I'm loosing feet with what is going on here with ME vs EM. Regarding the former, I understand Ron states it is not incompatible with GR, so not with SR, so not with Lorentz invariance. But it can predict the result of a situation that GR cannot predict, namely situation of a ME thruster thrusting. This "hole" in GR was never noticed because such prediction for such situation never needed, kind of, so possible Machian "extension" (?) to GR forgotten. How could it be that a mundane device like a ME thruster could leave classic frameworks GR + QFT voiceless ?
I think the answer here is to note that as I said, GR does not address the issue fo the origin of inertia. Eistein liked Mach's explantion here. He was in fact the one who coined the name, and it helped him form GR, but GR is not contingent upon Mach's Principle, so you would not expect to see GR extended to include inertia manipulation. It was actually Dennis Sciama back in the 50's who first started connecting GR with MP. Woodward merely followed Sciama's lead when he stumbled upon the surprise in the derivations that showed there was a way to manipulate inertia present. He talks about this in detail in his book.
Thank you for the answer, but as expected in the question I don't find it satisfying. I won't read the book, main reason being I feel I should study complete and solid GR course first (and no time nor priority so far), so if you are getting tired of playing the popularization game for not enough involved audience I would understand.
So, with all my (admitted) shortcomings in understanding GR, seems to me it hasn't to be "extended" to predict that the total mass-energy content of a bulk material wont vary by a iota while it's vibrating (under harmonic self oscillations) : energy is swapping between kinetic energy and elastic energy in the intermolecular bonds but is the same magnitude, has the same gravitational pull, has the same inertia. "Inertia manipulation" would be just a particular configuration of accelerations and energy swapping between different forms, in a locally quite flat space-time, how could this be beyond the scope of GR as far as inertia is concerned ? Say for instance we study a battery, from empty, charging it will add mass_energy to it. The gained mass (say gravitational, as measured by weight on a scale) will be quite low but is clearly not 0 and predicted by SR, delta_m=delta_E/c² (sorry for the triviality). Now make an internal short-circuit so that this chemical potential energy discharges quickly, and converts to thermal agitation. There is no net gain nor loss of energy to the outside, so the hot depleted battery will weigh exactly as much as when cold and charged.
What is the aspect of an experiment of "inertia manipulation" that escapes this aptitude of SR (we don't even need GR here) of simply predicting that inertial mass amounts just to mass_energy content, and that a closed bulk system wont see any change in inertial mass, whatever happens inside ? And that an open bulk system can see a change in mass_energy content but only as much as mass_energy flow it incurs, and such flow will bring/carry away an equivalent momentum than would allow to "push heavy pull light", so we are left with 0 net thrust in the end ?
I can understand such Machian physics could predict such inertia manipulation, different from what SR would predict, but not how SR would fail to predict anything at all ! I mean, just show ME thruster design (and its internal power dynamics...) to a good physicist who don't know what it's supposed to do, you really think he/she will scratch head for a few days and conclude "how strange, we need an extended theory of inertia to predict how it will behave, classical frameworks have nothing to tell !" Really ?
As for the higher order anisotropies... this looks like a nice playground, full of hills and hollows. What a GR compatible Machian physics would have to say different from what would say GR : local inertias don't care ? Anyway, it claims to predict an effect that is astounding for most people working with GR under the form of a ME thruster thrusting. Can't the theory devise one other type of experiment that is at least as astounding and that could lend itself to more convincing reproducible results ? Call it an experiment in fundamental science (à la Michelson and Morley). Better credibility to the theory if it can expose itself to experimental falsifiability on other grounds that notoriously capricious propellentless drives. Are there such other falsifiable grounds?
Woodward makes the argument in his book, which I chided him about for failing at the kinds of detail I would have liked, but basically his argument is that the flatness we observe with WMAP data, does indeed require that Mach's Principle be correct. He says the issue is settled since WMAP. It's a complex issue and again, I think he should have gone slower though the argument and would perhaps make a wonderful academic paper in and of itself, but I don't know if he took the jibe seriously. I think he was writing again last summer but I don't know the subject or contents.
"Loosing feet with" sounds like an idiom from outside the English speaking world. Can I ask where you're from?
Yes, not far off England coasts but still not native speaker for sure, I'm French actually. "Perdre pied" (loosing foot, rather than feet...) meaning you can no longer reach the bottom with feet when standing in water. It's used as a way to admit you don't swim well and are no longer in a zone of comfort, and likely not to follow a particular lead but rather to drown swiftly. Beyond swimming... you get the picture, metaphorically.
I'm sure a lot of people have other conclusions to draw than correctness of Mach principle from the apparent flatness on cosmological scales. The question was rather, what other
lab experiments could be devised to check for the reality or falsify Machian theory ? Is a ME thruster the most simple arrangement where such effect would manifest ? Someone send me a life jacket please.