## Abstract

The laser, first operated in 1960, produced light with coherence properties that demanded explanation. While some attempted a treatment within the framework of classical coherence theory, others insisted that only quantum electrodynamics could give adequate insight and generality. The result was a sharp and rather bitter controversy, conducted over the physics and mathematics that were being deployed, but also over the criteria for doing good science. Three physicists were at the center of this dispute, Emil Wolf, Max Born’s collaborator on a canonical text on optics as a branch of classical electromagnetism, Roy J. Glauber, a student of Julian Schwinger and a high-energy particle theorist, and Leonard Mandel, both experimentalist and theorist and versed in the physics of photodetection. The story told here is thus one of three distinct research trajectories and of the explosion that occurred when, pushed into the well-financed field of laser studies, these trajectories collided.

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## Notes

Controversies with these two features are, of course, common in the history of science. See Dascal (1998).

See Milonni (1984).

Hasok Chang makes a plea for this sort of situation in Chang (2011).

The history of this experiment and the controversy it aroused are described in Silva and Freire (2013). Some minor mistakes in the description of the Brown–Twiss paper of January 1956 are corrected in

*Historical Studies in the Natural Sciences*Volume 45, #3 (2015).Mandel and Wolf themselves would reverse their opinion, based on Smith and Williams, in an article submitted in February 1963 (Mandel and Wolf 1963, p. 1315).

Golay was at Perkin-Elmer, an important laser firm.

Bracewell’s definition of the degree of coherence is so much like that of Wolf, which I discuss below, that it is worth knowing why he does not cite Wolf.

Wolf discusses his collaboration with Born in detail in Wolf (1983).

Wolf gives some of the progress of his thinking in the 1999 lecture “The Development of Optical Coherence Theory” (Wolf 1999).

See, for example, Wolf (1954).

Even in 1963, Wolf would remark “there seems to be a considerable lack of agreement about the precise meaning of the term ‘coherence’. Yet, in the domain of classical optics, a considerable clarification of this term has been obtained ... and a theory has been formulated which provides a satisfactory description of the majority of coherence effects ... from thermal sources” Wolf (1963b), quotation on p. 29.

Wolf (1963b), quotation on p. 30. This same generalizing tactic is also notable in Wolf’s earlier papers.

Mandel (1954). This, of course, is similar to the pre-World War II papers on how Brownian motion limits the accuracy of galvanometers.

For example, Mandel (1955).

Mandel (1958), quotation on p. 1038. Historical treatments of the wave-particle duality generally treat the pre-World War II period and include Folse (1985), Duncan and Janssen (2008) and Camilleri (2006). For aspects of Mandel’s encounter with Louis de Broglie’s brand of wave-particle dualism, see my manuscript, “Leonard Mandel and Experimental Tests of Quantum Mechanics,” available from the Center for History of Physics at the American Institute of Physics.

Because the uncertainty principle requires that the uncertainty in any one of the three spatial dimensions multiplied by the uncertainty in the conjugate component of the momentum must be equal to or larger than

*h*, the cell must be at least of size \(h^{3}\).Mandel’s use of statistical mechanics may reflect an influence of Reinhold Fuerth, an authority on classical and quantum statistics, who was at Birkbeck College when Mandel studied there and whom Mandel thanks “for some valuable discussions” (Mandel 1958, p. 1046).

Mandel (1961), quotation on p. 797. This high degeneracy was the reason Mandel and Wolf initially thought that the laser would show the HBT effect.

Magyar and Mandel (1963). The paper may be one of many indications of Mandel’s experimental prowess, for the ruby lasers were markedly ill-behaved. Subsequent papers would engage fully with Dirac.

David Kaiser describes life for young theorists at the Institute in these years in Kaiser (2005, pp. 87–93).

Bokulich (2008) discusses precisely this issue.

See the discussion of insight (i.e., understanding), and some references to the literature, in de Regt (2014).

See also note 8 on p. 2534 of his “Quantum Theory of Optical Coherence” (Glauber 1963b).

But Mandel’s conclusion (p. 65) would be “Although semiclassical theories have had considerable success in accounting for many observed effects, ... they fail completely in other cases, and no evidence exists that should cause us to think of giving up Q.E.D. in favor of a semiclassical theory.” See also my discussion of Edwin Jaynes’ crusade against QED in Bromberg (2006).

We may assume that these criteria (simplicity, convenience, generality and so on) reveal not only the authors’ opinions but also their beliefs about what arguments would be persuasive. Hence, they also throw some light on the methodological assumptions abroad in 1960s physics.

The word “function” is used loosely here and does not describe its mathematical status. Glauber addresses the relation between his work and Sudarshan’s in the final paragraphs of Glauber (1963c) and represents the two works as simultaneous and independent.

