A Commotion in the Stars: The Legacy of Christian Doppler

Christian Andreas Doppler (1803 – 1853) was born in Salzburg, Austria, to a longstanding family of stonemasons.  As a second son, he was expected to help his older brother run the business, so his Father had him tested in his 18th year for his suitability for a career in business.  The examiner Simon Stampfer (1790 – 1864), an Austrian mathematician and inventor teaching at the Lyceum in Salzburg, discovered that Doppler had a gift for mathematics and was better suited for a scientific career.  Stampfer’s enthusiasm convinced Doppler’s father to enroll him in the Polytechnik Institute in Vienna (founded only a few years earlier in 1815) where he took classes in mathematics, mechanics and physics [1] from 1822 to 1825.  Doppler excelled in his courses, but was dissatisfied with the narrowness of the education, yearning for more breadth and depth in his studies and for more significance in his positions, feelings he would struggle with for his entire short life.  He left Vienna, returning to the Lyceum in Salzburg to round out his education with philosophy, languages and poetry.  Unfortunately, this four-year detour away from technical studies impeded his ability to gain a permanent technical position, so he began a temporary assistantship with a mathematics professor at Vienna.  As he approached his 30th birthday this term expired without prospects.  He was about to emigrate to America when he finally received an offer to teach at a secondary school in Prague.

To read about the attack by Joseph Petzval on Doppler’s effect and the effect it had on Doppler, see my feature article “The Fall and Rise of the Doppler Effect in Physics Today, 73(3) 30, March (2020).

Salzburg Austria

Doppler in Prague

Prague gave Doppler new life.  He was a professor with a position that allowed him to marry the daughter of a sliver and goldsmith from Salzburg.  He began to publish scholarly papers, and in 1837 was appointed supplementary professor of Higher Mathematics and Geometry at the Prague Technical Institute, promoted to full professor in 1841.  It was here that he met the unusual genius Bernard Bolzano (1781 – 1848), recently returned from political exile in the countryside.  Bolzano was a philosopher and mathematician who developed rigorous concepts of mathematical limits and is famous today for his part in the Bolzano-Weierstrass theorem in functional analysis, but he had been too liberal and too outspoken for the conservative Austrian regime and had been dismissed from the University in Prague in 1819.  He was forbidden to publish his work in Austrian journals, which is one reason why much of Bolzano’s groundbreaking work in functional analysis remained unknown during his lifetime.  However, he participated in the Bohemian Society for Science from a distance, recognizing the inventive tendencies in the newcomer Doppler and supporting him for membership in the Bohemian Society.  When Bolzano was allowed to return in 1842 to the Polytechnic Institute in Prague, he and Doppler became close friends as kindred spirits. 

Prague, Czech Republic

On May 25, 1842, Bolzano presided as chairman over a meeting of the Bohemian Society for Science on the day that Doppler read a landmark paper on the color of stars to a meagre assembly of only five regular members of the Society [2].  The turn-out was so small that the meeting may have been held in the robing room of the Society rather than in the meeting hall itself.  Leading up to this famous moment, Doppler’s interests were peripatetic, ranging widely over mathematical and physical topics, but he had lately become fascinated by astronomy and by the phenomenon of stellar aberration.  Stellar aberration was discovered by James Bradley in 1729 and explained as the result of the Earth’s yearly motion around the Sun, causing the apparent location of a distant star to change slightly depending on the direction of the Earth’s motion.  Bradley explained this in terms of the finite speed of light and was able to estimate it to within several percent [3].  As Doppler studied Bradley aberration, he wondered how the relative motion of the Earth would affect the color of the star.  By making a simple analogy of a ship traveling with, or against, a series of ocean waves, he concluded that the frequency of impact of the peaks and troughs of waves on the ship was no different than the arrival of peaks and troughs of the light waves impinging on the eye.  Because perceived color was related to the frequency of excitation in the eye, he concluded that the color of light would be slightly shifted to the blue if approaching, and to the red if receding from, the light source. 

Doppler wave fronts from a source emitting spherical waves moving with speeds β relative to the speed of the wave in the medium.

