In wikipedia https://en.wikipedia.org/wiki/Equivalence_principle, there are three forms of equivalence principle ( equivalence of gravitational and inertial mass ) :
- Weak version (Galilean) :
- The trajectory of a point mass in a gravitational field depends only on its initial position and velocity, and is independent of its composition and structure.
- All test particles at the alike spacetime point, in a given gravitational field, will undergo the same acceleration, independent of their properties, including their rest mass.[7]
- All local centers of mass free-fall (in vacuum) along identical (parallel-displaced, same speed) minimum action trajectories independent of all observable properties.
- The vacuum world-line of a body immersed in a gravitational field is independent of all observable properties.
- The local effects of motion in a curved spacetime (gravitation) are indistinguishable from those of an accelerated observer in flat spacetime, without exception.
- Mass (measured with a balance) and weight (measured with a scale) are locally in identical ratio for all bodies (the opening page to Newton's Philosophiæ Naturalis Principia Mathematica, 1687).
Einstein version : The outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime.
Strong version : The strong equivalence principle suggests the laws of gravitation are independent of velocity and location. In particular, the gravitational motion of a small test body depends only on its initial position in spacetime and velocity, and not on its constitution. And the outcome of any local experiment (gravitational or not) in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime.
My question is, how these equivalence principles ( or possibly one of them ) leads to the idea that 'gravitation is manifestation of curved spacetime' ? Although I read associated book/data, I want to understand this concatenation of inspiration more logically and clearly. Can anyone helps?
