[Phys-l] hands-on physics activity, tangentially gravity-related

[John Denker <jsd@av8n.com>]

Here's an idea for you.

This involves some 100% real physics, and can be performed by
high-school students (and everybody else) as a hands-on activity.

To paraphrase Mark Twain, everybody talks about curved space,
but nobody does anything about curved space.

But we can fix that.  We can do things.

There are an almost-endless number of things you can do, starting
from the idea that masking tape will map out a geodesic for you.

To get a general idea of what I am talking about, see
  http://www.av8n.com/physics/geodesics.htm
but that's only the tip of the iceberg.

For starters, one simple thing you can do with a globe is to
construct the geodesic from Boston, MA to Coos Bay, OR and
observe that it passes _well_ north of Pierre, SD ... even
though all three places have nearly the same latitude.

   I have some metal globes and plastic globes that are unharmed
   by the application of tape.  (Globes with a paper surface might
   be problematic.)

You can also supply some saucers and shallow bowls, to be placed
upside-down on the table, to serve as parcels of local curvature.
Then run tape geodesic across the table and see how they remain
straight but are deflected by the curvature.

This can be understood at many levels, starting at a very superficial
level and proceeding to very profound levels.  High-school students
are not going to understand it very deeply, but IMHO the activity is
still worth doing.  This is the sort of thing that students should
be exposed to.  Then they can let it smolder for a few years, and
it will serve as the foundation for deeper understanding the next
time they see it.

You can supply cones and cylinders, which have zero extrinsic
curvature.  The students can get a clue about the difference between
intrinsic and extrinsic curvature by conformally wrapping a piece
of paper around the cone and/or cylinder.

In addition to globes, you can supply footballs and various weird-shaped
gourds ... all of which have nonzero intrinsic curvature.  Apply tape
to them and see what happens.  Pay particular attention to the fate
of lines of tape that start out parallel to one another;  this gives
a clear picture of /geodesic deviation/.

Another striking example of curvature can be found in FOLDIN'ART
sculptures:
  http://www.hasbro.com/default.cfm?page=ps_results&product_id=18368

There are some tremendous lessons to be learned by reverse-engineering
those things.  Think about the math and computer graphics that
went into designing them.



One particularly advanced application is the model of orbits in
a gravitational field, constructed as a curved space, as illustrated
at
  http://www.av8n.com/physics/geodesics.htm#fig-darts

That is over the head of most high-school students (and most adults
for that matter), because it requires some understanding of space-
time diagrams.  (People often ask, gravity means space is curved, in
what /direction/ is it curved.  The answer is that gravity causes a
great deal of curvature in the /time/ direction.  That drives
people nuts, until they see the construction in the aforementioned
figure.)

Note the contrast:

*) As a lesson in curvature, and the paths of things in curved space,
this activity is not even a model. It is a 100% non-fictional instance
of real tape interacting with real curvature.

*) At another level, tape can serve as a model of curvature-related
math and physics in applications such as
 -- Geodesy and navigation
 -- Physical optics
 -- General relativity
 -- et cetera.

In the GR case, we /model/ the worldlines using tape, and we /model/
the (x,t) directions using the (x,y) directions.  Thus the model does
not adhere 100% to the reality, but it is still a powerful model,
shedding much light on the reality.