Writing yesterday’s post I remembered doing a calculation a while ago which I filed away and never used again. Now that it has come back to my mind I thought I’d try it out on my readers (Sid and Doris Bonkers). I think the answer might be quite well known, as it is in a closed form, but it might be worth a shot if you’re bored.
The variable 
where 
Answers on a postcard through the comments box please..
A combination of circumstances – including being a bit poorly – has made me rather late in getting around to reading the papers released by the Planck consortium a couple of weeks ago. I’ve had a bit of time this Sunday so I decided to have a look. Naturally I went straight for, er, paper No. 24, which you can find on the arXiv, here.
I picked this one to start with because it’s about primordial non-Gaussianity. This is an important topic because the simplest theories of cosmological inflation predict the generation of small-amplitude irregularities in the early Universe that form a statistically homogeneous and isotropic Gaussian random field. This means that the perturbations (usually defined in terms of departures of the metric from a pure Robertson-Walker form) are defined by probability distributions which are invariant under translations and rotations in 3D space.
In a nutshell, such perturbations arise quite simply in inflationary cosmology as zero-point oscillations of a scalar quantum field, in a very similar way the Gaussian distributions that arise from the quantized harmonic oscillator. Assuming the fluctuations are small in amplitude the scalar field evolves according to
which is similar to that describing a ball rolling down a potential 
On the one hand, Gaussian fluctuations are great for a theorist because so many of their statistical properties can be calculated analytically: I played around a lot with them in my PhD thesis many moons ago, long before Planck, in fact long before any fluctuations in the cosmic microwave background were measured at all! The problem is that if we keep finding that everything is consistent with the Gaussian hypothesis then we have problems.
The point about this slow-rolling regime is that it is an attractor solution that resembles the physical description of a body falling through the air: eventually such a body reaches a terminal velocity defined by the balance between gravity and air resistance, but independent of how high and how fast it started. The problem is that if you want to know where a body moving at terminal velocity started falling from, you’re stumped (unless you have other evidence). All dynamical memory of the initial conditions is lost when you reach the attractor solution. The problem for early Universe cosmologists is similar. If everything we measure is consistent with having been generated during a simple slow-rolling inflationary regime, then there is no way of recovering any information about what happened beforehand because nothing we can observe remembers it. The early Universe will remain a closed book forever.
So what does all this have to do with Planck? Well, one of the most important things that the Planck collaboration has been looking for is evidence of non-Gaussianity that could be indicative of primordial physics more complicated than that included in the simplest inflationary models (e.g. multiple scalar fields, more complicated dynamics, etc). Departures from the standard model might just keep the window on the early Universe open.
A simple way of defining a parameter that describes the level of non-Gaussianity is as follows:
the parameter 
which is clearly consistent with zero. If this doesn’t look impressive, bear in mind that the typical fluctuation in the metric inferred from cosmological measurements is of order 
So it looks like only very unwise investors will be buying shares in cosmological non-Gaussianity at least in the short-term. More fundamentally we may be approaching the limit of what we can learn about inflation in particular, or even the early Universe in general, using the traditional techniques of observational cosmology. But there remain very intriguing questions that may yet shed light on the pre-inflationary epoch. Among these are the large-scale anomalies seen in the very same Planck data that have put such stringent limits on non-Gaussianity. But that question, described in Planck Paper 23, will have to wait for another day…
Here’s a refreshingly hard-nosed take on the recently-announced results from the Alpha Muon Spectrometer (which were rather excessively hyped, in my opinion…)
The Alpha Magnetic Spectrometer [AMS] finally reported its first scientific results today. AMS, a rather large particle physics detector attached to the International Space Station, is designed to study the very high-energy particles found flying around in outer space. These “cosmic rays” (as they are called, for historical reasons) have been under continuous study since their discovery a century ago, but they are still rather mysterious, and we continue to learn new things about them. They are known to be of various different types — commonly found objects such as photons, electrons, neutrinos, protons, and atomic nuclei, and less common ones like positrons (antiparticles of electrons) and anti-protons. They are known to be produced by a variety of different processes. It is quite possible that some of these high-energy particles come from physical or astronomical processes, perhaps very exciting ones, that we have yet to discover. And…
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Just time to post this neat picture I found on the BBC Website this morning:
Although these images were obtained using measurements of the cosmic microwave background made by Planck, they are not themselves maps of the radiation field itself. As photons produced in the early Universe travel through the Universe towards the observer, they are deflected by the gravitational field of intervening clumps of matter; this is called gravitational lensing. With a bit of effort this effect can be “inverted” to reveal the distribution of matter traversed by CMB photons, or at least a projection of that distribution along the line of sight. The good thing about this is that the maps show all the matter (through its gravitational effects) not just the luminous part that might be seen in a galaxy surveys, so they might provide more direct ways of testing cosmological theories.
