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The Einstein biographer Andrew Robinson, author of Einstein: A Hundred Years of Relativity , recently reminded me of the saga of Einstein’s blackboard. The blackboard, a well-known exhibit at the Oxford Museum for the History of Science, was used by Einstein in the second of three lectures he gave at Oxford University in 1931.

An image of the blackboard used in Einstein’s 2^nd Rhodes lecture at Oxford in April 1931 (reproduced by permission of the Hebrew University of Jerusalem). The analysis is taken from Einstein’s 1931 model of the cosmos.

I came across Einstein’s blackboard during the course of our first Einstein study, a translation and analysis of Einstein’s 1931 paper on cosmology. Although the paper is not very well known in the English-speaking world, it is a work of historical importance, as it constituted the first scientific publication in which Einstein formally rejected his static model of the universe and embraced the possibility of a cosmos of time-varying radius. In the paper, Einstein adopts Alexander Friedman’s 1922 analysis of relativistic cosmic models of time-varying radius and positive curvature, but sets the cosmological constant to zero, predicting a cosmos that expands and contracts over time (the model is sometimes known as the Friedman-Einstein model and should not be confused with the later Einstein-deSitter model of the cosmos). With the use of Edwin Hubble’s redshift/distance graph for the spiral nebulae, Einstein extracts estimates from his analysis of ρ ~ 10^-26 g/cm³ , P ~ 10⁸ light-years and t ~ 10¹⁰ years for the density of matter, the radius of the cosmos and the timespan of the cosmic expansion respectively. However, our analysis of the paper indicated that Einstein’s estimates contain a systematic numerical error.

Before submitting our paper on this to a journal, I discovered to my great surprise that Einstein’s 1931 paper is neatly summarized on the Oxford blackboard (see above). Although the blackboard is quite well known as an intriguing museum exhibit, it seems no-one had made the connection with a published paper. Even better, one extra line on the blackboard, not included in Einstein’s published paper, makes clear the source of the numerical errors in the paper.

The analysis is quite easy to follow: for a cosmos of radius P, the quantity D is defined on the top line of the blackboard as D= (1/c). (1/P).(dP/dt): essentially the Hubble constant divided by the speed of light. From his earlier analysis, Einstein has developed two independent relations from the Friedman equations that relate D to the radius and density of the cosmos respectively:  D² ~ 1/P²  and D²  ~ 1/3 kρ, shown as equations (1a) and (2a) on the blackboard. Using the contemporaneous Hubble constant of 500 kms^-1Mpc^-1, he thus extracts estimates of cosmic density, radius and timespan of expansion respectively,  displayed in the last three lines on the blackboard. However, these estimates contain errors as noted above, and the fourth line on the blackboard (not shown in Einstein’s published paper), makes the source of his error clear. Where Einstein obtains a value of 10^-53 cm^-2 for the quantity D², simple calculation shows that this quantity should have been D² ~ 10^-55 cm^-2 (or 10 ^-51 m^-2). It appears that Einstein stumbled in converting the Hubble constant to his customary cgs units, resulting in a density of matter that was too high by a factor of a hundred, a cosmic radius that was too low by a factor of ten, and a timespan for the expansion that was too high by a factor of ten (although the units of measurement are not specifically stated for the density estimate, cgs units are implied by the other calculations).

Thus Einstein’s blackboard helped us to solve the riddle of the anomalous estimates of his 1931 paper! Our paper on this made the cover of the European Physical Journal and you can read more about Einstein’s blackboard on this blog here and on wikipedia here.

Update

All of the above was interesting and good fun. However, I should say that our translation and analysis of Einstein’s 1931 paper yielded another, rather more serious result – namely that the 1931 paper is NOT a cyclic model, although it is often cited as the first cyclic model of the expanding universe. Einstein specifically rules out this possibility, pointing out that the model breaks down at the endpoints of the single ‘cycle’.

