Cautious Revolutionaries: Maxwell, Planck, Hubble*

Stephen G. Brush

Department of History and Institute for Physical Science and Technology,

University of Maryland, College Park, Maryland 20742.

(Received 22 August 2001; accepted 12 October 2001)

 

Three scientists exemplified the cautious behavior that we might like all scientists to display: indeed, they were so critical of their own ideas that they risked losing credit for them. Nevertheless they finally earned at least as much fame as they deserved, leaving historians to wonder about what they really believed. Maxwell initially rejected the kinetic theory of gases because two of its predictions disagreed with experiments; later he revived the theory, showed that one of those experiments had been misinterpreted, and eventually became known as one of the founders of the modern theory. Planck seems to have intended his 1900 quantum hypothesis as a mathematical device, not a physical discontinuity; later he limited it to the emission (not absorption) of radiation, thereby discovering "zero-point energy." Eventually he accepted the physical quantum hypothesis and became known as its discoverer. Hubble (with Humason) established the distance-velocity law, which others used as a basis for the expanding universe theory; later he suggested that redshifts may not be due to motion, and appeared to lean toward a static model in place of the expanding universe.

I. INTRODUCTION

It is well known that many successful scientists are very competitive. Having decided that their own discovery or theory is valid and important, they advocate it strongly and persistently, sparing no effort to get it published as fast as possible and to persuade everyone else to accept it. They may even exaggerate the strength of the evidence.1 Is aggressive behavior the only way to make your mark and win the rewards you deserve for your hard work? Is it true that -- as the saying goes -- you must blow your own horn no else will do it for you?

Scientists are also familiar with another kind of personality: the cautious researcher who checks and rechecks every data point and calculation before publishing it, and then eventually presents it in a rather tentative way not as a solid discovery, but a plausible hypothesis or experimental result whose ultimate significance remains to be determined. This kind of scientist may find great personal satisfaction in adding one more brick to the edifice of Scientific Knowledge, but rarely enjoys recognition by the public or great praise from other scientists. (Contrary to the egalitarian beliefs of some writers on science, only a small percentage of scientists do almost all the research that goes to form the core of established scientific knowledge.2) Sometimes these scientists are so discouraged by the rejection or silence of the scientific community that they drop out of research altogether.

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*Reprinted with permission from American Journal of Physics 70(2), 2002, pp 119-127. Copyright 2002, American Association of Physics Teachers. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Association of Physics Teachers.

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"Cautious" does not mean "non-competitive." The scientists I have in mind were certainly eager to make important discoveries and receive credit for them. They were cautious only in their public announcements. They would rather be right than first; their fear of being later found to have made a crucial mistake outweighed their fear of being scooped.

This paper deals with three exceptions to the above generalizations: scientists who presented their discoveries so cautiously that they might well have lost the credit for them to other, more aggressive scientists. Yet their publications did get cited, did arouse enthusiastic support from a few influential readers, and eventually earned for their authors at least as much recognition as they deserved. They probably did not think of themselves as "revolutionaries" but we may use that word when considering the impact of their achievements.

There is a common theme linking the ideas of Maxwell, Planck, and Hubble: the nature and significance of heat in space, called at various times since 1800 "infrared radiation," "radiant heat," " black body radiation," and, more recently, "cosmic microwave background radiation."3

II. MAXWELL

The Scottish physicist James Clerk Maxwell (1831-1879) is now known as a brilliant leader in two major areas: the statistical-molecular theory of gases and heat, and the electromagnetic theory of light and radiation.4 His work in the first led not only to the earliest generally-accepted estimate of the size of an atom (by Josef Loschmidt) but provided part of the foundation for the so-called "Probabilistic Revolution" that affected all areas of science between 1840 and 1940.5 His electromagnetic theory was confirmed by Heinrich Hertz's discovery of electromagnetic waves, which in turn led to remarkable advances in physics, astronomy, and technology.

In the 19th century, the value of Maxwell's work was appreciated by experts working on similar problems, but in the scientific community as a whole his achievements were less famous than those of Kelvin or Helmholtz. For example, when Albert Einstein studied at the Swiss Federal Polytechnical School ("ETH"), Maxwell's electromagnetic theory was not covered in any of the courses there so he had to study it on his own.6 In the 20th century, scientists belatedly realized that Maxwell's ideas had permanent value. His velocity distribution law still provides the basis for statistical mechanical calculations of the properties of fluids over the wide range of conditions where quantum effects are negligible or can be taken into account by adjusting parameters. His electromagnetic equations survived the Relativity Revolution and became an indispensable tool for electrical engineers as well as physicists. Astronomers continue to learn more about the universe by probing its messages through the spectrum of electromagnetic radiation predicted by those equations, while the rest of us learn perhaps more than we really need to know about human misbehavior from television. If the British counted their blessings more accurately they would give thanks to Maxwell for the help they got from radar in surviving the attacks of Hitler's bombers in 1940.

Physicist-historian Francis Everitt writes that Maxwell had an "architectural" mind. In contrast to Michael Faraday, who "worked by gradually collecting large arrays of facts," and Lord Kelvin, who "would take up a subject, work at it furiously for a few weeks, throw forth a string of novel ... ideas, and then drop everything and pass on," Maxwell prepared a few long papers, each giving "a new coherent view of some large subject, concise, complete in itself, yet opening the way to further discovery."7

Maxwell did not always follow a preconceived plan in developing his ideas: he sometimes first proposed a radically-speculative or artificial model to test his own understanding of the physics of a system, only to abandon it later in favor of a bold physical hypothesis or a more abstract mathematical formulation that did not commit him to any particular fundamental theory. Each plan was complete in itself though different from the others. In his 1861-62 paper "On Physical Lines of Force," Maxwell employed a mechanical model for electromagnetic interactions, in which magnetic lines of force (or magnetic field lines) were represented by vortices in a fluid ether. Small particles, described as ball bearings or idle wheels, were placed in the spaces between adjacent vortices; their function was to transmit the mechanical force from one vortex to another. If two neighboring vortices were rotating at the same rate, each particle would simply rotate in the opposite direction around a fixed point; but if one vortex spins faster than its neighbor, the particle would have a net translational motion in addition to its rotation. Maxwell showed that this translational motion corresponds to the electric current induced by a spatial variation in magnetic field lines. Thus the model, which eventually led him to his general theory of electric and magnetic fields, seemed to suggest that an electric current is a stream of particles. But in his later work on electromagnetic theory, Maxwell abandoned this model in favor of a set of equations relating the electric and magnetic fields. Everitt writes that "Maxwell's retreat from the vortex aether was an act of scientific caution."8 Elsewhere Maxwell considered more explicitly the idea that electricity might be composed of atomistic charged particles, exerting forces on each other, and rejected it. Instead, he preferred to deny action at a distance and attributed electric action "to tensions and pressures in an all-pervading medium."9

