Beta Phase: Square45 is currently in beta testing. Expect some features or content to be incomplete or missing.
45

Principle of Equivalence

The effects of gravity are indistinguishable from the effects of acceleration, forming the cornerstone of General Relativity's predictions.
📜

The statement of the theorem

The Principle of Equivalence asserts that in any sufficiently small, freely falling (local inertial) frame, the gravitational field effects vanish, allowing the spacetime to be approximated by flat Minkowski spacetime (ημν\eta_{\mu\nu}). Mathematically, this implies the existence of a coordinate transformation x′μ=x′μ(x)x'^\mu = x'^\mu(x) such that the connection coefficients vanish locally:\Γνρ′μ=0\Gamma'^{\mu}_{\nu\rho} = 0 \nThis condition ensures that the local physics is indistinguishable from that in the absence of gravity.