Ivan Debono

A notebook of useful things

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Happy 100th birthday, General Relativity

This year, professional physicists and the few geeks who are still interested in science (should we call them nerds?) are celebrating General Relativity’s centenary.

Great. What of it then?

General Relativity breaks the record for flowery adjectives in science.  It has been described as impossible to understand, poetic, beautiful, elegant and simple.

Book titles must be short and engaging. You are excused.

Book titles must be short and engaging. You are excused.

Surely it’s elegantly simple?


Simple? Einstein’s Zurich notebook. He makes a wrong assumption about weak gravitational fields on this page, and ends up the wrong path. He starts again on the next page, and arrives at the correct solution.

It’s hard to define ‘simple’ in scientific language. I more appropriate (and sober) description would be ‘complete’. General Relativity is the most complete theory of gravity known so far.

Why is it complete?

Because all gravitational phenomena we have observed so far can be modelled by General Relativity. It describes everything from falling apples, to the orbit of planets, the bending of light, the dynamics of galaxy clusters, and even black holes. The domain of validity of the theory covers a wide range of energy levels and scales. And scale is what physics is all about.

When the BICEP-2 experiment claimed to observe gravitational waves, there was a deeper (and probably more significant) result. It meant that General Relativity is valid up to the GeV energy scale, almost reaching the domain where quantum physics becomes the preferred description.

Can it describe the whole Universe?

Almost. Modern cosmology is based on General Relativity applied to a simple model of the Universe.

We have the field equations for gravity: the Einstein field equations.

We have the boundary conditions: homogeneity and isotropy, and the contents of the four-dimensional spacetime – matter or energy.

Put them together and you obtain a metric. Think of it as a generalised gravitational potential for the entire Universe.

Almost? What’s the catch?

The big questions in physics (we should really say Big Questions – they’re that important) , on this 100th birthday of General Relativity are the things that cannot be explained by this model: Dark Energy (the Universe doesn’t just expand, it accelerates), and  Inflation (the initial the matter-energy distribution was not homogeneous).

Einstein published most of his papers on General Relativity in 1914. Why are we celebrating 2015?

Because the essential element of General Relativity is the field equations. Einstein had been working on the problem for some years, starting in 1907. He arrived at the final, correct form  in 1915. And he was fully aware of the significance of this publication. He called it simply ‘The Field Equations of Gravitation’ (‘Feldgleichungen der Gravitation’,  in Akademie der Wissenschaften, Sitzungsberichte 1915 (part 2) pages 844-847).

From then on, it was a matter of working out the derivations.


Manuscript of ‘Grundlage der allgemeinen Relativitätstheorie’ (The Foundation of the General Theory of Relativity).


Printed and published. Job done.

Job done. Printed and published in Annalen der Physik (series 4), 49, 769–822, 1916.


Einstein in 1921.

Einstein in 1921.

Physics 2048

Among the multitude of 2048 spinoffs, it wasn’t long before someone thought of a physics twist to the game

Matt LeBlanc: LHC, or the Higgs boson.

James M Donnelly: Isotopic 256, or nucleosynthesis.

Musica universalis (14) – The inner space

Airwave (2000), Innerspace



Eugenio Calabi (1954), The space of Kähler metrics 

Shing-Tung Yau (1978), On the Ricci curvature of a compact kähler manifold and the complex Monge-Ampère equation

Probably not Thomas Bayes

Anyone who has Googled “Thomas Bayes” or searched Wikipedia will have come across this picture.


Most sites helpfully note that this is not an authentic portrait. The costume is anachronistic, and the illustration first appears about two hundred years after Bayes’s death. In fact there is no known portrait of probably the greatest name in probability and statistical theory.

We know very little about Thomas Bayes.

We do know that he was the son of Joshua and Ann Bayes, and was born in London or possibly Herfordshire, most likely in 1701. In 1719, he began to study logic and theology at the University of Edinburgh. When Bayes graduated, his father was the minister of the Presbyterian meeting house in Leather Lane. By 1731, Bayes moved to Tunbridge Wells, Kent, and became the Presbyterian minister of the Mount Sion chapel.

While there, Bayes published his first known work in 1731.  This is a theological rather than a mathematical text, with the rather self-explanatory title of Divine Benevolence or an Attempt to Prove That the Principal End of the Divine Providence and Government is the Happiness of His Creatures. 

His second work was published anonymously in 1736. It was called An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of the Analyst.

It is an interesting work which gives a glimpse of academic debate in 18th century England. In it, Bayes contradicts the criticisms of Bishop George Berkeley (author of The Analyst), who attacked the logical foundation of Isaac Newton’s calculus (“fluxions”). It contained enough mathematics in the introduction for Bayes to be elected Fellow of the Royal Society in 1742.