So Maxwell missed the discovery of the electron, but he also missed the mathematical vexations that frustrated all attempts to develop a consistent theory of the electron before the advent of relativity and quantum mechanics. Moreover, his general theory of electromagnetic waves eventually provided a place for forms of radiation other than light; in 1865 he wrote "we have strong reason to conclude that light itself (including radiant heat, and other radiations if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field."10

III. MAXWELL REJECTS THE KINETIC THEORY

At the time when Maxwell began his work on kinetic theory, that theory had already been formulated by several scientists, starting with Daniel Bernoulli in the 18th century. But it seemed incompatible with ideas about ether and the caloric theory of heat in the first half of the 19th century. It was not until mid-century that the general acceptance of the Law of Conservation of Energy made it plausible to think of heat as a form of molecular motion rather than a substance. But even then, there was some doubt about whether a molecule could simply move at constant speed in a straight lines until it collided with another molecule (or with the solid wall of its container); if, as was generally believed, space had to be filled with ether in order to allow the transmission of light according to the wave theory, wouldnít that ether resist the motion of molecules? Some physicists resolved that dilemma by postulating that molecules vibrated or rotated without much change in the position of their centers of gravity. Others argued that since radiant heat had been found to have wave properties similar to light, heat in general should be considered a wave motion of the ether. It was by no means clear in the 1850s that a gas theory that ignored the ether and radiant heat, while identifying temperature with the kinetic energy of molecules, could be successful.

When Maxwell first worked out his theory of a system of colliding elastic spheres, ignoring the ether and allowing the spheres to move freely through space, he was surprised to find that the velocity of the system would be independent of its density. (In his model, viscosity was attributed to the drift of molecules from fast-moving layers to slow-moving layers of gas; collisions of fast and slow molecules would tend to transfer momentum from faster to slower molecules. At higher densities, collisions would be more frequent but each collision would transfer less momentum.) He asked G. G. Stokes, an expert on the properties of fluids, if there were any experimental data available to test this prediction. Stokes told Maxwell about an 1829 observation of E. Sabine, which according to Stokes's own analysis indicated that the viscosity of a gas does vary with density. Thus in his 1860 paper on kinetic theory, referring to his theoretical prediction that viscosity should be independent of density, Maxwell wrote:

 

"Such a consequence of a mathematical theory is very startling, and the only experiment I have met with on the subject does not seem to confirm it."11

Maxwell also presented in this paper a theorem now known as the Equipartition Theorem (previously suggested by Waterston): in a system of particles in thermal equilibrium, each mechanical degree of freedom will have on the average the same kinetic energy . For example, if a gas such as oxygen is composed of diatomic molecules, and if a molecule is regarded as a system of two point masses bound together by any kind of force, or as a nonspherical particle, it will have 6 degrees of freedom: 3 for the motion of the mass (in the x, y and z directions) and 3 for the rotation around 3 possible axes. Then it follows from the Equipartition Theorem that the ratio of the specific heats at constant pressure and constant volume must be 4/3.

But careful experiments had shown that the actual ratio of specific heats of most diatomic gases is close to 1.40, significantly greater than 1.33. This result, Maxwell insisted, "seems decisive against the unqualified acceptance of the hypothesis that gases are such system of hard elastic particles. His 1860 paper ended with the sentence:

 

"Finally, by establishing a necessary relation between the motions of translation and rotation of all particles not spherical, we proved that a system of such particles could not possibly satisfy the known relation between two specific heats of all gases."12

Maxwell was even more emphatic about the failure of the kinetic theory to predict the right values of specific heats in the summary of a paper he read to the Oxford meeting of the British Association for the Advancement of Science:

 

"This result of the dynamical [kinetic] theory, being at variance with experiment, overturns the whole hypothesis, however satisfactory the other results may be."13

In spite of these statements Maxwell did not consider Sabine's experiment, as analyzed by Stokes, a sufficiently conclusive refutation of the kinetic theory to justify abandoning it completely. Stokes himself found that the results of Thomas Graham's experiments on the rate of flow of gases through narrow tubes were consistent with the assumption that viscosity is independent of density, but not with the alternative assumption that it is proportional to density. Maxwell wrote to a friend,14

 

"This seems rather a curious result, and an additional phenomenon explained by the 'collisions of particles' theory of gases. Still one phenomenon goes against that theory -- the relation between specific heat at constant pressure and at constant volume, which is in air 1.408, while it ought to be 1.333."

Obviously a direct measurement of viscosity was needed. Maxwell went to considerable effort to design and carry out his own experiments, with the help of his wife Katherine. He found that the viscosity of air, at a given temperature, remained constant when the pressure was varied between a half-inch and 30 inches of mercury, and this result, in agreement with research already published by O. E. Meyer, was confirmed by other physicists.

It turned out eventually that in computing the viscosity of air from Sabine's pendulum experiment, Stokes had implicitly assumed that the viscosity decreases in proportion to the density. That was a natural assumption for anyone to make before 1859; it must be valid in the limit of zero density, since if there is no gas present it canít exert any viscous force. It was only with the help of Maxwell's theory (based on assumptions that obviously would not apply in the zero-density limit) that one could correctly interpret the experiments designed to test the theory. So the outcome was not a refutation of the theory but a rather surprising and convincing confirmation of it. The alternative "static" theory of gases would certainly lead one to expect that viscosity should increase with density, as it in fact does for a liquid. Lord Rayleigh later wrote that "in the whole range of science there is no more beautiful or telling discovery than that gaseous viscosity is the same at all densities."15

Maxwell did not make any further attempt to resolve the other argument against the kinetic theory: its failure to explain the ratio of specific heats of diatomic gases. The theory predicted a value corresponding to six degrees of freedom, but experiments led to a ratio corresponding to only five. Ludwig Boltzmann and (independently) R.H. M. Bosanquet proposed that the sixth degree of freedom of such molecules might be unaffected by collisions and therefore would not contribute to the specific heat. About the same time (mid-1870s) it was discovered by A. Kundt and E. Warburg that the ratio for mercury vapor is almost precisely 1 2/3, the value predicted for a monatomic gas. Thus one could argue that the kinetic theory of specific heats is fundamentally sound but needs some minor adjustment to deal with diatomic (and polyatomic) molecules.

