Steuard Jensen
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steuard.bsky.social
Steuard Jensen
@steuard.bsky.social
520 followers 120 following 960 posts
Physics professor, Tolkien scholar, JoCoNaut, and all-around science nerd.
he/him
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steuard.bsky.social
The Andrew formerly known as Prince.
Screenshot of a New York Times headline and accompanying photo, reading: "Prince Andrew to Be Stripped of His Royal Title". (Andrew doesn't look too happy about this development.) [Subtitle: The extraordinary move caps his fall from grace over his ties to the convicted sexual predator Jeffrey Epstein.]
October 31, 2025 at 1:35 AM
steuard.bsky.social
It's getting cooler as we go deeper into autumn, which means my family has talked me into making the first homemade hot chocolate of the season. (I didn't take much convincing.) So delicious!
A mug full of freshly made hot chocolate sits on a green placemat on a wooden table. The mug is white ceramic, and the outside is covered with a Halloween scene with ghosts flying around haunted houses.
October 19, 2025 at 11:38 PM
steuard.bsky.social
I had a lovely time today hosting a couple groups of first graders in the Alma College planetarium to answer questions about the stars and the moon, and to read them "Moonshot" by Brian Floca (my very favorite book about space for kids). They were so enthusiastic, and had so many neat questions!
The cover of the book "Moonshot: The Flight of Apollo 11", by Brian Floca. The image on the cover is a drawn or painted illustration of a black night sky full of stars, with the moon centered near the top (a crescent of it illuminated, but the rest still dim but visible). Centered near the bottom of the cover is a detailed drawing of the joined spacecraft Columbia (a shiny silver metal cylinder covered with various hatches and attachments) and Eagle (a shiny golden boxy craft with four landing legs folded up along its corners). The cover includes medals/seals for a couple of children's book awards, but its biggest selling point is a quote from Michael Collins himself: "Reading Moonshot gave me the feeling I was back up in space."
October 14, 2025 at 7:54 PM
steuard.bsky.social
That equation kinda bugs me, maybe because I've never taught a Quantum course that didn't focus on Dirac notation. Operators don't act on functions, they act on states! So I'd write that result as shown in the image below (or maybe more equivalent, just "x-hat acting on x-ket equals x times x-ket").
Dirac notation for the action of the position operator x-hat acting on a state psi, and then written in the position basis. The first term is "x-bra acting on x-hat acting on psi-ket", which equals "x times the bracket of x-bra with psi-ket", which is by definition "x times the wavefunction psi(x)".
September 3, 2025 at 9:26 PM
steuard.bsky.social
7/? Last but not least, I've gone beyond most discussions of spacetime diagrams I've seen by adding basic support for showing "What would things look like in a *non-inertial* reference frame?" The app can draw plausible coordinates seen by a selected trajectory (with inevitable ambiguities).
The same diagram from earlier of an astronaut and their green-haired twin staying home. This time, though, a series of solid and dashed reddish lines criss-cross the diagram at various angles, illustrating how the astronaut might label time coordinates in their accelerated reference frame. (For each of the three different accelerated motion segments of the motion—rightward away from home, leftward to reverse toward home, and rightward to slow down while returning home—the red lines all come together at a single point "behind" the curve of the acceleration.) Three triangular wedge-shaped regions in the graph (extending outward from those singular points toward the sides of the graph) are shaded grey because the coordinate lines are ambiguous and overlapping there.
August 7, 2025 at 9:38 PM
steuard.bsky.social
6/? I've tried to make the app's user interface intuitive, but powerful under the hood: you can just click and drag events and trajectories on the diagram, or control their exact coordinates and velocities (and add new ones) down below. And of course you can play and pause the animation.
A screenshot of the app's user interface, including parts of the diagrams at the top (showing the motion of a house, a charging rhino, and a few flashes of light as seen in two different reference frames, along with animated motion panels below each one). In each diagram, one of the rhino images is selected (highlighted inside a yellow circle). Underneath the diagrams are a set of controls: undo/redo, animation play/pause, reference frame velocity selection, a panel showing detailed information about the selected event on the rhino's trajectory, controls for adjusting the diagram coordinates, and controls to load an example scenario or copy a permanent link to the current diagram state. Finally, sections at the bottom provide details and controls for any standalone events or any trajectories shown.