The birth centenary of the noted British astrophysicist Sir Fred Hoyle was celebrated on Friday at the Royal Astronomical Society with a one-day meeting of talks describing Sir Fred’s many contributions to 20^th century physics. While he is chiefly remembered in some quarters as the physicist who was ‘wrong on the big bang’, Sir Fred in fact made a number of seminal contributions to modern physics in several fields. Indeed, it was a treat to witness former collaborators and students recall his contribution to stellar evolution, stellar nucleosynthesis, astrobiology and cosmology, to name but a few.

I hadn’t been to the RAS before although I was elected a Fellow a few years ago, and I was stunned by its fantastic location in central London. It is housed in the famous Burlington House on Piccadilly, sharing the premises and courtyard with the Linnean Society, the Geological Society and the Royal Academy of Arts, a stone’s throw from Piccadilly Circus. As luck would have it, the Royal Academy are currently hosting a show of the work of the Chinese artist Weiwei, and his striking ‘Tree Sculpture’ filled the Burlington courtyard.

Burlington house on Piccadilly, housing five learned London societies, including the Royal Academy of Arts

Weiwei’s exhibit ‘Tree Sculpture’ in the Burlington courtyard. The RAS is located on the west wing of the courtyard.

The meeting opened with an introduction by Lord Martin Rees, who gave a comprehensive overview of Sir Fred’s works in a short, a ten-minute talk. This was followed by a description of Hoyle’s contribution to accretion physics by Professor Andrew Fabian of the Institute for Astronomy (IOA) in Cambridge, and talks on Hoyle’s work on nucleosynthesis by Professor Lynden-Bell (IOA) and Professor Malcolm Longair, Director of the Cavendish laboratory.

Professor Jayant Narlikar of the Inter-University Centre for Astronomy and Astrophysics (Pune, India) then gave the talk ‘Fred’s theories and ideas about gravity’. This was a rare treat – as a long term collaborator, Jayant made several important contributions to the development of Hoyle’s steady-state model of the universe (including the development of a new version of the model based on the principle of least action, and the development of the later ‘quasi-steady-state’ model), so it was most interesting to hear his take on the genesis of the steady-state cosmologies of Hoyle and Bondi and Gold.

Hoyle and Narlikar in 1966

Another treat was a talk by Professor Chandra Wickramasinghe of the University of Buckingham, ‘Fred Hoyle and the foundation of astrobiology’. This presented interesting insights into Chandra’s long collaboration with Sir Fred, from their early work on interstellar dust to their famous hypothesis that life on earth was seeded by comets. The latter work essentially founded the modern field of astrobiology, although they are not always credited for this.

Jayant’s talk was followed by a talk on Hoyle’s cosmology by Professor John Barrow of the Department of Applied Mathematics and Theoretical Physics at Cambridge. John gave a superb overview of Hoyle’s steady-state model of the universe, and of the battle royale between Hoyle’s theory group and Martin Ryle’s astronomy group at Cambridge during the 1950s. Most members of the audience were familiar with this story, but John brought out many points that are not well known – not least that the widespread skepticism concerning Hoyle’s hypothesis of the continuous creation of matter was something of a moot point. As demonstrated by Bill McCrea in 1951, a viable steady-state model can be constructed without this assumption. John also reminded the audience that today’s models of cosmic inflation are effectively steady-state cosmologies, and, if the eternal inflationary scenario is right, it is possible that the observed universe is a locally evolving patch in a global ensemble that is in a steady state!

Eternal inflation could give rise to evolving universes embedded in a global steady-state ensemble

I touched on both these points in my own talk ‘Steady-state cosmologies in context‘, although my main aim was to remind the audience that Hoyle’s steady-state model was a reasonable hypothesis at the time – and that the notion of a steady-state universe surfaced in cosmology on many occasions, from Arrhenius to Nernst, from Holmes to MacMillan. Further, not many people know that soon after the emergence of the first evidence for an expanding universe, several physicists considered the possibility of an expanding universe that remains in a steady state due to a continuous replenishment of matter, from Tolman to Einstein, from Schroedinger to Mimura. That said, my main focus was to discuss Einstein’s abandoned attempt at a steady-state model , an unpublished work discovered 2 years ago. (You can find more on Einstein’s attempt at a steady=state model here and here).

