Casimir forces on parallel plates

Casimir forces on parallel plates

In quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field. The typical example is of two uncharged metallic plates in a vacuum, like capacitors placed a few micrometers apart, without any external electromagnetic field. In a classical description, the lack of an external field also means that there is no field between the plates, and no force would be measured between them.^[1] When this field is instead studied using the QED vacuum of quantum electrodynamics, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force^[2]—either an attraction or a repulsion depending on the specific arrangement of the two plates. Although the Casimir effect can be expressed in terms of virtual particles interacting with the objects, it is best described and more easily calculated in terms of the zero-point energy of a quantized field in the intervening space between the objects. This force has been measured, and is a striking example of an effect purely due to second quantization.^[3][4] However, the treatment of boundary conditions in these calculations has led to some controversy. In fact "Casimir's original goal was to compute the van der Waals force between polarizable molecules" of the metallic plates. Thus it can be interpreted without any reference to the zero-point energy (vacuum energy) or virtual particles of quantum fields.^[5]

Dutch physicists Hendrik B. G. Casimir and Dirk Polder proposed the existence of the force and formulated an experiment (the "Casimir experiment") to detect it in 1948 while participating in research at Philips Research Labs. The classic form of the experiment, described above, successfully demonstrated the force to within 15% of the value predicted by the theory.^[6]

Because the strength of the force falls off rapidly with distance, it is only measurable when the distance between the objects is extremely small. On a submicron scale, this force becomes so strong that it becomes the dominant force between uncharged conductors. In fact, at separations of 10 nm—about 100 times the typical size of an atom—the Casimir effect produces the equivalent of 1 atmosphere of pressure (101.325 kPa), the precise value depending on surface geometry and other factors.^[7]

In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon; and in applied physics, it is significant in some aspects of emerging microtechnologies and nanotechnologies.^[8]

Overview[link]

The Casimir effect can be understood by the idea that the presence of conducting metals and dielectrics alters the vacuum expectation value of the energy of the second quantized electromagnetic field.^[9][10] Since the value of this energy depends on the shapes and positions of the conductors and dielectrics, the Casimir effect manifests itself as a force between such objects.

Vacuum energy[link]

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v t e

The causes of the Casimir effect are described by quantum field theory, which states that all of the various fundamental fields, such as the electromagnetic field, must be quantized at each and every point in space. In a simplified view, a "field" in physics may be envisioned as if space were filled with interconnected vibrating balls and springs, and the strength of the field can be visualized as the displacement of a ball from its rest position. Vibrations in this field propagate and are governed by the appropriate wave equation for the particular field in question. The second quantization of quantum field theory requires that each such ball-spring combination be quantized, that is, that the strength of the field be quantized at each point in space. At the most basic level, the field at each point in space is a simple harmonic oscillator, and its quantization places a quantum harmonic oscillator at each point. Excitations of the field correspond to the elementary particles of particle physics. However, even the vacuum has a vastly complex structure, so all calculations of quantum field theory must be made in relation to this model of the vacuum.

The vacuum has, implicitly, all of the properties that a particle may have: spin, or polarization in the case of light, energy, and so on. On average, most of these properties cancel out: the vacuum is, after all, "empty" in this sense. One important exception is the vacuum energy or the vacuum expectation value of the energy. The quantization of a simple harmonic oscillator states that the lowest possible energy or zero-point energy that such an oscillator may have is

Failed to parse (Missing texvc executable; please see math/README to configure.): {E} = \begin{matrix} \frac{1}{2} \end{matrix} \hbar \omega \ .

Summing over all possible oscillators at all points in space gives an infinite quantity. To remove this infinity, one may argue that only differences in energy are physically measurable; this argument is the underpinning of the theory of renormalization. In all practical calculations, this is how the infinity is always handled. In a deeper sense, however, renormalization is unsatisfying, and the removal of this infinity presents a challenge in the search for a Theory of Everything. Currently there is no compelling explanation for how this infinity should be treated as essentially zero; a non-zero value is essentially the cosmological constant and any large value causes trouble in cosmology.

Alternatively, a 2005 paper by Robert Jaffe of MIT states that "Casimir effects can be formulated and Casimir forces can be computed without reference to zero point energies. They are relativistic, quantum forces between charges and currents. The Casimir force (per unit area) between parallel plates vanishes as alpha, the fine structure constant, goes to zero, and the standard result, which appears to be independent of alpha, corresponds to the alpha → infinity limit," and that "The Casimir force is simply the (relativistic, retarded) van der Waals force between the metal plates."^[11]

Effects[link]

Casimir's observation was that the second-quantized quantum electromagnetic field, in the presence of bulk bodies such as metals or dielectrics, must obey the same boundary conditions that the classical electromagnetic field must obey. In particular, this affects the calculation of the vacuum energy in the presence of a conductor or dielectric.

Consider, for example, the calculation of the vacuum expectation value of the electromagnetic field inside a metal cavity, such as, for example, a radar cavity or a microwave waveguide. In this case, the correct way to find the zero point energy of the field is to sum the energies of the standing waves of the cavity. To each and every possible standing wave corresponds an energy; say the energy of the nth standing wave is Failed to parse (Missing texvc executable; please see math/README to configure.): E_n . The vacuum expectation value of the energy of the electromagnetic field in the cavity is then

Failed to parse (Missing texvc executable; please see math/README to configure.): \langle E \rangle = \frac{1}{2} \sum_n E_n

with the sum running over all possible values of n enumerating the standing waves. The factor of 1/2 corresponds to the fact that the zero-point energies are being summed (it is the same 1/2 as appears in the equation Failed to parse (Missing texvc executable; please see math/README to configure.): E=\hbar \omega/2 ). Written in this way, this sum is clearly divergent; however, it can be used to create finite expressions.

In particular, one may ask how the zero point energy depends on the shape s of the cavity. Each energy level Failed to parse (Missing texvc executable; please see math/README to configure.): E_n

depends on the shape, and so one should write Failed to parse (Missing texvc executable; please see math/README to configure.): E_n(s)
for the energy level, and Failed to parse (Missing texvc executable; please see math/README to configure.): \langle E(s) \rangle
for the vacuum expectation value. At this point comes an important observation: the force at point p on the wall of the cavity is equal to the change in the vacuum energy if the shape s of the wall is perturbed a little bit, say by Failed to parse (Missing texvc executable; please see math/README to configure.): \delta s

, at point p. That is, one has

Failed to parse (Missing texvc executable; please see math/README to configure.): F(p) = - \left. \frac{\delta \langle E(s) \rangle} {\delta s} \right\vert_p\,

This value is finite in many practical calculations.^[12]

Attraction between the plates can be easily understood by focusing on the 1-dimensional situation. Suppose that a moveable conductive plate is positioned at a short distance a from one of two widely separated plates (distance L apart). With a << L, the states within the slot of width a are highly constrained so that the energy E of any one mode is widely separated from that of the next. This is not the case in open region L, where there is a large number (about L/a) of states with energy evenly spaced between E and the next mode in the narrow slot---in other words, all slightly larger than E. Now on shortening a by da (< 0), the mode in the slot shrinks in wavelength and therefore increases in energy proportional to -da/a, whereas all the outside L/a states lengthen and correspondingly lower energy proportional to da/L (note the denominator). The net change is slightly negative, because all the L/a modes' energies are slightly larger than the single mode in the slot.

Derivation of Casimir effect assuming zeta-regularization[link]

In the original calculation done by Casimir, he considered the space between a pair of conducting metal plates at distance Failed to parse (Missing texvc executable; please see math/README to configure.): a

apart. In this case, the standing waves are particularly easy to calculate, since the transverse component of the electric field and the normal component of the magnetic field must vanish on the surface of a conductor. Assuming the parallel plates lie in the xy-plane, the standing waves are

Failed to parse (Missing texvc executable; please see math/README to configure.): \psi_n(x,y,z;t) = e^{-i\omega_nt} e^{ik_xx+ik_yy} \sin \left(k_n z \right)

where Failed to parse (Missing texvc executable; please see math/README to configure.): \psi

stands for the electric component of the electromagnetic field, and, for brevity, the polarization and the magnetic components are ignored here. Here, Failed to parse (Missing texvc executable; please see math/README to configure.): k_x
and Failed to parse (Missing texvc executable; please see math/README to configure.): k_y
are the wave vectors in directions parallel to the plates, and

Failed to parse (Missing texvc executable; please see math/README to configure.): k_n = \frac{n\pi}{a}

is the wave-vector perpendicular to the plates. Here, n is an integer, resulting from the requirement that ψ vanish on the metal plates. The energy of this wave is

Failed to parse (Missing texvc executable; please see math/README to configure.): \omega_n = c \sqrt{{k_x}^2 + {k_y}^2 + \frac{n^2\pi^2}{a^2}}

where c is the speed of light. The vacuum energy is then the sum over all possible excitation modes

Failed to parse (Missing texvc executable; please see math/README to configure.): \langle E \rangle = \frac{\hbar}{2} \cdot 2 \int \frac{A dk_x dk_y}{(2\pi)^2} \sum_{n=1}^\infty \omega_n

where A is the area of the metal plates, and a factor of 2 is introduced for the two possible polarizations of the wave. This expression is clearly infinite, and to proceed with the calculation, it is convenient to introduce a regulator (discussed in greater detail below). The regulator will serve to make the expression finite, and in the end will be removed. The zeta-regulated version of the energy per unit-area of the plate is

