Matter & Interactions I, Week 4

This week we formally wrapped our coverage (I hate that word) of special relativity. My goal never has been for students to do complicated numerical problems. Instead, I wanted them to understand the foundations of special relativity with an emphasis on the invariance of light’s speed, the loss of absolute simultaneity, and loss of absolute space, and the loss of absolute time. Really, the last three are consequences of the first. I also want them to know how we came to accept the invariance of light’s speed. If you search this blog on the “relativity” tag you’ll see examples of the kinds of questions I want students to be able to handle. Note especially that there’s no heavy mathematics in any of this. It’s almost entirely conceptual. There is some algebra, and there is a bit of right triangle geometry. The rest is just pure reasoning, which I don’t think introductory physics emphasizes enough these days.

In class, students spent most of the time on Overleaf writing up solutions/responses to questions from the Arons handout. In doing so, they made very useful suggestions for improvements to my mandi LaTeX package, and I have incorporated those into the latest build (which I have not yet pushed to CTAN). But as expected (and hoped for), writing these solutions forced them to read more carefully and this in turn caused them to raise the kind of questions I want them to get used to raising. Specifically, I assigned the following questions from Arons: 36.1, 36.2, 36.3, 36.4, 36.5, 36.7, 36.8, 36.10, 36.11, 36.12, 36.13, 36.14, 36.15, 36.17, 36.18, 36.19, 36.20, and 36.21. That’s a lot, but note that students were expected to be working these all along as they read through the relevant parts of the reading. However, as expected, most did not.

We also formulated our relativity standards this week. Here’s what we came up with:

  1. I can derive the expression for time dilation using a vertical light clock.
  2. I can derive the expression for length contraction using a horizontal light clock.
  3. I can describe a procedure for synchronizing two or more clocks using light or sound signals.
  4. I can explain why we treat light’s speed as an invariant.
  5. I can explain how simultaneity is relative.

I’ll be happy of students can demonstrate proficiency on these standards next week. We will also transition into the textbook next week, beginning with a discussion of vectors. I plan to do lots of things with vectors that aren’t in the text, and we’ll begin with VPython in earnest next week too.

As always, I welcome questions, comments, and constructive criticism.

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