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| In [[theoretical physics]], particularly in discussions of [[:Category:Theories of gravitation|gravitation theories]], a '''Mach principle''' is any of a class of principles which are more specific statements of [[Mach's principle]].
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| 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.)
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| ==Examples==
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| [[Hermann Bondi]] and Joseph Samuel have listed eleven distinct statements which can be called Mach principles, labelled by ''Mach0'' through ''Mach10''.<ref>{{cite arxiv | author=Bondi, Hermann; and Samuel, Joseph | title=The Lense–Thirring Effect and Mach's Principle | eprint=gr-qc/9607009 | date=July 4, 1996 }} A useful review explaining the multiplicity of "Mach principles" which have been invoked in the research literature (and elsewhere).</ref> Though their list is not necessarily exhaustive, it does give a flavor for the variety possible.
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| * ''Mach0'': The universe, as represented by the average motion of distant galaxies, does not appear to rotate relative to local inertial frames.
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| * ''Mach1'': Newton’s gravitational constant G is a [[dynamical field]].
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| * ''Mach2'': An isolated body in otherwise empty space has no inertia.
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| * ''Mach3'': Local inertial frames are affected by the cosmic motion and distribution of matter.
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| * ''Mach4'': The universe is spatially closed.
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| * ''Mach5'': The total energy, angular and linear momentum of the universe are zero.
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| * ''Mach6'': Inertial mass is affected by the global distribution of matter.
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| * ''Mach7'': If you take away all matter, there is no more space.
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| * ''Mach8'': <math>\Omega \ \stackrel{\mathrm{def}}{=}\ 4 \pi \rho G T^2</math> is a definite number, of order unity, where <math>\rho</math> is the mean density of matter in the universe, and <math>T</math> is the [[Hubble time]].
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| * ''Mach9'': The theory contains no absolute elements.
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| * ''Mach10'': Overall rigid rotations and translations of a system are unobservable.
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| ==See also==
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| * [[Mach's principle]]
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| * [[Democratic principle]]
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| ==References==
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| <references/>
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| [[Category:Theories of gravitation]]
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| [[Category:Gravitation]]
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| [[uk:Принцип Маха]]
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