But Maxwell refused to accept this solution on the grounds that it was not strictly deducible from any consistent mechanical model. He argued that none of the existing molecular models were wholly compatible with the properties of real gases. His view was that in theoretical physics one must maintain a high standard of mathematical rigor, even if this "leaves us no escape from the terrible generality" of the results: one can accept a theory as the best available at the time while at the same time recognizing oneself to be in a "state of thoroughly conscious ignorance which is the prelude to every real advance in knowledge."16

In hindsight, Maxwell's caution was inspired. The "paradox of specific heats" did turn out to be an anomaly of Newtonian mechanics, which could be resolved only with the help of quantum theory in the 20th century.

IV. PLANCK

The German physicist Max Planck (1858-1947) is generally considered to be the father of quantum theory, a theory that governs most physical and chemical phenomena. In addition to yielding accurate predictions of the observable properties of matter and radiation, quantum theory opens up to experimental testing some fascinating metaphysical questions.

In his biography of Planck, historian of science John Heilbron remarks: "A conservative in the root meaning, his particular effectiveness lay in his ability to adapt to, and even direct, current realities while saving, and acting on, traditional values ... he did not run after novelties." As a secretary of the Berlin Academy, Planck "always stayed cool and reasonable"; in controversies he played a moderating role.17

In addition to his quantum theory, Planck is also known for his view that scientists generally react cautiously to new ideas:

 

"A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it."18

This assertion, known to sociologists of science as "Planck's Principle," is often interpreted to mean that older scientists are likely to resist radical new ideas while younger scientists are more likely to welcome them.19

V. PLANCK REJECTS THE QUANTUM HYPOTHESIS

In the 1890s Planck was interested in the problem of "black body radiation": how does the thermal equilibrium distribution of electromagnetic waves in space depend on temperature and frequency? Thanks to Maxwell's electromagnetic theory, one could treat this problem -- heat in space --separately from the kinetic theory of gases, which dealt with heat as a mode of motion of atoms and molecules.20

In October 1900 Planck presented to the Berlin Physical Society a new formula for the frequency distribution of black-body radiation. The formula provided a very good fit to the latest experimental results so Planck tried to find a theoretical derivation of it. He had already developed a somewhat abstract model of "resonators" that are in thermal equilibrium with the radiation, and he already knew from his earlier thermodynamic analysis that the entropy of the system could be represented by a logarithmic formula, somewhat similar to Boltzmann's well-known formula for the entropy S of a system of molecules written in terms of the number of ways W of distributing the total energy of the system among them. In modern texts Boltzmann's formula is written S = k log W, where k is called "Boltzmann's constant." Boltzmann himself did not use this simple form because he recognized that if a molecule can have any energy on a continuous scale, W would be infinite; so he always wrote his formula for a difference of entropies between two states of the system and the logarithm of the ratio of corresponding values of W, giving finite quantities on both sides of the equation. He often calculated the values of W for the two states by assuming that energy was divided into discrete steps, calculating the ratio of the two values of W and finally taking the limit when the step size becomes zero. Planck followed this general approach though he did not precisely follow Boltzmann's procedure.

In his second 1900 paper, Planck assumed that the total energy of the resonators, E, is divided into P elements, each of energy ε = hν, where the new constant of nature h = 6.55 x 10-27 erg sec (now called "Planck's constant") and ν is the frequency of the resonator. If P is an integer one can calculate W. But, Planck wrote, if P "is not an integer, we take for P an integer in the neighborhood."21 [Emphasis added]

As the historian of science Olivier Darrigol points out, the last sentence "leaves no reason for doubt": "the energy of a single resonator was not thought to be restricted to multiples of ε."22 Planck was not actually proposing quantization of the resonator energies as a physical hypothesis, but only as a mathematical approximation to allow the use of a combinatorial formula for W: the number of ways of distributing something must be an integer. This allowed him to derive the empirically-correct distribution function for black-body radiation and, along with it, the new fundamental constant h; but it did not directly prove the validity of a quantum hypothesis.

This interpretation is consistent with Thomas Kuhn's argument, based on a comprehensive analysis of Planck's papers before and after 1900, that he did not propose a physical quantization in his 1900 paper. It was only in 1905 that such a hypothesis was proposed by Albert Einstein, in what is usually called his "photoelectric effect" paper.23

Kuhn's thesis was rejected or ignored by physicists and historians of physics for several years, but has recently started to gain support.24 One additional piece of evidence, which I have not seen cited by any historian in this connection,25 is in Planck's Nobel Lecture. Discussing the introduction of the constant h, he said it could be interpreted in two ways. It might be just a "fictitious quantity, in which case all the deductions from the radiation theory were largely illusory and were nothing more than mathematical juggling." Alternatively one could assume that "the radiation theory is founded on actual physical ideas ... - something quite new ..." replacing the "assumption of continuity of all causal relations." Which was it to be? To that question Planck gave the answer:26

 

"Experience has decided for the second alternative. That this decision should be made so soon and so certainly is not due to the verification of the law of distribution of energy in heat radiation, much less to my special derivation of the law, but to the restless, ever-advancing labour of those workers who have made use of the quantum of action in their investigations.

 

"The first advance in this work was made by A. Einstein..."

Presumably those who heard or read this statement, already "knowing" that Planck himself had discovered the quantum theory, assumed he was just being gracious in giving maximum credit to Einstein. I suggest we at least consider the possibility that his statement is literally correct.

On the other hand, one should note that when Planck rewrote and expanded his 1900 papers for publication in Annalen der Physik in 1901, he omitted the statement that if the number of quanta is not an integer one should take the nearest integer.27 Thus if you insist on giving the credit to Planck for originating the quantum theory, your case is a little stronger if you cite his 1901 paper rather than just the brief 1900 announcement.

