Quantum mechanics without imaginary numbers

I've been thinking about how the Schroedinger equation intimidates students because it is inherently complex:

(note the red i). This has led me in the past to say things like "quantum mechanics is weird because apparently the universe is both real and imaginary" and "we can only see the real parts". Now that last quote especially is suspect since what we can "see" is really the magnitude squared of the wavefunction:

which corresponds to the probability density of finding something in a particular location. But I'm coming around to a position where even the first quote above is suspect. It seems to me that you can rewrite the equation as two coupled equations:


Note how the 1's and 2's switch places. What I've done here is renamed the real part of as and the imaginary part of as . Only here I'm just numbering them and not really giving any preference to either. These two equations are totally equivalent to the original equation and what it says about the universe is that for every object you need to keep track of two things. In the end to make predictions about the object you'll need but note that I don't need imaginary numbers at all!

I think interpreting those two equation is of interest as well. Essentially the spatial curvature of one produces temporal changes in the other and vice versa. That's actually pretty cool as you could stare at a snapshot of both the two and predict what's going to happen in the next moment of time.

screencasting software

Well, the news came out last week about Google Video being shut down. I was not exactly happy given my plans for screencasting this coming spring semester. So I've spent the week trying to find some other alternatives. Here I'll put in a few of my findings. TeachTube Teachertube has similar lack of limits to file size and total number of uploads as Google Video. It's optimal resolution is half of Google's (320x240 vs 640x480) but Google actually reduces your videos to 320x240 after some processing anyways. You can mark you files as private and embed videos just like Google too. They have a semi-malfunctioning feature where you can upload support files to go along with the video. Overall it seems like a decent alternative to Google. Btw, the malfunctioning part is that when you click on the support files you're taken to a page with EVERY support file listed. WinFF I don't like the default file size that camstudio produces so I'm starting to use winFF to reduce it by roughly a factor of 2 by converting to .mp4 format from the avi format. The quality once it's on Google seems about the same. Jing Just today I started using Jing on my mac (it works on macs and windoze). It's pretty slick as the screen capture that it does seems to have very small file sizes (3.5MB/minute for full screen) AND they host your screencast for you at screencast.com for free! You get 2GB of space and 2GB/month bandwidth which is pretty good. What I really like about it is how easy it makes everything. You can keep it running in the background and when you make a video the controls are obvious and then when you're done it immediately puts it on screencast.com for you. All with one piece of software! There's also no delay between uploading and being able to view it. Plus they don't do any post-processing to reduce the quality. Of course the biggest downside is the 5 minute limit on videos but I'm willing to work with that! Elluminate Live This is software that Hamline has paid an academic license for. It's actually very slick. I used it yesterday during an interview I was a part of and I was very impressed. It's designed for online courses and I'm planning to use it immediately for my ongoing online course. I really like how you can grant microphone privileges to anyone logged in and how students can "raise their hand". It keeps track of who raised their hand first. Very cool. It also lets you share other windows on your screen so it would work very much like a screen cast. Well, we'll see how it goes this week . . .

Almost two weeks without tv

I don't really miss it. This past weekend there were a couple of times where just vegging in front of it sounded good but I knew there wasn't really anything on. On weeknights I've been busy cleaning the kitchen, brewing my iced tea for the next day, checking the discussion boards for my online class (online quantum mechanics, sounds fun, huh?), reading books, and posting to my blog. The boys are usually in bed by 8 and I go to bed around 10:30 so it's just 2.5 hours to fill. Dexter season 2 came in the mail recently and I am pining for it. I can't decide if that's allowed or not. I suppose I know deep down that it's not but it does sound like fun to watch. At least I wouldn't be watching commercials and I could pause it any time to deal with anything that comes up (I've been getting the evil eye from my wife for not responding to the kids when the tv's on). There's really no single show that I miss. I know Law and Order will always be there for me and things like Hulu.com seem to have the oldies but goodies so I don't feel like I have to watch something the night it premiers. Of course this is all during my j-term at Hamline when all I'm teaching is my online course. Once the spring semester starts I'll probably just use the time to get work done (like grading, the bane of my existence). We'll see.

Cereal with less than 10 g of sugar

In our continuing efforts to keep the kids healthy, I've decided to enforce a hard threshold of less than 10 g of sugar per serving in their cereal. I came to that number mostly arbitrarily but it's worked out pretty well. Almost every cereal you would think of as a sugar cereal has 10 or more and almost every healthy cereal has less than 10. We get plenty of stares in the cereal aisle at the grocery store. The boys pore over the ingredients list of all the cereals hoping to find one under the threshold. The first time was the most fun when they were happy to find some surprises:

• Honeycomb is over the limit but Chocolate Honeycomb isn't
• Fruity Pebbles is over the limit but Bam Bam Fruity Pebbles isn't
• Life is ok
• Fruit Loops is way over
• Any raisin cereal is WAY over (that's weird)

Buddy (9) argues quite often about cereals that have exactly 10:

Why can't we get ________?! It's 10, that's just one more than 9 and you let us get 9! (not 9 factorial, of course) It's just a tiny bit more!

I respond that there has to be a limit somewhere and that I'm not really all that happy about 9. We've had that conversation a number of times.

Update (12/13/2009): General Mills apparently reads my blog They're going to reduce the sugar in many cereals down to 9 g just so I'll buy more.  Cool!

