The Doctoral Students of Richard Feynman

15 downloads 180 Views 212KB Size Report
... during the last several years of his career, Feynman might have supervised several more students. 1 ... Feynman to the extent that he belonged in the first list. (Indeed, as I document ... California Institute of Technology. 1955. Koichi Mano.
The Doctoral Students of Richard Feynman T. S. Van Kortryk 120 Payne Street, Paris MO65275 [email protected]

Abstract I document 31 students who graduated to receive PhDs under Feynman’s supervision. I provide links to their theses and some data to quantify a part of their subsequent contributions in physics.

Introduction An ordinary genius is an ordinary fellow ... There is no mystery as to how his mind works. ... It is di¤erent with the magicians ... Even after we understand what they have done, the process by which they have done it is completely dark. They seldom, if ever, have students ... Richard Feynman is a magician of the highest caliber. — Mark Kac [1] As the centennial of Richard Feynman’s birth approaches, I attempt in this paper to dispel a minor myth about him. The myth is embodied in the words of Mark Kac that I have emphasized above, and in the following statement attributed to one of Feynman’s students, Philip Platzman [2]: “The reason why Feynman did not have many students was because he was very di¢ cult with them, because he didn’t really worry about students. ... He had a few students, but not many.” Thus a prevailing belief in the scienti…c community seems to be [3] Feynman had very few doctoral students who completed theses under his supervision. It may be surprising to most people to learn this is not true. The number of Feynman’s doctoral students is actually 31 3, with the uncertainty intended to take into account some unavailable documents as well as possible subjectivity on my part [4]. The lineup of students who completed their PhD research under Feynman’s discerning gaze began with Giovanni Lomanitz at Cornell in 1950, and concluded with Ted Barnes and Thomas Curtright at Caltech in 1977. In addition, two years after Feynman’s death he was listed as a co-advisor in Sandip Trivedi’s thesis, completed in 1990. While 31 is not an extremely large number of doctoral students for an academic career spanning four decades (e.g. compared to the 70+ dissertations supervised by Julian Schwinger during his …ve decades as an academic), nonetheless, 31 does amount on average to three PhDs for every four years of Feynman’s time as a professor. And again on average (assuming it takes …ve years to obtain a PhD) the supervision of that many students in forty years would be above the median expected from the results of an informal poll that suggests two to four graduate students at any one time is an optimal number to mentor. Moreover, were it not for illness during the last several years of his career, Feynman might have supervised several more students. 1

Among Feynman’s doctoral students the most recognized physicist is undoubtedly George Zweig, who was also mentored by Murray Gell-Mann, and who graduated from Caltech in 1964. Soon thereafter Zweig had a major impact on elementary particle physics through his independent invention of the “quark model” of hadrons. However, in my opinion, the research of Feynman’s other students has also had signi…cant impact and continues to in‡uence several areas of physics.

The Students There are PhDs and then there are Feynman PhDs. — Richard Sherman [2] From theses and PhD dissertation examination documents wherein it was either explicitly stated or otherwise clear that Feynman was the advisor or co-advisor , I …nd the 31 doctoral students listed here, the …rst three at Cornell, the others at Caltech: Giovanni Lomanitz (1950) Second order e¤ects in the electron-electron interaction Michel Baranger (1951) Relativistic Corrections to the Lamb Shift Laurie Brown (1951) Radiative corrections to the Klein-Nishina formula Albert Hibbs (1955) The growth of water waves due to the action of the wind William Karzas (1955) The e¤ects of atomic electrons on nuclear radiation Koichi Mano (1955) The self-energy of the scalar nucleon Gerald Speisman (1955) The neutron-proton mass di¤erence Truman Woodru¤ (1955) On the orthogonalized plane wave method for calculating ... Michael Cohen (1956) The energy spectrum of the excitations in liquid helium Samuel Berman (1959) Radiative corrections to muon and neutron decay Frank Vernon (1959) The theory of a general quantum system interacting ... dissipative system Willard Wells (1959) Quantum theory of coupled systems having application to masers Henry Hilton (1960) Comparison of the beta-spectra of boron 12 and nitrogen 12 Carl Iddings (1960) Nuclear size corrections to the hyper…ne structure of hydrogen Philip Platzman (1960) Meson theoretical origins of the non-static two nucleon potential Marvin Chester (1961) Some experimental and theoretical observations on ... EMF Elisha Huggins (1962) Quantum mechanics of the interaction of gravity ... Harold Yura (1962) The quantum electrodynamics of a medium Michael Levine (1963) Neutrino processes of signi…cance in stars George Zweig (1964) Two topics in elementary particle physics ... James Bardeen (1965) Stability and dynamics of spherically symmetric masses ... Howard Kabakow (1969) A perturbation procedure for nonlinear oscillations ... Robert Carlitz (1970) Elimination of parity doubled states from Regge amplitudes [5] Mark Kislinger (1970) Elimination of parity doublets in Regge amplitudes Finn Ravndal (1971) A relativistic quark model with harmonic dynamics [6] Richard Sherman (1971) Surface impedance theory for superconductors in ... magnetic …elds Arturo Cisneros (1973) I. Baryon-Antibaryon phase transition ... II. ... the Parton Model Steven Kau¤mann (1973) Ortho-positronium annihilation ... …rst order radiative corrections Frank (Ted) Barnes (1977) Quarks, gluons, bags, and hadrons Thomas Curtright (1977) Stability and Supersymmetry Sandip Trivedi (1990) Topics in quantum gravity From documents where Feynman was not described as an advisor or co-advisor, but was a member of the PhD examination committee although not the committee chairman, and/or was acknowledged in the thesis for moderate in‡uence and general advice, I …nd in addition: 2