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{\langle E(s) \rangle}{A} = \hbar \int \frac{dk_x dk_y}{(2\pi)^2} \sum_{n=1}^\infty \omega_n \vert \omega_n\vert^{-s}

In the end, the limit Failed to parse (Missing texvc executable; please see math/README to configure.): s\to 0

is to be taken. Here s is just a complex number, not to be confused with the shape discussed previously. This integral/sum is finite for s real and larger than 3. The sum has a pole at s = 3, but may be analytically continued to s = 0, where the expression is finite. The above expression is easily simplified to:

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{\langle E(s) \rangle}{A} = \frac{\hbar c^{1-s}}{4\pi^2} \sum_n \int_0^\infty 2\pi qdq \left \vert q^2 + \frac{\pi^2 n^2}{a^2} \right\vert^{(1-s)/2}

where polar coordinates Failed to parse (Missing texvc executable; please see math/README to configure.): q^2 = k_x^2+k_y^2

were introduced to turn the double integral into a single integral. The Failed to parse (Missing texvc executable; please see math/README to configure.): q
in front is the Jacobian, and the Failed to parse (Missing texvc executable; please see math/README to configure.): 2\pi
comes from the angular integration. The integral is easily performed and converges if Re[s] > 3, resulting in

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{\langle E(s) \rangle}{A} = -\frac {\hbar c^{1-s} \pi^{2-s}}{2a^{3-s}} \frac{1}{3-s} \sum_n \vert n\vert ^{3-s}

The sum clearly diverges at s in the neighborhood of zero, but if the damping of large-frequency excitations corresponding to analytic continuation of the Riemann zeta function to s = 0 is assumed to make sense physically in some way, then one has

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{\langle E \rangle}{A} = \lim_{s\to 0} \frac{\langle E(s) \rangle}{A} = -\frac {\hbar c \pi^{2}}{6a^{3}} \zeta (-3)

But Failed to parse (Missing texvc executable; please see math/README to configure.): \zeta(-3)=1/120

and so one obtains

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{\langle E \rangle}{A} = \frac {-\hbar c \pi^{2}}{3 \cdot 240 a^{3}}

The analytic continuation has evidently lost an additive positive infinity, somehow exactly accounting for the zero-point energy (not included above) outside the slot between the plates, but which changes upon plate movement within a closed system. The Casimir force per unit area Failed to parse (Missing texvc executable; please see math/README to configure.): F_c / A

for idealized, perfectly conducting plates with vacuum between them is

Failed to parse (Missing texvc executable; please see math/README to configure.): {F_c \over A} = - \frac{d}{da} \frac{\langle E \rangle}{A} = -\frac {\hbar c \pi^2} {240 a^4}

where

Failed to parse (Missing texvc executable; please see math/README to configure.): \hbar

(hbar, ħ) is the reduced Planck constant,

Failed to parse (Missing texvc executable; please see math/README to configure.): c

is the speed of light,

Failed to parse (Missing texvc executable; please see math/README to configure.): a

is the distance between the two plates.

The force is negative, indicating that the force is attractive: by moving the two plates closer together, the energy is lowered. The presence of Failed to parse (Missing texvc executable; please see math/README to configure.): \hbar

shows that the Casimir force per unit area Failed to parse (Missing texvc executable; please see math/README to configure.): F_c / A
is very small, and that furthermore, the force is inherently of quantum-mechanical origin.

NOTE: In Casimir's original derivation [1], a moveable conductive plate is positioned at a short distance a from one of two widely separated plates (distance L apart). The 0-point energy on both sides of the plate is considered. Instead of the above ad hoc analytic continuation assumption, non-convergent sums and integrals are computed using Euler-Maclaurin summation with a regularizing function (e.g., exponential regularization) not so anomalous as Failed to parse (Missing texvc executable; please see math/README to configure.): \vert\omega_n\vert^{-s}

 in the above.

More recent theory[link]

Casimir's analysis of idealized metal plates was generalized to arbitrary dielectric and realistic metal plates by Lifshitz and his students.^[13][14] Using this approach, complications of the bounding surfaces, such as the modifications to the Casimir force due to finite conductivity, can be calculated numerically using the tabulated complex dielectric functions of the bounding materials. Lifshitz' theory for two metal plates reduces to Casimir's idealized 1/a⁴ force law for large separations a much greater than the skin depth of the metal, and conversely reduces to the 1/a³ force law of the London dispersion force (with a coefficient called a Hamaker constant) for small a, with a more complicated dependence on a for intermediate separations determined by the dispersion of the materials.^[15]

Lifshitz' result was subsequently generalized to arbitrary multilayer planar geometries as well as to anisotropic and magnetic materials, but for several decades the calculation of Casimir forces for non-planar geometries remained limited to a few idealized cases admitting analytical solutions.^[16] For example, the force in the experimental sphere–plate geometry was computed with an approximation (due to Derjaguin) that the sphere radius R is much larger than the separation a, in which case the nearby surfaces are nearly parallel and the parallel-plate result can be adapted to obtain an approximate R/a³ force (neglecting both skin-depth and higher-order curvature effects).^[16][17] However, in the 2000s a number of authors developed and demonstrated a variety of numerical techniques, in many cases adapted from classical computational electromagnetics, that are capable of accurately calculating Casimir forces for arbitrary geometries and materials, from simple finite-size effects of finite plates to more complicated phenomena arising for patterned surfaces or objects of various shapes.^[16]

Measurement[link]

One of the first experimental tests was conducted by Marcus Sparnaay at Philips in Eindhoven, in 1958, in a delicate and difficult experiment with parallel plates, obtaining results not in contradiction with the Casimir theory,^[18][19] but with large experimental errors. Some of the experimental details as well as some background information on how Casimir, Polder and Sparnaay arrived at this point^[20] are highlighted in a 2007 interview with Marcus Sparnaay.

The Casimir effect was measured more accurately in 1997 by Steve K. Lamoreaux of Los Alamos National Laboratory,^[21] and by Umar Mohideen and Anushree Roy of the University of California at Riverside.^[22] In practice, rather than using two parallel plates, which would require phenomenally accurate alignment to ensure they were parallel, the experiments use one plate that is flat and another plate that is a part of a sphere with a large radius.

In 2001, a group (Giacomo Bressi, Gianni Carugno, Roberto Onofrio and Giuseppe Ruoso) at the University of Padua (Italy) finally succeeded in measuring the Casimir force between parallel plates using microresonators.^[23]

Regularisation[link]

In order to be able to perform calculations in the general case, it is convenient to introduce a regulator in the summations. This is an artificial device, used to make the sums finite so that they can be more easily manipulated, followed by the taking of a limit so as to remove the regulator.

The heat kernel or exponentially regulated sum is

Failed to parse (Missing texvc executable; please see math/README to configure.): \langle E(t) \rangle = \frac{1}{2} \sum_n \hbar |\omega_n| \exp (-t|\omega_n|)

where the limit Failed to parse (Missing texvc executable; please see math/README to configure.): t\to 0^+

is taken in the end. The divergence of the sum is typically manifested as

Failed to parse (Missing texvc executable; please see math/README to configure.): \langle E(t) \rangle = \frac{C}{t^3} + \textrm{finite}\,

for three-dimensional cavities. The infinite part of the sum is associated with the bulk constant C which does not depend on the shape of the cavity. The interesting part of the sum is the finite part, which is shape-dependent. The Gaussian regulator

Failed to parse (Missing texvc executable; please see math/README to configure.): \langle E(t) \rangle = \frac{1}{2} \sum_n \hbar |\omega_n| \exp (-t^2|\omega_n|^2)

is better suited to numerical calculations because of its superior convergence properties, but is more difficult to use in theoretical calculations. Other, suitably smooth, regulators may be used as well. The zeta function regulator

Failed to parse (Missing texvc executable; please see math/README to configure.): \langle E(s) \rangle = \frac{1}{2} \sum_n \hbar |\omega_n| |\omega_n|^{-s}

is completely unsuited for numerical calculations, but is quite useful in theoretical calculations. In particular, divergences show up as poles in the complex s plane, with the bulk divergence at s = 4. This sum may be analytically continued past this pole, to obtain a finite part at s = 0.

Not every cavity configuration necessarily leads to a finite part (the lack of a pole at s = 0) or shape-independent infinite parts. In this case, it should be understood that additional physics has to be taken into account. In particular, at extremely large frequencies (above the plasma frequency), metals become transparent to photons (such as X-rays), and dielectrics show a frequency-dependent cutoff as well. This frequency dependence acts as a natural regulator. There are a variety of bulk effects in solid state physics, mathematically very similar to the Casimir effect, where the cutoff frequency comes into explicit play to keep expressions finite. (These are discussed in greater detail in Landau and Lifshitz, "Theory of Continuous Media".)

Generalities[link]

The Casimir effect can also be computed using the mathematical mechanisms of functional integrals of quantum field theory, although such calculations are considerably more abstract, and thus difficult to comprehend. In addition, they can be carried out only for the simplest of geometries. However, the formalism of quantum field theory makes it clear that the vacuum expectation value summations are in a certain sense summations over so-called "virtual particles".