Doppler calculated the magnitude of the effect by taking a simple ratio of the speed of the observer relative to the speed of light.  What he found was that the speed of the Earth, though sufficient to cause the detectable aberration in the position of stars, was insufficient to produce a noticeable change in color.  However, his interest in astronomy had made him familiar with binary stars where the relative motion of the light source might be high enough to cause color shifts.  In fact, in the star catalogs there were examples of binary stars that had complementary red and blue colors.  Therefore, the title of his paper, published in the Proceedings of the Royal Bohemian Society of Sciences a few months after he read it to the society, was “On the Coloured Light of the Double Stars and Certain Other Stars of the Heavens: Attempt at a General Theory which Incorporates Bradley’s Theorem of Aberration as an Integral Part” [4]

Title page of Doppler’s 1842 paper introducing the Doppler Effect.

Doppler’s analogy was correct, but like all analogies not founded on physical law, it differed in detail from the true nature of the phenomenon.  By 1842 the transverse character of light waves had been thoroughly proven through the work of Fresnel and Arago several decades earlier, yet Doppler held onto the old-fashioned notion that light was composed of longitudinal waves.  Bolzano, fully versed in the transverse nature of light, kindly published a commentary shortly afterwards [5] showing how the transverse effect for light, and a longitudinal effect for sound, were both supported by Doppler’s idea.  Yet Doppler also did not know that speeds in visual binaries were too small to produce noticeable color effects to the unaided eye.  Finally, (and perhaps the greatest flaw in his argument on the color of stars) a continuous spectrum that extends from the visible into the infrared and ultraviolet would not change color because all the frequencies would shift together preserving the flat (white) spectrum.

The simple algebraic derivation of the Doppler Effect in the 1842 publication..

Doppler’s twelve years in Prague were intense.  He was consumed by his Society responsibilities and by an extremely heavy teaching load that included personal exams of hundreds of students.  The only time he could be creative was during the night while his wife and children slept.  Overworked and running on too little rest, his health already frail with the onset of tuberculosis, Doppler collapsed, and he was unable to continue at the Polytechnic.  In 1847 he transferred to the School of Mines and Forrestry in Schemnitz (modern Banská Štiavnica in Slovakia) with more pay and less work.  Yet the revolutions of 1848 swept across Europe, with student uprisings, barricades in the streets, and Hungarian liberation armies occupying the cities and universities, giving him no peace.  Providentially, his former mentor Stampfer retired from the Polytechnic in Vienna, and Doppler was called to fill the vacancy.

Although Doppler was named the Director of Austria’s first Institute of Physics and was elected to the National Academy, he ran afoul of one of the other Academy members, Joseph Petzval (1807 – 1891), who persecuted Doppler and his effect.  To read a detailed description of the attack by Petzval on Doppler’s effect and the effect it had on Doppler, see my feature article “The Fall and Rise of the Doppler Effect” in Physics Today, March issue (2020).

Christian Doppler

Voigt’s Transformation

It is difficult today to appreciate just how deeply engrained the reality of the luminiferous ether was in the psyche of the 19th century physicist.  The last of the classical physicists were reluctant even to adopt Maxwell’s electromagnetic theory for the explanation of optical phenomena, and as physicists inevitably were compelled to do so, some of their colleagues looked on with dismay and disappointment.  This was the situation for Woldemar Voigt (1850 – 1919) at the University of Göttingen, who was appointed as one of the first professors of physics there in 1883, to be succeeded in later years by Peter Debye and Max Born.  Voigt received his doctorate at the University of Königsberg under Franz Neumann, exploring the elastic properties of rock salt, and at Göttingen he spent a quarter century pursuing experimental and theoretical research into crystalline properties.  Voigt’s research, with students like Paul Drude, laid the foundation for the modern field of solid state physics.  His textbook Lehrbuch der Kristallphysik published in 1910 remained influential well into the 20th century because it adopted mathematical symmetry as a guiding principle of physics.  It was in the context of his studies of crystal elasticity that he introduced the word “tensor” into the language of physics.

At the January 1887 meeting of the Royal Society of Science at Göttingen, three months before Michelson and Morely began their reality-altering experiments at the Case Western Reserve University in Cleveland Ohio, Voit submitted a paper deriving the longitudinal optical Doppler effect in an incompressible medium.  He was responding to results published in 1886 by Michelson and Morely on their measurements of the Fresnel drag coefficient, which was the precursor to their later results on the absolute motion of the Earth through the ether. 