Fredrik Zachariasen (1956) Photodisintegration of the deuteron Paul Craig (1959) Observations of perfect potential ‡ow and critical velocities in super‡uid ... James Mercereau (1959) Di¤raction of Thermal Waves in Liquid Helium II Kenneth Wilson (1961) An investigation of the Low ... and the Chew-Mandelstam equations John Andelin (1966) Super‡uid drag in helium II Karvel Thornber (1966) I. Electronic Processes ... II. Polaron Motion ... Lorin Vant-Hull (1967) Veri…cation of long range quantum phase coherence ... William Press (1973) Applications of black-hole perturbation techniques Robert Wang (1976) A Study of Some Two-Dimensional Field Theory Models Don Page (1976) Accretion into and emission from black holes Stephen Wolfram (1980) Some topics in theoretical high-energy physics All of these were Caltech students. Originally I included Platzman in this second list. But upon looking at other documents I became convinced that his thesis was e¤ectively co-supervised by Feynman to the extent that he belonged in the …rst list. (Indeed, as I document later, Platzman’s personal listing in the Mathematics Genealogy Project states that Feynman was a co-advisor.) Similar remarks apply for Robert Carlitz [5] and Finn Ravndal [6]. If so, that would justify my head count of 31 “Feynman PhDs” to be a lower bound. It is interesting that Robert Wang’s thesis was o¢ cially written under Je¤rey Mandula’s guidance and …rst submitted in 1975. At that time Wang was examined by a committee that included Feynman who refused to accept the thesis as written. Consequently, Wang revised and resubmitted his thesis to have it …nally accepted in 1976 [3]. For this and other reasons I think one could argue that Feynman had the same or perhaps more in‡uence on Wang’s research and subsequent career as did Mandula. Nevertheless, I did not include Wang in the …rst list. Finally, I …nd several less compelling cases where Feynman was only a member of the dissertation examination committee at Caltech and was not particularly in‡uential for the research, so far as I can tell. I suspect there are many more such cases that I have not found, since on this point documentation is quite often incomplete and all committee members are not listed. For example: Lipes, Richard Gwin (1969) I. Application of multi-Regge theory ... II. High energy model .... Hill, Christopher Thaddeus (1977) Higgs scalars and the nonleptonic weak interactions. Dally, William J. (1986) A VLSI architecture for concurrent data structures. (restricted) Wawrzynek, John (1987) VLSI concurrent computation for music synthesis. (restricted) For the last two cases given above, I cannot access the theses to see if Feynman was acknowledged for signi…cant in‡uence.

Sources At the time of this writing, wikipedia lists only seven students claimed to have o¢ cially received PhDs with Feynman as the advisor, in somewhat random order: F. L. Vernon, Jr.; Willard H. Wells; Al Hibbs; George Zweig; Giovanni Rossi Lomanitz; Thomas Curtright; James M. Bardeen. However, this list is obviously far from complete, as documented by the Math Genealogy Project (MGP) and by the Caltech library archives. According to the MGP, also at the time of this writing, there were at least eleven other doctoral degrees completed under Feynman’s supervision in addition to those listed in wikipedia — one more at Cornell and ten more at Caltech: 3