Follow @telescoperThe reason I was out of the office yesterday was that I was in Cambridge, doing a PhD oral in the Cavendish Laboratory so the first thing to say is congratulations Dr Johnston! It was one of those viva voce examinations that turned out to be less of an examination than an interesting chat about physics. In fact the internal examiner, Prof. Steve Gull, seemed to spend more time asking me questions rather than the candidate!
Afterwards I met up with Anthony Lasenby, the candidate’s supervisor. Not surprisingly the main topic of our brief discussion was today’s impending announcement of results from Planck. Anthony is one of the folks who have been involved with Planck for about twenty years, since it began as a twinkle in the eye of COBRAS/SAMBA. I was looking forward to getting in bright and early this morning to watch the live streaming of the Planck press conference from Paris.
Unfortunately however, I could feel a bit of a lurgy coming on as I travelled to Cambridge yesterday. It got decidedly worse on the way home – it must have been the Cambridge air – and I even ended up passing out on the train from Victoria to Brighton. Fortunately, Brighton was the terminus so someone woke me up when we got there and I got home, coughing and spluttering. I suspect many cosmologists didn’t sleep well last night because of excitement about the Planck results, but in my case it was something else that kept me awake. Anyway, I didn’t make it in this morning so had to follow the announcements via Twitter. Fortunately there’s a lot of press coverage too; see the ESA site and a nice piece by the BBC’s redoubtable Jonathan Amos.
Anyway, without further ado, here’s Planck’s map of the cosmic microwave background:
It’s rather beautiful, in a pointillist kind of way, I think…
It will take me a while in my weakened state to complete a detailed study of the results – and I’m sure to return to them many times in the future, but I will make a couple of points now.
The first is that the papers and data products are all immediately available online. The papers will all appear on the arXiv. Open Access sceptics please take note!
The second is that the most interesting result (as far as I’m concerned) is that at least some of the cosmic anomalies I’ve blogged about in the past, such as the Axle of Elvis Axis of Evil and the famous colder-than-it-should-be cold spot, are still present in the Planck data:
The other results excite me less because, at a quick reading, they all seem to be consistent with the standard cosmological model. Of course, the north-south asymmetry is a small effect on could turn out to be a foreground (e.g. zodiacal emission) or an artefact of the scanning strategy. But if it isn’t a systematic it could be very important. I suspect there’ll be a rush of papers about this before long!
I’m sure to p0st much more about the Planck results in due course, but I think I’ll leave it there for now. Please feel free to post comments and reactions through the box below.
Follow @telescoperWell, Herschel may be going blind but it seems that just as one observatory gets ready to close its eyes on the Universe, another one gets ready to open them. Yesterday saw the official opening of the Atacama Large Millimetre Array (known to its friends as ALMA). What better way to celebrate the opening of this remarkable observatory than with an appropriately-named piece of music.
Con Alma is an original composition by Dizzy Gillespie who plays it on this track made with his big band in 1954, a period when Dizzy was experimenting with various fusions of bebop with Latin-American rhythms. It’s a deceptively complicated tune, with lots of changes of key to keep everyone on their toes. It may be more Cuban than Chilean in influence, but that’s the closest I could think of!
Follow @telescoperMost of the astronomers who read this blog will have heard the news that the Herschel Space Observatory is running out of the Helium that it has been using to keep it cool enough (~1.4K) to be sensitive to the far-infra-red radiation emitted by very distant objects.
There’s a gallery of wonderful images obtained by Herschel since it was launched in 2009 at the news item linked to above, but my favourite is one of the least photogenic:
Many of these fuzzy blobs correspond to immensely distant galaxies; what we see is starlight from very young stars absorbed by vast amounts of cosmic dust and then re-radiated in the infra-red. Understanding these sources is decidedly non-trivial and it will take many years to get all the information out that is hidden in images like this.
Anyway, one thing worth pointing out here is that what is going on now with Herschel is not some kind of failure. Quite the contrary, in fact. The original mission lifetime was planned to be three years, and Herschel has now been operating for nine months longer than that. The supply of Helium was always going to be the limiting factor as the spacecraft operates at the second Lagrange point of the Earth-Sun system, which is almost a million miles away and thus too far to be replenished. When the Helium does run out, Herschel will rapidly heat up to the point where its detectors are swamped. It will then be blind.
