https://www.quora.com/What-is-the-Mach-Principle-What-is-the-experimental-evidence-for-it-What-are-its-implications-on-physics-and-cosmology/answer/Marco-Pereira-1
My position about Mach's Principle is that it is unsupported and refuted by optical and gravitational detection of Neutron Star Collisions.
I identified the only support (Celestial Dynamics within the Solar System requires instantaneous positions to be used in the force calculation) as being the result of using the wrong (empirical Newton's Law of Gravitation) law.
This shouldn't come up as a surprise to anyone since we all know that Newton's Law failed to predict the right Mercury Perihelion Precession Rate.
Of course, nobody can use Einstein's equations for a multi-planet dynamical simulation.
My theory - the Hypergeometrical Universe Theory (HU) provides a trivial replacement for Newtonian Dynamics and Einstein's General Relativity.
In fact, HU fully replaces General and Special Relativity.
IN SUMMARY
To call a theory Machian is a bad thing.
Mach's Principle in its idea that all mass in the universe contributes to the local inertia is indeed problematical. However, there is assumptions that are usually ignored in both Newtonian and relativity. In these and may models, bodies (mass) depresses some type of background so that the negative gradient may be "gravity'. So, he problem is from whence this stuff/ background. Some assume it was thee before the Big Bang. These models have their (insurmountable) problems. The STOE suggests another, more useful solution in a slight change to Mach's Principle.
part of the discussion in:
https://www.youtube.com/watch?v=d0nkeV2dbWA
John Hodge
Only bad models have a problem describing this "mysterious background". In my theory, the mysterious background is just a flat Euclidian 4D spatial manifold. Simple as butter.
I don't think your suggested solution is simpler than just space, so I will not veer in that direction.
As I told you, I am still waiting for your predictions and the number of parameters associated with SN1a data.
Here is the data
https://supernova.lbl.gov/union/figures/SCPUnion2.1_mu_vs_z.txt
I am curious.
For example, for L-CDM you just have to present:
a) Friedmann Model with 7 parameters.
b) Picture of the fitting
Mach's principle, or, as I like to call it "Mocks principle" is essentially a refutation of Newton's second Law. It is positively one of the most idiotic ideas in physics, but because it is always expressed by respected scientists in awed tones nobody notices.
Even one of my favorite science educators Veritasium: https://www.youtube.com/watch?v=XRr1kaXKBsU
Isn't most of this video a semantic argument? Essentially, what Black-Shirt-Derek (BSD) is saying is that Newton's Law has a_{Newton}=(Net Force)/mass. The Net Force of Newton's Law included F_g=mg, where g is the gravitational field. While it is somewhat ambiguous, I think what BSD has done is re-defined acceleration to a_{Mach}=a_{Newton}-g. This claim was backed up with something Newton already knew: one does not actually feel a gravitational force in free-fall, nor is this force measured by an accelerometer. However, Newton, when he applied the scientific method, did not subscribe to any edict, saying "Thou shalt contain your experiment to the insides of a windowless elevator shaped compartment". He allowed himself to look out the window.
Newton's second states, essentially, that acceleration is equal to the net force on an object divided by its mass.
What mocks principle does is says, no... we're not going to do that. We're going to say that
amach = a-g = ∑Fng/m
Where Fng is the net non-gravitational force acting on the particle,
But then on top of that, we're going to add a whole bunch of other complete claptrap, to wow and amaze people, so it seems like we've just done something clever in conflating real and fictitious forces.
It's also one of those "Emperor's New Clothes" sorts of things, so if you point to the fact that you've spent a considerable amount of time in College Freshman physics making a distinction between real and fictitious forces, people in the general relativity community will cluck and guffaw about how foolish and uneducated you are to fail to conflate them, once Mach's principle is introduced.
Machs principle is a good example of what happens when a celebrity proposes nonsense...
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