Fresnel drag is the effect of light propagating through a medium that is in motion.  The French physicist Francois Arago (1786 – 1853) in 1810 had attempted to observe the effects of corpuscles of light emitted from stars propagating with different speeds through the ether as the Earth spun on its axis and traveled around the sun.  He succeeded only in observing ordinary stellar aberration.  The absence of the effects of motion through the ether motivated Augustin-Jean Fresnel (1788 – 1827) to apply his newly-developed wave theory of light to explain the null results.  In 1818 Fresnel derived an expression for the dragging of light by a moving medium that explained the absence of effects in Arago’s observations.  For light propagating through a medium of refractive index n that is moving at a speed v, the resultant velocity of light is

where the last term in parenthesis is the Fresnel drag coefficient.  The Fresnel drag effect supported the idea of the ether by explaining why its effects could not be observed—a kind of Catch-22—but it also applied to light moving through a moving dielectric medium.  In 1851, Fizeau used an interferometer to measure the Fresnel drag coefficient for light moving through moving water, arriving at conclusions that directly confirmed the Fresnel drag effect.  The positive experiments of Fizeau, as well as the phenomenon of stellar aberration, would be extremely influential on the thoughts of Einstein as he developed his approach to special relativity in 1905.  They were also extremely influential to Michelson, Morley and Voigt.

 In his paper on the absence of the Fresnel drag effect in the first Michelson-Morley experiment, Voigt pointed out that an equation of the form

is invariant under the transformation

From our modern vantage point, we immediately recognize (to within a scale factor) the Lorentz transformation of relativity theory.  The first equation is common Galilean relativity, but the last equation was something new, introducing a position-dependent time as an observer moved with speed  relative to the speed of light [6].  Using these equations, Voigt was the first to derive the longitudinal (conventional) Doppler effect from relativistic effects.

Voigt’s derivation of the longitudinal Doppler effect used a classical approach that is still used today in Modern Physics textbooks to derive the Doppler effect.  The argument proceeds by considering a moving source that emits a continuous wave in the direction of motion.  Because the wave propagates at a finite speed, the moving source chases the leading edge of the wave front, catching up by a small amount by the time a single cycle of the wave has been emitted.  The resulting compressed oscillation represents a blue shift of the emitted light.  By using his transformations, Voigt arrived at the first relativistic expression for the shift in light frequency.  At low speeds, Voigt’s derivation reverted to Doppler’s original expression.

A few months after Voigt delivered his paper, Michelson and Morley announced the results of their interferometric measurements of the motion of the Earth through the ether—with their null results.  In retrospect, the Michelson-Morley experiment is viewed as one of the monumental assaults on the old classical physics, helping to launch the relativity revolution.  However, in its own day, it was little more than just another null result on the ether.  It did incite Fitzgerald and Lorentz to suggest that length of the arms of the interferometer contracted in the direction of motion, with the eventual emergence of the full Lorentz transformations by 1904—seventeen years after the Michelson results.

            In 1904 Einstein, working in relative isolation at the Swiss patent office, was surprisingly unaware of the latest advances in the physics of the ether.  He did not know about Voigt’s derivation of the relativistic Doppler effect  (1887) as he had not heard of Lorentz’s final version of relativistic coordinate transformations (1904).  His thinking about relativistic effects focused much farther into the past, to Bradley’s stellar aberration (1725) and Fizeau’s experiment of light propagating through moving water (1851).  Einstein proceeded on simple principles, unencumbered by the mental baggage of the day, and delivered his beautifully minimalist theory of special relativity in his famous paper of 1905 “On the Electrodynamics of Moving Bodies”, independently deriving the Lorentz coordinate transformations [7]

One of Einstein’s talents in theoretical physics was to predict new phenomena as a way to provide direct confirmation of a new theory.  This was how he later famously predicted the deflection of light by the Sun and the gravitational frequency shift of light.  In 1905 he used his new theory of special relativity to predict observable consequences that included a general treatment of the relativistic Doppler effect.  This included the effects of time dilation in addition to the longitudinal effect of the source chasing the wave.  Time dilation produced a correction to Doppler’s original expression for the longitudinal effect that became significant at speeds approaching the speed of light.  More significantly, it predicted a transverse Doppler effect for a source moving along a line perpendicular to the line of sight to an observer.  This effect had not been predicted either by Doppler or by Voigt.  The equation for the general Doppler effect for any observation angle is

Just as Doppler had been motivated by Bradley’s aberration of starlight when he conceived of his original principle for the longitudinal Doppler effect, Einstein combined the general Doppler effect with his results for the relativistic addition of velocities (also in his 1905 Annalen paper) as the conclusive treatment of stellar aberration nearly 200 years after Bradley first observed the effect.