August 7, 2025 at 9:38 PM
steuard.bsky.social
5/? The app can show coordinate grids for two different reference frames on the same diagram (the diagram frame grid looks normal; the other frame is tilted), and can also draw the corresponding diagram as seen in the other frame. This visualization clarifies sooo many puzzles and "paradoxes"!
A screenshot of my spacetime diagram web app, showing diagrams describing the same events and motion in two different inertial frames ("Home Frame" on the left and "Other Frame" on the right). Each diagram shows a "graph paper" grid with the vertical axis labeled "t" or "t prime" and the horizontal axis labeled "x" or "x prime". Faintly in the background of each is a tilted diamond-like grid showing the coordinate grid of the other frame. Each diagram shows three lines going up the page (toward higher t), but they go straight up in the Home Frame and up along parallel diagonal lines in the Other Frame. There are also 45° lines going upward from a shining event marked at the origin. A yellow horizontal line is drawn across each diagram at the same height somewhere in the middle. Below each diagram is a flat panel showing the locations of each object at the time corresponding to the height of the yellow line: two firecrackers, a person with green hair in the middle, and a couple of blue dots between them. In the scenario below the Other Frame diagram, the firecracker on the left has just exploded.
August 7, 2025 at 9:38 PM
steuard.bsky.social
4/? My app also calculates how each observer in a diagram will measure time: one brain-bending idea in relativity is that clocks tick differently depending on how you see them moving. Here's an illustration of the "twin paradox", where the twin on a rocket ages less than the one who stays home.
A simple spacetime diagram labeled "Home Frame", showing a graph paper grid with vertical axis labeled "t" and horizontal "x". A green line representing a person with green hair extends straight up the graph just left of the origin, while a blue line representing an astronaut follows a curving path. The astronaut's line goes straight up from the bottom of the graph to the origin (right next to the green line) and then bends to the right, curving smoothly to a maximum point (six lines up in time and four lines over in space) before curving back to its original x position and straightening back up (next to the green line) to the top of the graph. Red-ish dots representing years of travel are marked along each line, with the green line's dots spaced evenly at each gridline while the blue line's dots are spread wide apart in sections where the graph is tilted farthest from vertical. A yellow line extends horizontally across the diagram near the top. Below the diagram, a thin panel shows the location of each of the two people at the time represented by the yellow line, directly below the points where each of their lines intersects the yellow line. Under each picture is a number corresponding to the number of red dots since the origin at that time: seven for the green hair and five for the astronaut.
August 7, 2025 at 9:38 PM
steuard.bsky.social
3/? The basic idea (described better at the link!) is that motion back and forth along a straight line can be represented as a graph with time going *up*: a horizontal slice (in yellow) shows where on the line each object is at that time. My app animates the motion, to translate diagrams to reality.
A simple spacetime diagram labeled "Home Frame", showing a graph paper grid with vertical axis labeled "t" and horizontal "x". An orange line representing a house extends straight up the graph through the origin, while a green line representing a runner tilts up and to the right, and a blue line representing an airplane tilts more steeply to the right. A yellow line extends horizontally across the diagram near the top. Below the diagram, a thin panel shows the location of each of the three objects at the time represented by the yellow line, directly below the points where each of their lines intersects the yellow line.
August 7, 2025 at 9:38 PM
steuard.bsky.social
1/? Ever wanted to understand Einstein's theory of special relativity? I'm feeling remarkably proud of a web page/app I've written that introduces the idea using "spacetime diagrams" (and lets you play with them yourself).
steuard.github.io/spacetime/in...
🎢🧪 #ITeachPhysics
A screenshot of my spacetime diagram web app, showing diagrams describing the same events and motion in two different inertial frames ("Home Frame" on the left and "Other Frame" on the right). Each diagram shows a "graph paper" grid with the vertical axis labeled "t" or "t prime" and the horizontal axis labeled "x" or "x prime". Faintly in the background of each is a tilted diamond-like grid showing the coordinate grid of the other frame. Each diagram shows three lines going up the page (toward higher t), but they go straight up in the Home Frame and up along parallel diagonal lines in the Other Frame. There are also 45° lines going upward from a shining event marked at the origin. A yellow horizontal line is drawn across each diagram at the same height somewhere in the middle. Below each diagram is a flat panel showing the locations of each object at the time corresponding to the height of the yellow line: two firecrackers, a person with green hair in the middle, and a couple of blue dots between them. In the scenario below the Other Frame diagram, the firecracker on the left has just exploded.
