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Gravity - Can it exist in 1 Dimension?

Gravity - Can it exist in 1 Dimension?

Consider a closed loop containing two point masses m and M. The loop is a 1D space.

What's the gravitational force between the two masses?

Newton's formula for the gravitational force F between two masses m and M in 3D space is..


where G is a constant and r is the distance between the two masses.

The r^2 term is good in a 3D space, but in general it's r^(n-1) where n is the dimension of the space. So putting n=1 for 1D space we get..

r^(1-1)=r^0=1 so F=G*M*m

Which means F is independent of distance. Gravity has the same strength no matter how far apart the two objects are!

So each object feels the exact same gravitational force to the right and left and the net force is zero. Gravity does not exist in 1D space!

Of course, these calculations have been done using Newton's theory of gravity. I wonder if we would get the same result with Einstein's General Theory of Relativity, which is now 100 years old but still "state-of-the-art" in gravitational theories.

Content written and posted by Ken Abbott
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