Despite the generally positive reception of Einstein’s theory of special relativity, some of its consequences were anathema to many physicists at the time.  A key stumbling block was the question whether relativistic effects, like moving clocks running slowly, were only apparent, or were actually real, and Einstein had to fight to convince others of its reality.  When Johannes Stark (1874 – 1957) observed Doppler line shifts in ion beams called “canal rays” in 1906 (Stark received the 1919 Nobel prize in part for this discovery) [8], Einstein promptly published a paper suggesting how the canal rays could be used in a transverse geometry to directly detect time dilation through the transverse Doppler effect [9].  Thirty years passed before the experiment was performed with sufficient accuracy by Herbert Ives and G. R. Stilwell in 1938 to measure the transverse Doppler effect [10].  Ironically, even at this late date, Ives and Stilwell were convinced that their experiment had disproved Einstein’s time dilation by supporting Lorentz’ contraction theory of the electron.  The Ives-Stilwell experiment was the first direct test of time dilation, followed in 1940 by muon lifetime measurements [11].


Further Reading

D. D. Nolte, “The Fall and Rise of the Doppler Effect“, Phys. Today 73(3) 30, March 2020.


Notes

[1] pg. 15, Eden, A. (1992). The search for Christian Doppler. Wien, Springer-Verlag.

[2] pg. 30, Eden

[3] Bradley, J (1729). “Account of a new discoved Motion of the Fix’d Stars”. Phil Trans. 35: 637–660.

[4] C. A. DOPPLER, “Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels (About the coloured light of the binary stars and some other stars of the heavens),” Proceedings of the Royal Bohemian Society of Sciences, vol. V, no. 2, pp. 465–482, (Reissued 1903) (1842).

[5] B. Bolzano, “Ein Paar Bemerkunen über die Neu Theorie in Herrn Professor Ch. Doppler’s Schrift “Über das farbige Licht der Doppersterne und eineger anderer Gestirnedes Himmels”,” Pogg. Anal. der Physik und Chemie, vol. 60, p. 83, 1843; B. Bolzano, “Christian Doppler’s neuste Leistunen af dem Gebiet der physikalischen Apparatenlehre, Akoustik, Optik and optische Astronomie,” Pogg. Anal. der Physik und Chemie, vol. 72, pp. 530-555, 1847.

[6] W. Voigt, “Uber das Doppler’sche Princip,” Göttinger Nachrichten, vol. 7, pp. 41–51, (1887). The common use of c to express the speed of light came later from Voigt’s student Paul Drude.

[7] A. Einstein, “On the electrodynamics of moving bodies,” Annalen Der Physik, vol. 17, pp. 891-921, 1905.

[8] J. Stark, W. Hermann, and S. Kinoshita, “The Doppler effect in the spectrum of mercury,” Annalen Der Physik, vol. 21, pp. 462-469, Nov 1906.

[9] A. Einstein, “”Über die Möglichkeit einer neuen Prüfung des Relativitätsprinzips”,” vol. 328, pp. 197–198, 1907.

[10] H. E. Ives and G. R. Stilwell, “An experimental study of the rate of a moving atomic clock,” Journal of the Optical Society of America, vol. 28, p. 215, 1938.

[11] B. Rossi and D. B. Hall, “Variation of the Rate of Decay of Mesotrons with Momentum,” Physical Review, vol. 59, pp. 223–228, 1941.

Physicists in Revolution: Arago, Riemann, Jacobi and Doppler

The opening episode of Victoria on Masterpiece Theatre (PBS) this season finds the queen confronting widespread unrest among her subjects who are pressing for more freedoms and more say in government. Louis-Phillipe, former King of France, has been deposed in the February Revolution of 1848 in Paris and his presence at the Royal Palace does not help the situation.

