“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 not CBS, so we miss Cronkite’s commentary. The late afternoon video is a simple animation; the famous 16-mm film — only later synchronized with the audio — would return to Earth with the astronauts 4 days later.

The tension is palpable. The cartoon lander reaches the surface at the expected time, but Aldrin’s monotone readouts continue. Absence of video heightens the audio. Mission control radios “60 seconds” of fuel remaining. Then “30 seconds”. I hold my breath. At last, Aldrin reports “Contact light” — we have touched the moon — followed by Armstrong’s famous, “Houston … Tranquility Base here, the Eagle has landed”. Of the landing site, my mother observes, “They’ve already named it”.

No one wants to cook, so we go to McDonald’s for dinner. As we drive, I see a small shop with photos of the three astronauts in its window. The streets are still. The world seems stopped.

10:56:15 PM EDT, Sunday, July 20, 1969

10:56:15 PM EDT, Sunday, July 20, 1969

As Collins orbits the moon solo, Armstrong and Aldrin forgo a scheduled sleep period, moving forward the moonwalk. Finally video — live from the surface of the moon —  shows a LEM landing leg, first inverted but quickly rectified. Armstrong describes the surface as “almost like a powder”. Again I hold my breath, a lump in my throat. “Okay. I’m going to step off the LEM now … that’s one small step for [a] man, one giant leap for mankind.” I don’t hear the indefinite article, but I immediately grasp the meaning. Armstrong reads the plaque, “We came in peace for all mankind”. Aldrin practices locomotion, which “would get rather tiring”. The president phones. We leave Aunt Nora’s as the astronauts prepare to return to the LEM.

The next morning I sit on my living room floor reading two newspapers: The New York Times, with its simple banner headline “Men Walk on Moon” — which still brings me tears of joy, triumph, and wonder as I write this 50 years later — and the local newspaper, with its astonished “Now Do You Believe!”.

My Monday morning newspapers, July 21, 1969

My Monday morning newspapers, July 21, 1969

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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, e^{i \varphi} = \cos \varphi + i \sin \varphi.

The animation below traces the Wooster W in epicycles of 100 circles-moving-on-circles in the complex plane. Algebraically, the trace is a complex discrete Fourier series \sum c_n e^{i n \omega t} =\sum r_n e^{i (n\omega t + \theta_n)}, where r_n are the circle radii, \theta_n are carefully chosen phase shifts, \omega is the fundamental angular frequency, and t is time.

Using Fourier analysis, any reasonable path can traversed by a moon orbiting a moon orbiting a moon orbiting ... a planet orbiting a star

Using Fourier analysis, any reasonable path can traversed by a moon orbiting a moon orbiting a moon orbiting … a planet orbiting a star

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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 Δν_{\text{Cs}} = 9\,192\,631\,770~\text{s}^{−1} defines the second.

Then light speed constant c = 299\,792\,458~\text{m}\cdot\text{s}^{−1} defines the meter.

Then Planck’s constant h = 6.626\,070\,15\times 10^{−34}~\text{kg}\cdot\text{m}^{2}\cdot\text{s}^{−1} defines the kilogram.

Then electron charge constant e = 1.602\,176\,634\times 10^{−19}~\text{A}\cdot{\text{s}} defines the Ampere.

Then Boltzmann’s constant k = 1.380\,649\times 10^{−23}~\text{kg}\cdot\text{m}^{2}\cdot\text{K}^{−1}⋅\text{s}^{−2} defines the Kelvin.

And Avogadro’s constant N_{\text{A}} = 6.022\,140\,76\times 10^{23}~\text{mol}^{−1} defines the mole.

And luminous efficacy constant K_{\text{cd}} = 683~\text{cd}\cdot\text{sr}\cdot\text{s}^{3}\cdot\text{kg}^{−1}\cdot\text{m}^{−2} defines the candela.

(Where “sr” is the steradian or square radian, the 3D analogue of the 2D radian.) Discussion continues about the mole and the candela, including whether they should even be base units. The new definitions break the relationship between the C-12 mass, the dalton, the kilogram, and Avogadro’s constant, and the candela is arguably a photo-biological quantity.

I wish my phone number were 919-263-1770.

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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 times further but a thousand times larger (billions rather than millions of solar masses).

For Astronomy Table lunch at Kitt’s Soup & Bread, I quickly created the graphic below to illustrate various radii of a mass M Schwarzschild black hole, a good approximation to this rotating Kerr black hole. The event horizon with reduced circumference R_s = 2 G M / c^2 is the point of no return, the causal disconnection from which even light can’t escape. The innermost stable circular orbit at 3R_s marks the inner edge of the accretion disk. Massless particles like photons can orbit even closer, at the 1.5R_s photon sphere, where you can see your back by looking straight ahead! The ring of light (mainly 1.3 mm synchrotron radiation) in the EHT photo comes from photons with impact parameter \sim 2.6R_s that just graze the photon sphere and can orbit multiple times before spiraling in or out.

