Christian Doppler

Chapter 1 · Too Frail for the Trade

A stonemason's son, and years without a post

1803 – 1835 · Salzburg · Vienna · Prague

Christian Andreas Doppler was born at Salzburg in November 1803 into a family of *stonemasons* — a prosperous and long-established business.

He was expected to enter it, and he was physically too weak. He had poor health all his life.

A mathematician consulted about the boy suggested he be sent to study mathematics instead, so he went to the Polytechnic Institute in Vienna and then completed his schooling at Salzburg before studying mathematics, astronomy and mechanics.

And then he could not get a job.

He worked as an *assistant* at the Vienna Polytechnic for four years, and when that ended he could find nothing. For a period he worked as a *bookkeeper* in a cotton mill. He applied for academic posts across the Austrian Empire — repeatedly, in some cases dozens of times — and was rejected.

By 1835 he had given up. He sold his possessions, made arrangements to *emigrate to America*, and had gone as far as obtaining the necessary papers when an offer arrived from *Prague*: a post teaching mathematics at a secondary school, with an appointment at the Technical Academy to follow.

He took it and stayed.

The Prague years were productive and gruelling. His teaching load was enormous — at one point he was examining thousands of students a year — and his health, never good, deteriorated under it. He complained bitterly in letters about having no time for research.

It was in these conditions, in 1842, that he read the paper he is remembered for.

“The colour of the light emitted by a star must be altered by its motion towards or away from the observer.”

— Christian Doppler, Über das farbige Licht der Doppelsterne (1842)

Why this matters

Doppler had sold his possessions and obtained papers to emigrate to America when the Prague offer arrived — the principle was very nearly never stated.

You have the sold possessions and the letter from Prague. What would you ask him?

Ask Doppler

• “How close did you come to emigrating?”
• “What was it like being unable to get a post for years?”
• “What did being too frail for the family trade mean?”
• “How do you do research with that teaching load?”
• “What would you have done in America?”

Chapter 2 · Crowding and Stretching

The principle, argued from geometry alone

1842 · Prague

On 25 May 1842 Doppler read a paper to the Royal Bohemian Society of Sciences: *Über das farbige Licht der Doppelsterne* — On the Coloured Light of Double Stars.

The principle is simple enough to picture.

A source emits waves at a steady rate. If the source and the observer are *stationary* relative to one another, the waves arrive at the rate they were emitted.

Now let the source move *toward* the observer. Each successive wave is emitted from a position slightly closer than the last, so it has less distance to travel and arrives sooner than it otherwise would. The waves are *crowded together*: the observed frequency is *higher*, the wavelength shorter.

Let the source move *away*, and each wave is emitted from further off. The waves are *stretched out*: frequency *lower*, wavelength longer.

And the same holds if the *observer* moves instead. What matters is the *relative* motion.

The argument is entirely *geometrical*. It says nothing about what the waves are made of, what medium they travel in, or what mechanism produces them. It follows from the emitter and receiver changing separation between one wave and the next.

Doppler saw the consequence immediately, and it is the boldest part of the paper: because the argument does not depend on the nature of the wave, it must apply to *light* as well as to sound.

That is a substantial claim in 1842, when the nature of light was disputed and nobody had measured any such effect for it.

He stated the principle in general, for any wave.

Why this matters

The argument is purely geometrical, which is why Doppler could assert it must hold for light — the reasoning does not depend on what the wave is.

You have the crowded waves and the general claim. What is your question?

Ask Doppler

• “Why do the waves crowd together when the source approaches?”
• “Does it matter whether the source or the observer moves?”
• “Why must it apply to light too?”
• “What made you confident about a geometrical argument?”
• “Had anybody noticed the effect for sound before?”

Chapter 3 · The Thing He Wrote the Paper to Explain

Double stars, and an application that fails

1842 – 1850s · Prague · Vienna

Doppler's *motivation* was an astronomical puzzle. Some double stars appear *coloured* — one component reddish and the other bluish, or both tinted.

His proposal: the stars in a binary system orbit one another, so at any moment one is moving toward us and the other away. If motion shifts the frequency of light, the approaching star should look *bluer* and the receding one *redder*.

It is a beautiful idea and it is *wrong*, for a reason of *magnitude*.

The orbital velocities of stars in binary systems are on the order of tens of kilometres per second. Light travels at three hundred thousand kilometres per second. The ratio is a few parts in ten thousand, which produces a shift in wavelength far too small to alter a star's apparent colour perceptibly.

And there is a second problem, pointed out at the time. A star emits a *continuous spectrum* across all visible wavelengths. Shifting the whole spectrum slightly moves some light out of the visible range at one end and moves some in at the other. The overall colour barely changes at all.

The observed colours of double stars have other causes — genuine differences in surface temperature, and contrast effects in the observer's eye.

*Josef Petzval*, a colleague in Vienna and an accomplished mathematician, attacked the paper publicly and at length. His criticisms of the double-star application were substantially correct, though he also attacked the underlying principle in ways that were not, and the dispute was bruising and personal.

Doppler defended the astronomical application well past the point where it was tenable.

So he wrote a paper to explain double-star colours, got that entirely wrong, and stated in passing a principle that turned out to be one of the most useful in physics.

Why this matters

The one thing Doppler wrote the paper to explain is the one thing his principle does not explain — the stellar velocities are far too small.

You have the coloured stars and the failed explanation. What would you ask?

