I was reminded today that 4th December is the anniversary of the death, in 1131, of the Persian astronomer, mathematician and poet Omar Khayyam. That in turn reminded me that just over year ago I received a gift of a sumptuously illustrated multi-lingual edition of the Rubáiyát of Omar Khayyám:
Edward Fitzgerald‘s famous English translation of these verses is very familiar, but it seems there’s a more of Fitzgerald than Khayyam in many of the poems and the attribution of many of the original texts to Khayyam is dubious in any case. Whatever you think about this collection, I think it’s a bit unfortunate that Khayyam is not more widely recognized for his scientific work, which you can read about in more detail here.
Anyway, as we approach the end of 2022 many of us will be remembering people we have lost during the year so here is a sequence of three quatrains (XXII-XXIV) with an appropriately elegiac theme:
For some we loved, the loveliest and the best That from his Vintage rolling Time hath pressed, Have drunk their Cup a Round or two before, And one by one crept silently to rest.
And we, that now make merry in the Room They left, and Summer dresses in new bloom, Ourselves must we beneath the Couch of Earth Descend–ourselves to make a Couch–for whom?
Ah, make the most of what we yet may spend, Before we too into the Dust descend; Dust into Dust, and under Dust to lie, Sans Wine, sans Song, sans Singer, and–sans End!
I’m glad I was too busy today to respond earlier to a junk science story that has been doing the rounds, in the Guardian, in Quantaand even in Physics World to name but a few. Had I had time to write something as soon as I’d seen these pieces of tripe I would probably have responded with more expletives than would be seemly even for this blog. This sort of crap makes me rather angry, you see.
Meaningless Illustration
The story is basically that a group of scientists have created a “wormhole in space-time” that enables quantum teleportation.
Of course they have done no such thing. The paper, like so many stories hyped beyond the bounds of reason, is published in Nature. There are some interesting things in this publication, but nothing to justify the absurd claims that have propagated into the media. The authors must take some of the blame for allowing such tosh to be spread about in their names. I don’t think it will do them any good in the long run.
At least I hope it doesn’t.
You can read it for yourself and make your own , but my take is the following:
Did the authors create a wormhole (even a baby one) in a laboratory? Definitely not.
Did they discover anything whatsoever to do with quantum gravity? No way.
Did they even simulate a wormhole in a lab? Not even close.
Did they even make progress towards simulating a wormhole in a lab? Still no.
Apart from all that it’s fine.
The author of the Quanta article, Natalie Wolchover, writes:
Researchers were able to send a signal through the open wormhole, though it’s not clear in what sense the wormhole can be said to exist.
Au contraire, it’s absolutely clear that no wormhole can be said to exist in any sense whatsoever.
I hope this clarifies the situation.
UPDATE: I see that Peter Woit has gone to town on this on his blog here.
Just a quick post to advertise the fact that the Department of Theoretical Physics at Maynooth University is inviting applications for a Postdoctoral Fellowship Position in Computational and Theoretical Astrophysics. The successful applicant will join the Research Group led by Dr John Regan and is expected to develop their own independent research program within the confines of a research project investigating the formation, growth, and demographics of Black Holes in the early Universe. The group, currently consisting of four PhD students and one additional postdoctoral researcher, is currently engaged in numerous research topics with the goal of understanding early black hole formation. In line with this we are currently implementing an ambitious research project using the EnzoE exascale class code to run large volume, high resolution simulations focused on the first billion years of black hole formation. The successful candidate will be expected to contribute significantly to this research effort but are free to pursue their own research lines under this remit.
For more information, including deadlines and the applications procedure, please see the AAS Jobs register advertisement here.
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!
In yesterday’s Mechanics lecture I decided to illustrate the use of energy conservation arguments with an application to the pole vault. I have done this a few times and indeed wrote a blog post about it some years ago. At the time I wrote that post however the world record for the pole vault was held by the legendary Ukrainian athlete Sergey Bubka at a height of 6.14m which he achieved in 1994. That record stood for almost 20 years but has since been broken several times, and is now held by Armand Duplantis at a height of 6.21m.
