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The person who is freely falling "feels" weightless, but by
our definition of weight as the force of gravity, the person is not
weightless.
When we are clear and unambiguous with students, they
might be conflicted for a while, but they are not dissatisfied. And
unless I've completely forgotten my general relativity, there is no
weight in that theory. There is mass and there is curvature of space-
time. Objects follow their path in space-time. Unless they are
obstructed by an object such as the Earth, they are not accelerating
and they experience no force of gravity. I am prepared to be wrong on
that, because it's been a while.