My description of Planck as a cautious revolutionary does not depend only on the validity of Kuhn's and Darrigol's interpretations of his 1900 paper but also on the following facts, which do not seem to be controversial:

(1) Even in the 1900 paper he never suggested (as Einstein did in 1905) that electromagnetic radiation in space is quantized; his quantum hypothesis, whether physical or mathematical, applies only to the amount of energy possessed by a resonator and to the amount that can be emitted or absorbed.

(2) The next year he retreated from that position, denying for example that the absorption of energy is quantized and suggesting that the resonator in general will possess a non-integer number of quanta. But this cautious behavior did not cost him the credit for inventing the quantum hypothesis; in fact it led indirectly to a new discovery.

(3) In Planck's 1910 paper on the theory of heat radiation, he refused to accept Einstein's hypothesis that electromagnetic radiation is quantized. Planck warned that one should not be so hasty in throwing out the wave theory of light, after all the struggles to establish it and all its successes in explaining and predicting so many phenomena. He still believed in the strict validity of Maxwell's equations for empty space, thus excluding the possibility of discrete energy quanta in a vacuum.28

(4) The following year Planck published a "new radiation hypothesis."29 He now argued that his original assumption -- that a resonator can absorb energy only in discrete amounts --is really untenable, because of the following thought experiment. Suppose the oscillator is irradiated with radiation of very low intensity. In this case it will take a long time for the incoming energy to add up to the required quantum value h ; this is especially true for high-frequency radiation, which is present only in small amounts according to the Planck distribution formula. But one can simply remove the source of radiation after a short time, before a single quantum has been absorbed. The resonator will then have absorbed only part of a quantum and cannot get any more, in contradiction to the hypothesis that absorption can occur only in integer multiples of a quantum. Because of this difficulty, Planck assumed instead that absorption is continuous, while emission is discrete.

According to Planck's new hypothesis, a resonator will in general have energy

U = n + x

where n is an integer and x can have any value between 0 and 1. Now suppose we cool down a large number of such resonators to absolute zero temperature, allowing each to emit all of its n quanta. Then the remaining energies of the resonators will be distributed uniformly between 0 and 1, with the average value being 2ε = 2hν. Thus Planck discovered what was later called (and derived from quantum mechanics) the zero-point energy of a quantum system. Contrary to classical physics, atomic particles still have a finite amount of energy even at absolute zero temperature.


VI. HUBBLE

The American astronomer Edwin P. Hubble (1889-1953) is widely known as the founder of the "expanding universe" concept, which provided the empirical basis for the 20th-century revolution in cosmology. Using the period-luminosity correlation for Cepheid variable stars, discovered by Henrietta Swan Leavitt at the Harvard Observatory, Hubble was able to estimate the distances of a number of galaxies. Vesto Melvin Slipher at the Lowell Observatory in Arizona had measured the shifts of lines in the spectra of these galaxies, and found that most of them were toward the red end of the spectrum; if they are due to the Doppler effect, these "red shifts" can be used to compute the speed at which the galaxies are moving away from us. Combining the distances d with the speeds v, Hubble proposed in 1929 his famous law, now written in the form v = Hd, where H is "Hubble's constant." In words, each galaxy (on the average) is moving away from us at a speed proportional to its distance. The simplest interpretation of Hubble's Law is that the galaxies were once very close together and have been moving apart since then, so that the universe is gradually expanding at a constant rate; the beginning of the expansion was 1/H years ago.

Norriss Hetherington, an historian of science who has thoroughly examined Hubble's publications and manuscripts, points out that his approach to science was strongly influenced by his early training and experience in law: "Reading Roman law in Oxford [where he was a Rhodes Scholar] and practising as an attorney in the United States were good preparation for a subsequent career in science."30 Knowing that any evidence presented in court would face critical scrutiny by lawyers for the other side, one must forestall valid criticism by finding and fixing any weaknesses in one's case before going to court. Scientists must realize that their observations can be affected by their own theoretical preconceptions, and shouldnít be trusted until checked by others who donít have a vested interest in getting a particular result. Hubble wrote to a junior colleague whose independent observations might provide strong support for Hubble's views: "keep a skeptical point of view and look for discrepancies rather than consistency."31 Hubble's reputation as an astronomer would be endangered if it turned out that he had overlooked important negative evidence in his zeal to establish the Expanding Universe.

VII. HUBBLE REJECTS THE EXPANDING UNIVERSE

Following the publication of Einstein's general theory of relativity in 1916, Willem de Sitter and other astronomers explored cosmological models in which stars moved (or appeared to move) away from us at speeds proportional to their distance, so that the universe as a whole is expanding. Hubble probably learned about de Sitter's theory at an international conference in 1928, and asked his collaborator Milton L. Humason to obtain observational evidence to test it.

In his 1929 paper, Hubble proposed a "roughly linear relation between velocities and distances among nebulae" but did not mention the inference that the universe of nebulae (galaxies, we would now say) is expanding, though other astronomers were quick to make that inference.32 In 1930, annoyed because de Sitter had failed to give him explicit credit for discovering the velocity-distance relation, Hubble wrote to de Sitter:

 

The possibility of a velocity-distance relation among nebulae has been in the air for years -- you, I believe, were the first to mention it. But our preliminary note in 1929 was the first presentation of the data where the scatter due to uncertainties in distances was small enough as compared to the range in distances to establish the relation. In that note, moreover, we announced a program of observations for the purpose of testing the relation at greater distances ... the results have steadily confirmed the earlier relation. For these reasons I consider the velocity-distance relation, its formulation, testing and confirmation, as a Mount Wilson contribution and I am deeply concerned in its recognition as such.33

Nothing modest or cautious about that!

