Author: John F. Lindner

  • The Ringed Planets

    John F. Lindner

    When I was a kid, Saturn was the ringed planet. But today, we know that all of the outer planets have rings. The James Webb Space Telescope has now imaged each of them in infrared revealing their distinctive structures, including Jupiter‘s very faint ring (located by the arrow and dashed curve). The planet images below…

  • Simplest Chaos

    John F. Lindner

    The motion of one of the simplest dynamical systems, a torqued, damped, nonlinear pendulum, can be infinitely complicated. Consider a simple pendulum of length and mass rigidly connected to an axle of radius wrapped by a rope that hangs down one side with a mass climbing up and down it, as in the attached animation.…

  • Vampire Ein Stein

    John F. Lindner

    Just a couple of months after announcing the remarkable discovery of a single shape that forces a non-periodic tiling of the plane, Smith, Myers, Kaplan, and Goodman-Strauss have announced an improved aperiodic monotile or ein stein. (Ein stein is “one stone” in German.) The hat and turtle shapes tile the plane only non-periodically, but with their…

  • The Temperature of the Vacuum

    John F. Lindner

    Quantum field theory predicts that the temperature of empty space should depend on the observer’s motion, increasing proportionally with acceleration. Here I attempt an accessible introduction to this striking effect, related to Hawking radiation and discovered independently by Fulling, Davies, and Unruh, assuming only sophomore-level physics (including hyperbolic functions) with some assistance from Mathematica. Hyperbolic…

  • A Century of Compton Scattering

    John F. Lindner

    One hundred years ago today the Physical Review published research on light scattering electrons that would earn its author, Wooster graduate Arthur Compton, a Physics Nobel Prize. By relativistically conserving spacetime momentum, as in the diagram below, and treating light as particles now called photons, Compton discovered that deflecting an electron through an angle stretches…

  • We Are Going

    John F. Lindner

    After half a century confined to low-Earth orbit, and as soon as late next year, humans will once again leave Earth and voyage to Moon. The reality of this exciting adventure crystallized earlier this month when NASA announced the diverse and inspiring Artemis II crew: Clockwise from left in the photo below are Christina Koch,…

  • Behold, an Ein Stein!

    John F. Lindner

    This academic year has been thrilling: first nuclear fusion breakeven, now an ein stein! Last week, a preprint at arxiv.org by David Smith et al. announced an “ein stein”, or one stone, a shape that forces a non periodic tiling of the plane, ending a half-century quest by many researchers, including me. A retiree and…

  • Generalizing Coulomb’s Law

    John F. Lindner

    The forces between two electric charges in arbitrary motion are complicated by velocity, acceleration, and time-delay effects. The forces need not even lie along the line joining the two charges! Suppose a source charge is at position with velocity and acceleration , and a test charge is at position with velocity and acceleration . Let…

  • Triple EVA

    John F. Lindner

    Since the mid 1960s, all space walks or extra-vehicular activities (EVAs) have involved just one or two astronauts — except once. In May 1992, on the STS-49 mission, the crew of the space shuttle Endeavour was attempting to rescue a stranded communications satellite, Intelsat 603. After repeated two-person EVAs failed to capture the satellite, NASA and the…

  • 5-Color Theorem

    John F. Lindner

    On 1852 October 23, Francis Guthrie noticed that he needed only 4 colors to color the counties of England so no two bordering counties shared the same color. This works for any map, but only in 1976, and with the aid of a computer, did Kenneth Appel and Wolfgang Haken finally prove the 4-color theorem. Here I outline…

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