In 1848 a wave of spontaneous revolution swept across Europe.  It was not a single revolution of many parts, but many separate revolutions with similar goals.  Two essential disruptions of life occurred in the early 1800’s.  The first was the partitioning of Europe at the Congress of Vienna from 1814 to 1815, presided over by Prince Metternich of Austria, that had carved up Napoleon’s conquests and sought to establish a stable order based on the old ideal of absolute monarchy.  In the process, nationalities were separated or suppressed.  The second was the industrialization of Europe in the early 1800’s that created economic upheaval, with masses of working poor fleeing effective serfdom in the fields and flocking to the cities.  Wages fell, food became scarce, legions of the poor and starving bloomed.  Because of these influences, European society had become unstable, supercooled beyond a phase transition and waiting for a seed or catalyst to crystalize the continent into a new state of matter. 

When the wave came, physicists across Europe were caught in the upheaval.  Some were caught up in the fervor and turned their attention to national service, some lost their standing and their positions during the inevitable reactionary backlash, others got the opportunities of their careers.  It was difficult for anyone to be untouched by the 1848 revolutions, and physicist were no exception.

The Spontaneous Fire of Revolution

The extraodinary wave of revolution was sparked by a small rebellion in Sicily in January 1848 that sought to overturn the ruling Bourbons.  It was a small rebellion of little direct consequence to Europe, but it succeeded in establishing a liberal democracy in an independent state that stood as a symbol of what could be achieved by a determined populace.  The people of Paris took notice, and in the sudden and unanticipated February Revolution, the French constitutional monarchy under Louis-Phillipe was overthrown in a few days and replaced by the French Second Republic.  The shock of Louis-Phillipe’s fall reverberated across Europe, feared by those in power and welcomed by those who sought a new world order.  Nationalism, liberalism, socialism and communism were on the rise, and the opportunity to change the world seemed to have arrived.  The Five Days of Milan in Italy, the March Revolution of the German states, the Polish rebellion against Prussia, and the Young Irelander Rebellion in Ireland were all consequences of the unstable conditions and the unprecidented opportunities for the people to enact change.  None of these uprisings were coordinated by any central group.  It was a spontaneous consequence of similar preconditions that existed across nearly all the states of Europe.

Arago and the February Revolution in Paris

The French were no newcomers to street rebellions.  Paris had a history of armed conflict between citizens manning barricades and the superior forces of the powers at be.  The unforgettable scene in Les Misérables of Marius at the barricade and Jean Valjean’s rescue through the sewers of Paris was based on the 1832 June Rebellion in Paris.  Yet this event was merely an echo of the much larger rebellion of 1830 that had toppled the unpopular monarchy of Charles X, followed by the ascension of the Bourgeois Monarch Louis Phillipe at the start of the July Monarchy.  Eighteen years later, Louis Phillipe was still on the throne and the masses were ready again for a change.  Alexis de Tocqueville saw the change coming and remarked, “We are sleeping together in a volcano. … A wind of revolution blows, the storm is on the horizon.”  The storm would sweep up a generation of participants, including the French physicist Francois Arago (1786 – 1853).

Lamartine in front of the Town Hall of Paris on 25 February 1848 (Image by Henri Félix Emmanuel Philippoteaux in public domain).

Arago is one of the under-appreciated French physicists of the 1800’s.  This may be because so many of his peers have become icons in the history of physics: Fourier, Fresnel, Poisson, Laplace, Malus, Biot and Foucault.  The one place where his name appears—the Spot of Arago—was not exclusively his discovery, but rather was an experimental demonstration of an effect derived by Poisson using Fresnel’s new theory of diffraction.  Poisson derived the phenomenon as a means to show the absurdity of Fresnel’s undulatory theory of light, but Arago’s experimental demonstration turned the tables on Poisson and the emissionists (followers of Newton’s particulate theory of light).  Yet Arago played a role behind the scenes as a supporter and motivator of some of the most important discoveries in optics.  In particular, it was Arago’s encouragement and support of the (at that time) unknown Fresnel, that helped establish the Fresnel theory of diffraction and the wave nature of light.  Together, Arago and Fresnel established the transverse nature of the light wave, and Arago is also the little-known discoverer of optical rotation.  As a young scientist, he attempted to measure the drift of the ether, which was a null experiment that foreshadowed the epochal experiments of Michelson and Morley 80 years later.  In his later years, Arago proposed the methodology for measuring the speed of light in both stationary and moving materials, which became the basis for the important measurements of the speed of light by Fizeau and Foucault (who also attempted to measure ether drift).

