Free Quantum Man: Richard Feynman's Life in Science by Lawrence M. Krauss Page A

established explicitly how quantum mechanics could be formulated in terms of a Lagrangian. In so doing, Feynman had taken the first step in completely reformulating quantum theory.
    I ADMIT TO being skeptical about whether Feynman really outdid Dirac that morning in Princeton. Certainly anyone who understands Dirac’s paper can see that almost all of the key ideas are there. Why Dirac didn’t take the next step to see if they could actually be implemented is something we will never know. Perhaps he was satisfied enough that he had demonstrated a possible correspondence but never felt it would be particularly useful for any practical purposes.
    The only information we have that Dirac never actually proved to himself that his analogy was exact is Feynman’s later recollection of a conversation with Dirac at the 1946 bicentennial celebration at Princeton. Feynman describes asking Dirac if he knew that his “analogy” could be made exact by a simple constant of proportionality. Feynman’s recollection of the conversation goes as follows:
    Feynman: “Did you know that they were proportional?”
    Dirac: “Are they?”
    Feynman: “Yes.”
    Dirac: “Oh, that’s interesting.”
    For Dirac, who was known to be both terse and literal in the extreme, this was a long conversation, and it probably speaks volumes. For example, Dirac married the sister of another famous physicist, Eugene Wigner. Whenever he introduced her to people, he introduced her as “Wigner’s Sister,” not as his wife, feeling apparently that the latter fact was superfluous (or perhaps merely demonstrating that he was as misogynistic as many of his colleagues at the time).
    More relevant perhaps is a story I heard regarding the famous Danish physicist Niels Bohr, who apparently was complaining about this far-too-quiet postdoctoral researcher, Dirac, who the equally famous physicist Ernest Rutherford had sent him from England. Rutherford then told Bohr a story about a person who goes into a pet shop to buy a parrot. He is shown a very colorful bird and told that it speaks ten different words, and its price is $500. Then he is shown a more colorful bird, with a vocabularly of one hundred words, with a price of $5,000. He then sees a scruffy beast in the corner and asks how much that bird is. He is told $100,000. “Why?” he asks. “That bird is not very beautiful at all. How many words then does it speak?” None, he is told. Flabbergasted, he says to the clerk, “This bird here is beautiful, and speaks ten words and is $500. That bird over there speaks a hundred words and is $5,000. How can that scruffy little bird over there, who doesn’t speak a single word, be worth $100,000?” The clerk smiles and says, “That bird thinks.”
    W HAT DIRAC HAD intuited in 1933, and what Feynman picked up immediately and explicitly (although it took him awhile to describe it in these terms), is that whereas in classical mechanics the Lagrangian and the action function determine the correct classical path by assigning simple probabilities to the different classical paths between a and c— ultimately assigning a probability of essentially unity for the path of least action and essentially zero for every other path—in quantum mechanics the Lagrangian and the action function can be used to calculate, not probabilities, but probability amplitudes for transitions between a and c . And that moreover in quantum mechanics many different paths can have nonzero probability amplitudes.
    While working out this idea with a simple example Feynman discovered—before Jehle’s surprised eyes that morning in the library at Princeton—that if he tried to calculate probability amplitudes using this prescription for very short travel times he could obtain a result that was identical with the result obtained in traditional quantum mechanics from Schrödinger’s equation. What’s more, in the limit where systems get big, so that classical laws of motion govern the system and