Between the two talks on Sir Fred’s cosmology, Nicola Hoyle gave a fascinating description of her personal recollections of her grandfather. It included many intriguing photos and pieces of information I hadn’t seen before. The meeting ended with a talk by Professor John Faulkner of the University of California at Santa Cruz on Sir Fred’s contribution to our understanding of stellar structure and evolution, after which we all trooped off to the beautiful library of Geological Society on the other side of the square for coffee.

All in all, a superb conference in memory of a superb physicist. The meeting was organized by Simon Mitton of Cambridge University. You can find the programme here and slides for my own talk on the ‘Seminars’ page of this blog.

After the meeting, speakers were treated to dinner at the famous RAS Dining Club, and I rolled back to my hotel through the gardens of Buckingham Palace. On Saturday, I took a hop-on hop-off open bus tour of London and it was a great success. In particular, I caught a young string orchestra rehearsing Correlli and Vivaldi concerti in St Martin in the Fields, and a superbly talented string quartet playing Brahms’s Hungarian Dances in Covent Garden, not to mention a relaxing stroll  along the Embankment in the afternoon sun. I’d forgotten what London can be like on a Saturday afternoon, must visit the RAS more often!

The best way to see London

Update

There is a detailed summary of the meeting in this month’s issue of Astronomy and Geophysics

I  had a most enjoyable day on Friday at the mathematical physics department of Maynooth University, or NUI Maynooth, to give it its proper title. I was there to attend an international masterclass in particle physics. This project, a few years old, is a superb science outreach initiative associated with CERN, the European Centre for Particle Physics particle in Geneva, home of the famous Large Hadron Collider (LHC). If you live on planet earth, you will probably have heard that a famous particle known as the Higgs boson was recently discovered at the LHC. The idea behind the masterclasses is to give secondary school students the opportunity to “become a particle physicists for a day” by performing measurements on real data from CERN.

The day got off to a great start with a lecture on “Quarks, leptons and the forces of nature” by Dr. Paul Watts, a theoretical physicist at Maynooth. An excellent introduction to the world pf particle physics, I was amused by Paul’s cautious answer to a question on the chances of finding supersymmetric particles at the LHC. What the students didn’t know was that Paul studied under the late Bruno Zumino, a world expert on supersymmetry, and one of the pioneers of the theory. Paul’s seminar was followed by another lecture, “Particle Physics Experiments and the Little Bang” , an excellent a talk on the detection of particles at the LHC by Dr Jonivar Skullerud, another physicist at Maynooth. In between the two lectures. we all trooped outside in the hope of seeing something of today’s solar eclipse . I was not hopeful, given that the sky was heavily overcast until about 9.30. Lo and behold, the skies cleared in time and we all got a ringside view of the event through glasses supplied by Maynooth physics department! Now that’s how you impress visitors to the college…

Viewing the eclipse

After lunch we had the workshop proper. Each student was assigned a computer on which software had been installed that allowed them to analyse particle events from the ALICE detector at the LHC (lead ion collisions). Basically, the program allowed the students to measure the momentum and energy of decay products of particles from the tracks produced in collisions, allowing them to calculate the mass of the parent particle and thus identify it. As so often, I was impressed how quickly the students got the hang of the program – having missed the introduction thanks to a meeting, I was by far the slowest in the room. We all then submitted our results, only to find a large discrepancy between the total number of particles we detected and the number predicted by theory! We then all returned to the conference room, and uploaded our results to the control room at the LHC. It was fun comparing our data live with other groups around Europe and discussing the results. Much hilarity greeted the fact that many of the other groups got very different results, and the explanation for that (but what many groups really wanted to know was  whether we got a good look at the eclipse in Ireland).