More interesting is the understanding that the sums over the energies of standing waves should be formally understood as sums over the eigenvalues of a Hamiltonian. This allows atomic and molecular effects, such as the van der Waals force, to be understood as a variation on the theme of the Casimir effect. Thus one considers the Hamiltonian of a system as a function of the arrangement of objects, such as atoms, in configuration space. The change in the zero-point energy as a function of changes of the configuration can be understood to result in forces acting between the objects.

In the chiral bag model of the nucleon, the Casimir energy plays an important role in showing the mass of the nucleon is independent of the bag radius. In addition, the spectral asymmetry is interpreted as a non-zero vacuum expectation value of the baryon number, cancelling the topological winding number of the pion field surrounding the nucleon.

Wormholes[link]

This section requires expansion.

Exotic matter with negative energy density may be required to stabilize a wormhole.^[24] Morris, Thorne and Yurtsever pointed out that the quantum mechanics of the Casimir effect can be used to produce a locally mass-negative region of space-time,^[25] and suggested that negative effect could be used to stabilize a wormhole to allow faster than light travel.

In physics, a wormhole is a hypothetical topological feature of spacetime that would be, fundamentally, a "shortcut" through spacetime. For a simple visual explanation of a wormhole, consider spacetime visualized as a two-dimensional (2D) surface. If this surface is folded along a third dimension, it allows one to picture a wormhole "bridge". (Please note, though, that this is merely a visualization displayed to convey an essentially unvisualisable structure existing in 4 or more dimensions. The parts of the wormhole could be higher-dimensional analogues for the parts of the curved 2D surface; for example, instead of mouths which are circular holes in a 2D plane, a real wormhole's mouths could be spheres in 3D space.) A wormhole is, in theory, much like a tunnel with two ends each in separate points in spacetime. This concept has been used extensively in science fiction.

Analogies and the dynamic Casimir effect[link]

A similar analysis can be used to explain Hawking radiation that causes the slow "evaporation" of black holes (although this is generally visualised as the escape of one particle from a virtual particle-antiparticle pair, the other particle having been captured by the black hole).

The dynamical Casimir effect is the production of particles and energy from an accelerated boundary, often referred to as a moving mirror^[26] or motion-induced radiation.

Constructed within the framework of quantum field theory in curved spacetime, the dynamical Casimir effect has been used to better understand acceleration radiation; i.e. the Unruh effect.

Moving mirrors create entropy, particles, energy and gravitational-like effects. In analogy to the event horizon of a black hole, an accelerated mirror amplifies quantum field vacuum fluctuations.

An experimental verification of the dynamical Casimir effect was first achieved in May 2011 at Chalmers University of Technology, in Gothenburg, Sweden.^[27][28]

Repulsive forces[link]

There are few instances wherein the Casimir effect can give rise to repulsive forces between uncharged objects. In a seminal paper, Evgeny Lifshitz showed (theoretically) that in certain circumstances (most commonly involving liquids), repulsive forces can arise.^[29] This has sparked interest in applications of the Casimir effect toward the development of levitating devices. An experimental demonstration of the Casimir-based repulsion predicted by Lifshitz was recently carried out by Munday et al.^[30] Other scientists have also suggested the use of gain media to achieve a similar levitation effect,^[31] though this is controversial^{[citation needed]} because these materials seem to violate fundamental causality constraints and the requirement of thermodynamic equilibrium.

Applications[link]

It has been suggested that the Casimir forces have application in nanotechnology,^[32] in particular silicon integrated circuit technology based micro- and nanoelectromechanical systems, silicon array propulsion for space drives, and so-called Casimir oscillators.^[33]

See also[link]

Physics portal

• Casimir pressure
• Scharnhorst effect
• Van der Waals force

References[link]

Further reading[link]

Introductory readings[link]

• Casimir effect description from University of California, Riverside's version of the Usenet physics FAQ.
• A. Lambrecht, The Casimir effect: a force from nothing, Physics World, September 2002.
• Casimir effect on Astronomy Picture of the Day

Papers, books and lectures[link]

• H. B. G. Casimir, and D. Polder, "The Influence of Retardation on the London-van der Waals Forces", Phys. Rev. 73, 360–372 (1948).
• Casimir, H. B. G. (1948). "On the attraction between two perfectly conducting plates". Proc. Kon. Nederland. Akad. Wetensch. B51: 793. http://www.historyofscience.nl/search/detail.cfm?pubid=2642&view=image&startrow=1. 
• S. K. Lamoreaux, "Demonstration of the Casimir Force in the 0.6 to 6 µm Range", Phys. Rev. Lett. 78, 5–8 (1997)
• M. Bordag, U. Mohideen, V.M. Mostepanenko, "New Developments in the Casimir Effect", Phys. Rep. 353, 1–205 (2001), arXiv. (200+ page review paper.)
• Kimball A.Milton: "The Casimir effect", World Scientific, Singapore 2001,ISBN 981-02-4397-9
• Bressi, G.; Carugno, G.; Onofrio, R.; Ruoso, G. (2002). "Measurement of the Casimir Force between Parallel Metallic Surfaces". Physical Review Letters 88 (4): 041804. arXiv:quant-ph/0203002. Bibcode 2002PhRvL..88d1804B. DOI:10.1103/PhysRevLett.88.041804. PMID 11801108. 
• Kenneth, O.; Klich, I.; Mann, A.; Revzen, M. (2002). "Repulsive Casimir Forces". Physical Review Letters 89 (3): 033001. arXiv:quant-ph/0202114. Bibcode 2002PhRvL..89c3001K. DOI:10.1103/PhysRevLett.89.033001. 
• J. D. Barrow, "Much ado about nothing", (2005) Lecture at Gresham College. (Includes discussion of French naval analogy.)
• Barrow, John D. (2000). The book of nothing: vacuums, voids, and the latest ideas about the origins of the universe (1st American ed.). New York: Pantheon Books. ISBN 0-09-928845-1.  (Also includes discussion of French naval analogy.)
• Jonathan P. Dowling, "The Mathematics of the Casimir Effect", Math. Mag. 62, 324–331 (1989).

Temperature dependence[link]

• Measurements Recast Usual View of Elusive Force from NIST
• V.V. Nesterenko, G. Lambiase, G. Scarpetta, Calculation of the Casimir energy at zero and finite temperature: some recent results, arXiv:hep-th/0503100 v2 13 May 2005

External links[link]

• Casimir effect article search on arxiv.org
• G. Lang, The Casimir Force web site, 2002
• J. Babb, bibliography on the Casimir Effect web site, 2009

Richard Feynman
File:Richard Feynman Nobel.jpg
Born	Richard Phillips Feynman (1918-05-11)May 11, 1918 Far Rockaway, Queens, New York, U.S.
Died	February 15, 1988(1988-02-15) (aged 69) Los Angeles, California, U.S.
Residence	United States
Nationality	American
Fields	Physics
Institutions	Manhattan Project Cornell University California Institute of Technology
Alma mater	Massachusetts Institute of Technology (B.S.), Princeton University (Ph.D.)
Doctoral advisor	John Archibald Wheeler
Other academic advisors	Manuel Sandoval Vallarta
Doctoral students	F. L. Vernon, Jr.[1] Willard H. Wells[1] Al Hibbs[1] George Zweig[1] Giovanni Rossi Lomanitz[1] Thomas Curtright[1]
Other notable students	Douglas D. Osheroff Robert Barro W. Daniel Hillis
Known for	Feynman diagrams Feynman point Feynman–Kac formula Wheeler–Feynman absorber theory Bethe–Feynman formula Feynman sprinkler Feynman Long Division Puzzles Hellmann–Feynman theorem Feynman slash notation Feynman parametrization Sticky bead argument One-electron universe Quantum cellular automata
Influences	Paul Dirac
Notable awards	Albert Einstein Award (1954) E. O. Lawrence Award (1962) Nobel Prize in Physics (1965) Oersted Medal (1972) National Medal of Science (1979)
Spouse	Arline Greenbaum (m. 1941–1945) «start: (1941)–end+1: (1946)»"Marriage: Arline Greenbaum to Richard Feynman" Location: (linkback:http://en-wiki.pop.wn.com/index.php/Richard_Feynman)(died) Mary Lou Bell (m. 1952–1954) «start: (1952)–end+1: (1955)»"Marriage: Mary Lou Bell to Richard Feynman" Location: (linkback:http://en-wiki.pop.wn.com/index.php/Richard_Feynman) Gweneth Howarth (m. 1960–1988) «start: (1960)–end+1: (1989)»"Marriage: Gweneth Howarth to Richard Feynman" Location: (linkback:http://en-wiki.pop.wn.com/index.php/Richard_Feynman) (his death)
Signature
Notes He was the father of Carl Feynman and adoptive father of Michelle Feynman. He was the brother of Joan Feynman.