But Hubble and Humason almost immediately started to back away from their claim to have discovered a velocity-distance relation, substituting the more empirical claim that they had found a redshift-distance relation, without committing themselves as to whether the redshift is due to velocity or some other cause. In 1931 Humason wrote "It is not at all certain that the large red-shifts observed in the spectra are to be interpreted as a Doppler effect, but for convenience they are expressed in terms of velocity and referred to as apparent velocities."34

In later years Hubble consistently avoided any definite statement that the red-shifts of distant galaxies are due to motion (though he admitted that this interpretation did apply to nearby ones) or that the universe is actually expanding. Thus one may say that Hubble "discovered the expanding universe" in the same sense that Planck "discovered the quantum": he established an empirical formula that seemed to imply the theory and indeed led others to adopt it (and later to assume that he must have adopted it himself) -- yet he drew back from explicitly advocating it as a true statement about the world, and even on some occasions suggested that the theory is false.

One reason for Hubble's caution was that the "age of the universe" estimated from his redshift-distance relation using the data available in the 1930s, if one assumes that the redshifts are due to motion, would be only about 2 billion years. The British astronomer-physicist James Jeans had estimated that the stars are roughly 1000 times as old as that, assuming that they derive their energy from the mutual annihilation of positive and negative particles.35 Hubble was probably alluding to this estimate when he remarked in 1934 that 2 billion years is a "suspiciously short time scale -- a small fraction of the estimated age of some stars -- and

 

"the apparent discrepancy suggests the advisability of further discussion of the interpretation of red-shifts as evidence of motion. ... the cautious observer refrains from committing himself to the present interpretation and employs the colorless term 'relative velocity.'"36

While Hubble conceded that the Doppler interpretation of red shifts may be provisionally accepted "until evidence to the contrary is forthcoming" and is in fact "widely accepted" by cosmologists, it cannot be considered definitely established. And, as he often did in lectures and popular articles during the 1930s and 1940s, he put in a plug for an on-going project: "The 200-inch telescope [not completed until 1948] will definitely answer the question of the interpretation of red-shifts, whether or not they do represent motions."37

The Jeans time scale was abandoned by other astronomers in the 1930s as other sources of stellar energy were investigated. But another problem had already arisen, from geochronology: the age of the Earth, estimated from radiometric dating, is probably at least 3 billion years. This discrepancy led several cosmologists to revise the simple assumption of uniform expansion of the universe, and was one of the reasons why Fred Hoyle, Hermann Bondi and Thomas Gold proposed their "steady state" cosmology in 1948.38

In the meantime Hubble's work with the American cosmologist Richard C. Tolman led to another way to answer the question. They looked at two simple models based on the assumption that red-shifts (a) are or (b) are not velocity shifts, and applied them to the observational data on the distribution of galaxies. For (a), the universe "is represented by a homogeneous expanding model obeying the relativistic laws of gravitation" while for (b), they used "a static Einstein model of the universe, combined with the assumption that photons lose energy on their journey to the observer by some unknown effect..." This alternative kind of redshift was apparently inspired by the speculations of F. Zwicky and W. D. Macmillan, and was later called the "tired light" hypothesis.39 The conclusion of the Hubble-Tolman collaboration was that model (a) could be made to fit the data only by assuming a rather high curvature, high density and small size of the universe; it would imply that the "average" nebulae now observed emitted their light about 300 million years in the past, nearly comparable to the "time of cosmic expansion -- possibly of the order of 109 to 1010 years."36 Model (b) was more satisfactory.

Hubble did not explicitly advocate the tired light hypothesis, rather he took the position that it was not his responsibility as an observer to determine the correct theoretical interpretation of his data. But he went further than that, with rather explicit statements that the "expanding models are definitely inconsistent with the observations unless a large positive curvature (small, closed universe) is postulated," which gives an unreasonably high density as well as a "small scale both in space and time."41 On the other hand the non-expanding model (b) gives a "rather simple and thoroughly consistent picture." It is "more economical and less vulnerable, except for the fact that, at the moment, no other satisfactory explanation [of the red shift] is known." Moreover, the expanding model (a) assigns a unique location to the observer [we are at the center of the expansion] which is "unwelcome and a priori improbable."42

Hubble continued to express skepticism about the validity of the expanding universe up until the time of his death in 1953, citing both the astronomical data, which favored a static model, and geochronology, which gave an age of the earth greater than the age of the allegedly-expanding universe.43

The conflict between astronomical and geological time scales was eliminated in the 1950s when the astronomers revised their distance scale. This was in part due to new observations made with the 200-inch telescope which, as Hubble had predicted, resolved the red-shift problem and put the expanding-universe theory on a firmer foundation. By doubling and then quadrupling (or more) the distances of most galaxies, these observations increased the age of the universe to more than 10 billion years, at least twice the age of the earth even when the latter was increased to its current value of about 4.5 billion years. If Hubble had lived just a few more years he probably would have accepted the expanding universe theory.

While the expansion of the time-scale removed one of the justifications for the steady-state cosmology, Hoyle and other British scientists continued to support it as an alternative to the "big bang" cosmology developed by Lemaître, Gamow, Alpher and Herman. That controversy was finally settled in favor of the big bang by the confirmation in 1965 of the prediction that the universe should now be permeated by black body radiation. The discovery of this "cosmic microwave background radiation" by Penzias and Wilson, and the subsequent verification that its frequency distribution fits Planck's formula fairly well, persuaded astronomers (except Hoyle and a few of his followers) to abandon the steady state theory.44 Further analysis of this radiation is now uncovering clues to the early history of the universe.


VIII. SHOULD SCIENTISTS BE CAUTIOUS?

Scientists are often advised to be severely critical of their own theories and data, to find their defects before publication rather than suffer the embarrassment of having others find them. But once a discovery is published, it seems necessary to defend it vigorously, in order to preserve one's reputation and increase the chances of getting resources (grants, tenure) to do more research. Even worse than making a mistake is the nightmare of seeing someone else get the credit for your discovery because you didnít publish it quickly or prominently enough. Worst of all, it might seem, is to publish an idea, then later announce that it is wrong, then even later, after your work has been forgotten, learn that it was really right after all!

Maxwell, Planck, and Hubble deserve our respect for following the rules of the game even when it was against their own short-term interests to do so: to insist on high standards of mathematical reasoning and empirical proof at the risk of losing the credit for their discoveries. Each story had a happy ending in the 20th century. Maxwell is generally acknowledged as one of the major creators of the kinetic theory of gases even though he didnít resolve the specific heats anomaly. Planck is widely regarded as the father of the quantum theory even though, as Frank Sulloway says, he was a "cautious laterborn" who "spent a lifetime resisting [his own] radical insights."45 Hubble is almost universally considered the founder of the expanding universe theory46 in spite of his reluctance to advocate it. Were they just lucky to get so much credit for these achievements?