Giovanni Lomanitz

Cornell University

1950

Laurie Brown

Cornell University

Albert Hibbs

California Institute of Technology

1955

Koichi Mano

California Institute of Technology

1955

Michael Cohen

1951

California Institute of Technology

Samuel Berman

1956

California Institute of Technology

1959

Frank Vernon

California Institute of Technology

1959

Willard Wells

California Institute of Technology

1959

Henry Hilton

California Institute of Technology

1960

Carl Iddings

California Institute of Technology

1960

Philip Platzman

California Institute of Technology

1960

Marvin Chester

California Institute of Technology

1961

Elisha Huggins

California Institute of Technology

1962

George Zweig

California Institute of Technology

1964

Finn Ravndal

California Institute of Technology

1971

Steven Kau¤mann

California Institute of Technology

1973

Thomas Curtright

California Institute of Technology

1977

Note that James Bardeen is the only PhD student in the wikipedia list who is not also in the MGP compilation. Also note that Philip Platzman is in the MGP list. I suppose that is because he requested to be classi…ed as a doctoral student of Feynman. Platzman’s personal listing in MGP supports my supposition. By way of comparison, and as a measure of the completeness of their database, Schwinger has only twenty of his students listed by the MGP. In any case, the mother lode of information about Feynman’s doctoral students can be found at the Caltech library. The following is a list of 25 PhD theses where Feynman is described as the advisor or co-advisor, as obtained by a direct search of the online database for theses provided by Caltech’s library at the time of this writing. 1990 Trivedi, Sandip P. (1990) Topics in quantum gravity. http://resolver.caltech.edu/CaltechTHESIS:03182015-100539813 1977 Barnes, Ted (F. E.) (1977) Quarks, gluons, bags, and hadrons. http://resolver.caltech.edu/CaltechETD:etd-09142007-135116 Curtright, Thomas Lynn (1977) Stability and supersymmetry. http://resolver.caltech.edu/CaltechETD:etd-12092004-161650 1973 Cisneros, Arturo (1973) I. Baryon-antibaryon phase transition at high temperature. II. Inclusive virtual photon-hadron reactions in the parton model. http://resolver.caltech.edu/CaltechTHESIS:03022016-151750147 4

Kau¤mann, Steven Kenneth (1973) Ortho-positronium annihilation: steps toward computing the …rst order radiative corrections. http://resolver.caltech.edu/CaltechTHESIS:04042014-111059101 1971 Sherman, Richard David (1971) Surface impedance theory for superconductors in large static magnetic …elds. http://resolver.caltech.edu/CaltechTHESIS:03022016-130412002 1970 Kislinger, Mark Brecher (1970) Elimination of parity doublets in Regge amplitudes. http://resolver.caltech.edu/CaltechTHESIS:03022016-141707222 1969 Kabakow, Howard Arthur (1969) A perturbation procedure for nonlinear oscillations (The dynamics of two oscillators with weak nonlinear coupling). http://resolver.caltech.edu/CaltechTHESIS:04102013-145406345 1965 Bardeen, James Maxwell (1965) Stability and dynamics of spherically symmetric masses in general relativity. http://resolver.caltech.edu/CaltechETD:etd-04152003-164152 1964 Zweig, George (1964) Two topics in elementary particle physics: The reaction [photonneutron going to pion-nucleon] at high energies. K leptonic decay and partially conserved currents. http://resolver.caltech.edu/CaltechETD:etd-12112002-091415 1963 Levine, Michael Jerry (1963) Neutrino processes of signi…cance in stars. http://resolver.caltech.edu/CaltechTHESIS:01022013-143533677 1962 Huggins, Elisha R. (1962) Quantum mechanics of the interaction of gravity with electrons: theory of a spin-two …eld coupled to energy. http://resolver.caltech.edu/CaltechTHESIS:08182011-085110085 Yura, Harold Thomas (1962) The quantum electrodynamics of a medium. http://resolver.caltech.edu/CaltechTHESIS:08182011-105631962 1961 Chester, Marvin (1961) Some experimental and theoretical observations on a con…gurational EMF. http://resolver.caltech.edu/CaltechETD:etd-03172006-141326

5

1960 Hilton, Henry Hoyt (1960) Comparison of the beta-spectra of boron 12 and nitrogen 12. http://resolver.caltech.edu/CaltechETD:etd-06222006-090249 Iddings, Carl (1960) Nuclear size corrections to the hyper…ne structure of hydrogen. http://resolver.caltech.edu/CaltechETD:etd-06202006-084058 1959 Berman, Samuel Morris (1959) Radiative corrections to muon and neutron decay. http://resolver.caltech.edu/CaltechETD:etd-01272006-161000 Vernon, Frank L. (1959) The theory of a general quantum system interacting with a linear dissipative system. http://resolver.caltech.edu/CaltechETD:etd-02242006-154616 Wells, Willard Henry (1959) Quantum theory of coupled systems having application to masers. http://resolver.caltech.edu/CaltechETD:etd-02222006-081649 1956 Cohen, Michael (1956) The energy spectrum of the excitations in liquid helium. http://resolver.caltech.edu/CaltechETD:etd-03192004-153651 1955 Hibbs, Albert R (1955) The growth of water waves due to the action of the wind. http://resolver.caltech.edu/CaltechETD:etd-12152003-113247 Karzas, William James (1955) The e¤ects of atomic electrons on nuclear radiation. http://resolver.caltech.edu/CaltechETD:etd-01072004-095620 Mano, Koichi (1955) The self-energy of the scalar nucleon. http://resolver.caltech.edu/CaltechETD:etd-01142004-152723 Speisman, Gerald (1955) The neutron-proton mass di¤erence. http://resolver.caltech.edu/CaltechETD:etd-01222004-092833 Woodru¤, Truman Owen (1955) On the orthogonalized plane wave method for calculating energy Eigen-values in a periodic potential. http://resolver.caltech.edu/CaltechETD:etd-01272004-091647 By way of comparison, a direct search for Gell-Mann as advisor turns up 15 theses in the Caltech library database. Among these, Hilton, Levine, and Zweig are shown to be co-advised by Feynman and Gell-Mann. Beyond these publicly accessible sources, the largest amount of documentation that is available to me concerns Thomas Curtright, who has provided this excerpt from his thesis examination committee papers [3]:

