Abstract
The equivalence principle was explained by Einstein using the didactic “mental experiment” of a uniform gravitational field inside an elevator. The Earth gravitational field is not really uniform so the question about how to create a uniform gravitational field is legitimate. To this aim, instead of using metrics depending on spatial coordinates, we have studied a cosmological - like metric and we have found that, under suitable assumptions, it is possible to measure a uniformly accelerated motion for the test particles moving inside the elevator.
Highlights
Albert Einstein constructed his General Relativity starting from two postulates: the equivalence principle and the principle of general covariance
We have shown that a uniform gravitational field in an Einstein’s elevator, can be obtained starting from a cosmological - like metric that generates a spacetime contraction
We have found a solution of geodesic equations that leads to the right peculiar velocity for the particles inside the elevator if a suitable choice of the scale factor is made
Summary
Albert Einstein constructed his General Relativity starting from two postulates: the equivalence principle and the principle of general covariance. We have devoted two previous papers to that subject, one from the classical point of view [2], and the other one [3] for quantum regime Different forms of this principle are used in textbooks, but we prefer the simple definition given by Pauli ”In Newtonian theory, a frame of reference located in a homogeneous gravitational field is perfectly equivalent, from a mechanical point of view, to a uniformly accelerated reference frame. Regardless of the final result, from the didactic point of view, it may be enough to face the problem of defining the properties of a uniform gravitational field and to underline the differences with respect to the space of uniformly accelerated observers, which we do in section 2 and 3 of the paper.
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