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Can anyone please explain me Mach's principle, i.e the definition of inertia he has given? I am really not getting what spin and universe have to do with inertia because what we are taught in our schooldays is as simple as

inertia is the measure of mass of a system, i.e the ability of a body to resist the change in the state of a body.

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What today is commonly referred to as Mach's principle was not proposed by Ernst Mach. The idea was proposed by Einstein, but he called it 'Mach's principle' and unfortunately Einstein did this in such a way that readers are under the impression that Mach proposed it.
(Presumably Einstein opted to attribute the idea to Mach because Einstein came to the idea from something that Mach had written.)

A historically accurate name would be: Einstein's Mach's principle.

Today there are multiple versions in circulation; it's not a well defined concept.

Historians of physics describe that Einstein abandoned Einstein's Mach's principle in the mid 20's.
(Einstein didn't publicly announce that, but historians of physics point out that Einstein ceased mentioning Einstein's Mach's principle in his articles altogether, whereas just a few years earlier Einstein had claimed that Einstein's Mach's principle was fundamentally important for General Relativity.)

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