I was at this point going to make a cheap joke to the effect that after years on its own in the dark preoccupied with images of heavenly bodies, it was entirely predictable that Herschel would go blind. But I decided not to. I’ll save that kind of off-colour remark for Twitter…
ps. Coincidentally, on this day (March 13th) in 1781, William Herschel discovered the planet Uranus. The telescope is named in Herschel’s honour because he was also the first person to demonstrate the existence of infra-red radiation.
Follow @telescoperAs I mentioned last week, one of the main items on the agenda at the moment is recruitment of new PhD students. As usual, this finds me having to operate on both sides of the fence, playing a role in selecting students whilst also trying to advise students on how to target their applications, prepare for interview, and choose between offers (for those who manage to get a place).
In my field (astrophysics), the primary route for funding a PhD comes through the Science and Technology Facilities Council (STFC) which operates a national deadline (31st March) before which candidates can not be required to make a decision. This deadline sets the timescale for departments to decide too, as we clearly want to make sure all our first choice applicants get their offers before the cutoff date.
The national deadline prevents students from being pressured into making decisions before they have heard back from all the institutions to which they have applied, so in that sense it’s a good idea. On the other hand, it does mean that there’s often frantic activity on deadline day as offers are accepted or declined. Reserves have to be contacted quickly when a favoured candidate withdraws to go somewhere else and not all of them may still be available. A student who has been waiting anxiously without a first-choice offer may suddenly receive a lifeline on deadline day.
Getting offers is one thing, but deciding between them is quite another. There are many things to take into account, and the criteria are by no means clear. I’m not the only person to have been thinking about this. There are personal matters, of course. Is it a nice place? Are the people friendly? Do you think you can get on with your potential supervisor? That sort of thing. But there’s also the actual research. Is the project really what you want to do? Is is likely to open up a future career in research, or just be a dead end? Is the mixture of theory and experiment (or observation) what you would like?
One of the issues that often arises when I discuss research with potential PhD students is how structured the project is. Some projects are mapped out by the supervisor in great detail, with specific things to be done in a specific order with well-defined milestones against which progress can be measured. Others, especially but not exclusively theoretical ones, are much more of the nature of “here’s an interesting idea – let’s study it and see where it leads”. Most PhDs are somewhere between these two extremes, but it’s probably true that experimental PhDs are more like the former, whereas theoretical ones are more like the latter. Mine, in theoretical astrophysics, ended up evolving quite considerably from its starting point.
I’ve always been grateful to my supervisor for allowing me the freedom to follow my own curiosity. But I think it was essential to be given an initial focus, in the form of a specific project to cut my teeth on. Getting a calculation finished, written up and published gave me the confidence to start out on my own, but I did need a lot of guidance during that initial phase. We a;ll need to learn how to walk before we can run.
Another aspect of this is what the final thesis should look like. Should it be a monolithic work, focussed on one very specific topic, or can it be an anthology of contributions across a wider area? Again, it’s a question of balance. I think that a PhD thesis should be seen as a kind of brochure advertising the skills and knowledge of the student that produced it. Versatility is a good quality, so if you can do lots of different things then your thesis should represent that. On the other hand, you also need to demonstrate the ability to carry out a sustained and coherent piece of research. Someone who flits around knocking out lots of cutesy “ideas papers” may get a reputation for being a bit of a dabbler who is unable or unwilling to tackle problems in depth. The opposite extreme would be a person who is incapable of generating new ideas, but excellent once pointed in a specific direction. The best scientists, in my opinion, have creative imagination as well as technical skill and stamina. It’s a matter of balance, and some scientists are more balanced than others. There are some (scary) individuals who are brilliant at everything, of course., but us mere mortals have to make the most of our limited potential.
The postdoc market that lies beyond your PhD is extremely tough. To survive you need to maximize the chances of getting a job, and that means being able to demonstrate a suitability for as many opportunities as possible that come up. So if you want to do theory, make sure that you know at least something about observations and data analysis. Even if you prefer analytic work, don’t be too proud to use a computer occasionally. Research problems often require you to learn new things before you can tackle them. Get into the habit of doing that while you’re a student, and you’re set to continue for the rest of your career. But you have to do all this without spreading yourself too thin, so don’t shy away from the chunky calculations that keep you at your desk for days on end. It’s the hard yards that win you the match.
