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Thinking about space and time in Switzerland

This week, I spent a very enjoyable few days in Bern, Switzerland, attending the conference ‘Thinking about Space and Time: 100 Years of Applying and Interpreting General Relativity’. Organised by Claus Beisbart, Tilman Sauer and Christian Wüthrich, the workshop took place at the Faculty of Philosophy at the University of Bern, and focused on the early reception of Einstein’s general theory of relativity and the difficult philosophical questions raised by the theory. The conference website can be found here and the conference programme is here .

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The university of Bern, Switzerland

Of course, such studies also have a historical aspect, and I particularly enjoyed talks by noted scholars in the history and philosophy of 20th century science such as Chris Smeenk (‘Status of the Expanding Universe Models’), John Norton (‘The Error that Showed the Way; Einstein’s Path to the Field Equations’), Dennis Lehmkuhl (‘The Interpretation of Vacuum Solutions in Einstein’s Field Equations’), Daniel Kennefick (‘A History of Gravitational Wave Emission’) and Galina Weinstein (‘The Two-Body Problem in General Relativity as a Heuristic Guide to the Einstein-Rosen Bridge and the EPR Argument’). Other highlights were a review of the problem of dark energy (something I’m working on myself at the moment) by astrophysicist Ruth Durrer and back-to-back talks on the so-called black-hole information paradox from physicist Sabine Hossenfelder and philosopher Carina Prunkl. There were also plenty of talks on general relativity such as Claus Kiefer’s recall of the problems raised at the famous 1955 Bern conference (GR0),  and a really interesting talk on Noether’s theorems by Valeriya Chasova.


Walking to the conference through the old city early yesterday morning


Dr Valereria Chasova giving a talk on Noether’s theorems

My own talk, ‘Historical and Philosophical Aspects of Einstein’s 1917 Model of the Universe’, took place on the first day, the slides are here. (It’s based on our recent review of the Einstein World which has just appeared in EPJH). As for the philosophy talks, I don’t share the disdain some physicists have for philosophers. It seems to me that philosophy has a big role to play in understanding what we think we have discovered about space and time, not least in articulating the big questions clearly. After all, Einstein himself had great interest in the works of philosophers, from Ernst Mach to Hans Reichenbach, and there is little question that modern philosophers such as Harvey Brown have made important contributions to relativity studies. Of course, some philosophers are harder to follow than others, but this is also true of mathematical talks on relativity!

The conference finished with a tour of the famous Einstein Haus in Bern. It’s strange walking around the apartment Einstein lived in with Mileva all those years ago, it has been preserved extremely well. The tour included a very nice talk by Professor Hans Ott , President of the Albert Einstein Society, on AE’s work at the patent office, his 3 great breakthroughs of 1905, and his rise from obscurity to stardom in the years 1905-1909.

Einstein’s old apartment in Bern, a historic site maintained by the Albert Einstein Society

All in all, my favourite sort of conference. A small number of speakers and participants, with plenty of time for Q&A after each talk. I also liked the way the talks took place in a lecture room in the University of Bern, a pleasant walk from the centre of town through the old part of the city (not some bland hotel miles from anywhere). This afternoon, I’m off to visit the University of Zurich and the ETH, and then it’s homeward bound.


I had a very nice day being shown around  ETH Zurich, where Einstein studied as a student


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Imagine taking a mountain lift from the centre of town to lectures!

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Revolutions in Science at UCD

Earlier today , I gave my first my undergraduate lecture at University College Dublin (UCD). The lecture marked the start of a module called Revolutions in Science, a new course that is being offered to UCD students across the disciplines of science, engineering business, law and the humanities.


As far as I know, this is the first course in the history and philosophy of science (HPS) offered at an Irish university and I’m delighted to be part of the initiative. I’ve named my component of the module Science, Society and the Universe – a description of the evolution of ideas about the universe, from the Babylonians to the ancient Greeks, from Ptolemy to Copernicus, from Newton to Einstein (it’s a version of a module I’ve taught at Waterford Institute of Technology for some years).

Hopefully, the new module will be the start of a new trend. It has long surprised me that interdisciplinary courses like this are not a staple of the university experience in Ireland. Certainly, renowned universities like Harvard, Oxford and Cambridge all have strong HPS departments with associated undergraduate modules offered to students across all disciplines. After all, such courses offer a very nice mix of history, philosophy and science, not to mention a useful glimpse into the history of ideas.


In the meantime, I think I will really enjoy being back at my alma mater once a week. I can’t believe how UCD has developed into a really attractive campus

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A new year, a new semester

I always enjoy the start of the second semester. There’s usually a great atmosphere around the college – after long weeks of quiet, it’s great to see the students back and all the restaurants, shops and canteens back open. The students themselves always seem to be in good form too. I suspect it’s the prospect of starting afresh with new modules, one of the benefits of semesterisation.

I’m particularly enjoying the start of term this year as I managed to finish a hefty piece of research before the teaching semester got under way. I’ve been working steadily on the project, a review of a key paper published by Einstein in 1917, since June 1st, so it’s nice to have it off my desk for a while. Of course, the paper will come back in due course with corrections and suggestions from the referees, but I usually enjoy that part of the process.

In the meantime, I’d forgotten how much I enjoy teaching, especially in the absence of a great cloud of research to be done in the evenings. One of the courses I’m teaching this semester is a history of the atomic hypothesis. It’s fascinating to study how the idea emerged from different roots: philosophical considerations in ancient Greece, considerations of chemical reactions in the 18th and 19th century , and considerations of statistical mechanics in the 19th century. The big problem  was how to test the hypothesis: at least until a brilliant young patent clerk suggested that the motion of small particles suspended in water might betray the presence of millions of water molecules.  Einstein’s formula was put to the test by the French physicist Jean Perrin in 1908, and it is one of Einstein’s great triumphs that by 1910, most scientists no longer talked of the ‘atomic hypothesis’, but of ‘atoms’.