In addition to his duties as the director of the National Observatory and as the perpetual secretary of the Academie des Sciences (replacing Fourier), he entered politics in 1830 when he was elected as a member of the chamber of deputies.  At the fall of Louis-Phillipe in the February Revolution of 1848, he was appointed as a member of the steering committee of the newly formed government of the French Second Republic, and he was named head of the Marine and Colonies as well as the head of the Department of War.  Although he was a staunch republican and supporter of the people, his position put him in direct conflict with the later stages of the revolutions of 1848. 

The population of Paris became disenchanted with the conservative trends in the Second Republic.  In June of 1848 barricades were again erected in the streets of Paris, this time in opposition to the Republic.  Forces were drawn up on both sides, although many of the Republican forces defected to the insurgents, and attempts were made to mediate the conflict.  At the barricade on the rue Soufflot near the Pantheon, Arago himself approached the barricades to implore defenders to disperse.  It is a measure of the respect Arago held with the people when they replied, “Monsieur Arago, we are full of respect for you, but you have no right to reproach us.  You have never been hungry.  You don’t know what poverty is.” [1] When Arago finally withdrew, he feared that death and carnage were inevitable.  They came at noon on June 23 when the barricade at Porte Saint-Denis was attacked by the National Guards.  This started a general onslaught of all the barricades by Republican forces that left 1,500 workers dead in the streets and more than 11,000 arrested.  Arago resigned from the steering committee on June 24, although he continued to work in the government until the coup d’Etat by Louis Napolean, the nephew of Napoleon Bonaparte, in 1852 when he became Napoleon III, Emperor of the Second French Empire. Louis Napoleon demanded that all government workers take an oath of allegiance to him, but Arago refused.  Yet such was the respect that Arago commanded that Louis Napoleon let him continue unmolested as the astronomer of the Bureau des Longitudes.

Riemann and Jacobi and the March Revolution in Berlin

The February Revolution of Paris was followed a month later by the March Revolutions of the German States.  The center of the German-speaking world at that time was Vienna, and a demonstration by students broke out in Vienna on March 13. Emperor Ferdinand, following the advice of Metternich, called out the army who fired on the crowd, killing several protestors.  Throngs rallied to the protest and arms were distributed, readying for a fight.  Rather than risk unreserved bloodshed, the emperor dismissed Metternich who went into exile to London (following closely the footsteps of the French Louis-Phillipe).  Within the week, the revolutionary fervor had spread to Berlin where a student uprising marched on the royal palace of King Frederick Wilhelm IV on March 18.  They were met by 20,000 troops. 

The March 1848 revolution in Berlin (Image in the public domain).

Not all university students were liberals and revolutionaries, and there were numerous student groups that formed to support the King.  One of the students in one of these loyalist groups was a shy mathematician who joined a loyalist student militia to protect the King.  Bernhard Riemann (1826 – 1866) had come to the University of Berlin after spending a short time in the Mathematics department at the University in Göttingen.  Despite the presence of Gauss there, the mathematics department was not considered strong (this would change dramatically in about 50 years when Göttingen became the center of German mathematics with the arrival of Felix Klein, Karl Schwarzschild and Hermann Minkowski).  At Berlin, Riemann attended lectures by Steiner, Jacobi, Dirichlet and Eisenstein. 

On the night of the uprising, a nervous Riemann found himself among a group of students, few more than 20 years old, guarding the quarters of the King, not knowing what would unfold.  They spent a sleepless night that dawned on the chaos and carnage at the barricades at Alexander Platz with hundreds of citizens dead.  King Wilhelm was caught off guard by the events, and he assured the citizens that he would reorganize the government and yield to the demonstrator’s demands for parliamentary elections, a constitution, and freedom of the press.  Two days later the king attended a mass funeral for the fallen, attended by his generals and ministers who wore the german revolutionary tricolor of black, red and gold.  This ploy worked, and the unrest in Berlin died away before the king was forced to abdicate.  This must have relieved Riemann immensely, because this entire episode was entirely outside his usual meek and mild character.  Yet the character of all the unrelated 1848 revolutions had one thing in common: a sharp division among the populace between the liberals and the conservatives.  As Riemann had elected to join with the loyalists, one of his professors picked the other side.

