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74

PROPERTY FROM THE FAMILY OF RICHARD P. FEYNMAN

FEYNMAN, RICHARD P.
"TWO OBJECTIVES. (1) TO POINT OUT THE PECULIAR POINT. (2) TO FORMULATE A ME IN A DEFINITE NUMBER OF ASSUMPTIONS (NON-RELATIVISTIC SCHRÖD)," CA 1946-51.
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74

PROPERTY FROM THE FAMILY OF RICHARD P. FEYNMAN

FEYNMAN, RICHARD P.
"TWO OBJECTIVES. (1) TO POINT OUT THE PECULIAR POINT. (2) TO FORMULATE A ME IN A DEFINITE NUMBER OF ASSUMPTIONS (NON-RELATIVISTIC SCHRÖD)," CA 1946-51.
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FEYNMAN, RICHARD P.
"TWO OBJECTIVES. (1) TO POINT OUT THE PECULIAR POINT. (2) TO FORMULATE A ME IN A DEFINITE NUMBER OF ASSUMPTIONS (NON-RELATIVISTIC SCHRÖD)," CA 1946-51.
Autograph manuscripts, 5 pp (8 1/2 x 11 & 8 x 10 1/2 in) in pencil on plain white paper (2 sheets), and Cornell watermarked paper (2 sheets).
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FEYNMAN DERIVES THE SCHRÖDINGER EQUATION VIA THE FEYNMAN PATH INTEGRAL, SHOWING THE EQUIVALENCE OF THESE DISTINCT, BUT COMPLEMENTARY FORMULATIONS OF QUANTUM MECHANICS.

"Will you understand what I am going to tell you?... No, you're not going to be able to understand it. ...I don't understand it. Nobody does." (Feynman on the Path Integral)

By 1925-26, Heisenberg's Matrix Mechanics & Schrödinger's Equation, both based on so-called “Hamiltonian” methods, were the algebraic & differential cornerstones of the "new" quantum physics, garnering their inventors the 1932 & 1933 Nobel Prizes, respectively.  A generation later, Feynman formulated a entirely distinct and original way of thinking about quantum particles, encoded in his celebrated Feynman Path Integral, based on a complementary “Lagrangian” viewpoint, having its roots in an obscure 1933 paper of Feynman's hero, Paul Dirac.  In the first manuscript, possibly written at some point before coming to Cornell, perhaps while still at Princeton, Feynman brilliantly uses his Path Integral to “derive” the Schrödinger Equation. This bit of magic, in its first incarnation dating to a chance 1941 Princeton chat over beers with Herbert Jehle (a student of Schrödinger recently escaped from Nazi Germany), has been famously recounted many times.  The key insight hinged on Dirac’s use of the word “analogue,” which Feynman had mistakenly interpreted as “equal”; once Jehle explained the next day that Dirac’s language implied “proportional”, rather than equal, Feynman was unleashed. In a flash, the equivalence between Hamiltonian & Lagrangian formulations of quantum mechanics was established, the proportionality constant (essentially “A” in the manuscript...) calculated, and with this creative assault upon the black board, Feynman had hurled himself (as well as the stunned Jehle, along for the ride) far beyond Dirac, and forged a powerful new tool of quantum physics:

“Jehle told Feynman he made an important discovery. He was struck by the unabashed pragmatism in Feynman’s handling of the mathematics, so different than Dirac’s more detached, more aesthetic tone. ‘You Americans!’ he said. ‘Always trying to find a use for something.’” (Gleick, pp. 128-9)

Following his time at Los Alamos, and after his arrival at Cornell, Feynman returned to these fundamental questions of quantum mechanics. In the second manuscript, on Cornell watermarked paper, he again invokes the essential Feynman notion of a “sum over histories”, highlighting the key mathematical object Fo(2,1), known as the "free-particle propagator,” bottom recto, before turning his attention, au verso, to the Dirac Equation.  Eventually, these ideas, greatly extended, were consolidated in the 1965 Caltech classic, Quantum Mechanics and Path Integrals, by Feynman & Hibbs (lot 109).

Ironically, Feynman had been exposed, in apocryphal fashion, to classical Lagrangian mechanics by Abram Bader, his legendary High School physics teacher (Feynman Lectures, vol II, ch. 19) but had surprisingly rejected, indeed throughout his entire MIT days..., this elegant approach in favor of more direct, workman-like force analyses. Nevertheless, his eventual embrace of the Lagrangian formulation at this critical point not only cleared the way for the resolution of his Princeton PhD work with Wheeler, (see below), but more importantly laid the architectural foundation for his functional integration techniques, with their implicit homage to the Least Action Principle, permitting him to craft his very own special brand of QED, entirely complementary to that of his fellow Laureates Schwinger & Tomonoga. 

The 3rd Cornell page refers, most likely, to the original 1941 "Absorber Theory" of Feynman and Wheeler — or perhaps a 1949 electromagnetic extension (Rev. Mod. Phys. 21, 425) — with its associated focus on radiation reaction effects and, amusingly here, captures a specific eureka moment ("Sum = 0 to this order!) when the calculation reveals that there is "No light received at large distances." In the original formulation, the clever inclusion of an "advanced" (i.e., traveling backward in time) component to the traditional "retarded" solution established the possibility that emission of radiation will not be realized lest there be absorbers in place everywhere, all of the time — a Nobel-calibre, yet impish tip of the hat to the proverbial question: "If a tree falls in a forest, and no one is there..." (Gleick, pp. 110-123).

Beautiful, clean examples of Feynman's brilliance. 

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