Problem set answers for MITs 8.033 using real valued quaternions

Problem set 1

Problem sets 2-6 are at another site, Doing Special Relativity with Quaternions

The Back Story

In early 1997, I had a meeting with a famous physicist to discuss my research project. Actually, I sat outside his door and talked with him to and from the chinese food truck. He thought my project was "Interesting, but not very interesting." The reason was that I had a few math widgets, but no theory. I thanked him for his time.

Now I had to find a theory. This is a crazy assignment. I decided to begin my search by posing a question: define a brief definition of time that must be two sentences or less and only be about phyiscs or math, not philosophy. My runon sentence answer used quaternions as a definition of events in space-time.

To test the hypothesis, I asked the professor who taught the class if I could audit 8.033, Classical and Relativitic Mechanics (it is now online). He approved. As a test of quaternions as an essential tool for physics, I had three ground rules for the assigned problems:

  1. Each problem had to be solved the standard way
  2. Each problem had to be solved using real-valued quaternions
  3. If any problem could not be solved with real-valued quaternions, there would be no need to look further into quaternions

It turned out that all 53 assigned problems were solved using real-valued quaternions. That was the start of my ongoing study. To avoid the book being overrun with the problem set answers, they were moved to a separate book.