August 7, 2025 at 9:38 PM
steuard.bsky.social
Staying at the Madonna Inn in San Luis Obispo on a short getaway fore our 25th anniversary. Our room is fun, with stained glass windows and a rock waterfall shower. Lovely!

The pillows, though, all feel like they're stuffed with jackets guests have accidentally left behind over the past 70 years.
The William Tell bedroom at the Madonna Inn. The exterior walls are built of huge rough stones and feature stained glass windows showing the famous "shoot an apple off your son's head" story. (The carpet is patterned red to match the apple, and the interior walls are bright red.) The rock-walled shower in our bedroom includes both an ordinary shower head and a waterfall off of a rock shelf up above.
July 28, 2025 at 3:14 AM
steuard.bsky.social
A still shot from Terminator 2, showing the shape shifting T1000 robot in the form of John's foster mother. She is holding out one arm, which has taken the shape of a sharp metal blade (dripping with blood). The shape is oddly reminiscent of the recalled steamers' pointy ends in the quoted skeet.
July 17, 2025 at 10:48 PM
steuard.bsky.social
I'd been looking forward to taking a long bike ride this morning before it got too hot, but it turns out there's a Canadian wildfire causing nasty air quality across Michigan. Definitely not safe conditions to push myself for a 40 mile ride! Hopefully it'll clear up in a couple days.
A map of air quality from map.purpleair.com showing air quality levels as colored circles. Green markers for good air are shown through the Dakotas to the west and past Lakes Huron and Erie to the east-southeast, but red and purple bad air spreads southeast from a source in eastern Saskatchewan through Minnesota, Wisconsin, and Michigan.
July 13, 2025 at 2:52 PM
steuard.bsky.social
Just got treated to a Star Wars medley by the carillon bells at the National Cathedral.
A view up the hill through a garden to the carillon bell tower of the National Cathedral in Washington, DC.
June 21, 2025 at 5:06 PM
steuard.bsky.social
4:00pm: Capitol selfie on the way to a Metro station

4:30pm: Looking across the street as we scurry into our hotel under an umbrella.

Things evidently got exciting while we were underground!
Me in the foreground in a burgundy polo with Ms13 peeking out from behind with a grin. Behind us is the US Capitol building under a beautiful clear blue sky. A scene of two-story row houses along a narrow, wet street covered in fallen leaves under a grey, cloudy sky. Leaning up against the houses is a giant tree half again as tall as they are (the trunk may be two feet across?) that was knocked down by an intense thunderstorm.
June 19, 2025 at 9:23 PM
steuard.bsky.social
Visiting the Smithsonian Museum of Natural History's famous Cheese Assortment collected by Apollo astronauts and thinking of @scalzi.com.
Part of a display of various rocks and dust brought back from the Moon at the Smithsonian Museum of Natural History.
June 18, 2025 at 7:53 PM
steuard.bsky.social
Oh, what the heck. Purely for the vibes of the moment, here's proof that astrophotography should be left to people passionate enough to do it right. I still think it's fun to be able to look back in my photo library and remember adventuring out with Ms13 in the middle of the night. :)
A very blurry and somewhat distorted photo of the moon just a few minutes after totality was reached in a lunar eclipse. Despite the low photo quality, you can see that the ball of the moon is mostly rust-colored against the dark black of space, but the top edge still shows slightly brighter, whiter coloration because it's not very far from the edge of the Earth's umbral shadow.
March 14, 2025 at 7:03 AM
steuard.bsky.social
Looks the same to me: i.redd.it/q1dcw0o1ktfd...
A political ad for AfD in Germany, featuring a blonde man and woman making a roof shape over their kids by apparently heiling Hitler at each other.
January 5, 2025 at 5:53 PM
steuard.bsky.social
Continuing the holiday season by making my grandmother's Christmas spritz cookies. It's really fun to feel this connection to those older generations!
