How Physics Got Precise

Or some events from the history of physics

that happen to intrigue the speaker

Daniel Kleppner

Massachusetts Institute of Technology

How Physics Got Precise

Or some events from the history of physics

that happen to intrigue the speaker

Daniel Kleppner

Massachusetts Institute of Technology

The Length of the Year

Determinations of t he length of the yearexpressed in mean solar days

Author Place Date Error(seconds)

? Babylon c. 700 BC 344

Hipparchus Egypt 150 BC 430

? Mexico AD 700 -20

Da Yen China AD 723 190

Al-Zarquali Arabia AD 900 2

Ulugh Beg Samarkand AD 1400 30

Copernicus Europe AD 1500 34

Tycho Brahe Europe AD 1600 3

Xing Yunlu China AD 1620 3

Source: E.G. Richards, Mapping Time,The Calendar and it History, Oxford, 1998

The year 1600 and the dawn of modern science

On January 1, 1600, Johannes Kepler set out for

Prague to work for Tycho Brahe. For me, this event

marks the birth of modern science. The delivery

was difficult.

Jo hannes Kepler

J ohannes Kepler, Keppler, Khepler, Kheppler, orKeplerus, the founder of modern astronomy, wasconceived on May 16, A.D. 1571, at 4:37 A.M., andwas born on December 27 at 2:30 P.M., after apregnancy lasting 224 days, 9 hours, and 53minutes.

The five differe nt ways of spelling his name are allhis own, and so are the figures relating toconception, pregnancy and birth, recorded in ahoroscope which he cast f or himself .

Taken from: Alfred Koestler, The Sleepwalkers, Macmillan Co., N.Y. 1959.

1609 Kepler publishes Astronomica Nova

A NEW ASTRONOMY Based on Causationor A PHYSIC S OF THE SKY

derived from I nvestigations of theMOTION S OF THE STA R MARS

Founded on Observations ofTHE NOBLE TYCHO BRAHE

Contains first two planetary laws1) Planets travel around the sun not in circles but in elliptical orbits

with sun at a focus2) Speed is not uniform: law of equal areas

1619 Kepler publishes HarmoniaMundi

Principal findings:

A. the Third Law of Planetary Motion: the square of the period is proportional to the cube of the radius

B. Celestial music is created by the planets as they move along their orbits at varying speeds

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

1609, July, Galileo learns of telescope

1609, December, Galileo starts systematic observations

1610, March, Galileo publishes The Starry Messenger

Refractive indices for different colors, to six figures, five significant figures

Page from Galileo’s notebook, Jan. 1610

Date of observation

Hours after sunset

Ganymede

time (hours)

dis

tan

ce

(Jupit

er

dia

mete

rs)

Plotted by Alber Liau

time (hours)

Europadis

tan

ce

(Jupit

er

dia

mete

rs)

Plotted by Alber Liau

Europa: period = 84.223 hours from Kepler: 85 hours

Ganymede: period = 171.71 hours from Kepler: 172 hours

1682: more precise measurements are available

Measurements taken from…

from

Principia, Book III,The System of theWorld,Motte translation

translated by AndrewMotte, 1729, revised byFlorian Cajori, U. of Cal. Press,Berkeley, 1947

from

Principia, Book III,The System of theWorld,Motte translation

translated by AndrewMotte, 1729, revised byFlorian Cajori, U. of Cal. Press,Berkeley, 1947

from

Principia, Book III,The System of theWorld,Motte translation

translated by AndrewMotte, 1729, revised byFlorian Cajori, U. of Cal. Press,Berkeley, 1947

from

Principia, Book III,The System of theWorld,

Law of Universal Gravitation

“And therefore (by Rule 1 and 2)the force by which the moon is retained in its orbit is the verysame force which we commonlycall gravity;…

from

Principia, Book III,The System of theWorld,

…15 1/12 Paris feet, …or, more accurately, 15 feet, 1 inch and 1 line 4/9

A Problem of Units

Towards the end of the 18th century there wastotal confusion in units and standards

“Contemporaries estimated that under the cover of some eight hundred names, the Ancien Regime of France employed a staggering 250,000 different units of weights and measures.”

Ken Alder, the Measure of All Things,Free Press, 2002

The rod, 16 men of assorted heightcoming from church. F.C. Cochrane, Measures for Progress, NBS, 1996

The Enlightment and a Triumph of Reason:

A system of units based on Nature, not Mankind

A Metric System: metric distance, metric mass, metric time, metric calendar,. . .

First triumph of the Metric Revolution: a new unit of length--the meter

Definition: the meter is 1 ten millionth the distance from the equator to the pole

Realization of the meter:

Survey, by triangulation, the distance between two latitudes along a convenient meridian, for instance the meridian between Barcelona and Dunquerque. Expeditions launched in 1792; Méchain toBarcelona, Delambra to Dunquerque. Their work concluded in 1798.

A great story, see The Measure of All Things, by Ken Alder, Free Press, 2002

“scale of30,000toises”

Paris!

A digression-- the advance of precision by

Joseph von Fraunhofer, 1783-1829

-Genius of optical instruments

-Inventor of the diffraction grating

-A life of rags to riches

The dispersive power of various glasses,Munich, 1814

Absorption lines in the solar spectrum,the “Fraunhofer lines”, 1814

Table of refractive indices of various glasses and materials.

Thinking aboutdiffraction, 1814.

Fraunhofer inventsdiffraction gratingin 1818.

Fraunhofer’s shop

NEEDED: A BETTER METER1873 “Convention of the Meter” signed Bureau Internationale des Poids et Mesures established

New definition of meter discussed1889 Meter redefined in terms of artifact Pt-Ir bar

1889 meterand kilogramMeanwhile…

1879: letter from Maxwell to

head of U.S. Naval observatory

Michelson-Morley experiment, December 1887

Experimentalfringe shift

1/8 TheoreticalShift

Michelson and Morley present their results for the fringe shift due to motion through the ether, December, 1887

Directly following that paper, another.