Richard Phillips Feynman ( /ˈfaɪnmən/; May 11, 1918 – February 15, 1988)^[2] was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics (he proposed the parton model). For his contributions to the development of quantum electrodynamics, Feynman, jointly with Julian Schwinger and Sin-Itiro Tomonaga, received the Nobel Prize in Physics in 1965. He developed a widely used pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, which later became known as Feynman diagrams. During his lifetime, Feynman became one of the best-known scientists in the world. In a 1999 poll of 130 leading physicists worldwide by the British journal Physics World he was ranked as one of the ten greatest physicists of all time.^[3]

He assisted in the development of the atomic bomb and was a member of the panel that investigated the Space Shuttle Challenger disaster. In addition to his work in theoretical physics, Feynman has been credited with pioneering the field of quantum computing,^[4][5] and introducing the concept of nanotechnology.^[6] He held the Richard Chace Tolman professorship in theoretical physics at the California Institute of Technology.

Feynman was a keen popularizer of physics through both books and lectures, notably a 1959 talk on top-down nanotechnology called There’s Plenty of Room at the Bottom and the three volume publication of his undergraduate lectures, The Feynman Lectures on Physics. Feynman also became known through his semi-autobiographical books (Surely You’re Joking, Mr. Feynman! and What Do You Care What Other People Think?) and books written about him, such as Tuva or Bust!.

He also had a deep interest in biology, and was a friend of the geneticist and microbiologist Esther Lederberg, who developed replica plating and discovered bacteriophage lambda.^[7] They had several mutual physicist friends who, after beginning their careers in nuclear research, moved into genetics, among them Max Delbrück and Aaron Novick.

Biography[link]

Early life[link]

Richard Phillips Feynman was born on May 11, 1918,^[8] in Far Rockaway, Queens, New York.^[9] His family originated from Russia and Poland; both of his parents were Ashkenazi Jewish.^[10] They were not religious and by his youth Feynman described himself as an “avowed atheist”.^[11] Feynman (in common with the famous physicist Edward Teller) was a late talker; by his third birthday he had yet to utter a single word. The young Feynman was heavily influenced by his father, Melville, who encouraged him to ask questions to challenge orthodox thinking. From his mother, Lucille, he gained the sense of humor that he had throughout his life. As a child, he had a talent for engineering, maintained an experimental laboratory in his home, and delighted in repairing radios. His younger sister Joan also became a professional physicist.^[12][13]

Education[link]

In high school, his IQ was determined to be 125—high, but “merely respectable” according to biographer James Gleick.^[14] Feynman later scoffed at psychometric testing. In the year 1933, in which he turned 15, he taught himself trigonometry, advanced algebra, infinite series, analytic geometry, and differential and integral calculus.^[15] Before entering college, he was experimenting with and re-creating mathematical topics, such as the half-derivative, using his own notation. In high school, he was developing the mathematical intuition behind his Taylor series of mathematical operators.^[16]

His habit of direct characterization sometimes rattled more conventional thinkers; for example, one of his questions, when learning feline anatomy, was “Do you have a map of the cat?” (referring to an anatomical chart).

Feynman attended Far Rockaway High School, a school also attended by fellow laureates Burton Richter and Baruch Samuel Blumberg.^[17] A member of the Arista Honor Society, in his last year in high school, Feynman won the New York University Math Championship; the large difference between his score and those of his closest competitors shocked the judges.^[18]

He applied to Columbia University, but was not accepted.^[19][20] Instead he attended the Massachusetts Institute of Technology, where he received a bachelor’s degree in 1939, and in the same year was named a Putnam Fellow. While there, Feynman took every physics course offered, including a graduate course on theoretical physics while only in his second year.

He obtained a perfect score on the graduate school entrance exams to Princeton University in mathematics and physics—an unprecedented feat—but did rather poorly on the history and English portions.^[18] Attendees at Feynman’s first seminar included Albert Einstein, Wolfgang Pauli, and John von Neumann. He received a Ph.D. from Princeton in 1942; his thesis advisor was John Archibald Wheeler. Feynman’s thesis applied the principle of stationary action to problems of quantum mechanics, inspired by a desire to quantize the Wheeler–Feynman absorber theory of electrodynamics, laying the groundwork for the “path integral” approach and Feynman diagrams, and was titled “The Principle of Least Action in Quantum Mechanics”.

This was Richard Feynman nearing the crest of his powers. At twenty-three … there was no physicist on earth who could match his exuberant command over the native materials of theoretical science. It was not just a facility at mathematics (though it had become clear … that the mathematical machinery emerging from the Wheeler–Feynman collaboration was beyond Wheeler’s own ability). Feynman seemed to possess a frightening ease with the substance behind the equations, like Albert Einstein at the same age, like the Soviet physicist Lev Landau—but few others.

— James Gleick, Genius: The Life and Science of Richard Feynman

The Manhattan Project[link]

This unreferenced section requires citations to ensure verifiability.

Feynman (center) with Robert Oppenheimer (right) relaxing at a Los Alamos social function during the Manhattan Project

At Princeton, the physicist Robert R. Wilson encouraged Feynman to participate in the Manhattan Project—the wartime U.S. Army project at Los Alamos developing the atomic bomb. Feynman said he was persuaded to join this effort to build it before Nazi Germany developed their own bomb.

He was assigned to Hans Bethe’s theoretical division, and impressed Bethe enough to be made a group leader. He and Bethe developed the Bethe–Feynman formula for calculating the yield of a fission bomb, which built upon previous work by Robert Serber.

He immersed himself in work on the project, and was present at the Trinity bomb test. Feynman claimed to be the only person to see the explosion without the very dark glasses or welder’s lenses provided, reasoning that it was safe to look through a truck windshield, as it would screen out the harmful ultraviolet radiation.

As a junior physicist, he was not central to the project. The greater part of his work was administering the computation group of human computers in the Theoretical division (one of his students there, John G. Kemeny, later went on to co-design and co-specify the programming language BASIC). Later, with Nicholas Metropolis, he assisted in establishing the system for using IBM punched cards for computation. Feynman succeeded in solving one of the equations for the project that were posted on the blackboards. However, they did not “do the physics right” and Feynman’s solution was not used.

Feynman’s other work at Los Alamos included calculating neutron equations for the Los Alamos “Water Boiler”, a small nuclear reactor, to measure how close an assembly of fissile material was to criticality. On completing this work he was transferred to the Oak Ridge facility, where he aided engineers in devising safety procedures for material storage so that criticality accidents (for example, due to sub-critical amounts of fissile material inadvertently stored in proximity on opposite sides of a wall) could be avoided. He also did theoretical work and calculations on the proposed uranium hydride bomb, which later proved not to be feasible.

Feynman was sought out by physicist Niels Bohr for one-on-one discussions. He later discovered the reason: most physicists were too in awe of Bohr to argue with him. Feynman had no such inhibitions, vigorously pointing out anything he considered to be flawed in Bohr’s thinking. Feynman said he felt as much respect for Bohr as anyone else, but once anyone got him talking about physics, he would become so focused he forgot about social niceties.

Due to the top secret nature of the work, Los Alamos was isolated. In Feynman’s own words, “There wasn’t anything to do there”. Bored, he indulged his curiosity by learning to pick the combination locks on cabinets and desks used to secure papers. Feynman played many jokes on colleagues. In one case he found the combination to a locked filing cabinet by trying the numbers a physicist would use (it proved to be 27–18–28 after the base of natural logarithms, e = 2.71828…), and found that the three filing cabinets where a colleague kept a set of atomic bomb research notes all had the same combination. He left a series of notes as a prank, which initially spooked his colleague, Frederic de Hoffmann, into thinking a spy or saboteur had gained access to atomic bomb secrets. On several occasions, Feynman drove to Albuquerque to see his ailing wife in a car borrowed from Klaus Fuchs, who was later discovered to be a real spy for the Soviets, transporting nuclear secrets in his car to Santa Fe.

On occasion, Feynman would find an isolated section of the mesa to drum in the style of American natives; “and maybe I would dance and chant, a little”. These antics did not go unnoticed, and rumors spread about a mysterious Indian drummer called “Injun Joe”. He also became a friend of laboratory head J. Robert Oppenheimer, who unsuccessfully tried to court him away from his other commitments after the war to work at the University of California, Berkeley.

Feynman alludes to his thoughts on the justification for getting involved in the Manhattan project in The Pleasure of Finding Things Out. As mentioned earlier, he felt the possibility of Nazi Germany developing the bomb before the Allies was a compelling reason to help with its development for the US. However, he goes on to say that it was an error on his part not to reconsider the situation when Germany was defeated. In the same publication, Feynman also talks about his worries in the atomic bomb age, feeling for some considerable time that there was a high risk that the bomb would be used again soon so that it was pointless to build for the future. Later he describes this period as a “depression.”

