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After the Moonwalk
Iconic is Neil Armstrong’s photograph of Buzz Aldrin during the first moon walk, with Armstrong reflected in Aldrin’s visor. Much less well-known is this pair of photographs taken just after the moon walk. To my eyes, Armstrong seems exhausted but happy; Aldrin seems satisfied … and over his shoulder, almost casually, is a window, and…
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“Contact Light”
Our TV is broken, so Aunt Nora invites us to her apartment. (Aunt Nora isn’t really our aunt, but she introduced our parents to each other, so that’s what we call her.) My brother Jim and I lie on the floor close to the TV, while the adults sit on the couch. We watch NBC…
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Wooster Epicycles
A vector is the sum of its components, a mechanical vibration is a combination of its normal mode motions, a quantum state is a superposition of its eigenstates, and any “nice” function is a Fourier sum of real or complex sinusoids, . The animation below traces the Wooster W in epicycles of 100 circles-moving-on-circles in the…
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Redefining SI
Today the SI (Système international d’unités) base units are redefined. The following are now exact. Memorize these numbers! Cs-133 transition frequency constant defines the second. Then light speed constant defines the meter. Then Planck’s constant defines the kilogram. Then electron charge constant defines the Ampere. Then Boltzmann’s constant defines the Kelvin. And Avogadro’s constant defines the mole. And luminous efficacy constant defines…
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Black Hole Radii
I set the alarm for 8:55 AM. Brutal, but I wanted to watch live the National Science Foundation Event Horizon Telescope news conference. I was expecting the first image of a black hole, and the EHT team did not disappoint. But the black hole was not the Milky Way’s Sgr A*, but M87*, a thousand…
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The Longest Day
The December solstice is the longest day of the year, despite being the northern hemisphere’s shortest daylight. Earth’s sidereal day is the time to rotate 360° with respect to distant stars, about 23 hours and 56 minutes, and its solar day is the time between successive noons, about 24 hours. Earth’s obliquity (tilt) and revolution (orbit) require…
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Relativistic Colors
Metallium, Inc. is attempting to manufacture coins made from as many different metals (and elements) as possible, typically 99 to 99.9% pure. My Metallium coin collection currently includes aluminum, titanium, iron, nickel, copper, zinc, silver, tin, and gold coins. Most metals are silvery gray because they absorb ultraviolet light and reflect visible light. However, relativistic…
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720° untangles 360° tangles
Despite growing up in three dimensions, as a kid I did not recognize one of 3D’s deep and subtle properties: full rotations tangle, but double rotations untangle! Following physicist Paul Dirac, twist a belt one full turn about its length. The 360° single twist cannot be undone without changing the belt buckles’ orientations, although the twist…
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Luna’s Convex Orbit
Luna orbits Earth and Earth orbits Sol (where Luna is Earth’s moon and Sol is Earth’s star, the sun). As a kid, I thought Luna’s solar orbit formed a loopy spirograph pattern. Instead, Luna’s orbit is convex! Neglecting the eccentricity and tilts of the orbits and the incommensurability of the periods, Luna’s counterclockwise path around…
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1+2+3+… = -1/12?
In quantum electrodynamics, the bare charge of an electron is infinite, but the renormalized dressed charge is finite. The bare electron shields itself by polarizing the virtual electron-positron pairs of the nearby quantum vacuum to reduce its coupling at large distances to in natural units, where the “I” decorating the equals sign denotes an informal relationship. Renormalization techniques help…
Author: John F. Lindner
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Nice post, John! Thanks for writing these. I always enjoy them.
David Smith’s ein stein is an awesome shape!
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Thanks, Mark! I enjoy reading your posts as well.