Here he is breaking the record on July 24th 2022 in Eugene, Oregon:
He seemed to clear that height quite comfortably, actually, and he’s only 23 years old, so I dare say he’ll break quite a few more records in his time but the fact that world record has only increased by 7cm in almost 30 years tells you that the elite pole vaulters are working at the limits of what the human body can achieve. A little bit of first-year physics will convince you why.
Basically, the pole is a device that converts the horizontal kinetic energy of the vaulter , as he/she runs in, to the gravitational potential energy acquired at the apex of his/her vertical motion, i.e. at the top of the vault.
Now assume that the approach is at the speed of a sprinter, i.e. about , and work out the height that the vaulter can gain if the kinetic energy is converted with 100% efficiency. Since the answer to that little sum turns out to be about 5 metres.
This suggests that 6.21 metres should not just be at, but beyond, the limit of a human vaulter, unless the pole were super-elastic. However, there are two things that help. The first is that the centre of mass of the combined vaulter-plus-pole does not start at ground level; it is at a height of a bit less than 1m for an an average-sized person. Nor does the centre of mass of the vaulter-pole combination reach 6.21 metres.
The pole does not go over the bar, but it’s pretty light so that probably doesn’t make much difference. However, the centre of mass of the vaulter actually does not actually pass over the bar. That doesn’t happen in the high jump, either. Owing to the flexibility of the jumper’s back the arc is such that the centre of mass remains under the bar while the different parts of the jumper’s body go over it.
Moreover, it’s not just the kinetic energy related to the horizontal motion of the vaulter that’s involved. A human can in fact jump vertically from a standing position using elastic energy stored in muscles. In fact the world record for the standing high jump is an astonishing 1.9m. In the context of the pole vault it seems likely to me that this accounts for at least a few tens of centimetres.
Despite these complications, it is clear that pole vaulters are remarkably efficient athletes. And not a little brave either – as someone who is scared of heights I can tell you that I’d be absolutely terrified being shot up to 6.21 metres on the end of a bendy stick, even with something soft to land on!
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.
I thought quite a few readers of In the Dark might be interested that there’s a new open-access journal starting up called Philosophy of Physics. It’s published by LSE Press. See this post for more details.
Thank you very much to everyone in the Governing Board and the Society who contributed to realizing our key initiative!
Special thanks go to David Wallace for having accepted to act as the journal’s founding Editor-in-Chief. Read his announcement on the LSE Press’s blog here.
Please consider submitting your best work to Philosophy of Physics. In order to do so, you should become a member of the Society. It’s free for students and unwaged people, £10 for postdocs, and £20 for others. Once you are a member, you will find instructions on how to submit a paper inside the members’ area, as explained here.
There’s a new interactive map of the Universe created by astronomers at Johns Hopkins University using data from the Sloan Digital Sky Survey. You can read all about it here There’s also a nice video to watch:
The picture at the top of this post is not the actual map, it’s just a publicity poster. You can play with the fully interactive version here.
This reminds me that when I started as a researcher in cosmology, back in 1985, the biggest galaxy redshift survey available had only just over a thousand galaxies in it and probed only a tiny fraction of the volume of the Universe that has now been mapped, i.e. only out to a redshift of about 0.05.
Well it seems there has been progress and, according to the Irish Times, a proposal to join CERN is going to be tabled by the Minister Simon Harris. This follows a long hiatus after a move reported in the news here in Ireland several years ago of a report from a Committee of the Houses of the Oireachtas making the case for Ireland to join CERN. You can download the report here (PDF) and you’ll find this rather striking graphic therein:
You will see that there are only three European countries other than Ireland that don’t have any form of membership or other agreement with CERN: Latvia, Bosnia-Herzegovina, Moldova. The fact that almost everyone else is in is not in itself necessarily a good argument for Ireland to join, but it does make one wonder why so many other countries have found it important to join or have an agreement with CERN while Ireland has not.