Ask Doppler

• “Why is a star's motion too slow to change its colour?”
• “What actually makes double stars look coloured?”
• “Why defend the application for so long?”
• “How much of Petzval's criticism was fair?”
• “Can a principle survive a failed application?”

Chapter 4 · Trumpeters on an Open Railway Carriage

Buys Ballot's test, 1845

1845 · Utrecht · Maarssen

The principle needed testing, and the test is one of the most charming experiments in physics.

*Christoph Buys Ballot*, a Dutch meteorologist, was sceptical of Doppler — he thought the effect real but doubted Doppler's treatment — and set out to check it properly in 1845.

Sound was the obvious choice, because sound travels at about 340 metres per second, and the newly built *railways* could move a source at a substantial fraction of that. A train at 40 miles an hour is going at about five per cent of the speed of sound, which produces a pitch shift of nearly a semitone — clearly audible.

The difficulty is *measuring* it in 1845. There is no electronic frequency meter, no recording device, and no way to capture a sound for later analysis.

Buys Ballot's solution was to use *people* as instruments.

He hired a locomotive on the line between Utrecht and Maarssen and put a group of *trumpeters* on an open carriage, playing and holding a single sustained note.

On the platform he stationed musicians with *perfect pitch* — trained to identify a note by ear alone — with instructions to write down the note they heard as the train approached and again as it receded.

The train ran back and forth for two days, at various speeds.

The results matched the prediction. The approaching note was heard sharp, the receding note flat, and the size of the shift corresponded to the speed.

It is a genuinely well-designed experiment. Buys Ballot had no instrument capable of the measurement, so he used the best available frequency detectors — human beings with absolute pitch — and controlled the source with a locomotive.

It is also, quietly, the first experimental use of a railway to do physics.

Why this matters

With no instrument able to measure frequency, Buys Ballot used musicians with perfect pitch as detectors and a locomotive as a moving source.

You have the trumpeters and the men on the platform. What is your question?

Ask Doppler

• “How do you measure a frequency shift in 1845?”
• “Why does a train produce an audible shift?”
• “What did Buys Ballot think of your paper?”
• “Is using people as instruments good practice?”
• “Why do you hear a passing siren change pitch?”

Chapter 5 · The Red Shift

Mendel, an early death, and an expanding universe

1847 – 1853 and after · Vienna · Venice

In 1847 Doppler moved to the Mining Academy at Schemnitz, and in 1850 became the first *Director of the Institute of Physics* at the University of Vienna — the position he had wanted all his life.

Among his students at Vienna was a young Augustinian friar named *Gregor Mendel*, who was sent by his monastery to train as a teacher. Doppler taught him physics and, importantly, encouraged the *statistical* treatment of experimental data — counting, tabulating and analysing large numbers of observations rather than describing individual cases.

Mendel went back to his monastery and applied exactly that approach to pea plants, counting thousands of them, and founded genetics.

Doppler's health failed. He had a chronic lung disease, probably tuberculosis, aggravated by years of overwork. He travelled to *Venice* in 1852 hoping the climate would help, and died there in March 1853, aged *forty-nine*.

He was buried in Venice, and the grave was subsequently lost.

The principle he stated has become one of the most widely used in physics and technology.

*Radar speed cameras* bounce a radio wave off a moving car and measure the frequency shift. *Weather radar* measures the motion of raindrops in a storm the same way. *Medical ultrasound* uses it to measure blood flow, so a Doppler scan can show blood moving through a heart or a fetal circulation, in colour, in real time.

And in astronomy it did what Doppler wanted, by a route he did not foresee. Not by changing a star's *colour*, but by shifting the positions of the *spectral lines* Kirchhoff had shown identify the elements. Those lines are at precisely known wavelengths, so a shift is measurable however small.

*Vesto Slipher* measured such shifts in spiral nebulae from 1912 and found most of them *red-shifted*, receding. *Edwin Hubble* in 1929 showed the recession speed is proportional to distance.

That is the expanding universe, and it rests on the principle a man read to a society in Prague in 1842, in a paper about the colours of double stars, which he got wrong.

Why this matters

The red shift of spectral lines, not of a star's overall colour, is what made Doppler's principle work in astronomy — and it produced the evidence for an expanding universe.

You have Mendel, Venice and the expanding universe. What would you ask him?

Ask Doppler

• “What did you teach Gregor Mendel?”
• “Why do spectral lines work where colour does not?”
• “How does a Doppler ultrasound see blood moving?”
• “What would you make of an expanding universe?”
• “Does it matter that you were wrong about the stars?”

What Doppler changed

The Doppler effect is the working principle of speed cameras, weather radar, medical ultrasound and the measurement of galaxy red-shifts — the last of which became the evidence for an expanding universe eighty years after his death. He also taught Gregor Mendel and encouraged the statistical treatment of experimental data that founded genetics.

A debate that continues

The double-star colour explanation that motivated the whole paper is wrong, and Doppler defended it past the point where it was tenable; Josef Petzval's public attack was partly justified and partly not, and the dispute was bruising.

Keep exploring — ask Doppler

• “What else does relative motion change?”
• “How long should you defend an application?”
• “Which of your students surprised you most?”

Related lives

• Gregor Mendel — Father of Genetics
• Edwin Hubble — Who Made the Universe Much Larger
• Gustav Kirchhoff — Who Read The Sun's Chemistry
• Marin Mersenne — Who Counted A Musical Note

Related themes

Waves and frequency · The Doppler effect · Red shift and the expanding universe