Uploading our results via a conference call with the contol room at the LHC, CERN

All in all, a wonderful way for students to get a glimpse of life in the world of the LHC, to meet active particle physics researchers, and to link up with students from other countries. See here for the day’s program.

I spent most of the bank holiday weekend at a conference in beautiful Castletown House in County Kildare. Castletown House is well-known as a venue for classical music concerts but I had never been there for a conference before!

Castletown House in Co. Kildare

The conference was Irish Quantum Foundations, this year’s meeting of the Irish Quantum Field Group. Organised by Eoin O’Colgain of the University of Oviedo in conjunction with theoretical physicists at the Dublin Institute for Advanced Studies, the National University of Ireland, Maynooth and Trinity College Dublin, it was most enjoyable.  Of course,  I’m not a quantum theorist (or any other sort of theorist) but as well as many talks on quantum field theory and string theory, there were seminars on recent advances in experimental particle physics and cosmology. You can find the programme and abstracts here – highlights for me were  a seminar on the recent results from the Planck satellite by Steven Gratton of Cambridge University and a talk on recent studies of the internal structure of the proton at LHCb by Ronan McNulty of University College Dublin.

The conference also featured a public science lecture on the Higgs boson by Peter Higgs of Edinburgh University. Yes, the man himself! Peter’s visit to Ireland received quite  bit of media attention and his lecture certainly didn’t disappoint. About 400 young people turned up in Maynooth University late on Friday afternoon to hear him describe how his work in quantum theory led him postulate the existence of the Higgs boson in 1964. Younger colleagues from Edinburgh then described the successful search for the Higgs at the Large Hadron Collider and how the discovery fits into modern physics. It was a very enjoyable outreach event and I think the point, that what once seemed an abstruse piece of theoretical physics went on to become a major lynchpin of modern physics , was well-made. A nice touch was that Professor Higgs was introduced by Dr Brian Dolan, a quantum theorist at Maynooth who informed the assembled students and visitors that he had studied under Higgs as a student at at Edinburgh!

Peter Higgs being congratulated by Dr Fabiola Gianotti of the ATLAS experiment at CERN , on the day of the announcement of the discovery of a Higgs-like particle at the LHC

The last talk of the conference was a memorial lecture in honour of my father, Lochlainn O’Raifeartaigh. The lecture was given by Professor Nathan Seiberg of the Institute of Advanced Studies at Princeton, a very appropriate choice – Nathan is a world-renowned figure in quantum field theory and string theory, particularly for his work in supersymmetry. This work is closely related to that of Lochlainn, in fact several of my father’s last papers were on the Seiberg-Witten model. Nathan gave a superb overview of some new advances in supersymmetry, carefully drawing out the connections between his own work and that of Lochlainn in many instances. Dad always said that he thought his work on supersymmetry breaking was probably his best and it’s good to know that scientific work can live on, just as music and literature do.

At question time, I asked Nathan about his thoughts on the lack of evidence for supersymmetry at the LHC so far (a lack of evidence that is leading some commentators to declare supersymmerty dead in the water). Like so many theorists, he had a very general overview:

“Even if supersymmetry is not realized in the energy range explored by the LHC, it is still and will always be important.  The impact of supersymmetry on theoretical physics and on mathematics has already been huge and it will continue to be essential…there are many parallels with other theoretical ideas that did not solve the problems they were designed to solve but turned out to be crucial in other contexts.”

Of course this is true – gauge theory in particular is full of examples of  advances that seemed to run into a wall, and were later found to be extremely important in other contexts. (Yang-Mills theory is a good example).

All in all, a superb conference – photos will be available on the conference website soon.

Update

I had a very nice conversation with Peter Higgs on Friday about Lochlainn, he remembered him well and was very complimentary about his work. He also pointed out that Irish students, physicists and engineers were losing out by Ireland’s non-membership of CERN, a point he also made on national TV (see link here, the interview is 20 mins in). I got my photo taken with Peter, but it came out looking like Jackson Pollock painting!