Carl Gustav Jacob Jacobi (1804 – 1851) had been born in Potsdam and had obtained his first faculty position at the University of Königsberg where he was soon ranked among the top mathematicians in Europe.  However, in his early thirties he was stricken with diabetes, and the harsh winters of Königsberg became to difficult to bear.  He returned to the milder climate of Berlin to a faculty position at the university when the wave of revolution swept over the city.  Jacobi was a liberal thinker and was caught up in the movement, attending meetings at the Constitution Club.  Once the danger to Wilhelm IV had passed, the reactionary forces took their revenge, and Jacobi’s teaching stipend was suspended.  When he threatened to move to the University of Vienna, the royalists relented, so Jacobi too was able to weather the storm. 

The surprising footnote to this story is that Jacobi delivered lectures on a course on the application of differential equations to mechanics in the winter semester of 1847 – 1848 right in the midst of the political turmoil.  His participation in the extraordinary political events of that time apparently did not hamper him from giving one of the most extraordinary sets of lectures in mathematical physics.  Jacobi’s lectures of 1848 were the greatest advance in mathematical physics since Euler had reinterpreted Newton a hundred years earlier.  This is where Jacobi expanded on the work of Hamilton, establishing what is today called the Hamilton-Jacobi theory of dynamics.  He also derived and proved, using Liouville’s theorem of 1838, that the volume of phase space was an invariant in a conservative dynamical system [2].  It is tempting to imagine Jacobi returning home late at night, after rousing discussions of revolution at the Constitution Club, to set to work on his own revolutionary theories in physics.

Doppler and the Hungarian Revolution

Among all the states of Europe, the revolutions of 1848 posed the greatest threat to the Austrian Empire, which was a beaurocratic state entangling scores of diverse nationalities sprawled across the largest state of Europe.  The Austrian Empire was the remnant of the Holy Roman Empire that had succumbed to the Napoleonic invasion.  The lands that were controlled by Austria, after Metternich engineered the Congress of Vienna, included Poles, Ukranians, Romanians, Germans, Czechs, Slovaks, Hungarians, Slovenes, Serbs, Albanians and more.  Holding this diverse array of peoples together was already a challenge, and the revolutions of 1848 carried with them strong feelings of nationalism.  The revolutions spreading across Europe were the perfect catalyst to set off the Hungarian Revolution that grew into a war for independence, and the fierce fighting across Hungary could not be avoided even by cloistered physicists.

Christian Doppler (1803 – 1853) had moved in 1847 from Prague (where he had proposed what came to be called the Doppler effect in 1842 to the Royal Bohemian Society of Sciences) to the Academy of Mines and Forests in Schemnitz (modern Banská Štiavnica in Slovakia, but then part of the Kingdom of Hungary) with more pay and less work.  His health had been failing, and the strenuous duties at Prague had taken their toll.  If the goal of this move to an obscure school far from the center of Austrian power had been to lead a peaceful life, Doppler’s plans were sorely upset.

The news of the protests in Vienna arrived in Schemnitz on the 17th of March, and student demonstrations commenced immediately.  Amidst the uncertainty, Doppler requested a leave of absence from the summer semester and returned to Vienna.  It is not clear why he went there, whether to be near the center of excitement, or to take advantage of the free time to pursue his own researches.  While in Vienna he read a treatise before the Academy on galvano-electric effects.  He returned to Schemnitz in the Fall to relative peace, until the 12th of December, when the Hungarians rejected to acknowledge the new Emperor Franz Josef in Vienna, replacing his Uncle Ferdinand who was forced to abdicate, and the Hungarian war for independence began.

Görgey’s troops crossing the Sturec pass. Their ability to evade the Austrian pursuit was legendary (Image by Keiss Károly in the public domain).

