We know that the equivalence principle explains the slowing down of time, since, with respect to an inertial observer the time difference between sending two successive light pulses at the head of the rocket is greater than that of receiving them at the tail.

How it explains curvature of space?

  • 1
    $\begingroup$ 1. Do you want to know about expansion or curvature? 2. The equiv principle cannot on its own show you all the spatial properties, but some useful intuitions can be obtained from the rotating disk in flat spacetime. $\endgroup$ Jul 20, 2021 at 10:13
  • $\begingroup$ I know it cannot show all the properties. We won't have tidal forces in a local reference frame. But can it give some intuitions about space expansion? $\endgroup$
    – Nayeem1
    Jul 20, 2021 at 10:24

1 Answer 1


Curvature represents tidal effects, and the equivalence principle is by definition only applicable to regions of spacetime where tidal effects are too small to notice. So the equivalence principle on its own cannot tell you about curvature.

However, if you couple the equivalence principle with some basic observations then you can infer that curvature is needed. Specifically, the equivalence principle implies that an object in free fall has a worldline which is locally straight (a geodesic). Now, couple this with observations of tidal effects. For example, consider two objects dropped from rest at the same altitude over a planet. Initially they are at rest with respect to each other, then the distance between them reduces.

So, per the equivalence principle we have two straight lines. Since they are initially at rest their world lines are initially parallel. And yet the distance between them reduces, in principle (drill holes through the planet) they will intersect at the center of the planet.

This combination (straight initially parallel lines that intersect) is not possible in flat spacetime, but is possible if spacetime is curved.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.