My new diet

I'm trying to be a little more healthy this year so I'm trying to follow my new diet more closely. It's actually very simple: if it's homemade, you can eat all you want. I figure that all the weird preservatives and other added chemicals (like the ominous MSG, for example) in packaged foods can't be good for you so even if the homemade food is not that great for you, if you fill up on it you'll hopefully be less likely to eat the pre-packaged stuff. I'm also trying to kick the fake sugar habit by drinking iced tea when I can (with just lemon added). I've been thinking about the diet for a while (probably since back when I was on the South Beach diet) but the momentum really got going when the big boys and I watched a cooking show on PBS that showed how to make homemade macaroni and cheese. The boys actually said it looked good! I jumped all over that and we went to get the ingredients right away. I don't think we made it that night but it was pretty soon afterwards. They did like it, though not as much as they thought, and I pigged out (it's homemade, after all). That night I didn't snack on anything! My goals for dieting are three-fold: 1. fit into my clothes (not that big of a deal since I can always just buy bigger ones); 2. Be able to run up and down the basketball court or play at least 5 games of SocCourt without needed to fall over and hyperventilate; 3. actually I was going to say stay below some embarrassing weight but I find that if (2) is fine, I don't actually care. I'll admit that tonight we had Mickey D's for dinner but I'm still trying my best to eat healthy things when I can.

Screencasting in modern physics

This is a continuation of my earlier post on screencasting. Here I'll talk about my plans to use screencasting in my upcoming Modern Physics course for sophomore physics majors at Hamline. Here are some of the contributing factors for why I decided to do this:

1. I never feel like I work enough examples in class (often I won't do any!).
2. I would like to do more all-class quizzes. I first saw these in my HS physics course with Mr. Erpelding 20 years ago. You come in, ask a question, and expect the answer on the board after a fixed amount of time. After the allotted time you ask random students follow up questions. In the end everyone gets the same grade. In HS we'd take the whole period but I've done it in as short as 10 minutes.
3. Sites like cramster.com have made it difficult to know if students are doing their own homework. I always encourage my students to work together but in the end I want them to own it. I was at a Physics Chairs conference this past summer (sounds like fun, huh?) and a lot of people were trying to figure out what to do to combat this. A number of times people talked about quizzes taking the place of homework in the gradebook but the common response was that class time is too precious.
4. This past summer in my graduate classes I assigned four homework problems a night. Instead of grading all of them as I've done in the past (continually falling behind as I teach them for 8 hours a day every day for two weeks) I rolled a four-sided die every morning and then used that homework problem as the quiz the first thing in the morning. That way I only had to grade one problem per person per day. The students commented that they liked the system as at night they just needed to make sure they understood the problem and didn't have to obsess about every point possible. The four-sided die was fun because the students knew that it was completely random and they didn't need to waste time trying to guess which problem I was going to pick.

Ok, so here's the plan: For every class I will type up my notes (as usual) but then I'll record and post a screencast of the notes. Effectively it'll be a lecture without an audience. Students will be expected to both read the book and watch the screencast before class. They then use my online summary web page to submit a summary and a question about the material. In class I'll simply do four things: 1. Give a quiz on a random homework problem from the previous day, 2. answer any questions they've posted, 3. work some examples on the new material, 4. give an all-class quiz. The plan addresses all of the concerns above as I'll have plenty of time in class since I won't be lecturing the new material. Some concerns I have include:

1. The student's exposure to my lecture does not allow interactivity (they can post their questions to my summary page but they'll have to wait for class for the answer)
2. If the students don't do the work outside of class they'll fall behind quite quickly. In a recent class I committed to not talking about material students didn't ask about and I stuck to my guns by continuing to ask both homework and exam questions about that material.
3. Can I stay on top of all those screencasts?

For the first one above there's been some interesting research done recently. Apparently students in a similar class felt that the flexibility they had in being able to watch the screencasts whenever they liked (and the ability to pause and rewind) outweighed the lack of interactivity. I'm currently optimistic about this experiment. I'll add more posts about it when the semester starts.

Screencasting

I've recently taken up screencasting to aid in my teaching. I started with a fully online class I taught last fall and I'm planning to do a lot more of it in an in-person class this spring. I use free software on windows machines (Camstudio) that can record a portion of screen while also recording your voice. It saves the movie as an .avi file (ugh) but then I upload it to google video and they turn it into a flash movie (just like youtube). A few cool things about how I'm using it:

1. You can set the software to have the region being recorded follow your mouse around.
2. You can highlight your mouse so it's easier to see.
3. Google Video does not have a limit on either file size or total number of files uploaded
4. Google Video has a desktop uploader so you can upload a bunch at a time
5. Google Video allows you to set the movie as private so only those you give the address to can see it.

In this post I'll talk about how I used it in the fully online class and in a future post I'll talk about how I plan to use it for an in-person class. Homework: In my online class I set up groups that work on hints for the rest of the class on single homework problems. I provide for them the solution to that problem and a screencast of the solution. I simply pull up the pdf scanned copy of the solution and record my voice describing the calculations while pointing at the appropriate sketch/equation/description. The students tell me that they learn much more from that than simply reading the solution as sometimes I'm a little terse with my descriptions and often I skip (trivial?) algebraic steps. Lectures: Each week we cover a chapter in the text. Before the week starts I type up my notes on what I call a Daily outline (here's an example). That system allows me to easily typeset equations, put in Mathematica calculations (that are adjustable on the fly!) and link to any animations I've made. I also put in links to other cool descriptions. Then I make a screencast of the page (see below for that same example) where I can fill in the details and walk the students through any external links.