Gravitational Time Dilation - Definition

Definition

Clocks which are far from massive bodies (or at higher gravitational potentials) run faster, and clocks close to massive bodies (or at lower gravitational potentials) run slower. This is because gravitational time dilation is manifested in accelerated frames of reference or, by virtue of the equivalence principle, in the gravitational field of massive objects.

It can also be manifested by any other kind of accelerating reference frame such as an accelerating dragster or space shuttle. Spinning objects such as merry-go-rounds and ferris wheels are subjected to gravitational time dilation as a consequence of centripetal acceleration.

This is supported by the general theory of relativity due to the equivalence principle that states that all accelerated reference frames are physically equivalent to a gravitational field of the same strength. For example, a person standing on the surface of the Earth experiences exactly the same effect as a person standing in a space ship accelerating at 9.8 m/sec2 (that is, generating a force of 9.8 N/kg, equal to the gravitational field strength of Earth at its surface). According to general relativity, inertial mass and gravitational mass are the same. Not all gravitational fields are "curved" or "spherical"; some are flat as in the case of an accelerating dragster or spacecraft. Any kind of g-load contributes to gravitational time dilation.

• In an accelerated box, the equation with respect to an arbitrary base observer is, where
  • is the total time dilation at a distant position,
  • is the acceleration of the box as measured by the base observer,
  • is the "vertical" distance between the observers and
  • is the speed of light

When is much smaller than, the linear "weak field" approximation may also be used.

• On a rotating disk when the base observer is located at the center of the disk and co-rotating with it (which makes their view of spacetime non-inertial), the equation is, where
  • is the distance from the center of the disk (which is the location of the base observer), and
  • is the angular velocity of the disk.

(It is no accident that in an inertial frame of reference this becomes the familiar velocity time dilation ).