Early academic career[link]

Following the completion of his Ph.D. in 1942, Feynman held an appointment at the University of Wisconsin–Madison as an assistant professor of physics. The appointment was spent on leave for his involvement in the Manhattan project. In 1945, he received a letter from Dean Mark Ingraham of the College of Letters and Science requesting his return to UW to teach in the coming academic year. His appointment was not extended when he did not commit to return. In a talk given several years later at UW, Feynman quipped, “It’s great to be back at the only university that ever had the good sense to fire me”.^[21]

After the war, Feynman declined an offer from the Institute for Advanced Study in Princeton, New Jersey, despite the presence there of such distinguished faculty members as Albert Einstein, Kurt Gödel, and John von Neumann. Feynman followed Hans Bethe, instead, to Cornell University, where Feynman taught theoretical physics from 1945 to 1950.^[16] During a temporary depression following the destruction of Hiroshima by the bomb produced by the Manhattan Project, he focused on complex physics problems, not for utility, but for self-satisfaction. One of these was analyzing the physics of a twirling, nutating dish as it is moving through the air. His work during this period, which used equations of rotation to express various spinning speeds, soon proved important to his Nobel Prize-winning work. Yet because he felt burned out, and had turned his attention to less immediately practical but more entertaining problems, he felt surprised by the offers of professorships from other renowned universities.^[16]

Despite yet another offer from the Institute for Advanced Study, Feynman rejected the Institute on the grounds that there were no teaching duties: Feynman felt that students were a source of inspiration and teaching a diversion during uncreative spells. Because of this, the Institute for Advanced study and Princeton University jointly offered him a package whereby he could teach at the university and also be at the Institute. That he also turned this down suggests the effects of his depression^{[not in citation given]}. (see Surely You’re Joking Mr. Feynman!). Somewhat later, feeling better, Feynman accepted an offer from the California Institute of Technology (Caltech) — and as he says in his book Surely You’re Joking Mr. Feynman! — because a desire to live in a mild climate had firmly fixed itself in his mind while installing tire chains on his car in the middle of a snowstorm in Ithaca.

Feynman has been called the “Great Explainer”.^[22] He gained a reputation for taking great care when giving explanations to his students and for making it a moral duty to make the topic accessible. His guiding principle was that if a topic could not be explained in a freshman lecture, it was not yet fully understood. Feynman gained great pleasure^[23] from coming up with such a “freshman-level” explanation, for example, of the connection between spin and statistics. What he said was that groups of particles with spin ½ “repel”, whereas groups with integer spin “clump.” This was a brilliantly simplified way of demonstrating how Fermi–Dirac statistics and Bose–Einstein statistics evolved as a consequence of studying how fermions and bosons behave under a rotation of 360°. This was also a question he pondered in his more advanced lectures and to which he demonstrated the solution in the 1986 Dirac memorial lecture.^[24] In the same lecture, he further explained that antiparticles must exist, for if particles only had positive energies, they would not be restricted to a so-called “light cone.”

He opposed rote learning or unthinking memorization and other teaching methods that emphasized form over function. He put these opinions into action whenever he could, from a conference on education in Brazil to a State Commission on school textbook selection. Clear thinking and clear presentation were fundamental prerequisites for his attention. It could be perilous even to approach him when unprepared, and he did not forget the fools or pretenders.^[25]

During one sabbatical year, he returned to Newton’s Principia Mathematica to study it anew; what he learned from Newton, he passed along to his students, such as Newton’s attempted explanation of diffraction.^{[citation needed]}

Caltech years[link]

The Feynman section at the Caltech bookstore

Feynman did significant work while at Caltech, including research in:

• Quantum electrodynamics. The theory for which Feynman won his Nobel Prize is known for its accurate predictions.^[26][27] This theory was begun in the earlier years during Feynman’s work at Princeton as a graduate student and continued while he was at Cornell. This work consisted of two distinct formulations, and it is a common error to confuse them or to merge them into one. The first is his path integral formulation, and the second is his Feynman diagrams. Both formulations contained his sum over histories method in which every possible path from one state to the next is considered, the final path being a sum over the possibilities (also referred to as sum-over-paths.)^[28] For a number of years he lectured to students at Caltech on his path integral formulation of quantum theory. The lecture notes have recently been reedited by Daniel F. Styer and published as a Dover paperback. Not only did Styer correct several hundred typographical and other minor errors, but he included many footnotes explaining, for example, several places where the author used heuristic or plausible reasoning. The second formulation of quantum electrodynamics (using Feynman diagrams) was specifically mentioned by the Nobel committee. The logical connection with the path integral formulation is interesting. Feynman did not prove that the rules for his diagrams followed mathematically from the path integral formulation. Some special cases were later proved by other people, but only in the real case, so the proofs don’t work when spin is involved. The second formulation should be thought of as starting anew, but guided by the intuitive insight provided by the first formulation. Freeman Dyson published a paper in 1949 which, among many other things, added new rules to Feynman’s which told how to actually implement Renormalization. Students everywhere learned and used the powerful new tool that Feynman had created. Eventually computer programs were written to compute Feynman diagrams, providing a tool of unprecedented power. It is possible to write such programs because the Feynman diagrams constitute a Formal language with a grammar.

• Physics of the superfluidity of supercooled liquid helium, where helium seems to display a complete lack of viscosity when flowing. Applying the Schrödinger equation to the question showed that the superfluid was displaying quantum mechanical behavior observable on a macroscopic scale. This helped with the problem of superconductivity; however, the solution eluded Feynman.^[29] It was solved with the BCS theory of superconductivity, proposed by John Bardeen, Leon Neil Cooper, and John Robert Schrieffer.

• A model of weak decay, which showed that the current coupling in the process is a combination of vector and axial currents (an example of weak decay is the decay of a neutron into an electron, a proton, and an anti-neutrino). Although E. C. George Sudarshan and Robert Marshak developed the theory nearly simultaneously, Feynman’s collaboration with Murray Gell-Mann was seen as seminal because the weak interaction was neatly described by the vector and axial currents. It thus combined the 1933 beta decay theory of Enrico Fermi with an explanation of parity violation.

Richard Feynman at Fermilab

He also developed Feynman diagrams, a bookkeeping device which helps in conceptualizing and calculating interactions between particles in spacetime, notably the interactions between electrons and their antimatter counterparts, positrons. This device allowed him, and later others, to approach time reversibility and other fundamental processes. Feynman’s mental picture for these diagrams started with the hard sphere approximation, and the interactions could be thought of as collisions at first. It was not until decades later that physicists thought of analyzing the nodes of the Feynman diagrams more closely. Feynman famously painted Feynman diagrams on the exterior of his van.^[30]

From his diagrams of a small number of particles interacting in spacetime, Feynman could then model all of physics in terms of those particles’ spins and the range of coupling of the fundamental forces.^[31] Feynman attempted an explanation of the strong interactions governing nucleons scattering called the parton model. The parton model emerged as a complement to the quark model developed by his Caltech colleague Murray Gell-Mann. The relationship between the two models was murky; Gell-Mann referred to Feynman’s partons derisively as “put-ons”. In the mid 1960s, physicists believed that quarks were just a bookkeeping device for symmetry numbers, not real particles, as the statistics of the Omega-minus particle, if it were interpreted as three identical strange quarks bound together, seemed impossible if quarks were real. The Stanford linear accelerator deep inelastic scattering experiments of the late 1960s showed, analogously to Ernest Rutherford’s experiment of scattering alpha particles on gold nuclei in 1911, that nucleons (protons and neutrons) contained point-like particles which scattered electrons. It was natural to identify these with quarks, but Feynman’s parton model attempted to interpret the experimental data in a way which did not introduce additional hypotheses. For example, the data showed that some 45% of the energy momentum was carried by electrically neutral particles in the nucleon. These electrically neutral particles are now seen to be the gluons which carry the forces between the quarks and carry also the three-valued color quantum number which solves the Omega-minus problem. Feynman did not dispute the quark model; for example, when the fifth quark was discovered in 1977, Feynman immediately pointed out to his students that the discovery implied the existence of a sixth quark, which was duly discovered in the decade after his death.

After the success of quantum electrodynamics, Feynman turned to quantum gravity. By analogy with the photon, which has spin 1, he investigated the consequences of a free massless spin 2 field, and was able to derive the Einstein field equation of general relativity, but little more.^[32] However, the computational device that Feynman discovered then for gravity, “ghosts”, which are “particles” in the interior of his diagrams which have the “wrong” connection between spin and statistics, have proved invaluable in explaining the quantum particle behavior of the Yang–Mills theories, for example QCD and the electro-weak theory.

In 1965, Feynman was appointed a foreign member of the Royal Society.^[33] At this time in the early 1960s, Feynman exhausted himself by working on multiple major projects at the same time, including a request, while at Caltech, to “spruce up” the teaching of undergraduates. After three years devoted to the task, he produced a series of lectures that eventually became the Feynman Lectures on Physics, one reason that Feynman is still regarded as one of the greatest teachers of physics. He wanted a picture of a drumhead sprinkled with powder to show the modes of vibration at the beginning of the book. Outraged by many rock and roll and drug connections that could be made from the image, the publishers changed the cover to plain red, though they included a picture of him playing drums in the foreword. Feynman later won the Oersted Medal for teaching, of which he seemed especially proud.^[34]

His students competed keenly for his attention; he was once awakened when a student solved a problem and dropped it in his mailbox; glimpsing the student sneaking across his lawn, he could not go back to sleep, and he read the student’s solution. The next morning his breakfast was interrupted by another triumphant student, but Feynman informed him that he was too late.

Partly as a way to bring publicity to progress in physics, Feynman offered $1000 prizes for two of his challenges in nanotechnology, claimed by William McLellan and Tom Newman, respectively.^[35] He was also one of the first scientists to conceive the possibility of quantum computers.

