Talk:Einstein's Blackboard

Hello, it is not accurate to say that " the results were never published by Einstein subsequently". The equations shown on the blackboard are taken directly from Einstein's SAW paper of 1931, the so-called Friedman-Einstein model of the universe (Einstein, A. 1931. Zum kosmologischen Problem der allgemeinen Relativitätstheorie Sitzungsb.König. Preuss. Akad. 235-237) AS it happens, the blackboard played a role in uncovering a numerical error in Einstein's paper, as discussed in our paper on this O’Raifeartaigh, C. and McCann, B. (2014) ‘Einstein’s cosmic model of 1931 revisited: an analysis and translation of a forgotten model of the universe’. Eur. Phys. J. (H) 39 (1), pp. 63-85. Physics ArXiv preprint at http://arxiv.org/abs/1312.2192

Coraifeartaigh (talk) 21:54, 22 November 2015 (UTC)

Hello, again. Below is a fuller description of what Einstein's blackboard represents, complete with appropriate references. The sentence "the results were never published by Einstein subsequently" should be removed and this blurb inserted at that point.

In 2014, the Irish physicists Cormac O’Raifeartaigh and Brendan McCann pointed out [1] that the equations on Einstein’s blackboard are taken directly from a paper published by Einstein in April 1931 [2]. This little-known paper, sometimes known as the Friedman-Einstein model of the universe [3,4], marked 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 Friedman-Einstein model, Einstein adopted Friedman’s 1922 analysis of a cosmos of positive curvature and time-varying radius [5], but set the cosmological constant to zero, declaring it no longer necessary [2]. He then used Edwin Hubble’s observational value for the coefficient of expansion of the universe [6] to extract estimates from the Friedman equations of ρ ~ 10-26g/cm3 , P ~ 108 light-years and t ~ 1010 years for the density of matter, the radius of the cosmos and the timespan of the expansion respectively [2]. However, O’Raifeartaigh and McCann have shown [1] that these estimates contain an error, and should have been ρ ~ 10-28g/cm3 , P ~ 109 light-years and t ~ 109 years respectively. The source of Einstein’s error can be seen on the Oxford blackboard; while Einstein obtained a value of D2 ~ 10-53 cm-2 for the quantity defined in the top line as D=1/P dP/dt. 1/c , simple calculation shows that the contemporaneous Hubble constant of 500 km s-1Mpc-1 implied a value of D2 ~ 10-55 cm-2 (or 10 -51 m-2) [1].

[1] O’Raifeartaigh, C. and McCann, B. (2014) ‘Einstein’s cosmic model of 1931 revisited: an analysis and translation of a forgotten model of the universe’.Eur. Phys. J. (H) 39 (1), pp. 63-85. Physics ArXiv preprint athttp://arxiv.org/abs/1312.2192 [2] Einstein, A. 1931. Zum kosmologischen Problem der allgemeinen Relativitätstheorie Sitzungsb.König. Preuss. Akad. 235-237 [3] North, J.D. 1965. The Measure of the Universe: A History of Modern Cosmology . Oxford University Press p132

[4] Rindler, W. 1969. Essential Relativity: Special, General and Cosmological. Van Nostrand Reinhold Company New York p261 [5] Friedman, A. 1922. Über die Krümmung des Raumes. Zeit. Physik. 10 : 377-386 [6] Hubble, E. 1929. A relation between distance and radial velocity among extra-galactic nebulae. Proc. Nat. Acad. Sci. 15: 168-173 Coraifeartaigh (talk) 21:08, 23 November 2015 (UTC)

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