My AP Physics C: E&M class finished all the content we needed to get through with a few weeks to spare, so I decided (amidst their great excitement) to do a unit on relative motion and special relativity. Thankfully, the physics education twitter community is awesome, and I’ve been rescued from what would otherwise be certain doom with this unit, especially given that I had almost as much to learn about it as my students. Special thanks to @LCTTA and @kellyoshea for equipping me with a life preserver before I dove out into such choppy waters.
Through my various readings and video watchings, I came across this fantastic video by MinutePhysics. Take a moment to watch it before reading further; it’s only a 2 minute video, and it’ll save me a lot of typing. The inspiration for this activity came from what he call’s the switch-a-roo, in particular when “rotates” the slices vs. just sliding them (at about 1:03).
Beginnings of an activity
My idea is really nothing more than making strips of paper that students can slide and rotate much like the “slices” shown in the MinutePhysics video. This will be given to them after a week of basic relative motion, so frames of reference and relative velocity are part of their vocabulary now. This will also go right after an introduction to the Michelson-Morley experiment and their “discovery” that the speed of light is constant in all frames of reference.
There will be two objects in motion relative to one another along with a photon. Both objects and the photon start at the same position. One object remains stationary, the other moves away with a constant velocity as does the photon in the same direction. Here’s how I’m imagining this might go:
Change the frame of reference such that the other object is at rest.
From this:To this:How does this violate the rules of special relativity? I would be looking for them to notice what’s in green above. I’m also curious as to what discussion the jaggedness of the photon’s line (look closely at the second picture) might generate.
How can you perform a switch-a-roo that doesn’t violate the rules of special relativity? I’m a little unsure how to guide them towards a condition for …doesn’t violate the rules of special relativity beyond that they have to keep the photon line “unbroken.” That makes it work out right, but I’d like it a little more grounded in physics. However, even if I can’t figure that out, it at least allows them to see the creation of a new time axis.
What do you think lines parallel to the bottom of each strip mean? It’s a new time axis! This will rely on their previous discussions about spacetime diagrams (which we’ve done for only non-relativistic scenarios in preparation for this part) about lines parallel to the time axis indicate constant position and vice-versa.
Does time in the new frame tick at the same rate as the first frame? Justify you claim with evidence and reasoning. This one’ll be a zinger! Time dilation!
Some other follow-up questions that I’ve yet to think of. Suggestions? Does the new frame have the same position axis as the old one? If not, what would a new one look like? See the next section on why I might ask this as I thought of it while typing it out. However, upon further reflection, I’m not even sure this can be done? Even if not through this particular example, it’s still a great discussion to have.
Some other follow-up questions that I’ve yet to think of. Suggestions?
What I like: I think the most effective (and coolest) thing about this is that it gives students some kind of visual for how to think about time dilation and why the constancy of the speed of light necessitates such an effect. Linking the effects of special relativity to one of the key postulates in relativity, the speed of light in vacuum is constant in all frames of reference, was something that I never really understood until recently, and I want my students to appreciate that link. I think it also helps them appreciate the genius of the theory in that everything works out just fine if you just abandon the idea of absolute simultaneity. It sounds so simple when you say it like that, but it’s really rather profound!
It also sets them up for utilizing spacetime diagrams for relativistic scenarios, especially if we want to get into drawing the new time and position axes for a moving frame on top of those for a stationary frame, as shown here:
What I don’t like: I begin the activity by them seeing that applying a regular ‘ol switch-a-roo (i.e., the Galilean transformation) makes light travels a shorter distance in the same amount of time, thus violating special relativity. And that’s a great starting place, I think. But there’s not really a way to circle back to that to verify that the new switch-a-roo (i.e., the Lorentz transformation) succeeds where the old one fails. I see how that happens when the new position axis is drawn (like in the SparkNotes picture above), but I’m not sure my students will see that. Perhaps I should just ask them to discuss whether or not a new position axis is needed and, if so, what would it look like? Hmm..
I’ll be giving this to my students in a few days, and I’m hoping for the best!