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Einstein's Blackboard is ablackboard^[1] which physicistAlbert Einstein (1879–1955) used on 16May 1931 during his lectures while visiting theUniversity of Oxford in England.^[2][3][4] The blackboard is in the collection of the History of Science Museum inOxford.^[5][6] The equations in the blackboard are related to the cosmological model known asFriedmann–Einstein universe.

The lecture in which the blackboard was used was the second of three, delivered atRhodes House inSouth Parks Road. Einstein's visit to give the Rhodes Lectures, and also to receive an honoraryDoctor of Science degree from Oxford University on 23 May 1931, was hosted by the physicistFrederick Lindemann.^[7] Einstein's first lecture was onrelativity, the second oncosmology, and the third onunified field theory. All the lectures were delivered inGerman. A brief report of the second lecture was given inThe Times^[8] and inNature.^[9] A summary of all three lectures can be found in the Archives of the Oxford Museum for the History of Science.^[10]

The blackboard was rescued with another board by dons (including the chemistE. J. Bowen, zoologistGavin de Beer, and historian of scienceRobert Gunther^[11][12][3]) and formally donated by theWarden of Rhodes House, SirFrancis James Wylie.^[13][14] The writing on the blackboard, althoughephemeral in nature, is of historic interest because the equations displayed are taken from a model of the universe proposed by Einstein in May 1931 known asFriedmann–Einstein universe.^[15][16][17] The last three lines on the blackboard are estimates of the density of matter in the universeρ, the radius of the universeP and the timespant of the expansion of the universe respectively. It has recently been shown that these estimates contain a systematic numerical error.^[16]

The blackboard is considered a "mutant" object or artefact because it no longer serves the philosophical purpose of a blackboard, namely temporary information storage. By keeping Einstein's writings on it for ever, the blackboard became something else and can only regain to its original purpose by being wiped.^[18][19][20] A second blackboard used by Einstein during the lecture was also donated to the museum, but was accidentally wiped clean by a museum cleaner.^[21][22]

Einstein returned to Oxford again in 1932 and 1933 before he settled atPrinceton University in the United States for the rest of his life.^[23]

The blackboard reads

Blackboard

${\displaystyle D=\frac{1}{c}\frac{1}{\ell }\frac{\mathrm{d}\ell }{\mathrm{d}t}=\frac{1}{c}\frac{1}{P}\frac{\mathrm{d}P}{\mathrm{d}t}}$

${\displaystyle D^2=\frac{1}{P^2}\frac{P_0-P}{P}\sim \frac{1}{P}}$

1a

${\displaystyle D^2=\frac{\kappa \rho }{3}\frac{P_0-P}{P_0}\sim \kappa \rho }$

2a

${\displaystyle D^2\sim {10}^{-53}}$

${\displaystyle \rho \sim {10}^{-26}}$

${\displaystyle P\sim {10}^8\text{l.y.}}$

${\displaystyle t\sim {10}^{10}({10}^{11})\text{y}}$

where the variables refer to Friedmann–Einstein universe, where${\displaystyle D}$ is defined in the equations,${\displaystyle c}$ is thespeed of light,${\displaystyle \ell }$ is thescale factor,${\displaystyle P}$ is the radius of the universe (measured in light years) and${\displaystyle P_0}$ its maximal value,${\displaystyle \rho }$ is the mean density of matter,${\displaystyle t}$ is time and the age of the universe (last line, measured in years), and${\displaystyle \kappa }$ is theEinstein's gravitational constant.

In 2013, it was pointed out^[16][17][24] that the equations on the Oxford blackboard had been taken directly from a key paper on relativistic cosmology written by Einstein in April 1931 and published in the Proceedings of the Royal Prussian Academy of Science on 9 May that year.^[15] The paper, known as the Friedmann–Einstein universe, is of historic significance because it constituted the first scientific publication in which Einstein embraced the possibility of a cosmos of time-varying radius. In the paper,^[15] Einstein adoptsAlexander Friedmann's 1922 analysis^[25] of relativistic models of a universe of time-varying radius and positive curvature, but sets thecosmological constant to zero, declaring it redundant, predicting a universe that expands and contracts over time. With the use ofEdwin Hubble's observations^[26] of a linear redshift/distance relation for the spiral nebulae, Einstein extracts from his model estimates ofρ ~ 10⁻²⁶ g/cm³,P ~ 10⁸ light-years andt ~ 10¹⁰ years for the density of matter, the radius of the cosmos and the timespan of the cosmic expansion respectively. These values are displayed in the last three lines on the Oxford blackboard (although the units of measurement are not specifically stated for the density estimate,cgs units are implied by the other calculations).

It has also been noted^[16][24] that the numerical estimates of cosmic parameters in Einstein's 1931 paper – and on the blackboard – contain a systematic error. Analysis of the 1931 paper shows that, given the contemporaneous Hubble constant of 500 km s⁻¹Mpc⁻¹, Einstein's estimates of cosmic density, radius and timespan should have beenρ ~ 10⁻²⁸ g/cm³,P ~ 10⁸ light-years andt ~ 10⁹ years respectively. One line on the blackboard, not included in the published paper, makes the nature of Einstein's error clear. In the fourth line on the blackboard, Einstein obtains a value of 10⁻⁵³ cm⁻² for the quantityD², defined in the top line of the blackboard as

${\displaystyle D=\frac{1}{c}\frac{1}{P}\frac{\mathrm{d}P}{\mathrm{d}t}}$,

i.e., theHubble constant divided by the speed of light. Simple calculation shows that the contemporaneous value of the Hubble constant in fact implied a value ofD² ~ 10⁻⁵⁵ cm⁻² (or 10⁻⁵¹ m⁻²) for this quantity. It appears that Einstein stumbled in convertingmegaparsecs to cm, giving 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.^[16] These errors were corrected in a later review of relativistic cosmology written by Einstein in 1945.^[27]

A blackboard used by Einstein in a public lecture at theUniversity of Nottingham on 6 June 1930 was also preserved after the lecture and is part of the university's archives.^[28]The blackboard is presently on display inside a protective frame and screen, within the university's Department of Physics and Astronomy. During term time it can be seen by academics and students within the classroom it's in. Visitors to campus can see it on display during university open days, if they take a tour of the department.

When translated, it reads as a table of contents in English:

• Introductory remarks
• Concept of the body
• Special relations between bodies
• Concept of space in mathematics (byRené Descartes)
• Newtonian space
• Concept of the field (byMichael Faraday,James Clerk Maxwell andHendrik Lorentz)
• Special relativity theory
• General theory of relativity and geometry
• Unified field theory

• Einstein in Oxford (2024 book)

• Einstein's Blackboard podcast
• Photo: Einstein's blackboard,TripAdvisor, 2014
• Oxford – Einstein's blackboard,Flickr, 2013
• Einstein’s Blackboard,IELTS

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