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.

The broad notion is that “mass there influences inertia here”. Any statement which — though possibly far more specific than this — follows in this spirit may be classified as a “Mach principle”. **The truth of these statements depends on the particular statement.** (The truth also depends on the theory of gravity, though Einstein’s general relativity is the most frequently discussed theory.)

**Examples**

Hermann Bondi and Joseph Samuel have listed eleven distinct statements which can be called *Mach principles*, labelled by *Mach0* through *Mach10*. 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.*Mach2*: An isolated body in otherwise empty space has no inertia.*Mach3*: Local inertial frames are affected by the cosmic motion and distribution of matter.*Mach4*: The universe is spatially closed.*Mach5*: The total energy, angular and linear momentum of the universe are zero.*Mach6*: Inertial mass is affected by the global distribution of matter.*Mach7*: If you take away all matter, there is no more space.*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.*Mach10*: Overall rigid rotations and translations of a system are unobservable.

— Wikipedia on *Mach principle*

2014.06.22 Sunday ACHK