Measurement

The Measurers, Hendrik van Balen

MeasurementWhen you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind. William Thompson, aka Lord Kelvin

‘MY GOODNESS, IT’S 12:15.0936420175. TIME FOR LUNCH.’

Errors in Physics

doh!

“Any measurement that you make without the knowledge of its uncertainty is completely meaningless.”

Walter Lewin, MIT Professor of Physics

Scientific knowledge is a body of statements of varying degrees of certainty — some most unsure, some nearly sure, but none absolutely certain.

Richard Feynman

1600 Kepler Guessing Infinite

1667 Galileo Lanterns Really fast

1676 Olaus Roemer Jupiter's satellites 214,000

1726 James Bradley Stellar Aberration 301,000

1849 Armand Fizeau Toothed Wheel 315,000

1862 Leon Foucault Rotating Mirror 298,000 ± 500

1879 Albert Michelson Rotating Mirror 299,910 ± 50

1907 Rosa, Dorsay Electromagnetic constants 299,788 ± 30

1926 Albert Michelson Rotating Mirror 299,796 ± 4

1947 Essen, Gorden-Smith Cavity Resonator 299,792 ± 3

1958 K. D. Froome Radio Interferometer 299,792.5 ± 0.1

1983 Adopted Value 299,792.458 exact!

Significant Figures and the Pursuit of Glory!

Hubble Space Telescope (HST)

Telescope Mirror

• Problem: images were fuzzier than expected (e.g. star on right should appear as a single point)

• Telescope mirror was too flat on the edges by 2.2 micrometers (μm)

• 2.2 micrometers (μm) = 0.0000022 m

• Human hair thickness = about 0.1 mm (1000 microns)!

Hubble images: before and after correction

Moral: significant figures matter in measurement!!!