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Originally posted by Shadowy Man
Divergent as in if you take the divergence (Del dot F) of the force field you get a non-zero value.
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I think that is the same as the issue of tidal forces...ie if you're in an elevator and you measure the direction of gravity on either side of the elevator, the force will be pointing in a slightly different direction.
For those who aren't familiar with this idea,
this page has a good illustration:
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Notice the emphasis on the idea that these statements are only true locally. In a laboratory which has some finite extent, these statements are not true anymore. Imagine an observer accompanied by two widely separated objects in the freely falling lab. In a non-uniform gravitational `field' such as that produced by a planet, the free fall of the objects towards the centre of the planet will be noticeable to the observer for large enough separation. In the case of the planet, the objects are not stationary in the lab, but slowly moving towards one another, apparently under some type of `force'. If the observer did not know that he was freely falling, he would conclude that there was a force between these objects from his observations.
In the figure below, the situation on the left is that of an observer in empty space (or freely falling in a uniform gravitational field), while the situation on the right is in free fall in a radial field. In this latter situation, the observer sees an apparent force move the two objects closer together.
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I found an interesting comment on this issue
here:
Quote:
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An interesting addendum regarding the so-called "tidal forces" felt by an extended object in free-fall is the following. Since we are not assuming a uniform field, the test object experiences these forces. For example, a ten foot 2x4 in the presence of a strong gravitational field would become concave in shape. The force on the center of the plank, being closer to the center of the gravitating mass, would be greater than that on each end of the plank. To the extent that the body is deformable, the tidal forces would bend the plank. However, if we also do not have uniform acceleration, but instead apply the accelerative force to the center of the plank, the inertia of the ends of the plank would result in a similar deformation. The plank would again be concave in the direction of acceleration. In this way, a non-uniform gravitational field can be replaced by an equivalent, non-uniform acceleration, and we can apply the principle of equivalence even to extended objects (this is what Einstein did when introducing the dynamic, or parameterized, metric in general relativity), though there is neither a theoretical nor a practical reason for doing so.
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06-17-2003, 07:30 AM
