Tag Archives: teaching

A Simple Introduction to Special Relativity

einstein2

Think Einstein’s theory of Special Relativity is beyond you? Think again.

It sounds intimidating. But what most people don’t realize is that it only requires a knowledge of the Pythagorean theorem, the definition of velocity (or really just speed, in the sense of distance divided by time), some basic algebra, and a willingness to embrace an unintuitive new understanding of time (and distance).

Here’s a simple introduction that I wrote for my 9th and 10th grade students at Village High School in May of 2010:

Relativity

Feel free to share it, copy it, distribute it, shred it, or burn it.

Okay, I admit that there’s actually a lot more to Special Relativity than what’s discussed in this little paper. The first three inescapable conclusions that emerge from the theory are that (1) time slows down in a moving reference frame (“time dilation”); (2) moving objects are shortened (“length contraction”); and (3) events that are simultaneous in one reference frame occur at different times in other reference frames. What’s hard to wrap your mind around is that these effects are not just matters of perception. Rather, the times and lengths actually change.

Those three effects are only the beginning, though. From them can be derived all sorts of other fascinating phenomena. Velocities, energies, momenta, and forces also change from one reference frame to another. The most amazing thing about Special Relativity, in my opinion, is the fact that the magnetic force is actually just a consequence of these time and length transformations.* One could say that the magnetic force isn’t even a real force. It’s an effect that arises as a consequence of relativity whenever an electric charge moves. (That’s why the “electromagnetic force” is considered to be just one force.) In fact, you can set up a situation in which, from the point of view of one person who’s sitting still, there’s a magnetic field; but from the point of view of another person who’s moving in a certain way, there is no magnetic field. It all depends on your point of view.

It’s tempting to go one step further and draw parallels between the physical theory of relativity and various philosophical ideas — relativism in ethics, culture, and religion, for example. It seems like there’s a scientific basis for saying that ideas that are right from one point of view might be wrong in another, and vice versa. But in fact, such thinking is contrary to the very heart of special relativity. The physical theory is built on the following two axioms: (1) The speed of light is always exactly the same in any reference frame; and (2) The laws of physics are always exactly the same in any reference frame. Thus, special relativity is actually a theory of absolutes. In fact, Einstein himself wanted to call it “Invariance Theory.”** It was other people who gave it the name “Relativity.”

* Haskell, Richard. “Special Relativity and Maxwell’s Equations.”

** Isaacson, Walter. Einstein: His Life and Universe.

Preparing Students for Real Life

schoolHouse

The Houston Chronicle published an article about a new plan to train students, especially in low-income areas, for specific careers. The skills listed in the article are “process technology” (in “chemical, refining, and manufacturing careers”), “electronic engineering,” “network and computer administration,” “logistics and global supply,” and “pharmacy technology.”

Now this is what I’m talking about. If executed well, programs like this could have a significant positive impact on our education system and society in general. This is right in line with some of my proposals in my education essay, namely:

  1. Make the curriculum more practical.
  2. Encourage early specialization.
  3. Reduce the emphasis on “preparation for college.”
  4. Develop trade schools.

The most important thing here is that we give kids something constructive to do. If we give them practical skills and enable them to start working, kids who otherwise might have felt worthless and directionless and turned to gangs and drugs would instead feel like contributing members of society who have some say. That’s the kind of change that will make America a better place to live in.

I hope this program receives the support it needs in order to have a chance at success.

Here’s a link to the article in the Chronicle:

HISD looking to help graduates land jobs

An Interesting Physics Problem: The Airport Walkway

airportWalkway

In December 2008, one of my favorite students emailed me an interesting physics problem:

Suppose you’re in an airport and you need to get from point A to point B. For part of the way, there’s a moving walkway; the rest of the way, there isn’t. You walk at your normal speed, both on the moving walkway and on the floor. The questions are:

1. If you have to stop to tie your shoe, should you do it on the floor or on the walkway? (Your goal is to make the trip in as short a time as possible.)

2. If you can run for a short, fixed period of time, do you save more time by running on the walkway or on the floor?

3. How do the answers to (1) and (2) change if you take special relativity into account?

I wrote up a solution, which I’m very proud of. Here it is:

Airport Walkway Problem

What’s Needed for Effective Education Reform?

After spending four years teaching high school math and physics, I am now entering graduate school to pursue research in applied physics. I wanted to write down my thoughts on teaching and, in particular, on the state of our education system, while the experience was still fresh in my mind. I did so back in June, and I am now ready to post the finished product online. It ended up being a 45-page essay. It’s more for myself than for anyone else, but I think some people will find it interesting. So here it is (as a PDF):

What’s Needed for Effective Education Reform?

In the essay, I make some unconventional proposals, including:

  • doing away with grades entirely
  • doing away with grade levels entirely
  • doing away with the high school diploma entirely
  • encouraging early specialization
  • developing a culture of respect for teachers
  • disciplining students in more effective ways

Enjoy.