There has been quite a bit of mention in the media this last week or so that it is 100 years since Albert Einstein published his ground-breaking theory of gravity – the general theory of relativity. Yet, there seems to be some confusion as to when this theory was first published, in some places you will see 1915, in others 1916. So, I thought I would try and clear up this confusion by explaining why both dates appear.

## From equivalence to the field equations

Everyone knew that Einstein was working on a new theory of gravity. As I blogged about here, he had his insight into the equivalence between acceleration and gravity in 1907, and ever since then he had been developing his ideas to create a new theory of gravity.

He had come up with his principle of equivalence when he was asked in the autumn of 1907 to write a review article of his special theory of relativity (his 1905 theory) for *Jahrbuch der Radioaktivitätthe* (the Yearbook of Electronics and Radioactivity). That paper appeared in 1908 as *Relativitätsprinzip und die aus demselben gezogenen Folgerungen* (On the Relativity Principle and the Conclusions Drawn from It) (Jahrbuch der Radioaktivität, 4, 411–462).

In 1908 he got his first academic appointment, and did not return to thinking about a generalisation of special relativity until 1911. In 1911 he published a paper *Einfluss der Schwerkraft auf die Ausbreitung des Lichtes* (On the Influence of Gravitation on the Propagation of Light) (Annalen der Physik (ser. 4), 35, 898–908), in which he calculated for the first time the deflection of light produced by massive bodies. But, he also realised that, to properly develop his ideas of a new theory of gravity, he would need to learn some mathematics which was new to him. In 1912, he moved to Zurich to work at the ETH, his alma mater. He asked his friend Marcel Grossmann to help him learn this new mathematics, saying “You’ve got to help me or I’ll go crazy.”

Grossmann gave Einstein a book on non-Euclidean geometry. Euclidean geometry, the geometry of flat surfaces, is the geometry we learn in school. The geometry of curved surfaces, so-called Riemann geometry, had first been developed in the 1820s by German mathematician Carl Friedrich Gauss. By the 1850s another German mathematician, Bernhard Riemann developed this geometry of curved surfaces even further, and this was the Riemann geometry textbook which Grossmann gave to Einstein in 1912. Mastering this new mathematics proved very difficult for Einstein, but he knew that he needed to master it to be able to develop the equations for general relativity.

These equations were not ready until late 1915. Everyone knew Einstein was working on them, and in fact he was offered and accepted a job in Berlin in 1914 as Berlin wanted him on their staff when the new theory was published. The equations of general relativity were first presented on the 25th of November 1915, to the Prussian Academy of Sciences. The lecture *Feldgleichungen der Gravitation* (The Field Equations of Gravitation) was the fourth and last lecture that Einstein gave to the Prussian Academy on his new theory (Preussische Akademie der Wissenschaften, Sitzungsberichte, 1915 (part 2), 844–847), the previous three lectures, given on the 4th, 11th and 18th of November, had been leading up to this. But, in fact, Einstein did not have the field equations ready until the last few days before the fourth lecture!

The peer-reviewed paper of the theory (which also contains the field equations) did not appear until 1916 in volume 49 of *Annalen der Physik* – *Grundlage der allgemeinen Relativitätstheorie* (The Foundation of the General Theory of Relativity) Annalen der Physik (ser. 4), 49, 769–822. The paper was submitted by Einstein on the 20th of March 1916.

In a future blog, I will discuss Einstein’s field equations, but hopefully I have cleared up the confusion as to why some people refer to 1915 as the year of publication of the General Theory of Relativity, and some people choose 1916. Both are correct, which allows us to celebrate the centenary twice!

You can read more about Einstein’s development of the general theory of relativity in our book *10 Physicists Who Transformed Our Understanding of Reality. *Order your copy here.