Maxwell's case is a little different from the others because he saw fairly soon that the "refutations" he produced for the kinetic theory were either based on dubious data or affected only a small part of the domain of the theory; they donít affect the validity of the greater part of his work and the viscosity problem may even have inspired him, at least indirectly, to develop his more sophisticated formulation (not relying on the mean-free-path approximation). Even if his early doubts had been more widely known, they would have had little effect on his reputation or his place in the history of science.

The Planck case is more controversial: he was perhaps initially more confused than cautious, become cautious later on in restricting quantization to emission. Kuhn's thesis met with strong resistance from physicists who felt that it was unfair to take credit away from Planck and give it to Einstein, who already had so much credit for relativity. Planck (unlike Maxwell and Einstein), did not have a lot of other widely-recognized achievements: the quantum was his major claim to fame. One wonders how many physicists actually read Planck's 1900 papers before Einstein published his version of quantum theory in 1905, and whether his contribution would have been considered so important if Einstein, Bohr and others had not developed it much farther than Planck was willing to.

The persistence of the belief that Hubble advocated the expanding universe theory is puzzling, since his opposition to it was widely known in the astronomical community during his lifetime. A science journalist reported that the 1935 Hubble-Tolman analysis "which casts doubt on the reality of the expansion ... has come like a bombshell into the camp of the theorists and is providing a major topic of conversation among astronomers, cosmologists, mathematicians and other universe explorers."47 Several astronomers who knew Hubble, and historians who have examined the original sources, agree that he rejected the velocity interpretation of red-shifts and was skeptical about the reality of expansion.48 Yet this knowledge does not seem to have spread to the younger generation of astronomers and science writers.

Nevertheless our three cautious revolutionaries do deserve the credit they now receive. Maxwell did discover that gas viscosity is independent of density, and he did lay the foundations for the modern kinetic theory. Planck did propose the first quantum theory (even if it was intended only as a mathematical fiction). Hubble was the first to support with solid evidence a velocity-distance law for nebulae.

Historians of science are now skeptical of the concept of "discovery" as a discrete event for which a particular person or persons should get "credit" or "priority." It is not the job of the historian to decide who should get credit for a discovery, but rather to study who does get credit and why. If in these three rather important cases credit was given to someone who actually followed the rules about how scientists should behave, by being cautious and self-critical about the validity of a result even after it was published, then perhaps we do not have to believe that credit always goes to the wrong person49 or that aggressive self-promotion and exaggeration is the best way to become a successful scientist. Maybe nice guys do not always finish last.


ACKNOWLEDGMENTS

This paper is based on research supported in part by a Fellowship from the John Simon Guggenheim Memorial Foundation, and by the General Research Board of the University of Maryland. For important improvements and corrections I thank Phyllis Brush, Francis Everitt, Norriss Hetherington, Patrick McCray, and Spencer Weart.


REFERENCES AND NOTES

1. F. Reif, "The Competitive World of the Pure Scientist," Science 134 (1961), 1957-1962. Some of the evidence for Reif's description of this world is disputed by R. V. Pound, "Weighing Photons, II" Physics in Perspective, 3 (2001), 4-51. See also S. G. Brush, "Should the History of Science be Rated X?" Science, 183 (1974), 1164-1172; Donald Kennedy, "Good News, Bad News," Science 293, 761 (2001), and (for a specific recent example) Charles Seife, "Berkeley Crew Unbags Element 118," Science 293, 777-778 (2001).

2. "Experimental science has progressed thanks in great part to the work of men astoundingly mediocre, and even less than mediocre. That is to say, modern science, the root and symbol of our actual civilization, finds a place for the intellectually commonplace man and allows him to work therein with success. ... In this way the majority of scientists help the general advance of science while shut up in the narrow cell of their laboratory, like the bee in the cell of its hive." José Ortega y Gasset, Revolt of the Masses, translated from the Spanish edition of 1930 (Norton, New York, 1932), pp. 122-23. This thesis, now known by sociologists of science as the "Ortega Hypothesis," has been refuted (at least for modern physics) by Jonathan R. Cole and Stephen Cole, "The Ortega Hypothesis," Science, 178 (1972), 368-75. The basic premise goes back to Francis Bacon; see his New Organon (1620), available in several modern editions. He argued that anyone of moderate intelligence could make significant contributions to science by diligently following the correct (i.e., Baconian) method. While he used his method to provide inductive evidence that heat is atomic motion, Bacon is notorious for his refusal to accept Copernican astronomy and Gilbert's geomagnetic theory.

3. For general background, details and references see the book by Gerald Holton and Stephen G. Brush, Physics, The Human Adventure: From Copernicus to Einstein and Beyond (Rutgers Univ. Press, New Brunswick, NJ, 2001) and its website bibliography.

4. This and the following sections are based mostly on my book The Kind of Motion We Call Heat: A History of the Kinetic Theory of Gases in the 19th Century (North-Holland/American Elsevier, Amsterdam & New York, 1976). For biographical information see C. W. F. Everitt, James Clerk Maxwell: Physicist and Natural Philosopher (Charles Scribner's Sons, New York, 1975); Lewis Campbell and William Garnett, The Life of James Clerk Maxwell, with a New Preface and Appendix with Letters by Robert H. Kargon (Johnson Reprint Corp., New York, 1969). A complete scholarly edition of his letters and papers is being published by P. M. Harman, The Scientific Letters and Papers of James Clerk Maxwell (Cambridge University Press, New York, 1990-). A good philosophical discussion of Maxwell's kinetic theory is given by Peter Achinstein, Particles and Waves: Historical Essays in the Philosophy of Science (Oxford University Press, New York, 1991).

5. The Probabilistic Revolution, edited by Lorenz Krüger et al. (MIT Press, Cambridge, MA, 1987).

6. The Collected Papers of Albert Einstein, Volume 1, edited by John Stachel et al. (Princeton University Press, Princeton, 1987), p. xxxix. See also Bruce J. Hunt, The Maxwellians (Cornell University Press, Ithaca, NY, 1991); Jed Z. Buchwald, From Maxwell to Microphysics: Aspects of Electromagnetic Theory in the Last Quarter of the Nineteenth Century (University of Chicago Press, Chicago, 1985).