Many of his lectures and other miscellaneous talks were turned into books, including The Character of Physical Law and QED: The Strange Theory of Light and Matter. He gave lectures which his students annotated into books, such as Statistical Mechanics and Lectures on Gravity. The Feynman Lectures on Physics^[36] occupied two physicists, Robert B. Leighton and Matthew Sands as part-time co-authors for several years. Even though they were not adopted by most universities as textbooks, the books continue to be bestsellers because they provide a deep understanding of physics. As of 2005, The Feynman Lectures on Physics has sold over 1.5 million copies in English, an estimated 1 million copies in Russian, and an estimated half million copies in other languages.^{[citation needed]}

In 1974, Feynman delivered the Caltech commencement address on the topic of cargo cult science, which has the semblance of science but is only pseudoscience due to a lack of “a kind of scientific integrity, a principle of scientific thought that corresponds to a kind of utter honesty” on the part of the scientist. He instructed the graduating class that “The first principle is that you must not fool yourself—and you are the easiest person to fool. So you have to be very careful about that. After you’ve not fooled yourself, it’s easy not to fool other scientists. You just have to be honest in a conventional way after that.”^[37]

In 1984–86, he developed a variational method for the approximate calculation of path integrals which has led to a powerful method of converting divergent perturbation expansions into convergent strong-coupling expansions (variational perturbation theory) and, as a consequence, to the most accurate determination^[38] of critical exponents measured in satellite experiments.^[39]

In the late 1980s, according to “Richard Feynman and the Connection Machine”, Feynman played a crucial role in developing the first massively parallel computer, and in finding innovative uses for it in numerical computations, in building neural networks, as well as physical simulations using cellular automata (such as turbulent fluid flow), working with Stephen Wolfram at Caltech.^[40] His son Carl also played a role in the development of the original Connection Machine engineering; Feynman influencing the interconnects while his son worked on the software.

Feynman diagrams are now fundamental for string theory and M-theory, and have even been extended topologically.^{[citation needed]} The world-lines of the diagrams have developed to become tubes to allow better modeling of more complicated objects such as strings and membranes. However, shortly before his death, Feynman criticized string theory in an interview: “I don’t like that they’re not calculating anything,” he said. “I don’t like that they don’t check their ideas. I don’t like that for anything that disagrees with an experiment, they cook up an explanation—a fix-up to say, ‘Well, it still might be true.’” These words have since been much-quoted by opponents of the string-theoretic direction for particle physics.^[41]

Challenger disaster[link]

The 1986 Space Shuttle Challenger disaster

Feynman played an important role on the Presidential Rogers Commission, which investigated the Challenger disaster. During a televised hearing, Feynman demonstrated that the material used in the shuttle's O-rings became less resilient in cold weather by immersing a sample of the material in ice-cold water. The Commission ultimately determined that the disaster was caused by the primary O-ring not properly sealing due to extremely cold weather at Cape Canaveral.^[42]

Feynman devoted the latter half of his book What Do You Care What Other People Think? to his experience on the Rogers Commission, straying from his usual convention of brief, light-hearted anecdotes to deliver an extended and sober narrative. Feynman’s account reveals a disconnect between NASA’s engineers and executives that was far more striking than he expected. His interviews of NASA’s high-ranking managers revealed startling misunderstandings of elementary concepts. For instance, NASA managers claimed that there was a 1 in 100,000 chance of a catastrophic failure aboard the shuttle, but Feynman discovered that NASA's own engineers estimated the chance of a catastrophe at closer to 1 in 100. He concluded that the NASA management’s space shuttle reliability estimate was fantastically unrealistic, and was particularly angered that NASA used these figures to recruit Christa McAuliffe into the Teacher-in-Space program. He warned in his appendix to the commission’s report (which was included after he threatened not to sign the report), “For a successful technology, reality must take precedence over public relations, for nature cannot be fooled.”^[43] He also rebuked some mathematicians for their exclusivity, saying “I have great suspicion that [mathematicians] don’t know that this stuff is wrong and that they’re intimidating people.”^[44]

Ethnic identification[link]

Though raised Jewish and born to Ashkenazi parents, Feynman himself was not only atheist, but distanced himself from being labelled Jewish even on ethnic grounds. He routinely refused to be included in lists or books that classified people by race. He asked to not be included in Tina Levitan’s, The Laureates: Jewish Winners of the Nobel Prize, writing, "To select, for approbation the peculiar elements that come from some supposedly Jewish heredity is to open the door to all kinds of nonsense on racial theory," and adding "…at thirteen I was not only converted to other religious views but I also stopped believing that the Jewish people are in any way 'the chosen people'".^[45][46]

Personal life[link]

While researching for his Ph.D., Feynman married his first wife, Arline Greenbaum (often spelled Arlene). She was diagnosed with tuberculosis, but she and Feynman were careful, and he never contracted it. She succumbed to the disease in 1945. In 1946 Feynman wrote a letter to her but kept it sealed until after his death.^[47] This portion of Feynman’s life was portrayed in the 1996 film Infinity, which featured Feynman’s daughter Michelle in a cameo role.

He was married a second time in June 1952, to Mary Louise Bell of Neodesha, Kansas; this marriage was brief and unsuccessful:

He begins working calculus problems in his head as soon as he awakens. He did calculus while driving in his car, while sitting in the living room, and while lying in bed at night.

—Mary Louise Bell divorce complaint^[48]p.168

He later married Gweneth Howarth from Ripponden, Yorkshire, who shared his enthusiasm for life and spirited adventure.^[49] Besides their home in Altadena, California, they had a beach house in Baja California, purchased with the prize money from Feynman’s Nobel Prize, his one third share of $55,000. They remained married until Feynman’s death. They had a son, Carl, in 1962, and adopted a daughter, Michelle, in 1968.^[49]

Feynman had a great deal of success teaching Carl, using discussions about ants and Martians as a device for gaining perspective on problems and issues; he was surprised to learn that the same teaching devices were not useful with Michelle.^[50] Mathematics was a common interest for father and son; they both entered the computer field as consultants and were involved in advancing a new method of using multiple computers to solve complex problems—later known as parallel computing. The Jet Propulsion Laboratory retained Feynman as a computational consultant during critical missions. One co-worker characterized Feynman as akin to Don Quixote at his desk, rather than at a computer workstation, ready to do battle with the windmills.

Feynman traveled widely, notably to Brazil, where he gave courses at the CBPF (Brazilian Center for Physics Research) and near the end of his life schemed to visit the Russian land of Tuva, a dream that, because of Cold War bureaucratic problems, never became reality.^[51] The day after he died, a letter arrived for him from the Soviet government giving him authorization to travel to Tuva. Out of his enthusiastic interest in reaching Tuva came the phrase “Tuva or Bust” (also the title of a book about his efforts to get there), which was tossed about frequently amongst his circle of friends in hope that they, one day, could see it firsthand. The documentary movie Genghis Blues mentions some of his attempts to communicate with Tuva, and chronicles the successful journey there by his friends.

Responding to Hubert Humphrey’s congratulation for his Nobel Prize, Feynman admitted to a long admiration for the then vice president.^[52] In a letter to an MIT professor dated December 6, 1966, Feynman expressed interest in running for the governor of California.^[53]

Feynman took up drawing at one time and enjoyed some success under the pseudonym “Ofey”, culminating in an exhibition dedicated to his work. He learned to play a metal percussion instrument (frigideira) in a samba style in Brazil, and participated in a samba school.

In addition, he had some degree of synesthesia for equations, explaining that the letters in certain mathematical functions appeared in color for him, even though invariably printed in standard black-and-white.^[54]

According to Genius, the James Gleick–authored biography, Feynman tried LSD during his professorship at Caltech.^[18] Somewhat embarrassed by his actions, Feynman largely sidestepped the issue when dictating his anecdotes; he mentions it in passing in the “O Americano, Outra Vez” section, while the “Altered States” chapter in Surely You’re Joking, Mr. Feynman! describes only marijuana and ketamine experiences at John Lilly’s famed sensory deprivation tanks, as a way of studying consciousness.^[16] Feynman gave up alcohol when he began to show early signs of alcoholism, as he did not want to do anything that could damage his brain—the same reason given in “O Americano, Outra Vez” for his reluctance to experiment with LSD.^[16]

In Surely You’re Joking, Mr. Feynman!, he gives advice on the best way to pick up a girl in a hostess bar. At Caltech, he used a nude/topless bar as an office away from his usual office, making sketches or writing physics equations on paper placemats. When the county officials tried to close the place, all visitors except Feynman refused to testify in favor of the bar, fearing that their families or patrons would learn about their visits. Only Feynman accepted, and in court, he affirmed that the bar was a public need, stating that craftsmen, technicians, engineers, common workers “and a physics professor” frequented the establishment. While the bar lost the court case, it was allowed to remain open as a similar case was pending appeal.^[16]

Feynman has a minor acting role in the film Anti-Clock. He is credited as “The Professor.”^[55]

Death[link]

Feynman developed two rare forms of cancer, Liposarcoma and Waldenström's macroglobulinemia, dying shortly after a final attempt at surgery for the former on February 15, 1988, aged 69.^[18] His last recorded words are noted as “I’d hate to die twice. It’s so boring.”^[18][56]

Popular legacy[link]

Alan Alda, the stage, screen and television actor, studied writings about Richard Feynman’s life during the 1990s in preparation for playing the role of Feynman on stage in a yet-to-be developed play. Playwright Peter Parnell was commissioned by Alda to write a two-character play about a fictional day in the life of Feynman set two years prior to Feynman’s death from cancer, based upon Alda’s biographical research. The play, entitled QED, premiered at the Mark Taper Forum in Los Angeles, CA in 2001. The play was then presented at the Vivian Beaumont Theatre on Broadway; with both presentations starring Alan Alda as the scientist, Richard Feynman.