There are sad tidings in Ireland this week with the news that Professor Alex Montwill, Ireland’s best-known particle physicist, has died. Alex was an outstanding  physicist in the field of experimental particle physics and the best teacher I ever had, inspiring generations of physics students with his legendary undergraduate lectures on the physics of the elementary particles and the puzzles of the quantum world. If I can pass on even a morsel of his great knowledge to my own students, my career will have been worthwhile.

Professor Alex Montwill of the UCD particle physics group

The biography below is reproduced from the Institute of Physics

Professor Emeritus of Experimental Physics at UCD, Alex Montwill was one of the first Irish scientists to work at CERN in the late 1950’s. From about that time onwards he was head of the Fundamental Particle research group at UCD which later became members of the European Nuclear Emulsion Collaboration. The collaboration carried out extensive studies in hypernuclear physics and subsequently made the first observation of the creation and decay of a particle containing a charmed quark. Apart from over 40 years’ teaching at UCD,  Alex lectured at City College New York and at the University of Minnesota, Minneapolis. He presented some 150 Science slots on RTE1 radio in 1980’s and 1990’s. He is co-author with Ann Breslin of the book entitled ‘Let there be light’ which was published in 2008 by Imperial College Press. Alex’s hobbies were bridge and chess in both of which he represented Ireland in international competition.

I would like to add: Alex and Ann published a second book ‘ The quantum adventure’ just this year. It’s a fantastic read for anyone with an interest in quantum physics. Also, Alex chose the title ‘The laboratory of the mind‘ for his radio show, a title that gives you a feel for his deep interest in the philosophy of physics, an interest he passed on to generations of students. On a personal note, he knew my father well as a physicist and must have got a shock when I came along and was  a very ordinary student! Yet both Alex and Ann were  extremely supportive of my work in communicating the ideas of physics from the beginning.

As well as the countless students he inspired to take up physics as a career, Alex’s legacy can also be seen in today’s thriving particle physics group at UCD. This group, led by Professor Ronan Mc Nulty, is heavily involved in experiments at the LHCb detector at the Large Hadron Collider; these experiments probe the asymmetry between matter and antimatter, a puzzle of fundamental importance in particle physics.

Finally,  a most interesting ‘life-in-physics’ interview with Alex recorded by Dr Tony Scott on behalf of the IoP is available at:
http://www.iopireland.org/resources/audio/page_50891.html

Ar dheis Dé go raibh a anam

Last week saw the first release of new measurements of the cosmic microwave background by the Planck satellite . There have been many articles and blogposts on the results (see last post), all noting that the data fit well to the standard ‘ΛCDM’ model of a universe containing dark energy (69.2 +- .019 %), dark matter (25.8 ± 0.4%) and ordinary matter (4.82 ± 0.05%). Other results are a slightly revised value of the Hubble constant (67.3 +- 1.2 km/s/MPC) and a revised estimate of the period of expansion (13.8 billion years), aka ‘a new age for the universe’. However, there has been relatively little discussion of the implications of the Planck data for the theory of inflation.

As we saw in previous posts, the theory of cosmic inflation suggests that the universe underwent an extremely rapid, gigantic expansion in the first fractions of an instant, expanding in volume by a factor of about 10⁷⁸  in the time interval 10⁻³⁶ to 10⁻³² of the first second. Such numbers seem crazy in comparison with the relatively sedate expansion of space observed today (Hubble constant above), but inflation gives a very neat solution to several different problems associated with the big bang model; a lack of magnetic monopoles in the universe, the smoothness of the cosmic microwave background, and the fact that the geometry of space appears to be flat. Best of all, it can be shown that inflation provides a natural explanation for the tiny perturbations in the microwave background that gave rise to today’s galaxies (it is thought that quantum fluctuations in the infant universe were amplified by inflation to become the seeds of today’s galactic structures).

