Michele Besso (top right, with his wife Anna) worked with Einstein on his relativity paper. Credit: AIP/EMILIO SEGRE VISUAL ARCHIVES (top); CHRISTIE'S NEW YORK (bottom)

Got half a million dollars to spare? If so, you could become the owner of a manuscript that helped to reveal the contribution of Michele Besso, Albert Einstein's lifelong friend and collaborator, to the development of the general theory of relativity.

The 1913 Einstein–Besso Working Manuscript, containing more than 50 pages of handwritten text by Einstein and Besso, is part of a private collection of letters, manuscripts and books on twentieth-century theoretical physics that is due to be auctioned by Christie's in New York on 4 October.

Built up by publishing millionaire Harvey Plotnick, the Harvey Plotnick Library on the Development of Quantum Physics and the Theory of Relativity is considered the world's most important private collection of papers on modern physics. It includes around 2,500 items written by more than 100 of the twentieth century's most significant physicists. The total value of the collection is estimated at around US$2 million.

The Einstein–Besso Working Manuscript, which Christie's hopes will fetch between $500,000 and $700,000, is the collection's crown jewel. Besso, a Swiss engineer, was Einstein's most dependable sounding-board. The manuscript includes mathematical calculations, carried out by Besso under Einstein's guidance, which test whether early versions of Einstein's general-relativity equations could account for an anomaly in Mercury's orbit that Newton's theory of gravity couldn't fully explain.

The equations failed to solve the problem, but reformulated equations, finalized in 1915, were eventually successful. Along with other items of correspondence still held by the Besso family, the manuscript has helped science historians to piece together the working relationship between Einstein and Besso.

“Besso contributed more to the intellectual development of Einstein's general theory of relativity than has previously been realized,” says Jürgen Renn, a director of the Max Planck Institute for the History of Science in Berlin, and co-editor of the fourth volume of The Collected Papers of Albert Einstein (Princeton University Press, 1995), which includes a reproduction of the Einstein– Besso Working Manuscript. Renn, together with Michael Janssen, a science historian at the University of Minnesota, is preparing an article based on another previously unpublished manuscript by Besso, which underlines the significance of Besso's work in the development of the equations.

Other items in the Plotnick library include the doctoral thesis of Henri Becquerel, who discovered naturally occurring radioactivity, and that of Marie Curie, discoverer of the radioactive elements polonium and radium. There is also an offprint of Wilhelm Röntgen's 1895 announcement of his discovery of X-rays, and three handwritten letters by Werner Heisenberg to the Dutch physicist Samuel Goudsmit, discussing Goudsmit's discovery of electron spin.

Plotnick, who lives in Chicago, started his collection around 20 years ago. “I've always been interested in the history of physics,” he says. Having learnt enough about the development of quantum physics, Plotnick is selling in order to concentrate on his new interest in early Islamic art.

Most historians prefer important documents to be held by public institutions to safeguard access, but they accept that private ownership doesn't necessarily hinder their work. Plotnick has already given many historians access to the documents.