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Re: [Phys-L] Fwd: [PTSOS] spacetime simulator: flexible conduit?



On 07/18/2012 08:30 AM, Ken Caviness wrote:
In fact, the only "non-win" side I see to the tape & darts is that
it's not as cool as the marbles orbiting the mass on the trampoline.

So do the trampoline demo /also/.

1) Physicists are allowed to have fun. Even if the trampoline had no
value as a demo, you would be allowed to do it anyway.

2) The trampoline demo does have value. It does demonstrate some
interesting physics. Just don't call it a demo of curved spacetime,
because that is *not* on the list of things it demonstrates.

In particular, remember what I said about the blue things and the
triangular things. By using two analogies together, you can explain
the concept of "blue triangle" without ever showing anybody a blue
triangle.
http://www.av8n.com/physics/img48/blue-triangle.png

To make proper use of the trampoline demo, you don't need to change
the trampoline; you just need to change what you say about it.

*) There is a rule of thumb that says "physics is simple when analyzed
locally." Therefore back in the 1600s, the theory of universal
gravitation bugged people because the force "here" was explained by
a mass waaaay over "there". This sort of thing is called action-at-
a-distance and is always less desirable than local action. The
trampoline demonstrates how the interaction between two objects can
be explained in terms of three things with /local/ interactions,
namely object plus field plus object.

It must be emphasized that this is not a completely apt model of
general relativity, because the force depends on the slope not the
curvature ... but remember the blue triangles. The trampoline is
a good model of a field that intermediates the interaction of one
object with another.

*) You then follow that up by doing the tape geodesics also. This is
maybe not as eye-catching, but it is still interesting, especially
if you tie it in to couture, geography, navigation, aviation, optics,
classical physics, quantum physics, general relativity, et cetera.

Note how this upholds the rule of thumb that it is almost always
better to take the positive approach, namely presenting a correct
conception. This stands in contrast to the negative approach, namely
trying to suppress a misconception without providing any positive,
constructive replacement. Specifically, explaining what's good
about the tape model of geodesic deviation is incomparably better
than trying to explain what's wrong with the trampoline model.

*AFTER* they have use the tape etc. to figure out how curvature works,
you can spiral back and get them to understand that the trampoline
force law depends on slope not curvature ... with all that implies.

=============

There is also an opportunity for a metacognition lesson. You get to
talk briefly about the "blue triangle" issue and explain that a model
can be useful even when it is not a 1:1 model of the whole situation.
Sometimes it is necessary to have two or three models ... and then to
combine them using a leap of the imagination.

There is a great deal of abstraction and imagination in physics, and
in life in general. It is possible to firmly and clearly imagine a
blue triangle, even if you've never seen one.