## CUWiP 2018

Well, we’re so busy doing things here at Wooster Physics that we haven’t kept up the blogging about all our exciting activities.

Case in point — CUWiP 2018!

For the last several years, the American Physical Society has been hosting Conferences for Undergraduate Women in Physics (CUWiP). These are regional conferences around the US designed to help young women persist in physics by providing networking opportunities and information about graduate school and careers, in addition to talks about physics research.

We’ve been sending a delegation from Wooster to the nearest CUWiP for several years now, and it has been a really positive event.

This year, we had three Wooster students go to the local conference, which was at the University of Toledo. While there, they also got to meet up with Norah, a student from Hiram who did the Wooster REU over the summer.  Norah was presenting the results of her research with Dr. Lindner on Hannay Hoop-and-Bead Anholonomy.

Abigail and Norah!

Abigail Ambrose ’20 reports:

“One of my favorite speakers Dr. Karen Bjorkman, who is the Dean of the College of Natural Sciences and Mathematics at the University of Toledo. She is an astrophysicist and was an incredibly inspirational speaker.

We also got to go to a lot of different breakout sessions for everything from graduate school to REU applications and from writing papers to imposter syndrome. We all really want to go back and are super excited about some of the things we got to hear Michigan State planning for next year.”

Long day but still good!

And, just because I love it, here’s a picture from 2015 — what a great group of students!

Maggie, Laura, Justine, Popi, Catherine, Amanda, and Ziyi at CUWiP 2015

## Falcon Heavy

I was supervising Jr IS, but as I circulated around the lab, I watched the clock. Everyone was working quietly.

Just before launch, I snuck back to my office and closed the door. The SpaceX Falcon Heavy was surrounded by swirling clouds of condensation at Kennedy Space Center‘s historic Pad 39A. Amidst spectactors’ cheers and the sound suppression system’s deluge, the 27 Merlin rocket engines of the world’s largest launch vehicle ignited. I barely breathed for the first 2.5 minutes of flight under the three Falcon 9 boosters. The two side boosters detached, returned to Cape Canaveral, and landed side-by-side in a 1950s science fiction fantasy. While most test launches use mass simulators of concrete or steel, the payload fairing separated revealing Starman in the driver’s seat of a Tesla Roadster with Earth in the background.

Heart thumping, I returned to Jr IS. Everyone was working quietly.

Falcon Heavy boosters land side-by-side, like a 1950s science fiction fantasy, 2018 February 6

Tesla Roadster leaving Earth headed for beyond Mars

## The Impossible Problem

In 1969, Hans Freudenthal posed a puzzle that Martin Gardner would later call “The Impossible Problem”. Below is a 2000 version due to Erich Friedman.

I have secretly chosen two nonzero digits and have separately told their sum to Sam and their product to Pam, both of whom are honest and logical.

Pam says, “I don’t know the numbers”.
Sam says, “I don’t know the numbers”.
Pam says, “I don’t know the numbers”.
Sam says, “I don’t know the numbers”.
Pam says, “I don’t know the numbers”.
Sam says, “I don’t know the numbers”.
Pam says, “I don’t know the numbers”.
Sam says, “I don’t know the numbers”.
Pam says, “I know the numbers”.
Sam says, “I know the numbers”.

What are the numbers?

This beautiful problem may at first seem impossible, as you know neither the sum nor the product of the numbers, but the attached animation illustrates my solution.

Animated solution of “The Impossible Problem”. Matrix rows & columns are products and sums of nonzero digit pairs; filled squares indicate products & sums shared by pairs and not yet excluded by Pam or Sam

## Electronic Kilogram

The kilogram is the only metric unit still defined by an artifact. The International Prototype Kilogram, IPK or “Le Grand K”, is a golf-ball-sized platinum-iridium cylinder in a vault outside Paris. This year I expect the General Conference on Weights and Measures to replace the IKP by an electronic realization that balances gravitational and electrical power.

The Kelvin or Ampere balance suspends a horizontal wire loop of mass $m$, length $\ell$, and current $I$, by a radial magnetic field $B$. Integrate the magnetic force $\overrightharpoon{F}=q\overrightharpoon{v}\times\overrightharpoon{B}$ around the loop to find the force balance

$$m g = F = \left| \oint d \overrightharpoon{F} \right| = \left| \oint dq \,\overrightharpoon{v} \times \overrightharpoon{B}\right| = \left| \oint I d\overrightharpoon{\ell} \times \overrightharpoon{B}\right| =I \ell B$$

and solve for $m$. Unfortunately, $\ell$ and $B$ are difficult to measure accurately.

In 1975, Bryan Kibble proposed the calibration step of moving the current-less wire loop vertically at speed $v$. Integrate the force per charge $\overrightharpoon{F}/q=\overrightharpoon{v}\times\overrightharpoon{B}$  around the loop to find the induced voltage

$$V = \oint \overrightharpoon{E} \cdot d\overrightharpoon{\ell} = \oint \frac{\overrightharpoon{F}}{q}\cdot d\overrightharpoon{\ell} = \oint \overrightharpoon{v} \times \overrightharpoon{B} \cdot d\overrightharpoon{\ell} = v B \ell.$$

Eliminate $\ell$ and $B$ from the force and voltage expressions to find the virtual power

$$P = V I = v B L I = m g v$$

in Watts, and again solve for $m$. Accurately measure voltage $V$ by comparing to the superconducting Josephson-effect voltage

$$V =\frac{n_J f}{K_J},$$

where $K_J = 2 e / h = 0.48~\text{THz} / \text{mV}$ is the Josephson constant$n_J$ is the number of Josephson junctions, and $f$ is their microwave frequency. Convert current $I = V_R / R$ to voltage and resistance by Ohm’s law. Accurately measure resistance $R$ by comparing to the quantum Hall-effect resistance

$$R =\frac{R_K}{n_L},$$

where $R_K = h /e^2 = 26~\text{k}\Omega$ is the von Klitzing constant, and $n_L$ is the number of filled Landau levels. Accurately measure velocity $v$ and acceleration $g$ using interferometers.

