Confused at a higher level

The view from Carleton College's physics department

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Gotta do this

Posted by Arjendu on February 9, 2008

Well, if I don’t post now, I never will, because I feel like I am falling further behind at work (and my body falling apart isn’t helping any).

What’s on my plate? I am going to guess the same as for most people at small colleges. This is what takes time and piles up: Grading and writing letters of recommendation. Mostly grading. ‘Cos things without explicit deadlines don’t get done, is what I’ve found.

In ‘Revolutions’, we’re doing relativity (what I call Act II for my course, Act I being Newtonian physics, and Act III being quantum mechanics). I did a version of the ‘garage paradox’ in class last week involving a centipede and a butcher. For the non-physicists, let’s spell it out: There is an effect in relativity called length contraction so that moving objects shrink along their direction of motion.

In this specific problem, the centipede is of length 10 cm, and traveling at 0.6c. He races by a butcher with a pair of cleavers separated by 9 cm that the butcher slams down simultaneously, in his reference frame, of course, when he sees the centipede between them, which will happen at that speed. The paradox is that in the centipede’s reference frame, the cleavers are traveling at 0.6c, and so the separation between them is what shrinks, down to only 7.2 cm — how can he possibly survive in his reference frame? And yet the reality of his survival or death must be independent of reference frames.

The resolution of the paradox, for those who haven’t played this game before, is that the events — the slamming down of the cleavers — happen at different *times* in the centipede’s reference frame, so the separation between the two isn’t all that relevant.

I teach this paradox by asking students to work through a worksheet which asks very leading questions about the problem, and it’s a pleasure to see comprehension dawning on them as they work it out (it is *remarkable* how many kids used the calculators on their cell-phones). These are humanists, some of whom have never taken a physics class before — and almost all of whom will never see a physics class again — and here they are, figuring out how to deal with space, time, space-time. Later in the term I will ask them to create something based on their personal response to these issues. A few years ago, for that assignment Lisa G created 2 flip books that show the butcher’s and centipede’s perspectives respectively — you can flip through them, and of course, pause to register what is happening. Those flip books are a thing of joy, and I walk around the class, using them as a reward for students once they’ve worked out the paradox’s resolution for themselves. Or sometimes when they throw their hands up in despair at the end of the hour.

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3 Responses to “Gotta do this”

  1. Hi, I’m a physics student and I’m actually studying this now in class at my local state school. I’d love to see a copy of your sheet and work through it myself. Is it possible to ask you to email it to me, if you don’t feel like posting it online here?

    Thanks and keep blogging!

  2. arjendu said

    Brian, I don’t quite feel comfortable posting it, but a copy is on its cyber-way shortly (or at least as soon as I figure out an address for you).

  3. Sorry, I filled in my email address when leaving the comment, I thought you’d be able to see it. In any event, my email address is brian@brianpuccio.net.

    Thanks again!

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