Three trays of cookies sit on the kitchen counter: about two dozen light brown wreath shapes per tray. I am standing by the counter, gradually piping bright green frosting onto the bottom of each cookie to look like leaves spreading out to each side. Two trays of finished spritz cookies, lined up in rows (about two dozen per tray). Each is a light tan circular wreath shape of jagged shortbread. At the bottom of each wreath is a pattern of bright green frosting leaves spreading to each side, with three tiny red berries between them.
December 27, 2024 at 10:19 PM
steuard.bsky.social
Merry Christmas, everyone!
A nighttime view of a house decorated with white Christmas lights around the front porch and spiraling up the pillars. The yard is covered in a blanket of snow, and a row of luminarias lines the road. Nearly invisible in the darkness, a young teenager builds a tiny snowman beside the front walk.
December 25, 2024 at 12:02 AM
steuard.bsky.social
Baked this year's Swedish limpa bread a day in advance, so it'll make for a delicious breakfast in addition to part of our Christmas Eve smorgasbord.
A large oval loaf of bread is cooling on a wire rack. It is a fairly dark brown on its crust and lighter brown inside the five diagonal slashes across the top. A dusting of flour is still visible in a few places lower on the loaf.
December 24, 2024 at 3:39 AM
steuard.bsky.social
The gravy turned out to be as delicious as we'd hoped! I'm thankful for family and friends near and far this year, and for the support that we give to each other day after day (sometimes without even noticing that we're doing it).
A big plate of classic American Thanksgiving dinner, with turkey and mashed potatoes and stuffing all covered in homemade gravy and side portions of green beans, cranberry sauce, and a fresh baked roll.
November 29, 2024 at 2:02 AM
steuard.bsky.social
Turkey gravy in the process of coming together: one of my favorite parts of our traditional meal.
Two pots on a stove. The one on the left contains a thick layer of medium brown liquid and a whisk: flour and butter cooked into a roux, now with added broth. The one on the right contains darker brown clear broth, waiting to be added. (Not shown: pan drippings that will thoroughly darken the gravy and add amazing flavor.)
November 28, 2024 at 10:04 PM
steuard.bsky.social
8/? Bivectors turn out to describe magnetic fields well, too: the field's orientation inside a current loop matches the loop. (In 3D, you can always replace a bivector with the corresponding traditional vector using a right-hand rule.)

And in a mirror, bivector orientations behave 100% sensibly.
The same metal loop carrying a counterclockwise electric current as shown earlier, but this time instead of arrows illustrating the magnetic field as a vector we have shown oriented tiles illustrating the magnetic field as a bivector. The tiles inside the loop are parallel to the plane of the loop and all show counterclockwise orientations (matching the direction of the loop current). Beyond the loop, the tiles tilt to the side and around until they are perfectly flat in the plane of the loop (but now "upside down" so the side on top shows a clockwise orientation), and then beneath the plane of the loop continue tilting back in until they come back to where they started.
November 22, 2024 at 10:31 PM
steuard.bsky.social
7/? A *bivector* is the natural two-dimensional geometric quantity: instead of an arrow, you can visualize it as a tile whose area represents magnitude, tilted at a given angle, and with an orientation (clockwise/counterclockwise). (Shape doesn't matter.) Very intuitive for describing rotations!
This image repeats the earlier image of a merry-go-round and a ball swinging in circles on a string. But instead of using vectors to indicate angular velocity omega for each one, the angular velocity of each is shown as a flat tile whose attitude in space matches the angle of the original rotating system and which are labeled to indicate the direction of rotation in the corresponding plane: a counterclockwise arrow on top of the circular tile on the left and arrows along the edges of the rectangular tile on the right. Each tile is labeled as "omega-bivector", where the bivector nature is indicated by a double arrow decoration (pointing left and right) on top of the letter instead of a traditional vector sign. In fact, the (tilted) rectangular tile on the right for the swinging ball has been constructed from the tip-to-tail combination of the ball's position vector (from the center of the circle to the ball) followed by its momentum vector (mass times velocity in the ball's direction of motion). Technically, the result is the angular momentum bivector L rather than the angular velocity omega, but I didn't want to overcomplicate things. (This construction of a bivector parallelogram is called the wedge product of two vectors, and replaces the traditional cross product. The cross product result can be recovered by simply applying the right-hand rule to the bivector tile, with the new vector's length corresponding to the tile's area.)
November 22, 2024 at 10:31 PM