Showing posts with label P. A. M. Dirac. Show all posts
Showing posts with label P. A. M. Dirac. Show all posts

Friday, August 15, 2014

Feynman 3: The Bomb and then Depression

This is my third installment reviewing a biography about Richard Feynman called Quantum Man, one of the greatest physicists of all time.

So far:
Chapters 1-2: High school, MIT, and Princeton
Chapters 3-5: The Path to a Doctorate

Now chapters 6-7.

Chapter 6: Loss of Innocence
Finishing his PhD degree at Princeton was a condition for Richard and his fiancee Arline to get married. And so, even though she was deathly ill with tuberculous--and generating significant friction between Feynman and his mother--they got married. She would die two months before the bomb dropped on Hiroshima.

If you remember from last week, Feynman had helped work on the question of separating Uranium 235 from 238. He had worked with Robert Wilson's team on this, and it had been accomplished. Then next step was to build a nuclear reactor to do the separation, and this was taking place in Chicago with Enrico Fermi and John Archibald Wheeler, Feynman's doctoral mentor.

So Feynman went to Chicago. Soon after he arrived, he blew away the "theory group" by performing a calculation that had eluded them for months (78). Robert Oppenheimer picked Los Alamos as the place where the Manhattan Project would play out, and he picked Feynman to come with the first wave of scientists in 1943.

Oppenheimer was an unusual scientist because, as Feynman himself put it, he "was extremely human" (79). He not only understood the science. He had organizational skills and cared about people. He would notoriously regret the role he played in the creation of the atomic bomb. His words at the first successful testing were from the Bhagavad Gita: "Now I am become Death, the destroyer of worlds." Feynman merely grinned as he contemplated the physical causes of the mushroom cloud and sonic boom.

Feynman, once again working best in conversation, ended up almost by accident in a conversation in Los Alamos with a seasoned theoretician named Hans Bethe. Bethe would bounce ideas off of Feynman, who being very loud could be heard to cry out, "No, no! That's crazy." From Feynman's recollection, Bethe always proved to be right. From Bethe's recollection, Feynman was probably the most ingenious person in the whole division.

Bethe was the scientist who discovered that fusion fueled the sun. Bethe said of Feynman that "he could do anything, anything at all" (87). He was put in charge of the computing division. You have to wonder whether the Manhattan Project would have ended before the war if Feynman hadn't have been there.

For example, Feynman developed a mathematical method for integrating third-order differential equations that was more accurate than what they were doing with second-order differential equations. When several boxes full of the parts of an IBM computer arrived, Feynman and another person managed to put them together before the professionals from IBM arrived. It had never been done before.

Oppenheimer would say of Feynman that "He is by all odds the most brilliant young physicist here" (92).

Chapter 7: Paths to Greatness
As an academic Dean, I think I am somewhat unusual. I absolutely love knowledge for its own sake. My boss often quotes me as saying, "No one loves the irrelevant more than I do." But I am a pragmatist and a realist. In most cases, it doesn't matter how brilliant a teacher is if he or she can't teach. And in most cases, it doesn't matter how excellent your program is if no one is buying.

Of course there are top flight research institutions that are so heavily endowed that their professors can push the bounds of knowledge without a care and survive off of some small number of purely genius students. Feel free to hire me to teach there. But that is just not where the majority of academic institutions are. And, for all your pretense to greatness, most purists seem to have a penchant for self-destruction (and an overestimation of how great they are).

So I won't tell you what I wrote in the margins of this biography on reading about how the chair of Berkeley delayed making an offer to Feynman on Oppenheimer's recommendation. When he finally did, he had the gall to tell Feynman that no one had ever refused an offer from Berkeley's graduate department of physics.

Feynman did. He went to Cornell, who had the smarts to hire him two years earlier and give him a leave of absence while he was at Los Alamos. Stupid Berkeley.

But Feynman himself was pessimistic and depressed. What future was there, now that there was such a bomb. "What one fool can do, another can," he said (93). Indeed, it is amazing seventy years later that the bomb has not been used again.

It was natural that Feynman would feel like he had wasted three prime years of his intellect--the greatest discoveries of a physicist are usually made in one's twenties. His father had died of a stroke a year after his wife Arline. Teaching takes a whole lot more work than most imagine and back then there was no training in how to teach.

