Dynamics in Kaluza-Klein Gravity and a Fifth Force

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Abstract

Using a novel coordinate system, we rederive the field equations and equa tions of motion for 5-dimensional relativity in the general case where the metric can depend on all 5 coordinates (i.e., Kaluza-Klein theory without the cylinder restriction). We show that in general the fifth dimension produces a new dynamical force in 4-dimensional spacetime. This timelike fifth force is proportional to the 4-velocity of a particle and is thus unlike any known 4-force. We briefly examine the properties of some simple models, and suggest that the detection of the fifth force is the most promising way to investigate the existence of an extra dimension in nature.

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