On May 4, 2005, the United States Postal Service issued the American Scientists commemorative set of four 37-cent self-adhesive stamps in several configurations. The scientists depicted were Richard Feynman, John von Neumann, Barbara McClintock and Josiah Willard Gibbs. Feynman’s stamp, sepia-toned, features a photograph of a 30-something Feynman and eight small Feynman diagrams.^[57] The stamps were designed by artist Victor Stabin under the direction of U.S. Postal Service art director Carl T. Herrman.^[58]

The main building for the Computing Division at Fermilab is named the “Feynman Computing Center” in his honor.^[59]

The principal character in Thomas A. McMahon’s 1970 novel, Principles of American Nuclear Chemistry: A Novel, is modeled on Feynman.^{[citation needed]}

Real Time Opera premiered its opera Feynman at the Norfolk (CT) Chamber Music Festival in June 2005.^[60]

On the 20th anniversary of Feynman’s death, composer Edward Manukyan dedicated a piece for solo clarinet to his memory.^[61] It was premiered by Doug Storey, the principal clarinetist of the Amarillo Symphony.

In 2009–11, clips of an interview with Feynman were used by composer John Boswell as part of the Symphony of Science project in the second, fifth, seventh, and eleventh installments of his videos, “We Are All Connected”, “The Poetry of Reality”, “A Wave of Reason”, and “The Quantum World”.^[62]

In 1998, a photo of Richard Feynman giving a lecture was part of the poster series commissioned by Apple Computer for their “Think Different” advertising campaign.^[63]

In 2011 Feynman was the subject of a biographical graphic novel titled simply Feynman, written by Jim Ottaviani and illustrated by Leland Myrick.^[64]

Bibliography[link]

Selected scientific works[link]

• Feynman, Richard P. (2000). Laurie M. Brown. ed. Selected Papers of Richard Feynman: With Commentary. 20th Century Physics. World Scientific. ISBN 978-981-02-4131-5. 
• Feynman, Richard P. (1942). Laurie M. Brown. ed. The Principle of Least Action in Quantum Mechanics. Ph.D. Dissertation, Princeton University. World Scientific (with title Feynman’s Thesis: a New Approach to Quantum Theory). 2005. ISBN 978-981-256-380-4. 
• Wheeler, John A.; Feynman, Richard P. (1945). "Interaction with the Absorber as the Mechanism of Radiation". Rev. Mod. Phys. 17 (2–3): 157–181. Bibcode 1945RvMP...17..157W. DOI:10.1103/RevModPhys.17.157. 
• Feynman, Richard P. (1946). A Theorem and its Application to Finite Tampers. Los Alamos Scientific Laboratory, Atomic Energy Commission. OSTI 4341197. 
• Feynman, Richard P.; Welton, T. A. (1946). Neutron Diffusion in a Space Lattice of Fissionable and Absorbing Materials. Los Alamos Scientific Laboratory, Atomic Energy Commission. OSTI 4381097. 
• Feynman, Richard P.; Metropolis, N.; Teller, E. (1947). Equations of State of Elements Based on the Generalized Fermi-Thomas Theory. Los Alamos Scientific Laboratory, Atomic Energy Commission. OSTI 4417654. 
• Feynman, Richard P. (1948a). "Space-time approach to non-relativistic quantum mechanics". Rev. Mod. Phys. 20 (2): 367–387. Bibcode 1948RvMP...20..367F. DOI:10.1103/RevModPhys.20.367. 
• Feynman, Richard P. (1948b). "Relativistic Cut-Off for Quantum Electrodynamics". Physical Review 74 (10): 1430–1438. Bibcode 1948PhRv...74.1430F. DOI:10.1103/PhysRev.74.1430. 
• Wheeler, John A.; Feynman, Richard P. (1949). "Classical Electrodynamics in Terms of Direct Interparticle Action". Rev. Mod. Phys. 21 (3): 425–433. Bibcode 1949RvMP...21..425W. DOI:10.1103/RevModPhys.21.425. 
• Feynman, Richard P. (1949). "The theory of positrons". Phys. Rev. 76 (6): 749–759. Bibcode 1949PhRv...76..749F. DOI:10.1103/PhysRev.76.749. 
• Feynman, Richard P. (1949b). "Space-Time Approach to Quantum Electrodynamic". Phys. Rev. 76 (6): 769–789. Bibcode 1949PhRv...76..769F. DOI:10.1103/PhysRev.76.769. 
• Feynman, Richard P. (1950). "Mathematical formulation of the quantum theory of electromagnetic interaction". Phys. Rev. 80 (3): 440–457. Bibcode 1950PhRv...80..440F. DOI:10.1103/PhysRev.80.440. 
• Feynman, Richard P. (1951). "An Operator Calculus Having Applications in Quantum Electrodynamics". Phys. Rev. 84: 108–128. Bibcode 1951PhRv...84..108F. DOI:10.1103/PhysRev.84.108. 
• Feynman, Richard P. (1953). "The λ-Transition in Liquid Helium". Phys. Rev. 90 (6): 1116–1117. Bibcode 1953PhRv...90.1116F. DOI:10.1103/PhysRev.90.1116.2. 
• Feynman, Richard P.; de Hoffmann, F.; Serber, R. (1955). Dispersion of the Neutron Emission in U235 Fission. Los Alamos Scientific Laboratory, Atomic Energy Commission. OSTI 4354998. 
• Feynman, Richard P. (1956). "Science and the Open Channel". Science 123 (3191): 307. February 24, 1956. Bibcode 1956Sci...123..307F. DOI:10.1126/science.123.3191.307. PMID 17774518. 
• Cohen, M.; Feynman, Richard P. (1957). "Theory of Inelastic Scattering of Cold Neutrons from Liquid Helium". Phys. Rev. 107: 13–24. Bibcode 1957PhRv..107...13C. DOI:10.1103/PhysRev.107.13. 
• Feynman, Richard P.; Vernon, F. L.; Hellwarth, R.W. (1957). "Geometric representation of the Schrödinger equation for solving maser equations". J. Appl. Phys 28: 49. Bibcode 1957JAP....28...49F. DOI:10.1063/1.1722572. 
• Feynman, Richard P. (1959). "Plenty of Room at the Bottom". Presentation to American Physical Society. http://www.its.caltech.edu/~feynman/plenty.html. 
• Edgar, R. S.; Feynman, Richard P.; Klein, S.; Lielausis, I.; Steinberg, CM (1962). "Mapping experiments with r mutants of bacteriophage T4D". Genetics 47: 179–86. February 1962. PMC 1210321. PMID 13889186. //www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=1210321. 
• Feynman, Richard P. (1966). "The Development of the Space-Time View of Quantum Electrodynamics". Science 153 (3737): 699–708. August 12, 1966. Bibcode 1966Sci...153..699F. DOI:10.1126/science.153.3737.699. PMID 17791121. 
• Feynman, Richard P. (1974a). "Structure of the proton". Science 183 (4125): 601–610. February 15, 1974. Bibcode 1974Sci...183..601F. DOI:10.1126/science.183.4125.601. PMID 17778830. 
• Feynman, Richard P. (1974). "Cargo Cult Science" (PDF). Engineering and Science 37 (7). http://calteches.library.caltech.edu/51/02/CargoCult.pdf. 
• Feynman, Richard P.; Kleinert, Hagen (1986). "Effective classical partition functions". Phys. Rev., A 34 (6): 5080–5084. December 1986. Bibcode 1986PhRvA..34.5080F. DOI:10.1103/PhysRevA.34.5080. PMID 9897894. 

Textbooks and lecture notes[link]

The Feynman Lectures on Physics is perhaps his most accessible work for anyone with an interest in physics, compiled from lectures to Caltech undergraduates in 1961–64. As news of the lectures’ lucidity grew, a number of professional physicists and graduate students began to drop in to listen. Co-authors Robert B. Leighton and Matthew Sands, colleagues of Feynman, edited and illustrated them into book form. The work has endured, and is useful to this day. They were edited and supplemented in 2005 with “Feynman’s Tips on Physics: A Problem-Solving Supplement to the Feynman Lectures on Physics” by Michael Gottlieb and Ralph Leighton (Robert Leighton’s son), with support from Kip Thorne and other physicists.