Feynman was being showered with praise from all corners, but he felt like his best years were behind him. Others thought he was incredible. He felt stupid. "They were absolutely crazy" (96), he thought of offers from Princeton and the Institute for Advanced Study.

Bethe, upon hearing of Feynman's depression, remarked that, "Feynman depressed is just a little more cheerful than any other person... exhuberant" (97).

There is a great story about how hard it was for Feynman to finally write up his dissertation for publication. Apparently, two of his friends forced him to write it up while he was visiting them in the summer of 1947. They practically locked him up in a room. It was easy for him to express his ideas in conversational form. But to write them down in a beginning to end argument in detail, with everything exactly write. That he found a hard time doing.

[I know a couple people I'd frankly like to lock in a room to crank some of their gems out. On the other hand, one might argue that I would have written more scholarly pieces these last ten years if I hadn't started blogging.]

However, writing it up seemed to get him over a hump. Quantum mechanics began to be more visual for him. For the first time, he began to describe quantum mechanics in the language of sums over paths, with each path having an amplitude. It was a fundamental reformulation of quantum mechanics on which all the quantum mechanics since is based. His next task was to relativize it, to incorporate Einstein's relativity into his new version of the older model.

The rest of the chapter mostly flashes back to Dirac's relativizing of the original quantum mechanical equation of Schrodinger. We hear about the spin of particles called fermions, after Enrico Fermi. We hear about boson particles that don't spin. We hear of Wolfgang Pauli's exclusion principle and Dirac's theoretical discovery of antiparticles.

Meanwhile, Feynman was trying to find a way to picture the overall paths of these particles in a way that incorporated relativity the way Dirac had for a single particle at particular time and momentum...

Friday, July 04, 2014

Science Friday: Dirac's Antiparticles

Not long now. Here's chapter 5 of George Gamow's classic, Thirty Years That Shook Physics.

The previous posts were:

1a. Planck's Quantum
1b. Jumping Photons (Einstein and the Photoelectric Effect)
1c. The Compton Effect (Proof of Energy Packets)

2a. Thomson and Rutherford's Atoms
2b. Bohr's Contributions (How electrons fill the atom)

3a. Pauli Exclusion Principle (no two electrons at any one energy state)
3b. The Pauli Neutrino

4a. De Broglie's Wavy Particles
4b. Schrödinger's Wave Equation

5. Heisenberg's Uncertainty Principle

When I was at Florida State University in the summer of 1983 for Boy's State, I used some free time to find the office of P. A. M. Dirac and touch his door. He would die the next year.

One of the challenges of the burgeoning quantum mechanics of the late 1920s was that the Schrodinger equation did not account for relativistic factors that came into play with particles that might approach the speed of light. One factor that kept anyone from "relativizing" it was that the derivatives in the equation were of different orders, if I am understanding correctly. So part consisted of a first order derivative and another part of a second order derivative. It proved difficult to introduce Einstein's famous Lorentz transformation to such a mixed order equation.

So one evening in 1928 while Dirac sat in his Cambridge study at St. John's College, he thought to reduce the second order derivatives in such a way that the equation would consist entirely of first order derivatives. The hesitation to do this is that Schrodinger's equation, when of a first order level, includes imaginary numbers, that is, numbers that include the square root of -1 (i), which is difficult to conceptualize or really know what it means.

Nevertheless, it not only worked, allowing Dirac to create a relativistic version of Schrodinger's equation that would work when particles were approaching the speed light. It also accounted for another dimension of atomic description that had been discovered, namely, spin. The equation predicted that there were two values of spin that any electron could have in any orbital.

Another thing that his equation predicted were antiparticles. If one solution to his equation involved a negatively charged electron with positive mass, then another might be a positively charged electron. Dirac initially wondered if this "positive electron" might be the proton, but he did not have to wait long. In 1932, the existence of the "positron" was officially verified.

Richard Feymann would later suggest that a positron was an electron moving back in time, one of his many quirky ideas. When electron and positron meet, they annihilate and release 2mc squared of energy. Feymann suggested this was the electron changing directions in time.

The antiproton and antineutron would be discovered later. The question would arise. Are there equal portions of matter and antimatter in the universe? Might whole galaxies out there consist of antimatter, just as ours consists of matter?

Fun story about when Dirac first met Richard Feymann. Apparently he asked him, rather matter of factly, "I have an equation. Do you?"