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Re: gravitational embedding diagrams



At 02:03 PM 2/21/01 -0800, Leigh Palmer wrote:

embedding diagram ....... made with the
depression transformed into a peak! Why didn't the light rays get
deflected *away* from the Sun in that case, the naive listener might
easily think.

This is a most excellent point.

science museum exhibit in which ball bearings or coins are rolled to
simulate planetary orbits

We agree that the exhibit is misleading.

Box 1.6 of MTW. It is, in fact, just plain RONG,

Not so fast. M, T, and W are pretty smart dudes, way too smart to get
sucked in by something like that.

The difference is that they never roll ball bearings on their embedding
diagrams. They show light rays and sometimes they show ants walking
around, sensitive to distance but not to the pull of the embedding world's
gravity.

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

We can somewhat improve the museum exhibit as follows:
a) Use trained ants, or
b) Make a little "tricycle" as follows: two drive wheels in front, one
little castering freewheel in the back. The drive wheels always turn at
the same rate, and they don't slip, so they always travel the same distance.

-- On a planar surface, the tricycle moves in a straight line.

-- On a curved surface (curved up or down, it doesn't matter) the tricycle
will be deflected toward the pit or peak.

-- Unfortunately you can't demonstrate a closed orbit without using a pit
or peak so extreme that it has cylindrical walls. There would be technical
problems due to slippage. Maybe the demo would work in microgravity. Even
then there is only one closed orbit through a point, so you have to get the
initial conditions just right, which is hard. So basically the tricycle is
behaving like a photon in this model.

-- Maybe somebody can figure out a way to model a nonrelativistic particle.