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In theoretical physics, particularly in discussions of gravitation theories, a Mach principle is any of a class of principles which are more specific statements of Mach's principle.


Hermann Bondi and Joseph Samuel have listed eleven distinct statements which can be called Mach principles, labelled by Mach0 through Mach10.[1] Though their list is not necessarily exhaustive, it does give a flavor for the variety possible.

Mach0: The universe, as represented by the average motion of distant galaxies, does not appear to rotate relative to local inertial frames.
Mach1: Newton’s gravitational constant G is a dynamical field.
Mach4: The universe is spatially closed.
Mach8: \( \Omega \ \stackrel{\mathrm{def}}{=}\ 4 \pi \rho G T^2 \) is a definite number, of order unity, where \( \rho \) is the mean density of matter in the universe, and T is the Hubble time.
Mach9: The theory contains no absolute elements.


^ Bondi, Hermann; and Samuel, Joseph (July 4, 1996). "The Lense–Thirring Effect and Mach's Principle". arXiv:gr-qc/9607009. A useful review explaining the multiplicity of "Mach principles" which have been invoked in the research literature (and elsewhere).

See also

Mach's principle
Democratic principle

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