{"id":3327,"date":"2009-01-19T12:41:34","date_gmt":"2009-01-19T12:41:34","guid":{"rendered":"http:\/\/scienceblogs.com\/principles\/2009\/01\/19\/course-report-modern-physics\/"},"modified":"2009-01-19T12:41:34","modified_gmt":"2009-01-19T12:41:34","slug":"course-report-modern-physics","status":"publish","type":"post","link":"http:\/\/chadorzel.com\/principles\/2009\/01\/19\/course-report-modern-physics\/","title":{"rendered":"Course Report: Modern Physics"},"content":{"rendered":"

Back in the “Uncomfortable Questions” thread, Thony C<\/a> suggested that I should do running updates on the course I’m teaching now. I meant to get to this sooner, but last weekend’s bout with norovirus kind of got in the way…<\/p>\n

I like the idea, though, so below the fold are a bunch of comments on the classes I’ve had thus far this term:<\/p>\n

<\/p>\n

Class 1: Introduction to Relativity. I do a quick recap of the two classical physics classes that are pre-requisites for my class, showing the various conservation laws, and Maxwell’s equations. I then set up a version of the problem that led to relativity, showing that Maxwell’s equations predict a single value for the speed of light, independent of the speed of the source. Then I talk about the Michelson-Morley experiment, showing that there is no observable change in the speed of light from a moving object.<\/p>\n

This treatment is slightly ahistorical– it’s not clear whether Einstein knew about Michelson-Morley before he developed special relativity– but it provides a narrative that’s easy to follow, and gets the course off to a good start. Homework is a couple of math problems relating to the binomial approximation, which gets used over and over.<\/p>\n

Class 2: I start off by comparing the Galileian transformation to a proof that 1=2– it looks reasonable at first glance, but on closer inspection, it turns out to be flawed because of an error that’s subtle enough to be missed. In the case of a proof that 1=2, it’s usually a divide-by-zero; in the case of the Galileian transformation, it’s the assumption that time is the same for all observers.<\/p>\n

Then I go through the “light clock” thought experiment to show that moving observers will disagree about the timing of events, and derive the formula for time dilation. This is a special case of the Lorentz transformation, which is the next thing introduced, and I work through one example relating to muon creation and decay to demonstrate both time dilation and length contraction.<\/p>\n

As usual, I made a total hash of the explanation of length contraction. There’s a subtle definitional point about who measures what length that is really easy to screw up, and I was rushing to get things done before the end of class, and screwed it up completely. Based on the homework I just graded, they got the basic ideas, but more in spite of my lecture than because of it.<\/p>\n

Class 3: On the schedule, this is Paradox Day: I go through the “barn and pole” paradox to show the importance of keeping your frames straight and getting the timing of events right. Then it’s the “twin paradox,” talking about the distinction between inertial and non-inertial frames. This often confuses students into thinking that acceleration causes the time difference, so the homework includes reading an American Journal of Physics<\/cite> article<\/a> on a variation of the “twin paradox” in which both twins accelerate.<\/p>\n

I say “on the schedule,” because this was the day that the norovirus hit. I had to go to Albany to get Kate from her work, and hastily arranged for a colleague to cover my class.<\/p>\n

Class 4: I wrapped up the twin paradox (which my colleague hadn’t gotten to), and went through the transformation of velocities in special relativity. This is one of a half-dozen classes in this course that drive math majors crazy, as the quasi-derivations used to come up with the velocity addition formulae use a bunch of swashbuckling physicist tricks (“We have a dx here, and a dt there, so we divide through by dt, and hey, there’s the velocity, dx\/dt…”). There’s nothing actually wrong with it, but I don’t go through the formal steps needed to make that leap, and it always makes mathematicians squirm in their seats.<\/p>\n

Class 5: Relativistic momentum. The bulk of this class is taken up with a very long demonstration that the formula for relativistic momentum does, in fact, leave momentum as a conserved quantity in a two-dimensional elastic collision. Lots and lots of gory algebra, and it’s easy to get lost in the details. I’m not sure how well they got the idea, but it’s got to be done.<\/p>\n

Class 6: Relativistic energy. I go through the derivation of kinetic energy via the work-energy theorem (another wonderful swashbuckling physicist moment, where a “du\/dt” multipled by “dt” becomes just a “du,” magically changing the integration variable). I talk about the implications of E=mc2<\/sup>: pair creation and annihilation, binding energy, conservation of mass-energy. I end with one example of a particle physics problem, using the final energy and momentum of two decay products to find the mass and momentum of the original particle.<\/p>\n

Again, this was rushed a bit toward the end, but I think they got the idea.<\/p>\n

That’s pretty much it for relativity in this class. Today’s lecture is the Special Bonus Topic of showing how you can see a magnetic field as an electric field in a moving frame. It doesn’t lend itself to homework problems or exam questions, but it does bring everything together nicely.<\/p>\n

The first mid-term exam is on Thursday. Then it’s on to quantum mechanics.<\/p>\n","protected":false},"excerpt":{"rendered":"

Back in the “Uncomfortable Questions” thread, Thony C suggested that I should do running updates on the course I’m teaching now. I meant to get to this sooner, but last weekend’s bout with norovirus kind of got in the way… I like the idea, though, so below the fold are a bunch of comments on… Continue reading Course Report: Modern Physics<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"1","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,13,9,7],"tags":[],"class_list":["post-3327","post","type-post","status-publish","format-standard","hentry","category-academia","category-education","category-math","category-physics","entry"],"_links":{"self":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/3327","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/comments?post=3327"}],"version-history":[{"count":0,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/3327\/revisions"}],"wp:attachment":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/media?parent=3327"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/categories?post=3327"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/tags?post=3327"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}