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## Acknowledgments

I am grateful to Jed Z. Buchwald and Olival Freire Jr. for critical comments on earlier drafts and to Stephen E. Stich and Susan Vasakas for computer help.

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## Appendix

### Appendix

Wolf’s mutual coherence function may be written as

where the angle brackets denote an average over time. His complex degree of coherence is then obtained by normalizing this function (Wolf 1955).

If the absolute value of \(\gamma \) is unity, it is clear that \(\Gamma \) factors into two independent functions, in conformity with Glauber’s prescription for first-order coherence. Wolf’s terminology differs. Since \(\Gamma (P_1 ,P_2 ,\tau )\) connects two different space–time points, he calls it a second-order correlation.

In his 1957 paper on the HBT effect, Wolf calculates the correlation of the fluctuations in intensity at two space–time points. He writes the fluctuation at one of these points as

where

The correlation of the fluctuations at two points is then

For any two random functions *X*(*t*) and *Y*(*t*) that satisfy a two-dimensional Gaussian probability distribution, Wolf proves that

Setting \({X}={V}_{1}\) and \({Y}={V}_{2}\), Wolf is then able to equate the correlation of intensity fluctuations to \(2\langle V_1 \left( t \right) V_2 \left( {t+\tau } \right) \rangle ^{2}=2\Gamma ^{2}\) (In this publication, Wolf uses the symbol J for \(\Gamma \)).

Glauber writes the electric field operator, \(\vec {E}\), as \(\mathop \int \nolimits _{-\infty }^{+\infty } \varvec{e}\left( {\omega ,{\varvec{r}}} \right) e^{-i\omega t}\hbox {d}\omega .\)

Then, \(\vec {E}=\int \nolimits _{-\infty }^{0}\varvec{e}\left( {\omega ,{\varvec{r}}} \right) e^{-i\omega t}\hbox {d}\omega +\int \nolimits _{0}^{+\infty }\varvec{e}\left( {\omega ,{\varvec{r}}} \right) e^{-i\omega t}\hbox {d}\omega =\vec {E}^{-}+\vec {E}^{+}\).

He cites Dirac’s *Principles of Quantum Mechanics *as the authority for interpreting \(\hbox {E}^{+}\) as a photon annihilation operator. When it acts on a state with n photons, it produces a state with (\(n-1\)) photons, while \(\hbox {E}^{-}\) yields an (\(n+1\)) state:

“the probability per unit time that a photon be absorbed by an ideal detector at point **r** at time t is proportional to

Here \({\vert }{i}>\) is the state of the initial field and \({\vert }{f}>\) is the state of the final field and the sum is over all possible final states (\(\mu \) is an index that Glauber used to indicate the photon’s state of polarization) (Glauber 1963b, quotation on p. 2531).

The probability that n photons are absorbed at n photodetectors then becomes

For the case where the initial state of the field is imperfectly known, Glauber invokes the quantum mechanical density matrix and writes \(tr\left\{ {\rho E_{\mu }^{-}\left( {\varvec{r},t} \right) E_{\mu }^{+}\left( {\varvec{r},t} \right) } \right\} =G^{\left( 1 \right) }\left( {\varvec{r}t,\varvec{r}t} \right) \) for the average counting rate of an ideal photodetector. For an n photon coincidence, this becomes \(G^{\left( n \right) }=tr\big \{ \rho E^{-}\left( {\varvec{r}_1 ,t_1 } \right) \ldots E^{-}\left( {\varvec{r}_n ,t_n } \right) E^{+}\left( {\varvec{r}_{n+1} ,t_{n+1} } \right) \ldots E^{+}\left( {r_{2n} ,t_{2n} } \right) \big \}.\) Like Wolf, he arrives at a definition of coherence by normalizing these correlation functions. He sets \(g^{(n)}=G^{(n)}(x_1\ldots x_{2n} )/\prod \nolimits _j {\left\{ {G^{(1)}(x_j ,x_j )} \right\} ^{1/2}} \), where *x* stands for \(\mathbf{r}\) and *t*, and the product is evaluated for *j* ranging from 1 to 2*n*.

“If the field in question possesses nth-order coherence, it must, therefore, have \(g^{(j)}(x_1...x_j ,x_j ...x_1 )=1\) for \(j\le n\). It follows from the definition of the \(g^{(j)}\) that the corresponding values of the correlation functions ... factorize” (Glauber 1963b, 2534–2535).

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Bromberg, J.L. Explaining the laser’s light: classical versus quantum electrodynamics in the 1960s.
*Arch. Hist. Exact Sci.* **70**, 243–266 (2016). https://doi.org/10.1007/s00407-015-0166-8

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DOI: https://doi.org/10.1007/s00407-015-0166-8