matter dominated than massive ones. The unexpected discovery of two low-mass galaxies lacking dark matter immediately provoked concerns about the standard cosmology and ignited explorations of alternatives, including self-interacting dark matter and modified gravity. Apprehension grew after several cosmological simulations using the conventional model failed to form adequate numerical analogues with comparable internal characteristics (stellar masses, sizes, velocity dispersions and morphologies). Here we show that the standard paradigm naturally produces galaxies lacking dark matter with internal characteristics in agreement with observations. Using a state-of-the-art cosmological simulation and a meticulous galaxy-identification technique, we find that extreme close encounters with massive neighbours can be responsible for this. We predict that approximately 30 percent of massive central galaxies (with at least 1011 solar masses in stars) harbour at least one dark-matter-deficient satellite (with 108 – 109 solar masses in stars). This distinctive class of galaxies provides an additional layer in our understanding of the role of interactions in shaping galactic properties. Future observations surveying galaxies in the aforementioned regime will provide a crucial test of this scenario.
It’s quite an interesting result.
I’m reminded of this very well known paper from way back in 1998, available on arXiv here, by Priya Natarajan, Steinn Sigurdsson and Joe Silk, with the abstract:
We propose a scenario for the formation of a population of baryon-rich, dark matter-deficient dwarf galaxies at high redshift that form from the mass swept out in the Intergalactic Medium (IGM) by energetic outflows from luminous quasars. We predict the intrinsic properties of these galaxies, and examine the prospects for their observational detection in the optical, X-ray and radio wavebands. Detectable thermal Sunyaev-Zeldovich decrements (cold spots) on arc-minute scales in the cosmic microwave background radiation maps are expected during the shock-heated expanding phase from these hot bubbles. We conclude that the optimal detection strategy for these dwarfs is via narrow-band Lyman-α imaging of regions around high redshift quasars. An energetically scaled-down version of the same model is speculated upon as a possible mechanism for forming pre-galactic globular clusters.
It’s true that the detailed mechanism for forming dwarf galaxies with low dark matter densities is different in the two papers, but it does show that the issue being addressed by Moreno et al. had been addressed before. It seems to me therefore that the Natarajan et al. paper is clearly relevant background to the Moreno et al. one. I always tell junior colleagues to cite all relevant literature. I wonder why Moreno et al. decided not to do that with this paper?
Had Moreno et al. preprinted their paper before acceptance by Nature Astronomy I’m sure someone would have told them of this omission. This is yet another reason for submitting your papers to arXiv at the same time as you submit them to a journal rather than waiting for them to be published.
You may remember that we ran a very successful virtual Astrophysics & Cosmology Masterclass at Maynooth University last November. Now it’s time to announce the forthcoming International Masterclass on Particle Physics. This will take place on campus at Maynooth during the half-term break:
You can find more information, including instructions on how to book a place, here. The first such Masterclass at Maynooth took place in March 2012, so this year we will be celebrating the 10th anniversary.
These Masterclasses give secondary school students the opportunity to discover the world of quarks and leptons for themselves, by performing measurements on real data from CERN, meeting active particle physics researchers and linking up with like-minded students from other countries. We will join thousands of other secondary school students at more than 100 universities and laboratories around Europe and worldwide in a programme stretching over four weeks.
Physics at the most fundamental level – the smallest and most basic building blocks of matter – is an exotic world. But a few introductory talks and working with data from CERN will give the students insight into the fundamental particles of matter and the forces between them, as well as what went on during the Big Bang.
On Sunday afternoon, the students are introduced to particle physics, experiments and detectors in lectures given by active particle physics researchers. On Monday, after a virtual visit to the ALICE detector at CERN, they work on their own with data from ALICE Afterwards they participate in a video conference with students from other countries and moderators at CERN, where they discuss and compare their results.
For more information on the Particle Physics Masterclasses, see the International Masterclasses web site.
After a successful launch, subsequent deployment of its sunshield and mirrors, and arrival at its orbit around the Second Lagrange Point, the goal now for the James Webb Space Telescope is to align the optical components of the telescope to the required accuracy. This is not a simple task – each of the segments of the main mirror has to be aligned to within a fraction of a wavelength of the light it will observe (in the near-infrared part of the electromagnetic spectrum) – and it will take several months to complete. However, we did hear yesterday that the telescope has now seen “first light”, in the sense that the first photons have landed on its detectors. The first images to be formed will be blurry and distorted, but these will be used to adjust the components until they reach the required sharpness.
For more details of this process see here.
Incidentally, it is worth saying a little bit about L2, the second Lagrange point of the Earth-Sun system. As the diagram below shows, this orbits the Sun at a greater distance from the Sun than the Earth. According to Kepler’s Laws, and ignoring the Earth’s gravitation, a test particle placed in a circular orbit at this radius would move more slowly than the Earth and would not therefore hold a fixed position relative to the Earth and Sun as it went around. The effect of the Earth’s gravity however is to supply an extra force to speed it up a bit, so it can keep up and thus remain in a fixed configuration relative to both Earth and Sun.
The opposite applies to L1: an object placed here would, in the absence of Earth’s gravity, move more quickly and thus pull ahead of the Earth. Having the Earth there holds it back by just the right amount to maintain a fixed position in the rotating frame.
The interesting thing about L1 & L2 is that while they are both equilibrium points, they are both unstable to radial perturbations. An object placed at either of these points would move away if disturbed slightly. JWST does not therefore just sit passively at L2 – it moves in a so-called halo orbit around L2 a process which requires some fuel. It’s not that there’s an actual mass at L2 for it to orbit around, but that its motion produces a Coriolis Force that keeps it from moving away. It’s very clever, but does require a bit of energy to keep it in this orbit.
Unlike L1 & L2, the Lagrange Points L4 & L5 are stable and therefore attract all kinds of space junk, such as asteroids, cometary debris, and preprints by Avi Loeb.
Another interesting Lagrange Point is that Joseph-Louis Lagrange was born in 1736 in Turin, but that does not mean that he was Italian. At that time Italy did not exist as a political entity; in 1736 Turin was part of the Kingdom of Sardinia. Although born in the part of the world now known as Italy, he was never an Italian citizen. In fact he lived most of his life in Berlin and Paris and died in 1813, long before the Kingdom of Italy was founded (in 1861).
In the Dark 