Inflation posits an extremely rapid expansion of space in the first fractions of a second

Inflation has become an extremely successful paradigm in big bang cosmology, and today there are few non-inflationary explanations for the geometry of the universe or the formation of structure. But what exactly was the mechanism of inflation? There are over a hundred distinct models; although the WMAP satellite gave results that are consistent with the general idea, the data did not allow one to discriminate between the different models of inflation. So how about Planck?

The first result is that Planck gives a measurement of Ω_k = -0.0005 +- .07 for the curvature of space. This indicates a universe that is very close indeed to flatness. This result confirms and extends  many complementary measurements of the geometry of the universe and strengthens the case for inflation (essentially, inflation predicts that the universe expanded so quickly that any large-scale curvature was quickly smoothed out, just as a balloon blown up to gigantic proportions will appear flat to an observer). Explaining a spatial curvature that is exactly flat without inflation is extremely difficult as it requires a very special balance between the competing forces of expansion and gravity, so this is an important triumph for inflation.

A second profound result from Planck is that the ‘power’ spectrum of the perturbations in the microwave background has a ‘spectral index’ of 0.96 +-.009. This value, close to 1 but slightly less, is exactly consistent with almost all models of inflation. Best of all, the Planck data allow allow us to separate out two spectral parameters that could not be disentangled before (n_s and r, see here). The upshot is that the new data render some inflationary models very improbable, while others remain possible but with new constraints.

Inflationary models (lines and circles) vs the Planck data; points within dark blue and grey shading represent confidence intervals of 95% and 68% respectively

In particular, many complicated inflationary models such as power-law, double-field, and hybrid-model inflation are now effectively ruled out. (These results are backed by a lack of detection of non-Gaussianity in the CMB spectrum). Instead, the simplest ‘slow-roll single field’ type models are firmly in the frame of possibility (yellow and orange lines for example) . Intriguingly, it seems a Higgs-type field is also a possibility if it is strongly coupled to gravity.

Slow-roll inflation; a slowly decaying potential is required for inflation to end in a manner consistent with the observable universe

All in all, a spectacular vindication for inflation, a theory that was once considered far too contrived to be true. You can find more on this in the official summary of the Planck results here  (p36) or the specific Planck paper ‘Constraints on Inflation’ here.  This is how science progresses; painstaking analysis of models gives predictions that can be compared to emerging data. Many possible scenarios are ruled out, while others remain possible. Overall, it is important not to lose sight of the main result i.e. that the extraordinary phenomenon of cosmic inflation is almost certainly right and the simplest models are looking most likely! (Note that there is a misprint in the summary paper: the text on page 36 should refer to fig 26, not 23 – you saw it here first).

The next step is that more detailed observations by Planck may be able to detect a phenomenon known as B-mode polarization in the microwave background; if so, this could allow us to narrow the inflationary candidates down further, not to mention provide us with the first observation of gravitational waves.

Planck and the cyclic universe

One intriguing alternative to inflation is the ekpyrotic cyclic universe. In this model, the big bang is the result of a collision of two branes in a cyclic universe. Such models can reproduce all the characteristics of a standard big bang universe in a natural way, without the extra premise of inflation and its special initial conditions. As a bonus, the postulate of a big bang in the context of a cyclic universe is very attractive because it sidesteps difficult philosophical questions such as ‘when did the laws of physics become the laws of physics?’ or ‘when did spacetime become spacetime?’

During his presentation at Cambridge last week (see last post), Professor Paul Shellard mentioned that the new Planck data render many cyclic models, including the ekpyrotic universe, a lot less likely. At question time, I asked him what aspect of the new data disfavours the cyclic theories; it seems the lack of non-Gaussianities in the CMB spectrum rules out the conversion mechanism required by most cyclic models. However, Paul also suggested that the cyclic theorists would no doubt overcome this temporary setback by tweaking their models! I haven’t found much on this in the Planck papers so more on this later…