'What is logically simple is so difficult mathematically'
Albert Einstein (1879-1955). Autograph letter signed (‘A.E.’) to Michele Besso, [Princeton], 16 August 1949.
In German, two pages, 278 x 218mm. Envelope.
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Published in Pierre Speziali (ed.) Albert Einstein. Michele Besso. Correspondance 1903-1955. Paris: Hermann, 1972. No. 161
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'What is logically simple is so difficult mathematically': Einstein's generalised equations for gravitation.
Besso has asked Einstein to set out the generalised equations for gravitation which were the major preoccupation of Einstein's last years, and he complies with alacrity. 'You have expressed the wish that I should ride about a bit on my hobby horse for you ... I am persuaded that an essentially statistical theory, in spite of its great success, remains on the surface of things, and that one must ground oneself on the general relativity principle: generalisation of the gravitational equations for empty space'.
In this densely scientific manuscript, Einstein proceeds to walk Besso through the logic of these equations, which begin by replacing the symmetrical tensor gik with a non-symmetrical tensor: Einstein sets out the consequences in a series of equations, noting in passing the strains that the process places on the differential calculus involved, and interjecting in another place (perhaps with unintended irony), 'But it is not as simple as that'. He goes on: 'Now you will ask: did God whisper this in your ear? Unfortunately not. But the means is the following: there must be identities between the equations of the sort that they are compatible'. He explains the outlines of what he is looking for: 'These identities are the means for resolving the equations (but it doesn't happen "of its own accord")'.
He goes on: 'This is the framework of the thing': he will send Besso a paper which is about to be printed (Motion of particles in general relativity, 1949) which sets it all out. 'Whether there is anything true in the theory, I don't know, as I have been able to find no definitive solutions free of singularities. This is infamously difficult ...'. The letter concludes: 'The curse is that what is logically simple is so difficult mathematically'.
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