## Autograph Manuscript

AUTOGRAPH MANUSCRIPT EQUATIONS AND NOTES ON RELATIVITY AND PLANCK’S LAW.

On this page Einstein uses Planck’s law in his calculations on quantum physics. Under his first equation Einstein writes (translated): “Gravity effect on particles neglected: not possible, because gravity field generating effect of particles neglected. A more promising approach would be via equations.” Under his next equation he writes (translated): “For dia µ and a 14 equations required: Additionally, 4 equations by elimination of h of the gravity equations. Only possible if 4 identities exist.” Under his last, and most detailed equation, Einstein pens: “{ surface integral. Provided Ä T44 d V as surface integral applicable, then possible to calculate. The integral would have to be traceable to r, since this seems to be the only volume integral that can be calculated.”

These brief mathematical equations represented for Einstein partial success in his research into electromagnetism and gravity. All of these facts and figures relate to quantum physics and are rooted in Einstein's Theory of Relativity. In this fragment of a calculation, Einstein debates whether he can use an approximation to deal with the case of a system of particles moving under the influence of a weak gravitational field and an electromagnetic field. Although the gravitation field is weak, Einstein’s notations reveal that an approximation completely ignoring it would be unjustified, as the particles themselves are created or held together by gravitational forces. Therefore, he must deal with the full complexity of the field equations of General Relativity. Interestingly, part of this fragment features Planck's constant, noted in “4 equations by elimination of h of the gravity equations. Only possible if 4 identities exist,” and is written in a form that suggests a link to Einstein's Theory of General Relativity. Einstein was in many ways like a detective on a mystery trail, though in his case he was on the trail of nature’s mysteries. Like all good detectives, he had a style that consisted of taking facts that he knew were correct and forcing nature into a situation that would contradict this established truth. In this process he would reveal some new truths.

From the nature of the calculations, we estimate the date of this manuscript to be c1929. One 8x11.5 sheet, writing covering about 60% of one side. In very good condition, with intersecting folds (vertical fold a bit heavier), repaired tear to right edge, scattered light creases and wrinkles, and a few small stains, one of which touches the first mathematical expression.

*Scientific notations by Einstein are seldom encountered and highly desirable; this particular example—exploring quantum physics via Planck’s law—is both rare and significant*.

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