## time as distance

At Eisenhower, we’re into the space and solar system portion of the year.  Ms. Wyssenbach had a great activity for the students.  In an effort to get across the idea that “light years” are a measure of distance, we did an exercise.

Now experienced students know that the speed of light in a vacuum is constant, so any measurement of time is directly proportional to the distance the light travels.  A light year is therefore a known quantity (light travels about 3 x 10^8 meters per second, so one light year is about 9.5 x 10^15 meters or 9.5 trillion kilometers).   However, this concept can be very difficult to pick up for a naive learner… not the term “light year” per se or even the idea that light travels at a certain speed, because most students have heard of “traveling at the speed of light” or “light speed” or “light years” from television, movies, etc., but rather the concept of time as distance.

So, to tackle this, each student walked heel-to-toe style for exactly 1 minute and another student measured the distance walked in meters.  We did this 3 times for each student, and of course, they enjoyed the race and the “giant pizza cutter” measuring stick (a wheel with a 1 meter circumference that makes distance measurements fun and easy).  After the races and data collection, we returned to the classroom and got an average distance for the class.  This distance — the distance traveled in one minute by students walking heel to toe — was termed a “student minute.”  It turns out for the classes I observed, a “student minute” is 27 meters, rounded to the nearest whole meter.

Once we had this average, I started asking them questions.  The first hour, I tried a constructive approach to my questioning.

What is a student minute?  The average distance a student walks heel to toe in one minute.

How far is a student minute?  27 meters.

So how far is a student hour?  ummm.  hmmmm.  well...

Ok.  Let me ask another way.  How many minutes are in an hour?  60.

So how many student minutes are in a student hour? 60.

So how far is a student hour?  60 x 27 meters.

Ok. So how far is a student day? A student week?  A student month?  A student year? (you get the idea).

What is a light year?  umm.  hmm.  Is it how far light travels in one year?  Yes.

Now, is a light year a farther or shorter distance than a student year? Farther.

Why?  Because light is really fast.

Ok. So how far is a light minute?  WHOA.  minds exploding.  (not really, just some looks like duh… it’s the distance light travels in a minute which is much farther than a student minute because light travels really fast, which we already told you.)

But why do we pick light for our distance measure?  Because it’s cool?  Because it’s fast?  Because it doesn’t change speed?

The second hour, I took a deconstructive approach from the speed of light side of things.   I started right in with “Ok.  So how far is a light minute?”  This failed MISERABLY.  Nobody had any idea what I was talking about, and we got into this big discussion about whether we were measuring distance or time.  One student, who is pretty bright and very detail oriented, was completely confused.  I asked her what was confusing, and eventually we figured out that she was confused because we measured both time (1 minute exactly with a stop watch) and distance (with the pizza cutter thingy).  The fact that all of the times were held constant at 1 minute did not help her conceptually.  She understood much better when we compared the speed of students walking with the speed of light.

Overall, I think it was a very useful exercise to try and grasp the fundamental meaning of a light year as a distance.  Our next issue is scale.  We talked about why you would use a light year instead of an inch or a football field or a mile, but the numbers are  astronomical (sorry, I had to say it :))…

Anyway, the numbers are so big that I don’t think a real understanding of their relative magnitude is intuitively obvious to most students.  We’ll try and wrestle with that at some point as well.