In the context of General Relativity, the democratic principle allows quick, order-of-magnitude calculations for the strength of gravitomagnetic effects such as frame-dragging. While the principle is fairly intuitive, it does not have a rigorous mathematical definition.
John Wheeler (1990) on the practical application of Mach's principle to experiment (pp.232-233):
- "It is not necessary to enter into the mathematics of the theory to state its simple consequence ... Each mass has an "inertia-contributing" power, a voting power, equal to its mass, there, divided by the distance from there to here. "
According to the general principle of relativity, rotation is a relative property, and a state of motion that a satellite senses as being "absolutely non-rotating" is a local state, dictated partly by the relative rotation of the background stars, but also partly by the rotation of the body that the satellite orbits. Applying the democratic principle, we can calculate the influence of these two rotations on the satellite by calculating the relative contributions of these two collections of massenergy to the background gravitational field strength at the satellite's location, and then weighting their contributions on the satellite's "sense of rotation" accordingly.
See also
- Mach's principle
- Gravitoelectromagnetism
- General relativity
References
- Wheeler, John Archibald (1990). A journey into gravity and spacetime. W. H. Freeman. ISBN 0-7167-5016-3. See pp 232–233. This is a semi-popular book.