### Inventory no. 44725 - Former Display Label

THE EINSTEIN BLACKBOARD

The Einstein lectures at Oxford were given at a time of great excitement in the astronomical world, a time when Einstein's theories of general relativity were being combined in a whole variety of ways with astronomical data to explain the shifts towards the red in the spectra of distant galaxies. These red shifts, which increased with the distance of the galaxies observed, was generally thought to indicate an expansion of the universe as a whole. The mathematical models devised by 1931 to explain this phenomenon were very complicated, but at about this time Einstein was developing, together with Willem de Sitter (1872-1934), a relatively simple model, in which the pressure and the so-called 'cosmological constant' were ignored. Presumably Einstein chose this model for his lecture because of its simplicity. Furthermore, the cosmological constant, the arbitrary term {lamda}, which had been introduced by Einstein in 1917, a year after completing his General Theory of Relativity and Gravitation, required because of his assumption of a static universe, could be eliminated in the 1920s when Edwin Hubble (1889-1953) demonstrated that the galaxies were not immobile, but were receding from the observer. The consequences of eliminating {lamda} were described by De Sitter and Einstein in a joint paper 'On the Relation Between the Expansion and the Mean Density of the Universe', Proceedings of the National Academy of Sciences, vol. 18 (1932), pp. 213-4, and this is also the topic of this lecture.*

In the first line on the blackboard, D, the measure of expansion in the universe, is defined in terms of P (now usually denoted by R), the expansion factor (see the above article for full details). The expression for the density of matter in the universe, given by {rho} in the third line, is derived from the field equations. The last four lines contain numerical data (L. J = Licht Jahr [light year]; J = Jahr [year]). Thus, deriving in the first three lines an expression for D, the last four lines give the values for density, radius and age of the universe. A density of 10{-26 superscript} grams per cubic centimeter seemed feasible, but a radius of 10{8 superscript} light years rather small, indicating a much younger universe than was expected, which according to the last line was about 10, or perhaps 100 billion years (the bracket indicates an alternative figure, not a product of two figures).

Another blackboard used by Einstein is on display in the Department of Physics of the University of Nottingham. It is signed and dated 6 June 1930 and lists the topics discussed by Einstein on that day, including the concepts of space and fields in physics and mathematics, and the Special and General Theories of Relativity.

[* Note added 22/11/15: this paragraph is wrong. According to Cormac O'Raifeartaigh, the Einstein-de Sitter model was only devised and published in 1932. In Oxford he was lecturing on the less well-known Friedman-Einstein model of the universe; see http://arxiv.org/abs/1312.2192 ]

### Other narratives:

- Reflections on the Einstein blackboard
- Printed Pamphlet Accompanying The Rhodes Lectures, Oxford, 1931, by Albert Einstein
- The language of Einstein's lecture
- The Einstein blackboard
- Inv. 44725 - Nottingham blackboard
- Inv. 44725 - Newspaper coverage of Einstein's lectures