Understanding Mach Principle I cannot get the essence of Mach's Principle. 
In my undestanding, it states that the cause of the so-called "fictitious forces" which arise in non-uniform motion has to be found in the relative motion between the object under analysis and all other masses in the Universe.
Now, we now that the fictitious forces depend on the non-uniform motion of the OBSERVER and on the inertial-mass of the object under analysis --> the object under analysis contributes to these forces only with its mass, not with its relative motion.
So, I can't understand the conclusion:
 "The inertia of any object depends in its relative motion with respect to all other masses".
It seems to me that a more appropriate version should be:
"The inertia of an object depends on the relative motion of the OBSERVER with respect to all other masses".
But I am sure I am missing something.
Can you please help me understand?
 A: Mach's principle means many different things to many different people (Mach himself is long dead so cannot tell us what he meant). Wikipedia gives 11 different definitions: https://en.wikipedia.org/wiki/Mach%27s_principle#targetText=Mach's%20principle%20says%20that%20this,to%20the%20local%20inertial%20frame.&targetText=A%20very%20general%20statement%20of,scale%20structure%20of%20the%20universe%22.
The two versions you give are so similar that the level to which the principle has been "pinned down" is much less precise than the distinction you are trying to draw.
However,  my understanding is that the two versions you give do not differ significantly from one another anyway. Mach's principle (as I understand it) is essentially a deep suspicion of the fact that (according to our best understanding of physics) the following two hypothetical universes are different from one another:


*

*An infinite vacuum containing a single spanner.

*An infinite vacuum containing a single rotating spanner.


In the second case (for a spanner spinning on a generic axis) the internal molecules comprising the spanner will feel centrifugal forces which (for a realistic material) will lead to heating as the spanner flexes. (The energy is drawn from the rotation and the angular momentum is conserved by putting the spanner in a spin about a different axis, one in which its moment of inertia is higher so that equal angular momentum is possible with less rotational energy).
Examples like this (and rotating magnets, or buckets) are what upset people. The physics that would be predicted (IE heating and a change in axis of rotation) is actually the same for an observer in either reference frame (rotating or not), and it is this (observable) physics that is seen as suspicious.
