Explain Mach's principle to me please!

[ralph124c]

Earnst mach 9Austrain physicists0, and for whom the 'mach" number is named, came up with this idea before einstein. Can somebody please explain it to me? Are there any reasons to doubt it?

[Hyperelastic]

@Ernst Mach

The considerations just presented show, that it is not necessary to refer the law of inertia to a spacial absolute space. On the contrary, it is perceived that the masses that in the common phraseology exert forces on each other as well as those that exert none, stand with respect to acceleration in quite similar relations. We may, indeed, regard all masses as related to each other. That accelerations play a prominent part in the relations of the masses, must be accepted as a fact of experience; which does not, however, exclude attempts to elucidate this fact by a comparison of it with other facts, involving the discovery of new points of view.
(Mach, The Science of Mechanics, ch.2, vi-8, 288)

He is criticizing the notion of absolute acceleration, in so many words. Acceleration of a mass results in an inertial “force”, but Mach was a positivist and didn’t believe in absolute motion, because he assumed space was empty and therefore provided no natural frame of reference. His way around the problem was to hypothesize that inertia comes from the interaction of the mass with all other masses in the universe, so the acceleration that is important is the acceleration relative to most of the universe’s mass, which is in the far-flung “distant stars”. Even today, inertia cannot be explained in terms of simpler or deeper ideas.

I don’t think there is any physical theory in which Mach’s Principle is inherent. Part of the problem is that he didn’t state it mathematically, so it’s not absolutely clear what he meant (the second law of thermodynamics suffers from the same problem.) It’s not even really clear what Mach’s Principle is, because he talked around the subject quite a bit in The Science of Mechanics. It was only later that Einstein started talking about “Mach’s Principle”.

[Loopydude]

There is a Machian theory of “inertia” of charged particles, the Wheeler-Feynman Absorber Theory of radiation resistance. Without going into a redundant explanation of the theory (it’s historically significant, as playing with it helped lay some of the groundwork for Feynman’s path-integral formulation of QED), which can easily be Googled if you want more exposition, I guess the major problem (though not the only problem) with this idea is it requires a closed universe. Any extension of the theory within a quantum gravitational framework would also require a closed universe. Since observation appears to favor an “open” universe, perhaps, in general, Mach’s principle simply can’t work, or is, at least, evidentially disproven. I don’t know, and would be curious what physicists have to say on that subject.

[JasonFin]

The idea behind Mach’s principle is that there are no inherently inertial frames of motion; rather, which reference frames are inertial is determined by the arrangement of matter in the universe.

As mentioned here, there’s actually some disagreement among physicists as to whether General Relativity is a perfectly Machian theory.