How Physics Got Precise Or some events from

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

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.

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

distance (Jupiter diameters) Ganymede time (hours) Plotted by Alber Liau

distance (Jupiter diameters) Europa time (hours) Plotted by Alber Liau

1682: more precise measurements are available Europa: period = 84. 223 hours from Kepler: 85 hours Ganymede: period = 171. 71 hours from Kepler: 172 hours Measurements taken from…

from Principia, Book III, The System of the World, Motte translation translated by Andrew Motte, 1729, revised by Florian Cajori, U. of Cal. Press, Berkeley, 1947

from Principia, Book III, The System of the World, Motte translation translated by Andrew Motte, 1729, revised by Florian Cajori, U. of Cal. Press, Berkeley, 1947

from Principia, Book III, The System of the World, Motte translation translated by Andrew Motte, 1729, revised by Florian Cajori, U. of Cal. Press, Berkeley, 1947

from Principia, Book III, The System of the World, Law of Universal Gravitation “And therefore (by Rule 1 and 2) the force by which the moon is retained in its orbit is the very same force which we commonly call gravity; …

from Principia, Book III, The System of the World, A Problem of Units … 15 1/12 Paris feet, …or, more accurately, 15 feet, 1 inch and 1 line 4/9

Towards the end of the 18 th century there was total 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 height coming 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 to Barcelona, Delambra to Dunquerque. Their work concluded in 1798. A great story, see The Measure of All Things, by Ken Alder, Free Press, 2002

“scale of 30, 000 toises”

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 about diffraction, 1814. Fraunhofer invents diffraction grating in 1818.

Fraunhofer’s shop

NEEDED: A BETTER METER 1873 “Convention of the Meter” signed Bureau Internationale des Poids et Mesures established New definition of meter discussed 1889 Meter redefined in terms of artifact Pt-Ir bar 1889 meter and kilogram Meanwhile…

1879: letter from Maxwell to head of U. S. Naval observatory

Michelson-Morley experiment, December 1887

1/8 Theoretical Shift Experimental fringe shift 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 Wavelength of Sodium Light the actual and practical standard of Length.

So, the 1889 definition of meter in terms of artifact was 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 a series of papers, pushing the limits of interferometry. By studying the intensity of interference fringes as he extended one arm of his spectrometer over long distances, 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

Hydrogen fine structure “visibility of fringes” Balmer-alpha Balmer-beta reconstructed spectrum distance ---->

Comparison of Michelson’s 1892 results with state-of-the-art spectroscopy 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 vacuum of the orange-red line in the spectrum of the krypton-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 wobble and other small effects. In 1952, the International Astronomical Union proposed introducing “ephemeris time. ” The second is 1/31 556 925. 9747 of the tropical year 1900. Proposal was adopted in 1958.

Ephemeris time became legal in 1960. BUT… first atomic clock was demonstrated in 1954. Louis Essen and Jack Perry, Cesium atomic beam frequency standard NPL, 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 transition between 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 UT 1: based on Earth rotation UTC: Coordinated Universal Time: Leap seconds added to TA 1 keeps UTC within 0. 9 s of UT 1 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 on the 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 travels in 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 treatment of 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

A March of High Precision cesium clocks optical atomic clocks goal, February 2003 Courtesy T. W. Haensch

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 a comb of coherent optical frequencies. An early frequency comb generator

Optical Atomic Clock based on ultra-violet transition in mercury ion courtesy of Jim Bergquist Science, 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