7. C. W. F. Everitt, "Maxwell's Scientific Creativity," in Springs of Scientific Creativity, edited by Rutherford Aris, H. Ted Davis & Roger H. Stuewer (Univ. of Minnesota Press, 1983), 71-141, quote on p. 119.

8. Reference 7, p. 129. According to Sir Ambrose Fleming, Maxwell once said that "Because we can imagine a mechanism which can achieve some result we find in Nature, it does not in the least follow that it is done in that way." Fleming, "Physics and Physicists of the Eighteen Seventies," Nature, 143, 99-102 (1939), on p. 102.

9. Maxwell, "Address to the Mathematical and Physical Sections of the British Association," Report of the 40th Meeting of the British Association for the Advancement of Science (1870), 1-9; reprinted in Maxwell on Molecules and Gases, edited by E. Garber, S. G. Brush & C. W. F. Everitt (MIT Press, Cambridge, MA, 1986), pp. 90-104, quotation from p. 103. See also Maxwell's A Treatise on Electricity and Magnetism, 3rd edition (1891, Dover reprint 1954), vol. 1, pp. 380-81. For a detailed discussion of Maxwell's views see Jed Buchwald, From Maxwell to Microphysics (Ref. 6), Chapter 3; Daniel M. Siegel, Innovation in Maxwell's Electromagnetic Theory: Molecular Vortices, Displacement Current, and Light (Cambridge University Press, New York, 1991); essays by Siegel, Harman, and Buchwald in Wranglers and Physicists: Studies on Cambridge Physics in the Nineteenth Century, edited by P. M. Harman (Manchester University Press, Dover, NH, 1985).

10. J. C. Maxwell, "A Dynamical Theory of the Electromagnetic Field," Philosophical Transactions of the Royal Society, 155, 459-512 (1965), reprinted in The Scientific Papers of James Clerk Maxwell, edited by W. D. Niven (reprinted by Dover Publications, New York, 1965), quotation from Vol. 1, p. 535.

11. J. C. Maxwell, "Illustrations of the Dynamical Theory of Gases," Philosophical Magazine, series 4, 19 (1860), 19-32; 21 (1860), 21-37; reprinted, with related documents and commentary, in Garber et al., (Ref. 9); the quoted passage is on p. 300.

12. Garber et al., Ref. 9, p. 318.

13. J. C. Maxwell, "On the Results of Bernoulli's Theory of Gases as Applied to their Internal Friction, their Diffusion, and their Conductivity for Heat," Report of the 30th Meeting of the British Association for the Advancement of Science (Oxford, June and July 1960), Notes and Abstracts, pp. 15-16; reprinted in Garber et al. (Ref. 9), pp. 320-21.

14. Letter from Maxwell to H. R. Droop, 28 January 1862, reprinted in Garber et al (Ref. 9), p. 336, note 8.

15. Rayleigh (John William Strutt), "Clerk-Maxwell's Papers," Nature, 43 (1890), 26-27, reprinted in Rayleigh's Scientific Papers, Vol. III (Cambridge Univ. Press, 1902, reprinted by Dover, New York, 1964), pp. 426-48 (quotation from p. 427).

16. Maxwell, Review of A Treatise on the Kinetic Theory of Gases by H. W. Watson, Nature, 18 (1877), 242-46, reprinted in Maxwell on Heat and Statistical Mechanics, edited by Elizabeth Garber, Stephen G. Brush, and C. W. F. Everitt (Lehigh Univ. Press, Bethlehem, PA, 1995), pp. 156-67; quotation is from pp. 164-65. This book also contains a comprehensive bibliography of primary and secondary sources for Maxwell's work on kinetic theory (see pp. 495-525).

17. J. L. Heilbron, The Dilemmas of an Upright Man: Max Planck as Spokesman for German Science (Univ. of California Press, 1986), pp. 3, 62.

18. Max Planck, Scientific Autobiography and other Papers, translated by Frank Gaynor (Philosophical Library, New York, 1950), pp. 33-34.

19. D. L. Hull, P. Tessner, and A. Diamond, "Planck's Principle," Science, 202 (1978), 717-723; see also Hull, Science as a Process (Univ. of Chicago Press, 1988) and references therein.

20. Martin J. Klein, "Max Planck and the Beginnings of the Quantum Theory," Archive for History of Exact Sciences, 1, 461-479 (1962). This article is a good introduction to the subject, which helped to explode the myth of the "ultraviolet catastrophe." Many scientists had assumed that Planck proposed his theory in order to problem that when equipartition theorem is applied to the ether model of black body radiation, the integral of energy over frequency diverges at high frequencies. The myth was so widely disseminated that it inspired a children's book by Margaret Mahy, Ultra-Violet Catastrophe! Or the Unexpected Walk with Great-Uncle Magnus Pringle (Parentsí Magazine Press, New York, 1975). But Klein failed to note Planck's reluctance to propose an explicit physical quantization in 1900 (see below). See also Hans Kangro, Early History of Planck's Radiation Law (Crane, Russak, New York, 1976) for a survey of research on black-body radiation before Planck.

21. M. Planck, "Zur Theorie des Gesetzes der Energieverteilung im Normalspektrum," Verhandlungen der Deutschen Physikalische Gesellschaft 2 (1900), 237-245; translation by D. Ter Haar in H. Kangro (ed.), Planck's Original Papers in Quantum Physics (Taylor & Francis, London, 1972), pp. 38-45; quotation from page 40. I thank Joshua Rosenbloom for calling the last sentence to my attention.

22. O. Darrigol, From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory (Univ. of California Press, Berkeley, 1992), p. 73.

