Consider a doubled Pound-Rebka type experiment, where a source on the surface of the Earth, say, emits a pulse of radiation detected at some height h above the surface, and then the source emits another pulse a time t₀ after the first one. The spacetime diagram of height vs. time describing this will look roughly like a parallelogram: the base is the time t₀, the top (a distance h higher in the space direction) the reception time interval t', and the slanty sides the paths of the pulses at 45^o (to be consistent, in this view they should be curved by the acceleration we interpret the gravitational field as, but as long as the field is homogeneous the curves will still be parallel).

The Principle of Equivalence says the gravitational field of the Earth is equivalent to a frame accelerated at g, so over a time t one builds up a velocity v=gt. An observer will expect a Doppler shift in the pulse frequency of z=v/c=gt/c=gh, and indeed the Principle of Equivalence predicts a gravitational redshift of this amount. However, this redshift in frequency is equivalent to a change of time intervals, i.e. the Equivalence Principle says that the top and bottom time intervals are not the same: t' \ne t₀. The only way this can be consistent with our spacetime picture is to say that parallel lines are not parallel. Thus one is led inexorably to a picture of spacetime curvature.