Schwarzschild ("black shield") black hole with event horizon, unstable photon sphere, grazing photon sphere, and innermost stable circular orbit

Schwarzschild (“black shield”) black hole with event horizon, unstable photon sphere, grazing photon sphere, and innermost stable circular orbit

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December 22 is the Longest Day

December 22 is the longest day of the year, despite being near 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 an extra rotation (spin) of about 4 minutes to go from noon to noon. Because Earth is coincidentally at perihelion (nearest sun and moving fastest) during the December solstice (maximum tilt toward sun), these effects combine to produce the longest solar day, about 24 hours and 30 seconds.

The diagram discretely illustrates the difference between solar and sidereal days for planets with 3 different tilts. From the first row to the second, the planets orbit the sun as they spin 360° (in the sense of the green right-handed arrow). From the second row to the third, the planets spin through extra angles (in the sense of the yellow right-handed arrow), so that the marked longitudinal planes again includes the sun. Tilted planets must spin further, taking extra time, to extend a sidereal day to a solar day.

Planet (yellow) orbits sun (green) near perihelion through solar and sidereal days (rows) for 3 planetary tilts (columns). Longitudinal square rotates 360° for a sidereal day and >360° for a solar day.

Planet (yellow) orbits sun (green) near perihelion through solar and sidereal days (rows) for 3 planetary tilts (columns). Longitudinal square rotates 360° for a sidereal day and >360° for a solar day.

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March Meeting — Guest Blog by Carlos Owusu-Ansah ’21

Carlos in action at his poster, with Andrew Blaikie '13 and Daniel Blaikie '19.

Carlos in action at his poster, with Andrew Blaikie ’13 and Daniel Blaikie ’19.

I thought the March APS meeting was fantastic. It felt great to present our research findings to people who cared about what Dr. Lindner and I were working on at the College. I attended fun talks about astronomical phenomena and learned many cool things about the evolution of our solar system.

It is easy to think that physicists are an elite squad and that their subject matter is esoteric, but being so close and interacting with them made me realize that they are just like us and that learning about physical phenomena is really great fun. I am really happy to have been given this opportunity.

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March Meeting — Guest Blog by Katie Shideler ’21

Having never been to a physics conference, or even to the city of Boston, attending the annual American Physical Society’s March Meeting was all around a new and incredible experience. Being able to present my research to physicists from across the globe was nerve-racking but very insightful to get opinions of others who are far removed from the research I’m doing, so they brought in new perspectives I hadn’t thought of before.

Katie in front of her poster

Ready to start the poster session

My poster was set up next to a man who conducted similar research to me, so it was fascinating to see what he did differently with his system and how that changed the course of the experiment. Talking with him and exchanging ideas was one of my favorite parts of the conference.

Katie talks to another conference attendee by the poster

Deep in conversation with an interested attendee 

I also had the opportunity to sit in on numerous fascinating talks various researchers were giving. My favorite talk I went to talked about improving the design of the wheels on Mars Rovers, because NASA has been having problems with the Rovers getting stuck in the sand. This researcher and his team designed a new body for the Rover with new axes of rotation for the wheels to allow the Rover to keep moving and get itself out of the sand. It was pretty sweet to see clips of this thing moving through the sand. I also found this talk about nanorobots powered by lasers extremely interesting which seem to have the potential to make improvements in the medical fields.

Anyway, there were so many cool talks to go to I found it difficult to choose which ones to go watch. In addition to the awesome physics that was taking place, the city of Boston was extremely cool to explore and find local place to grab a coffee or a bite to eat. All in all, the March Meeting I would say was a success.

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Wooster in Boston

As mentioned earlier, I’m at the APS March Meeting in Boston this week.  There’s so much to say about all the talks that I’ve been to, etc, but in this post I’m just going to tell you about all the amazing Wooster connections!

First off, of course, we have five students here this year from the REU program last summer, and Dr. Leary and I are both here.  It’s fun to bring students to the meeting so that they can see how huge and diverse the larger world of physics is.  One of the great things that usually happens at the Meeting is that Wooster alumni come by to see our student posters.

Andrew and Carlos look at the poster

Andrew asks Carlos to fill him in on the latest progress in this work studying gravitational interactions for non-spherical objects

Tuesday morning I went to see Andrew Blaikie ’13 give a cool talk about graphene trampolines to be used as broadband bolometers.  Andrew is just about finished with his Ph.D. at Oregon.  He did a nice job with his talk, since he’s an old hand at the March Meeting by now.  Devoted readers of the blog will remember that we featured Andrew last year in the blog posts about the March Meeting in LA.  Andrew did the slash-slash project with Dr. Lindner for his Senior IS, so he came by the posters today to quiz Carlos Owusu-Ansah about his results with the latest incarnation of that research.