On a Method of making the Wave-length of Sodium Light the actual and practical standard of Length.

So, the 1889 definition of meter in terms of artifactwas obsolete when it was adopted. Michelson’s interferometric method was a) more precise- could measure one meter to about 1/100 of wavelength of light, ~2 parts in 10^8 b) more accurate- not susceptible to aging, temperature, bumps and bruises c) more practical- could be realized anywhere d) based on a natural unit.

In consequence, the artifact definition was more or less promptly set aside for a new definition….in 1960.

Meanwhile- starting in 1882, Michelson published aseries of papers, pushing the limits of interferometry.

By studying the intensity of interference fringes ashe extended one arm of his spectrometer over longdistances, Michelson

-Discovered the fine structure of hydrogen-Learned how to measure the width of spectral lines-Invented Fourier transform spectroscopy-Discovered pressure broadening-Confirmed Maxwell’s theory for the speeds of atoms

“visibility of fringes”

distance ---->reconstructed spectrum

Balmer-alpha

Balmer-beta

Hydrogen fine structure

Comparison of Michelson’s 1892 results with state-of-the-artspectroscopy in 1939.

Visibility curves and reconstructed spectra for two Hg isotopes. top: 3 line spectrum bottom: 2 line spectrum

Measurements of the speeds of atoms from the Doppler broadening of their spectral lines.

Finally, in 1960, a new legal definition of the meter was adopted, based on Michelson’s interferometric methods for counting wavelengths of light.

“The meter is 1650 763.73 wavelengths in vacuumof the orange-red line in the spectrum of thekrypton-86 atom.”

BUT, in 1959 the laser was invented, which revolutionized interferometry and soon made the new definition obsolete.

The story of TIME: Historic definition of the second: There are 86,400 seconds in one day

Problem: definition of day.Mean solar day: can be regarded as the

average time between successive sunrises.But, Earth’s rotation is slowing due to tidal

friction, and fluctuating due to Chandler wobbleand other small effects.

In 1952, the International AstronomicalUnion proposed introducing “ephemeris time.” Thesecond is 1/31 556 925.9747 of the tropical year1900. Proposal was adopted in 1958.

Ephemeris time became legal in 1960.BUT… first atomic clock was demonstrated in1954.

Louis Essen and Jack Perry,Cesium atomic beam frequency standardNPL, 1954

The definition of the second in terms of ephemeris time was obsolete before it was adopted. So..

in 1969 there was a new definition of the second

The second is the duration of 9192 631 770 periods of radiation corresponding to the transitionbetween the two hyperfine levels of the ground state of the cesium-133 atom.

A word about time scales:

TAI: average of primary and secondary atomic clocks around world

UT1: based on Earth rotation

UTC: Coordinated Universal Time: Leap seconds added to TA1 keeps UTC within 0.9s of UT1 This is the commonly propagated time scale.

From Splitting the Second,Tony Jones, IOP, 1992.

A problem in metrology:

Although time and frequency can easily be measured to 1 part in 10^13,

Wavelengths (i.e. distances) cannot be compared to better than 1 part in 10^10.

So, the speed of light cannot be measured to better than 1 part in 10^10.

Result: new definition of the meter based onthe distance light travels in a given time.

Realizing this new definition of the meter requires measuring the frequency of light, i.e. the frequency of a laser.

Frequency chain for measuring the frequency of a visible laser. NIST, ~1979.

New definition of the meter, 1983

The meter is the distance that light travelsin 1/299 792 458 of a second.

Unfortunately, for the next twenty years there was virtually no way to implement this definition.

Fortunately, this did not appear to cause any problems.

Changing styles of precision.

Three great syntheses in physics:

-Newton: Law of Universal Gravitation

-Maxwell: proof that light consists of electromagnetic waves, whose speed is given by the electric and magnetic force constants.

-Bohr: proof that the Rydberg constant is given by a specific combination of fundamental constants.

Bohr’s 1913 paper on his model of hydrogen.No uncertainties are stated.

The systematic treatmentof experimental uncertainty can be ascribed to R. T, Birge, who carried out the first evaluation of the fundamental constants.

The Physical Review Supplement later became the Review of Modern Physics.

The current state of high precision

The most accurately verified theory in physics is QED: theory and experiment have been found to agree to about 1 part in 10^11. This will soon be improved significantly.

A most unsatisfactory base unit in physics is mass, which continues to be an artifact at BIPM, Paris. This will not continue for much longer.

The most accurately measurable quantity continues to be time. Current accuracy is about 1 part in 10^15. Major improvements are expected.

An unsatisfactory (though pretty) base unit

opticalatomic clocks

cesiumclocks

goal,February 2003

CourtesyT.W. Haensch

A March of High Precision

The revolution in precision: optical frequency metrology--counting cycles of light--invented by T. W. Hänsch

Output from a modelocked (pulsed) laser. Here, the pulse rate is not synchronous with the carrier.

Synchronizing the carrier to form acomb of coherent optical frequencies.

An early frequency combgenerator

Optical Atomic Clockbased on ultra-violet transition in mercury ion

courtesy of Jim BergquistScience, 306, 1318, 2004

Is Time about to bite the dust--i.e. involve an artifact?

The gravitational red shift of time at the surface of the earth is about 1 part in 10^18 per meter. Thus, to define time to 1 part in 10^18, it will be necessary to fix where the clock is located.

Physics has progressed but human nature has not. There will undoubtedly be “lively debate” as to which laboratory gets the new second.

END