Hence the mass

$$m=\frac{VI}{gv}=VV_R\frac{1}{R}\frac{1}{gv}=n_J f\left(\frac{h}{2e}\right) n_J f_R\left(\frac{h}{2e}\right) n_L\left(\frac{e^2}{h}\right)\frac{1}{gv}=\frac{n_L n_J^2 f f_R h}{4gv}\propto h,$$

where $h=0.66~\text{zJ} / \text{THz}$ is the Planck constant. The Kibble or Watt balance thus defines mass in terms of the rate of change of a photon’s energy with its frequency.

The NIST-4 Kibble balance has measured the Planck constant to 13 parts per billion and is thus accurate enough to help redefine the kilogram. Credit: Jennifer Lauren Lee.

## Taylor Bowl

On Wednesday, September 13, 1989, I met with newly elected Physics Club officers Tom Taczak ’91, Dennis Kuhl ’90, Doug Halverson ’91, and Karen McEwen ’90 in Westminister House. I wrote in my diary, “first phys club meeting w. officers goes well”. That year we invented Taylor Bowl, an annual bowling competition between the Physics and Math clubs, both denizens of Taylor Hall, at the bowling lanes in Lowry Student Center. We intentionally chose an activity that either club could do, but that neither club could do well. The annual event was a great success for both clubs for nearly 30 years, but it ends with the demolition of Scot Lanes this month.

Physics at Taylor Bowl Montage

## Newton’s Can(n)on

One of my favorite illustrations is the cannon thought experiment from volume three of Isaac Newton‘s Principia Mathematica. Johannes Kepler argued that planets orbit elliptically with Sol at one focus. Galileo Galilei argued that terrestrial bodies fall parabolically in space and time. Living in the next generation and standing on their shoulders, Newton realized that Kepler’s ellipses and Galileo’s parabolas were extremes of the same continuum, the Newtonian synthesis, which he dramatized by imagining a cannon on a tall mountain shooting cannon balls at increasing horizontal speeds: a falling apple orbits Earth (but collides with its surface); the orbiting Luna falls toward Earth (but its tangential velocity prevents a collision).

In Newton’s famous thought experiment, subsuming both Galileo and Kepler,
cannonballs shot at ever increasing horizontal speed eventually fall around Earth

Low-resolution photograph of page 6 volume 3 of Newton’s Principia,
as it appears in the Voyager interstellar records now en route to the stars

## ein Stein

I’ve been fascinated by aperiodic tilings of the plane since Martin Gardner first wrote about them in Scientific American. In the 1960s, Robert Berger discovered a set of 20 426 prototiles or tile-types that can tile the plane but only with no translational periodicity — a wonderful mix of the expected and the surprising, a kind of visual music.

Over the years, the number of required prototiles has been greatly reduced. In the 1970s, Roger Penrose discovered a set of just two concave aperiodic prototiles. Robert Ammann then dissected these to discover a set of three convex aperiodic prototiles. Can a single prototile, one tile or stone, literally ein Stein in German, force a nonperiodic tiling? Despite several near misses and potential applications to quasicrystals, the existence of an ein Stein remains a fascinating unsolved problem.

Three convex Ammann tiles force a nonperiodic tiling of the plane.

Two concave Penrose tiles force a nonperiodic tiling of the plane.

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## Gossamer Flight

As a kid, I devoured the pages of Popular Science magazine and was fascinated by the quest for human-powered flight: Was a flying bicycle possible?

In the mid 1970s, I read that aerospace engineer Paul MacCready had assembled a team to build a large, lightweight, human-powered aircraft that could be rapidly repaired and redesigned. In 1977, after multiple iterations, cyclist Bryan Allen flew MacCready’s Gossamer Condor around a one-mile figure-eight course to win the first Kremer prize. Two years later, Allen flew MacCready’s improved Gossamer Albatross 22 miles across the English Channel to win the second Kremer prize.

Made with a carbon fiber frame and polystyrene ribs covered with transparent plastic film, each Gossamer aircraft had a long tapering wing behind a large horizontal stabilizer. Weighing less than the pilot-engine, the required power was only about 0.3 kW (or 0.4 hp). Currently, an outstanding Kremer prize is to fly a 26 mile marathon course in under an hour.

Bryan Allen powers and pilots Paul MacCready’s Gossamer Albatross across the English Channel in 1979.

Allen flies MacCready’s Gossamer Albatross II in NASA tests in 1980.

## The Cupola

In the sky is a castle, built in free fall, brick-by-brick, where the sun rises and sets every ninety minutes. The castle derives its energy from sunlight and recycles its water. Sealed against a vacuum, its inhabitants float and glide through its passageways and gaze down at Earth through its expansive cupola.

In an earlier age, the castle would be the magic of legend, but in ours, it’s the International Space Station. Assembled in low Earth orbit, its unique microgravity laboratories are powered by giant solar electric panels that rotate like windmills to track the sun. Arguably the most complex engineering project ever accomplished, the ISS is a model for international cooperation, where former cold-war enemies live and work together.

Astronaut Tracy Caldwell Dyson gazes down at Earth from the International Space Station’s cupola