In 1905, a young Albert Einstein developed a formula describing the motion of particles  suspended in a liquid, based on the hypothesis that the liquid was made up of millions of molecules. In 1908, the French physicist Jean Perrin demonstrated that the motion of such particles matched Einstein’s formula, giving strong support for the atomic hypothesis.  

For more on Perrin’s exeriment see here


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End of the second semester

It’s hard to believe we have almost reached the end of the second teaching semester. I’m always a bit sorry to see the end of classes, but I accept that it’s important that students are given time to reflect on what they have learnt. With that in mind, I don’t quite understand why exams start in early May rather than June.

As regards research, I can now get back to putting the finishing touches to a review paper I have been trying to finish for months. Mind you, thanks to the open-plan layout of offices in our college,  there will be more – not less – noise and distraction for the next few months as staff are no longer in class. Whoever came up with the idea that open-plan offices are a good idea for academics?

On top of finishing off my various teaching modules, I agreed to give a research seminar this week. The general theory of relativity, Einstein’s greatest contribution to science, is a hundred years old this month and I couldn’t resist an invitation to give a brief history of the theory, together with a summary of the observational evidence supporting many strange predictions of the theory – from black holes to the expanding universe, from the ‘big bang’ to gravitational waves. The talk took quite a bit of prep, but I think it went well and there were plenty of questions afterwards – a nice way to finish off the teaching semester.


The slides for the talk are here. Now the excitement is over and it’s back to the lonely business of writing research papers…


I gave a similar talk in University College Dublin yesterday. A tiring trip, but it’s always very satisfying to give a repeat performance.

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Skiing in Zermatt with the Ski Club of Great Britain

This week I’m back in Zermatt, Switzerland, one of my  all-time favourite ski resorts.I’m having a great week’s skiing with the Ski Club of Great Britain, a unique organisation that allows members to be guided around the mountain by Club Leaders who find all the best pistes and restaurants – not to mention a ready-made gang of cronies to hang out with after the lifts close. It really is a unique service they offer, perfect for the skier who arrives out solo.

Apres-ski with SKGB

The snow has been fine all week both on- and off-piste, if a bit icy in the mornings and a bit slushy in the afternoons. below you can see the well-known Gornergrat Observatory, right at the top of one of the main runs – can someone please organise a cosmology conference here ?

Gornergrat station and observatory above Zermatt with the Matterhorn in the background

Zermatt village is as gorgeous as ever, the archetypal Swiss ski resort, with superb restaurants, no cars and unbelievable views. I am often tempted to come down off the mountain early, just to stroll down the Hauptsrasse and look at the sights, but it hasn’t happened yet.

Zermatt Hauptstrasse

It’s not always the most relaxing of holidays, of course. First there’s the organisational challenge of getting oneself to the meeting point at 9 am sharp each morning with skis, poles, boots, hat, gloves, goggles, shades, transceiver, rucksack etc. I also had problems adjusting to the altitude for the first few days, plus my fancy skiboots have been killing me all week, not unusual when I haven’t used them in a while. I’ve had to become reconciled to the fact that off-piste is now pretty much beyond my fitness level. ..but none of that stuff matters much when you get up top!


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Centenary conference on the history of general relativity

In December, I attended a wonderful conference celebrating the centenary of the general theory of relativity, hosted by the Max Planck Institute for the History of Science in Berlin. The meeting, which took place in Berlin’s splendid Harnack Haus, was a  feast for anyone with an interest in Einstein’s theories or indeed the history of 20th century science.


Harnack Haus in Berlin

There were many talks by historians I have long admired, such as Helge Kragh,  Jurgen Renn, Jean EisenstaedtHannoch Gutfreund , Daniel KennefickChris Smeek and Dennis Lehmkuhl, to name a few. Topics covered included the genesis of general relativity in the 1910s, the low watermark of GR in the period 1940-1960, the history of gravitational waves, the renaissance of GR in the 1960s, the history of gravitational lensing, the history of the black hole information paradox and the history of relativistic cosmology. As regards the latter, I was delighted to give a talk on our recent work concerning Einstein’s cosmology. The program for the conference can be found here and videos of all the talks will soon be available . You can download the slides for my own talk here.


The conference room in Harnack Haus

Best of all, the history conference took place immediately after a conference on general relativity in the same venue,  organised by the Max Planck Institute for Gravitational Physics. Many delegates chose to attend both conferences , a double feast. It included  talks by noted researchers such as Rai Weiss, Paul Steinhardt, Joeseph Polchinski, Eric Adelberger, David Gross and Alexander Blum. Topics covered included black holes, gravitational waves, quantum gravity, the cosmological constant and tests of the equivalence principle. Many of the talks, although technical, took a historical approach: you can find the program here. I was particularly chuffed that Paul Steinhardt discussed my own group’s work on Einstein’s cosmology.


All in all, a superb week in Berlin, where it all started. I found the combination of a conference on physics with a conference on the history of physics very satisfying. It  fits very nicely with my conviction that the study of the history of science isn’t really a branch of historical study in the normal sense –  it’s more the study of the evolution of science. .


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Einstein’s blackboard and the Friedman-Einstein model of the cosmos

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 2nd 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:  D~ 1/P2  and D2  ~ 1/3 , 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.


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’.


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