When it comes to choosing supervisors, my advice would be to look for one who has a reputation for supporting their students, but avoid those who want to exert excessive control. I think it’s a supervisor’s duty to ensure that PhD student becomes as independent as possible as quickly as possible, but to be there with help and advice if things go wrong. Sadly there are some who treat PhD students simply as assistants, and give little thought to their career development.
But if all this sounds a bit scary, I’ll add just one thing. A PhD offers a unique challenge. It’s hard work, but stimulating and highly rewarding. If you find a project that appeals to you, go for it. You won’t regret it.
Follow @telescoperSome astronomy news that made a bit of a splash over the weekend was the announcement that the UK is to invest £88 million in the European Extremely Large Telescope. This amount is to be spread over 10 years, so isn’t quite as astronomical as it sounds, but in any case it is only the UK’s contribution to a project that involves large contributions from the other countries involved in the European Southern Observatory. The UK announcement isn’t the end of the story, in fact, as not all the money needed to make the project work is yet in place.
This is all good news, especially because not long ago it seemed quite likely that the UK would have to make a choice between the E-ELT and the Square Kilometre Array. Now it looks like we’re going to be involved in both of the world’s leading ground-based observational facilities. There is a price to be paid, of course. In order to accommodate these projects within the flat-cash budget of the Science and Technology Facilities Council, difficult choices had to be made, and some things have to go. Not everyone will be happy about the outcome, but Big Science requires Big Decisions.
Anyway, it was nice to see the Observer run a piece about this story, although I was a bit baffled by the implication of the caption going with the picture used to illustrate the story:
The European Extremely Large Telescope will study the Magellanic Cloud.
I’ll avoid asking “which Magellanic Cloud (Large or Small)?” and just point out that E-ELT will study a lot more than either or both! Still, people are more likely to read web articles if they include images, so I’ll end this piece with an appropriate one.
Random Astronomical Image
First, a serious announcement. It appears that the announcement of results from the Planck Mission will be streamed live from ESA HQ on 21st March from 10.00 to 12.00 CET (whatever that is). The UK will remain on GMT until 31st March so the ESA web server will probably crash at 9am British time on 21st March.
There’s a short press release making this announcement here. It says:
On Thursday 21 March 2013, the main scientific findings from the European Space Agency’s Planck spacecraft will be announced at a press briefing to be held at ESA’s Headquarter in Paris. Simultaneously with this event, data products and scientific papers based on the “nominal” operations period will be made public through the Planck Legacy Archive.
I was interested in the appearance of the word “nominal” in quotes in there so I searched for its meaning in the One True Chambers Dictionary, where I found:
nominal, adj relating to or of the nature of a name or noun; of names; by name; only in name; so-called, but not in reality; inconsiderable, small, minor, in comparison with the real value, hardly more than a matter of form…
Interesting. It seems that the “nominal” could mean, on the one hand, that ESA are being unusually modest about the importance of the forthcoming Planck results or, on the other, that there will now be a host of conspiracy theorists suggesting that the Planck results aren’t real….
That reminds me that years and years ago I had an idea for a crime novel with a plot that revolves around the murder of a prominent cosmologist just as some important scientific discovery is about to be announced. Suspicion gathers that the whole thing is an enormous hoax and the discovery bogus. But the experiment is shrouded in secrecy, and so expensive that it can’t easily be repeated, so who can tell, and how?
It’s very difficult to know for sure whether any scientific discoveries are genuine or not, even if the data and analysis procedures are made public. There’s always the possibility that everything might have been fabricated simulated, but in most cases the experiment can be repeated at a later date and the fraud eventually exposed, such as in the Schön Scandal. In Big Science, this may not be practicable. However, Big Science requires big teams of people and the chances are someone would blow the whistle, or try to…
Anyway, I know that there are people out there who take everything I write on this blog absurdly literally so I’ll spell it out that I am in no way suggesting that the Planck mission is a fraud. Or predicting that there’ll be a murder just before the announcements on March 21st. Any similarity purely coincidental and all that. And I’ve never had time to write the book anyway – perhaps a publisher might read this and offer me an advance as an incentive?
Moreover, going back to the Chambers Dictionary, I note the final definition omitted above
…according to plan (space flight)
So that’s that. Nothing sinister. I’m not sure how “nominal” acquired that meaning, mind you, but that’s another story…
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In the Dark 