Centrifugal Force in the Fourth Dimension
Newton's theory of gravitation says that a planet moves around the
sun because of the gravitational force. But Einstein's general theory of
relativity says that the planet chooses its shortest path around the sun
in the four dimensional world, but if Einstein is right, what is holding
the planets in orbit? My first guess would be centrifugal force but this
too uses the theory of gravity. Can you explain this?
The shortest path in four dimensional space - time turns out to be
the same ( almost ) as that predicted by Newtonian theory with forces.
Deviations are very small and can only be observed for Mercury's orbit.
For other planets, very high sensitive is required for detecting
Deviations can be large in some other cases as in the case of
binary pulsars. But these are non solar system objects.
4 dimensions is really a red herring, as far as your question is
concerned. Einstein REPLACES the notion of gravitational force by
the notion of warping space (or space-time, if you will). The result is
that the earth follows a geodesic path (shortest distance path) as it
travels around the sun because the sun's mass has warped space in such
a way as to keep the earth in its orbit.
That is about the best we can do without getting into the mathematics,
but when you are ready you might take a look at "Gravitation" by Misner,
Thorne and Wheeler.
Jack L. Uretsky
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Update: June 2012