Friday, August 08, 2014

Feynman 2: The Path to a Doctorate

A couple weeks ago, I started reviewing a biography about Richard Feynman called Quantum Man, one of the smartest physics geniuses of all time. It is incredibly humbling to read about him, a genius among geniuses. Sometimes we college professors slip into thinking we have something upstairs--we need a Feynman occasionally to knock the wind out of our presumptuous sails.

Chapters 1-2: High school, MIT, and Princeton

Chapter 3: A New Way of Thinking
We left off with Feynman at Princeton with John Archibald Wheeler, the one who coined the phrase "black hole." One of the things that struck me in the chapters today is the extent to which Feynman thrived in his early years by having someone to spar with intellectually. There's a certain kind of synergy that great designers or artists or thinkers can experience when they're bouncing ideas back and forth with others who are on the same wavelength. The whole becomes even greater than the sum of its parts. Wheeler was one such partner for Feynman.

Wheeler and Feynman had some crazy ideas together that did not end up in their first form, but turned out to be headed in promising directions. I mentioned in the last post the idea that certain photons might move back in time (he would later argue this of antiparticles). Another idea was that all elements were made up of electrons (quarks came closer later).

In 1941, Feynman the gifted grad student presented to the Princeton physics department professors (rather than to fellow students), with Albert Einstein, Wolfgang Pauli, John von Neumann, and other physics titans present.

We also meet the love of Feynman's life in this chapter, Arline. She would suffer and eventually die of tuberculosis, just as Feynman was reaching the end of the Manhattan Project.

While the theory Wheeler and Feynman cooked up about particles moving backward in time would not pan out eventually, it led Feynman to invent a new chapter in calculus. In the theory they were cooking up, "the path of a particle at a given time is affected by the path of another at a different time" (48). It was here that Feynman turned to Lagrange's principle of least action, mentioned in the previous post: "an object will take that path where the total sum of the difference between its kinetic energy at each point and its potential energy at each point is lowest."

So rather than think of events at specific times that cause events at a subsequent time, Feynman would focus on an overall space-time path.

Chapter 4: Alice in Quantumland
In this chapter, biographer Krauss spends a little time over-viewing some of the basics of quantum mechanics as they had developed in the two decades previous to Feynman's time at Princeton. He starts with Erwin Schrödinger's wave equation. His equation opened the door to the probability of finding a particle at any given place in space at a specific time. Strangely, it is not the equation itself but the square of the equation that gives this probability.

The equation by itself sometimes involves the square root of negative 1, which isn't a real number (literally ;-). It's called an "imaginary" number. But √-1 is all over quantum mechanics.

Because quantum mechanics works with probabilities, there is a sense in which a particle can take all the different possible paths from a to b. Feynman's idea was to look at the paths associated with the probabilities in Schrödinger's equation rather than the probabilities of where a particle is at any moment.

Chapter 5: Endings and Beginnings
At a beer party at a tavern in Princeton, Feynman ran into a European physicist named Herbert Jehle who happened to be in town. They got to talking and Feynman mentioned that he was trying to explore the path of particles using Lagrange's least action principle.  Jehle mentioned a paper that Paul Dirac had written on the subject in 1932.

According to Jehle, next day in the library, on the spot, working the math more quickly than he could follow, Feynman took Dirac's paper to the next level. Feynman would meet Dirac in 1946 and mention it to him. The almost entirely uncommunicative Dirac was said to say, "Oh, that's interesting." A story about another conversation between the two is that Dirac asked Feynman, "I have an equation, do you?"

I suspect that this was a conversation between the two greatest minds in physics in the twentieth century.

It was the moment that birthed what would become Feynman's thesis and his greatest contribution to quantum physics. He would develop a system of drawing probable paths of particles. He would show that his new approach to paths both reduced to Schrödinger's equation over short paths and to Newtonian ones on a large scale.

Meanwhile, World War 2 had started. In 1942, Feynman was tapped to work on the Manhattan Project. Robert Wilson, an instructor at Princeton in experimental physics, showed up at Feynman's office one day and asked if he was interested in helping him develop a method for separating Uranium 235 from Uranium 238. These are two isotopes of uranium--same type of atom but with different numbers of neutrons. U238 is stable (although it can become unstable plutonium). U235 is prone to deteroriate into Barium and Krypton, while releasing free neutrons that can then impact the nuclei of other U235 nuclei, setting off a chain reaction.

At first Feynman wasn't interested, but in the end couldn't turn down the opportunity. Wheeler thought he was close enough to finish his doctoral thesis in 1942 and urged him to turn it in. Feynman "had re-derived quantum mechanics in terms of an action principle involving a sum" (an integral). He had been able to apply Schrödinger's equation to situations where the standard equation didn't work. He had not yet incorporated relativity. That was what was needed for a full blown theory of quantum electrodynamics (QED).

Almost all of the most important theoretical advances in fundamental physics in the late twentieth century were made possible by Feynman's reformulation because it made it possible to bracket out Heisenberg's uncertainty principle here and there. Measurement of a quantum system by a physicist causes "the collapse of the wave function." The observer inevitably eliminates the possibility of other measurements by making one measurement. Feynman figured out a way to look at the whole picture in a way that did not engage individual moments of a particle's position and thus didn't collapse the function, if I understand correctly.

1 comment:

Martin LaBar said...

If you understand correctly, that's a great summary of the physics.