In 1752, Bayes retired from his ministry, but remained in Tunbridge Wells for the rest of his life.

Now begins the most interesting chapter of Bayes’s life as a scientist. He became interested in probability. It was a race against death.

Bayes became ill and executed his will on 12th December, 1760. Most of his estate was bequeathed to his brothers, sisters, nephews, and cousins. He also divided 200 pounds between John Boyl and and a certain Reverend Richard Price.

Bayes died in Tunbridge Wells, Kent on 7th April, 1761. After his death, the Reverend Richard Price received Bayes’ manuscript on probability. Richard Price edited the manuscript and introduced Bayes’ theorem to the Royal Statistical Society.

It was called Essay Towards Solving a Problem in the Doctrine of Chances and was published in the Philosophical Transactions of the Royal Society in 1763.


Diagram to illustrate Proposition 10 in the essay

I will leave the last word to the Revered Price himself:

Every judicious person will be sensible that the problem now mentioned is by no means merely a curious speculation in the doctrine of chances, but necessary to be solved in order to a sure foundation for all our reasonings concerning past facts, and what is likely to be hereafter. Common sense is indeed sufficient to show us that, from the observation of what has in former instances been the consequence of a certain cause or action, one may make a judgement what is likely to be the consequence of it another time and that the larger number of experiments we have to support a conclusion, so much more the reason we have to take it for granted. But it is certain that we cannot determine, at least not to any nicety, in what degree repeated experiments confirm a conclusion, without the particular discussion of the beforementioned problem; which, therefore, is necessary to be considered by any that would give a clear account of the strength of analogical or inductive reasoning; concerning, which at present, we seem to know little more than that it does sometimes in fact convince us, and at other times not; and that, as it is the means of acquainting us with many truths, of which otherwise we must have been ignorant; so it is, in all probability, the source of many errors, which perhaps might in some measure be avoided, if the force that this sort of reasoning ought to have with us were more distinctly and clearly understood.

The scourge of graduate unemployment

Berlin's trendence institute surveyed over 300,000 European graduates on their perceived career prospects Illustration: Christine Oliver for the Guardian

Berlin’s trendence institute surveyed over 300,000 European graduates on their perceived career prospects Illustration: Christine Oliver for the Guardian



Or what to do with millions of extra graduates.

Europe isn’t alone in facing the problem of graduate unemployment. The BRIC countries are feeling it too.

The numbers are staggering. In India one in three graduates up to the age of 29 is unemployed, according to a Labour Ministry report released last November. Total unemployment in the country is officially closer to 12%.

In China this month a record 7.26 million will graduate from the country’s universities – more than seven times the number 15 years ago.

Unemployment among new Chines graduates six months after leaving university is officially around 15%.

The real unemployment rate could be closer to 30% – some 2.3 million unemployed from this year’s graduating cohort alone, according to Joseph Cheng, professor of political science at City University of Hong Kong.

Meanwhile, back home in Europe, graduates expect to submit an average of 60 applications before landing their first job.  The average wait between graduation and employment is approaching six months. That’s the average.


Musica universalis (13) – The Higgs boson

John O’Callaghan (2014), One Special Particle



Robert Brout and François Englert (1964), Broken Symmetry and the Mass of Gauge Vector Mesons

Peter Higgs (1964), Broken Symmetries and the Masses of Gauge Bosons

Gerald Guralnik, C. Richard Hagen and Tom Kibble (1964), Global Conservation Laws and Massless Particles

The first known telescope

Giovanni Battista della Porta, Biblioteca dell’Accademia dei Lincei, Mss n° 12, c. 326 – Autograph

Giovanni Battista della Porta, Biblioteca dell’Accademia dei Lincei, Mss n° 12, c. 326 – Autograph


This sketch accompanies the first known description of a telescope. It is found in a letter from Giovanni Battista della Porta (c.1535-1615) dated 28th August, 1609 to Federico Cesi (1585-1630), in which he describes a telescope he examined in Naples in the summer of 1609.

The telescope was therefore invented by someone else, before 1609.

Here is della Porta’s description:  ‘It is a tube made of silver-plated tin, having a length of a one palm ad, three fingers in diameter, with a convex eyepiece at the end a: there is another tube [c] in the same tube, 4 fingers long, which enters into the first, and has a concave [lens] at the top’.

“È un cannello di stagno di argento, lungo un palmo ad, grosso di tre diti di diametro, che ha nel capo a un occhiale convesso: vi è un altro canal [c] del medesimo, di 4 diti lungo, che entra nel primo, et ha un concavo nella cima”.

Musica universalis (10) – The Standard Model

Rob Meloni (2013), Particle Theory 



Online particle physics information and references therein.


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