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Einstein's elevator thought experiment considered that in the Minkowski space-time of special relativity, all bodies fall identically.

What grounds did Einstein have to generalise this falling bodies observation to all physical processes to conclude that there is no conceivable physical experiment to distinguish between a homogenous gravitational field reference frame and a uniformly acceleration reference frame?

I believe this is about extending the weak equivalence principle to the Einstein's equivalence principle.

Maths
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A postulate or a physical principle doesn't have to be proven, doesn't have to be certified. It is a basic statement, a hypothesis that leads to results consistent with the experience. It is a "dogma of faith" that needs to be immune to any challenge.

I think the Equivalence Principle is valid because the inertial mass is also provided with a gravitational field. I want mean that; if inertial mass could be stripped of gravity, this principle couldn't be substantiated.

João Bosco
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    Could you please explain what you mean by "inertial mass is also provided with a gravitational field"? Thank you. – Maths Jan 03 '19 at 23:17
  • @AnmolGrover - I meant that when you apply a force on an object to test its inertial mass, the opposite resistance you feel is due solely to the inertia of the gravitational field of this body of test. But in the statement of this principle nobody never values ​​this fact. – João Bosco Jan 03 '19 at 23:35