One of Doppler’s former students from his days in Prague was appointed to command the newly formed Hungarian army.  General Arthur Görgey (1818 – 1916) moved to take possession of the northern mining towns (present day Slovakia) and occupied Schemnitz.  When Görgey learned that his old teacher was in the town he sent word to Doppler to meet him at his headquarters.  Meeting with a revolutionary and rebel could have marked Doppler as a traitor in Vienna, but he decided to meet him anyway, taking along one of his colleagues as a “witness” that the discussion were purely academic.  This meeting opens an interesting unsolved question in the history of physics. 

Around this time Doppler was interested in the dynamical properties of the pendulum for cases when the suspension wire was exceptionally long.  Experiments on such extreme pendula could provide insight into changes in gravity with height as well as the effects of the motion of the Earth.  For instance, Coriolis had published his paper on forces in rotating frames many years earlier in 1835.  Because Schemnitz was a mining town, there was ample access to deep mine shafts in which to set up a pendulum with a very long wire.  This is where the story becomes murky.  Within the family of Doppler’s descendants there are stories of Doppler setting up such an experiment, and even a night time visit to the Doppler house by Görgey.  The pendulum was thought to be one of the topics discussed by Doppler and Görgey at their first meeting, and Görgey (from his life as a scientist prior to becoming a revolution general) had arrived to help with the experiment [3]

This story is significant for two reasons.  First, it would be astounding to think of General Görgey taking a break from the revolution to do some physics for fun.  Görgey has not been graced by history with a benevolent reputation.  He was known as a hard and sometimes vicious leader, and towards the end of the short-lived Hungarian Revolution he displaced the President Kossuth to become the dictator of Hungary.  The second reason, which is important for the history of physics, is that if Doppler had performed this experiment in 1848, it would have preceded the famous experiment by Foucault by more than two years.  However, the paper published by Doppler around this time on the dynamics of the pendulum did not mention the experiment, and it remains an open question in the history of physics whether Doppler may have had priority over Foucault.

The Austrian Imperial Army laid siege to Schemnitz and commenced a short bombardment that displaced Görgey and his troops from the town.  Even as Schemnitz was being liberated, a letter arrived informing Doppler that his old mentor Stampfer at the University of Vienna was retiring and that he had been chosen to be his replacement.  The March Revolution had led to the abdication of the previous Austrian emperor and his replacement by the more liberal-minded Franz Josef who was interested in restructuring the educational system in the Austrian empire.  On the advice of Doppler’s supporters who were in the new government, the Institute of Physics was formed and Doppler was named as its first director.  He arrived in the spring of 1850 to take up his new post.

The Legacy of 1848

Despite the early successes and optimism of the revolutions of 1848, reactionary forces were quick to reverse many of the advances made for universal suffrage, constitutional government, freedom of the press, and freedom of expression.  In most cases, monarchs either retained power or soon returned.  Even the reviled Metternich returned to Vienna from exile in London in 1851.  Yet as is so often the case, once a door has been opened it is difficult to shut it again.  The pressure for reforms continued long after the revolutions faded away, and by 1870 many of the specific demands of the people had been instituted by most of the European states.  Russia was an exception, which may explain why the inevitable Russian Revolution half a century later was so severe.            

The revolutions of 1848 cannot be said to have had a long-lasting impact on the progress of physics, although they certainly had a direct impact on the lives of selected physicists.  The most lasting effect of the revolutions on science was the restructuring of educational systems, not only in Austria, but in many of the European states.  This was perhaps one of the first times when the social and economic benefits of science education to the national welfare was understood and implemented across Europe, although a similar recognition had occurred earlier during the French Revolution, for instance leading to the founding of the Ecole Polytechnique.  The most important, though subtle, effect of the revolutions of 1848 on society was the shift away from autocratic rule to democracy, and the freeing of expression and thought from rigid bounds.  The coming revolution in physics at the turn of the next century may have been helped a little by the revolutionary spirit that still echoed from 1848.


[1] pg. 201, Mike Rapport, “1848: Year of Revolution” (Basic Books, 2008)

[2] D. D. Nolte, The Tangled Tale of Phase Space, Chap. 6 in Galileo Unbound (Oxford University Press, 2018)

[3] Schuster, P. Moving the stars : Christian Doppler, his life, his works and principle, and the world after. Pöllauberg, Austria, Living Edition. (2005)