Melinda and Daniel, looking at a poster

Melinda listens to Daniel explain light sensitive BZ waves.

Walking around, I also bumped into Melinda Varga, who was at Wooster last year doing a post-doc with Erzsébet Regan that blends physics and biology.  She is still doing the postdoc but now is physically based at Harvard Medical Center.  She came to the poster session to ask our students about their work!

selfie with Hannah


I then also coincidentally sat down right next to Hannah Peltz Smalley!  Hannah was a Wellesley student who did the Wooster REU in 2017, and she is now a grad student at RPI.

Walking down the hallway to a session, I saw Nick Harmon ’04!  We chatted for a while to catch up.  He and his family recently moved to Indiana, where he started a position at the University of Evansville.

Amy Lytle, looking at some knitting

Amy Lytle investigates beautiful knit work at Elisabetta Matsumoto’s talk.

On Wednesday morning, there was session on Fabrics, Knits, and Knots that started with an invited talk by Elisabetta Matsumoto.  Many of you know that I am a knitter, so this was a cool “worlds collide” moment for me.  Afterward, I was up at the front looking at the demonstration pieces that Elisabetta had brought, and Amy Lytle ’01 tapped my elbow to say hi!  She graduated before I came to Wooster, but we’ve met many times by now.

Wednesday night, we had our group dinner, along with Popi Palchoudhuri ’16. She works here in Boston at E Ink, the maker of the ePaper technology that is in Amazon’s Kindle devices.  Popi is famous in beadpile history, both because she did the beadpile project as a first year summer student and again for IS, and also because of the quality of her lab notebook skills!

Maggie Donnelly, Wooster History '11 and academic publisher for physics

Maggie Donnelly, Wooster History ’11 and academic publisher for physics

Finally, I was walking around the exhibit hall one last time this afternoon.  I passed by the Institute of Physics booth, not planning to stop originally, but paused to ask a question about one of their display items.  The person I was talking to looked at my badge and said “College of Wooster!!”  It turns out that she was Maggie Donnelly ’11, a history major!  She was heavily involved in journalism at the College, took an editing job at an astrophysics journal once she left Wooster, and now loves being involved with academic publishing! One of her projects is the new Quantum Science and Technology journal by IOP, which you can see featured in the poster right beside her.  We talked for a while about the excellence of Wooster and what a wonderful community it is.  It was great to meet her.



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March Meeting 2019 Boston

I’m currently in Boston for the 2019 March Meeting, which is as exciting, overwhelming, and exhausting as usual!

Aerial view of Boston

Circling Boston to approach for landing. Keen viewers can see the Boston Commons (just on the far side of the river), the MIT campus (on the near side of the river, toward the right), and even the convention center (beyond the Commons)

You may remember last March Meeting, we were in LA, which was naturally nice and warm.  Boston welcomed the March Meeting with one of the first big snow storms of the season — about 8 inches of very wet, heavy snow — right in time for Monday morning.  Fortunately, I flew in on Sunday so had no trouble, but I heard of a local presenter who missed their invited 8 am talk because they couldn’t drive in.  The roads were definitely sloppy, but it was a beautiful snow.

Snowy street

Monday morning, outside the Parker House hotel.

Snowy scene

Snowy statue of Ben Franklin outside Old City Hall, just across from my hotel

I ended up walking into the convention center (about a mile) which was actually quite nice.  But I wished that I had brought boots.  I was impressed at how quickly the downtown sidewalks were being cleared.  The trouble was really at the intersections with the piles from the snow plows.

More snowy scenes

Snow on the Bass River, crossing toward the Convention Center

Once I arrived at the meeting, there were lots of interesting talks, of course.  I spent the morning in a session on Geophysical Applications of Granular Flows, with a series of really interesting invited talks. I learned a lot more about erosion and incipient flow — when does a fluid flowing over a granular material make those grains also flow?  When do grains that have been picked up and carried in the fluid drop down and settle?  It’s fluid dynamics and turbulence and granular materials all in one complicated problem!

More updates to come — but I need to get to the convention center this morning for our last day at the meeting!



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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 effects contract some of the atomic orbitals of copper and gold so they absorb some visible light and reflect the complementary colors. (Heuristically, in large atoms some electrons move at near light speed and appear more massive.) These colors are a striking example of relativistic physics in everyday life — and of the Dirac equation corrections to the Schrödinger equation.

My Metallium coin collection includes Al, Ti, Fe, Ni, Cu, Zn, Ag, Sn, AuAll are silvery gray except Cu and Au, whose colors result from relativistic changes to atomic orbitals.

My Metallium coin collection includes Al, Ti, Fe, Ni, Cu, Zn, Ag, Sn, Au coins. All are silvery gray except Cu and Au, whose colors result from relativistic changes to atomic orbitals.

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