As the document explains, if the Irish government were to decide to take Ireland into CERN then it would first have to become an Associate Member, which would cost around €1.2 million per year. That’s small potatoes really, and the financial returns to Irish industry and universities are likely to far exceed that, so the report strongly recommends this step be taken. This Associate member stage would last up to 5 years, and then to acquire full membership a joining fee of around €15.6 million would have to be paid, which is obviously a much greater commitment but in my view still worthwhile.
There were some positive noises when the document came out, but that was near the end of 2019. Not far into 2020 the pandemic struck and the idea sank without trace. Now it looks like the idea is alive again. It’s not exactly a done deal but at least there’s some movement.
While I strongly support the idea of Ireland joining CERN I do have a couple of concerns about the case as presented in the Oireachtas report.
One is that I’m very sad that the actual science done at CERN is downplayed in that report. Most of it is about the cash return to industry, training opportunities, etc. These are important, of course, but it must not be forgotten that big science projects like those carried out at CERN are above all else science projects. The quest for knowledge does have collateral benefits, but it a worthy activity in its own right and we shouldn’t lose sight of that.
My other (related) concern is that joining CERN is one thing, but in order to reap the scientific reward the government has to invest in the resources needed to exploit the access to facilities membership would provide. Without a related increase in research grant funding for basic science the opportunity to raise the level of scientific activity in Ireland would be lost.
Ireland recently joined the European Southern Observatory (ESO), a decision which gave Irish astronomers access to some amazing telescopes. However, there is no sign at all of Irish funding agencies responding to this opportunity by increasing funding for academic time, postdocs and graduate students needed to do the actual science. In one respect ESO is very like CERN: the facilities do not themselves do the science; we need people to do that. The jam for research is already spread very thinly in Ireland so having an extra thing to spread it on will not necessarily be a good thing for science in general.
In recent times I’ve posted quite a few times about the Hubble Tension and possible resolutions thereof. I also had polls to gauge the level of tension among my readers, like this one
and this one:
I’m not sure if these are still working, though, as I think I’ve reached the number of votes allowed on the basic free version of crowdsignal that comes with the free version of WordPress. I refuse to pay for the enhanced version. I’m nothing if not cheap. You can however still see the votes so far.
Anyway, there is a new(ish) paper on the arXiv by Mark Kamionkowski and Adam Riess that presents a nice readable introduction to this topic. I’m still not convinced that the Hubble Tension is anything more than an observational systematic, but I think this is a good discussion of what it might be if it is more than that.
Here is the abstract:
Over the past decade, the disparity between the value of the cosmic expansion rate directly determined from measurements of distance and redshift or instead from the standard ΛCDM cosmological model calibrated by measurements from the early Universe, has grown to a level of significance requiring a solution. Proposed systematic errors are not supported by the breadth of available data (and “unknown errors” untestable by lack of definition). Simple theoretical explanations for this “Hubble tension” that are consistent with the majority of the data have been surprisingly hard to come by, but in recent years, attention has focused increasingly on models that alter the early or pre-recombination physics of ΛCDM as the most feasible. Here, we describe the nature of this tension, emphasizing recent developments on the observational side. We then explain why early-Universe solutions are currently favored and the constraints that any such model must satisfy. We discuss one workable example, early dark energy, and describe how it can be tested with future measurements. Given an assortment of more extended recent reviews on specific aspects of the problem, the discussion is intended to be fairly general and understandable to a broad audience.
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, as he/she runs in, to the gravitational potential energy 
acquired at the apex of his/her vertical motion, i.e. at the top of the vault.
, and work out the height 
that the vaulter can gain if the kinetic energy is converted with 100% efficiency. Since 
the answer to that little sum turns out to be about 5 metres.
In the Dark 