Einstein Relatively Easy

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        Physically, this principle (sometimes referred as to EEP = Einstein's Equivalence Principle) postulates that there is no experiment done in a small confined space which can tell the difference between a uniform gravitational field and an equivalent acceleration.

Put in another way, according to this principle, all physic laws wih hold the same form in a free falling Local Inertial Frame (LIF) in presence of the gravitation and in an Inertial Frame in absence of gravitation.

Mathematically, this important observation states that in presence of a gravitational field, small enough free falling frames will be inertial, and that in these Local Inertial Frame (LIF), where the metric gμν reduces to ημν, the laws of physics from Special Relativity will hold true.

Refer to  the article The Equivalence Principle for more details.

Refer to the below youtube tutorial to get a good overview of the mathematical expression of the principle, i.e. how a local inertial frame (black colour) can be obtained by a general coordinate transformation at any point P of a manifold (blue colour)

 

Refer to the article 1907 Equivalence Principle first published expression to read the Einstein's first formulation of this principle.

 

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"Pas plus de cinq ou six semaines s'écoulèrent entre la conception de l'idée de la relativité restreinte et la rédaction de l'article correspondant."
Einstein à Carl Seelig, 11 Mars 1952

"N'importe quel étudiant dans les rues de Göttigen en connaît plus qu'Einstein sur les géométries à 4 dimensions. Et pourtant ce fut Einstein qui accomplit le travail, et non les mathématiciens."
David Hilbert

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