I …nd the succinctness to be both striking and amusing. 6

Some Citations of Papers Authored by Selected Feynman Students I now provide a restricted set of data to provide at least some support to the statement in the Introduction that Feynman’s students have had a signi…cant impact in physics. For this purpose, I will use data taken only from high-energy physics databases, in particular from INSPIRE. From that database I …nd the following citation summaries. To gauge them all, I begin with Richard Feynman:

Next, I give citation summaries for some of Feynman’s doctoral students, in alphabetical order. I have chosen those who tended to publish in elementary particle theory or closely related …elds. Frank (Ted) Barnes:

7

Sam Berman:

Laurie Brown:

Robert Carlitz:

8

Thomas Curtright:

Steven Kau¤mann:

Mark Kislinger:

9

Finn Ravndal:

Sandip Trivedi:

George Zweig:

10

This last result clearly shows some inadequacies of the database at hand. Citations to Zweig’s famous CERN preprints, that describe his independent invention of the quark model of hadrons, are not included in the INSPIRE database.

Summary From looking at many theses and papers by Caltech students, my overall impression is simply this: Feynman played a major role through his mentoring and supervision of doctoral students. He exerted tremendous in‡uence on graduate student research conducted at Caltech during his four decades there — perhaps even more than his widely perceived in‡uence on Caltech undergraduate studies. I conclude that it is not true Richard Feynman “had a few students, but not many.” Acknowledgements: I thank Professor Curtright for suggesting that there could very well be a widespread misunderstanding about the extent of Feynman’s mentoring of doctoral students — a conclusion he drew from many conversations with other physicists since the late 1970s — and that this constituted a distorted view of Feynman which should be corrected once and for all [3]. Finally, I thank Cosmas Zachos for his comments on various drafts of this manuscript.

References [1] M Kac, Enigmas of Chance: An Autobiography, University of California Press (1987). [2] J Mehra, The Beat of a Di¤ erent Drum: The Life and Science of Richard Feynman, Oxford University Press (1994) [3] T Curtright, private communication. [4] Regarding my subjectivity, see [5, 6]. [5] Robert Carlitz’s thesis was not available from the Caltech library when I originally compiled a list of Feynman’s doctoral students, but now it is. Therein I see that Carlitz’s advisor was Steven Frautschi and Feynman was not described as a co-advisor. In fact, Carlitz did not acknowledge Feynman for discussions at any point in his thesis — he only cited Feynman for an unpublished 1967 lecture. However, the main points of Carlitz’s thesis involve research that was carried out in collaboration with Mark Kislinger and published jointly with him in two papers. Now, in his thesis, Kislinger does acknowledge Feynman as his primary advisor. Moreover, in the second of his two papers with Carlitz, Kislinger “thanks R. P. Feynman for suggesting investigating this problem and for numerous helpful discussions.” Therefore, I consider Carlitz to have been co-advised by Feynman, despite the lack of any direct statements by Carlitz to con…rm this. [6] Finn Ravndal’s advisor was also Steven Frautschi, o¢ cially. Frautschi was the chairman of Ravndal’s dissertation examination committee, while Feynman was only a member of the committee. On the other hand, upon reading the acknowledgements in Ravndal’s thesis and considering what the entire thesis was about, it is clear that Feynman provided considerable guidance to Ravndal (also see [7]). Indeed, much of the research in the thesis was published jointly with Feynman and also Kislinger. In addition, Feynman appears as the advisor in Ravndal’s personal listing in the MGP, presumably because Ravndal wanted it so. [7] F Ravndal, “How I Got to Work with Feynman on the Covariant Quark Model” Int. J. Mod. Phys. A30 (2015) 1530009, arXiv:1411.0509 [physics.hist-ph]

11