23. T. S. Kuhn, Black-Body Theory and the Quantum Discontinuity: 1894-1912 (Oxford University Press, New York, 1978).

24. S. G. Brush, "Thomas Kuhn as a Historian of Science," Science & Education 9 (2000), 39-58. C. Carson, "The Origins of the Quantum Theory," Beamline, 30, no. 2 (Summer/Fall 2000), 6-19. O. Darrigol, Ref. 22., pp. 67-73; "Continuities and Discontinuities in Planck's Akt der Verzweiflung," Annalen der Physik (Leipzig) [ser. 8] 9 (2000): 851-960. H. Kragh, "Max Planck: The Reluctant Revolutionary," Physics World, 13, no. 12 (December 2000), 31-35

25. When I pointed out to Kuhn that he had not quoted this passage, which supported his thesis, he replied: "you are quite right that I did not use it, but I did call readersí attention to a more general version of the point on pp. 126 and 131. All three of Planck's autobiographical accounts of the origin of his theory fit my version of the story quite well." Letter from T. S. Kuhn to S. G. Brush, 10 January 1978.

26. M. Planck, Die Entstehung und bisherige Entwicklung der Quantentheorie [Nobel Prize Lecture] (Barth, Leipzig, 1920). Translation by R. Jones and D. H. Williams, in A Survey of Physical Theory (Dover, New York, 1960), pp. 102-114, quotation from p. 109.

27. M. Planck, "Ueber das Gesetz der Energieverteilung im Normalspectrum," Annalen der Physik [series 4] 4 (1901), 553-63 (see pp. 556-57).

28. M. Planck, "Zur Theorie der Wärmestrahlung," Annalen der Physik [series 4] 31 (1910), 758-68.

29. M. Planck, "Eine neue Strahlungshypothese," Verhandlungen der Deutsche Physikalische Gesellschaft, 13 (1911), 138-48

30. N. Hetherington, "Edwin Hubble:Legal eagle," Nature 319 (1986), 189-90, on p. 189

31. Letter from Hubble to N. Mayall, 23 February 1934, quoted by Hetherington, Ref. 30, note 12.

32. E. P. Hubble, "A Relation between Distance and Radial Velocity among extra-galactic Nebulae," Proceedings of the National Academy of Sciences, USA, 15 (1929), 168-73.

33. Hubble to de Sitter, 21 August 1930, quoted by N. S. Hetherington, "Philosophical Values and Observation in Edwin Hubble's Choice of a Model of the Universe," Historical Studies in the Physical Sciences, 13 (1982), 41-67, on p. 48. On de Sitter's cosmology, see J. D. North, The Measure of the Universe: A History of Modern Cosmology (Dover, New York, 1990).

34. M. L. Humason, "Apparent Velocity-Shifts in the Spectra of Faint Nebulae," Astrophysical Journal 74 (1931), 35-42.

35. Karl Hufbauer, "Astronomers take up the Stellar-Energy Problem, 1917-1920," Historical Studies in the Physical Sciences 11, 277-303 (1981).

36. E. P. Hubble, "The Realm of the Nebulae," Scientific Monthly 39 (1934), 193-202, on p. 199.

37. Ref. 36, p. 202.

38. S. G. Brush, "Is the Earth Too Old? The Impact of Geochronology on Cosmology, 1929-1952," in The Age of the Earth: From 4004 BC to AD 2002, edited by C. L. E. Lewis and S. J Knell (Geological Society, London, 2001), pp. 157-175.

39. F. Zwicky, "On the Red Shift of Spectral Lines through Interstellar Space," Proceedings of the National Academy of Science, 15 (1929), 773-779; "Remarks on the Redshift from Nebulae," Physical Review, 48 (1935), 802-806. W. D. MacMillan, "Velocities of the Spiral Nebulae," Nature, 129, 93.

40. E. P. Hubble & R. C. Tolman, "Two Methods of Investigating the Nature of the Nebular Red-Shift," Astrophysical Journal, 82 (1935), 302-37.

41. E. P. Hubble, "Effects of Red Shifts on the Distribution of Nebulae," Astrophysical Journal, 84 (1936), 517-54, quotations from pp. 517, 554.

42. E. P. Hubble, "Effects of Red Shifts on the Distribution of Nebulae," Proceedings of the National Academy of Sciences, USA, 22 (1936), 621-27, quotations from pp. 624-626.

43. S. G. Brush, Ref. 38.

44. S. G. Brush, "Prediction and Theory Evaluation: Cosmic Microwaves and the Revival of the Big Bang," Perspectives on Science, 1, 565-602 (1993).

45. F. J. Sulloway, Born to Rebel: Birth Order, Family Dynamics, and Creative Lives (Pantheon, New York, 1966), p. 194. According to Sulloway's theory, the temperament of scientists and their behavior in revolutions is strongly correlated with their birth order. He did not analyze Maxwell and Hubble from this viewpoint.

46. At least this belief is predominant in the United States; in other countries the credit may be given to de Sitter, Lemaitre, or Friedmann, with Hubble seen as merely confirming their theories. R,. W. Smith, The Expanding Universe (Cambridge University Press, New York, 1982); A. Pannekoek, A History of Astronomy (Barnes and Noble, New York, 1962, translated from the Dutch edition of 1951), pp. 488-489; E. A. Tropp, Y. Va. Frenkel, and A. D. Chernin, Alexandr A. Friedmann: The Man Who Made the Universe Expand (Cambridge University Press, New York, 1993), p. 218.

47. G. W. Gray, The Advancing Front of Science (Whittlesey House-McGraw-Hill, New York, 1937), pp. 66-67.

48. See the papers by Whitrow, Sandage, and Osterbrock, cited by S. G. Brush, Ref. 38; also Helge Kragh, Cosmology and Controversy (Princeton University Press, Princeton, NJ, 1996), p. 21; Mario Livio, The Accelerating Universe (Wiley, New York, 2000), p. 48; R. W. Smith, "Galaxies," in History of Astronomy: An Encyclopedia, edited by John Lankford (Garland, New York, 1997), pp. 221-225, on p. 224. Whitrow points out that Hubble's work with Tolman (ref. 40), which led him to reject the expanding universe model, was criticized by McVittie, Heckmann and others who disagreed with his "method of analyzing the observational results and disputed his conclusions ... these criticisms of Hubble's analysis came to be generally accepted." G. J. Whitrow, The Structure and Evolution of the Universe (Harper, New York, 1959), p. 44.

49. According to "Stigler's Law of Eponymy," no scientific discovery is named after its original discoverer; the law seems to be correct in a very large number of cases. Stephen M. Stigler, Statistics on the Table (Harvard University Press, Cambridge, 1999), Chapter 14.