• Feynman, Richard P. (1970). The Feynman Lectures on Physics: The Definitive and Extended Edition. 3 volumes (2nd ed.). Addison Wesley (published 2005, originally published as separate volumes in 1964 and 1966). ISBN 0-8053-9045-6.  Includes Feynman’s Tips on Physics (with Michael Gottlieb and Ralph Leighton), which includes four previously unreleased lectures on problem solving, exercises by Robert Leighton and Rochus Vogt, and a historical essay by Matthew Sands.
• Feynman, Richard P. (1961). Theory of Fundamental Processes. Addison Wesley. ISBN 0-8053-2507-7. 
• Feynman, Richard P. (1962). Quantum Electrodynamics. Addison Wesley. ISBN 978-0-8053-2501-0. 
• Feynman, Richard P.; Hibbs, Albert (1965). Quantum Mechanics and Path Integrals. McGraw Hill. ISBN 0-07-020650-3. 
• Feynman, Richard P. (1967). The Character of Physical Law: The 1964 Messenger Lectures. MIT Press. ISBN 0-262-56003-8. 
• Feynman, Richard P. (1981). Statistical Mechanics: A Set of Lectures. Addison Wesley. ISBN 0-8053-2509-3. 
• Feynman, Richard P. (1985b). QED: The Strange Theory of Light and Matter. Princeton University Press. ISBN 0-691-02417-0. 
• Feynman, Richard P. (1987). Elementary Particles and the Laws of Physics: The 1986 Dirac Memorial Lectures. Cambridge University Press. ISBN 0-521-34000-4. 
• Feynman, Richard P. (1995). Brian Hatfield. ed. Lectures on Gravitation. Addison Wesley Longman. ISBN 0-201-62734-5. 
• Feynman, Richard P. (1997). Feynman’s Lost Lecture: The Motion of Planets Around the Sun (Vintage Press ed.). London: Vintage. ISBN 0-09-973621-7. 
• Feynman, Richard P. (2000). Tony Hey and Robin W. Allen. ed. Feynman Lectures on Computation. Perseus Books Group. ISBN 0-7382-0296-7. 

Popular works[link]

• Surely You’re Joking, Mr. Feynman!: Adventures of a Curious Character, with contributions by Ralph Leighton, W. W. Norton & Co, 1985, ISBN 0-393-01921-7.
• What Do You Care What Other People Think?: Further Adventures of a Curious Character, with contributions by Ralph Leighton, W. W. Norton & Co, 1988, ISBN 0-393-02659-0.
• No Ordinary Genius: The Illustrated Richard Feynman, ed. Christopher Sykes, W. W. Norton & Co, 1996, ISBN 0-393-31393-X.
• Six Easy Pieces: Essentials of Physics Explained by Its Most Brilliant Teacher, Perseus Books, 1994, ISBN 0-201-40955-0.
• Six Not So Easy Pieces: Einstein’s Relativity, Symmetry and Space-Time, Addison Wesley, 1997, ISBN 0-201-15026-3.
• The Meaning of It All: Thoughts of a Citizen Scientist, Perseus Publishing, 1999, ISBN 0-7382-0166-9.
• The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman, edited by Jeffrey Robbins, Perseus Books, 1999, ISBN 0-7382-0108-1.
• Classic Feynman: All the Adventures of a Curious Character, edited by Ralph Leighton, W. W. Norton & Co, 2005, ISBN 0-393-06132-9. Chronologically reordered omnibus volume of Surely You’re Joking, Mr. Feynman! and What Do You Care What Other People Think?, with a bundled CD containing one of Feynman’s signature lectures.
• Quantum Man, Atlas books, 2011, Lawrence M. Krauss, ISBN 978039306471

Audio and video recordings[link]

• Safecracker Suite (a collection of drum pieces interspersed with Feynman telling anecdotes)
• Los Alamos From Below (audio, talk given by Feynman at Santa Barbara on February 6, 1975)
• Six Easy Pieces (original lectures upon which the book is based)
• Six Not So Easy Pieces (original lectures upon which the book is based)
• The Feynman Lectures on Physics: The Complete Audio Collection
• Samples of Feynman’s drumming, chanting and speech are included in the songs “Tuva Groove (Bolur Daa-Bol, Bolbas Daa-Bol)” and “Kargyraa Rap (Dürgen Chugaa)” on the album Back Tuva Future, The Adventure Continues by Kongar-ool Ondar. The hidden track on this album also includes excerpts from lectures without musical background.
• The Messenger Lectures, given at Cornell in 1964, in which he explains basic topics in physics. Available on Project Tuva for free (See also the book The Character of Physical Law)
• Take the world from another point of view [videorecording] / with Richard Feynman; Films for the Hu (1972)
• The Douglas Robb Memorial Lectures Four public lectures of which the four chapters of the book QED: The Strange Theory of Light and Matter are transcripts. (1979)
• The Pleasure of Finding Things Out (1981) (not to be confused with the later published book of same title)
• Richard Feynman: Fun to Imagine Collection, BBC Archive of 6 short films of Feynman talking in a style that is accessible to all about the physics behind common to all experiences. (1983)
• Elementary Particles and the Laws of Physics (1986)
• The Last Journey of a Genius, a BBC TV production in association with WGBH Boston (1989)
• Tiny Machines: The Feynman Talk on Nanotechnology (video, 1984)
• Computers From the Inside Out (video)
• Quantum Mechanical View of Reality: Workshop at Esalen (video, 1983)
• Idiosyncratic Thinking Workshop (video, 1985)
• Bits and Pieces — From Richard’s Life and Times (video, 1988)
• Strangeness Minus Three (video, BBC Horizon 1964)
• No Ordinary Genius (video, Cristopher Sykes Documentary)
• Richard Feynman — The Best Mind Since Einstein (video, Documentary)
• The Motion of Planets Around the Sun (audio, sometimes titled “Feynman’s Lost Lecture”)
• Nature of Matter (audio)

See also[link]

Notes[link]

References[link]

• Bethe, Hans A. (1991). The Road from Los Alamos. Masters of Modern Physics. 2. New York: Simon and Schuster. ISBN 0-671-74012-1. OCLC 24734608. 
• Edwards, Steven Alan (2006). The Nanotech Pioneers. Wiley. ISBN 978-3-527-31290-0. OCLC 64304124. 
• Feynman, Richard P. (1985). Ralph Leighton. ed. Surely You’re Joking, Mr. Feynman!: Adventures of a Curious Character. W. W. Norton & Co. ISBN 0-393-01921-7. OCLC 10925248. 
• Feynman, Richard P. (1986). Rogers Commission Report, Volume 2 Appendix F- Personal Observations on Reliability of Shuttle. NASA. http://history.nasa.gov/rogersrep/v2appf.htm. 
• Feynman, Richard P. (1987). Ralph Leighton. ed. "Mr. Feynman Goes to Washington". Engineering and Science (Caltech) 50 (1): 6–22. http://calteches.library.caltech.edu/48/2/1987Feynman.pdf. ^{[dead link]}
• Feynman, Richard P. (1988). Ralph Leighton. ed. What Do You Care What Other People Think?: Further Adventures of a Curious Character. W. W. Norton & Co. ISBN 0-393-02659-0. 
• Feynman, Michelle, ed. (2005). Perfectly Reasonable Deviations from the Beaten Track: The Letters of Richard P. Feynman. Basic Books. ISBN 0-7382-0636-9. http://books.google.com/?id=HpgNSVS6fUYC&pg=PA350&dq=feynman+atheist. , foreword by Timothy Ferris. (Published in the UK under the title: Don’t You Have Time to Think?, with additional commentary by Michelle Feynman, Allen Lane, 2005, ISBN 0-7139-9847-4.)
• Gribbin, John; Gribbin, Mary (1997). Richard Feynman: A Life in Science. Dutton. ISBN 0-525-94124-X. 
• Nobel Foundation (1972). "Richard P. Feynman, The Nobel Prize in Physics 1965: Biography". Nobel Lectures, Physics: 1963–1970. Amsterdam: Elsevier. ISBN 978-0-444-40993-5. http://nobelprize.org/nobel_prizes/physics/laureates/1965/feynman-bio.html. 
• Gleick, James (1992). Genius: The Life and Science of Richard Feynman. Pantheon Books. ISBN 0-679-40836-3. OCLC 243743850. 
• Hey, Tony; Walters, Patrick (1987). The quantum universe. Cambridge University Press. ISBN 978-0-521-31845-7. 
• Hillis, W. Daniel (1989). "Richard Feynman and The Connection Machine". Physics Today (Institute of Physics) 42 (2): 78. Bibcode 1989PhT....42b..78H. DOI:10.1063/1.881196. http://www.kurzweilai.net/articles/art0504.html?printable=1. 
• Leighton, Ralph (2000). Tuva Or Bust!:Richard Feynman’s last journey. W. W. Norton & Company. ISBN 0-393-32069-3. 
• LeVine, Harry (2009). The Great Explainer: The Story of Richard Feynman. Greensboro, North Carolina: Morgan Reynolds. ISBN 978-1-59935-113-1. 
• Schwinger, Julian (ed.) (1958). Selected Papers on Quantum Electrodynamics. Dover. ISBN 0-486-60444-6. http://books.google.com/books/about/Selected_papers_on_quantum_electrodynami.html?id=eYrl07GPkYkC. 
• Sykes, Christopher (1996). No ordinary genius : the illustrated Richard Feynman. New York: W.W. Norton. ISBN 0-393-03621-9. 
• "Anti-Clock(1979)". http://www.imdb.com/title/tt0166996/.