Imagine a second earth one lightyear away from our earth. Now imagine a bunch of scientists with a plane and some atomic clocks who are living on this second earth and who perform the Hafele-Keating Experiment, which is the experiment that was done in 1971 on our earth to prove the relativistic effects of kinematic and gravitational time dilation:
Joseph C. Hafele, a physicist, and Richard E. Keating, an astronomer, took four cesium-beam atomic clocks aboard commercial airliners. They flew twice around the world, first eastward, then westward, and compared the clocks against others that remained at the United States Naval Observatory. When reunited, the three sets of clocks were found to disagree with one another, and their differences were consistent with the predictions of special and general relativity. (Wikipedia)
Now lets suppose both earths are not moving or at least that they are not moving in relation to each other. Ignoring the gravitational time dilation, we can tell already from the experiment of 1971 that the atomic clocks on the fast moving plane will run a bit slower than the static atomic clocks on earth-two due to the kinematic time dilation of special relativity.
Because earth-one is not moving in relation to earth-two we can expect that if there was another atomic clock on earth-one it would run just as fast as the clocks on earth-two, hence also faster than the ones on the plane.
Now my question: Does this asynchronity between the time on earth-one and the time on the highspeed-plane flying around earth-two start the moment the plane starts (ignoring the short time of acceleration the plane needs) or does it start much later, when the light (information) of the flying plane arrives at earth-one (which would be one year delayed because of the distance of one lightyear between the two earths)?
In other words: Do the effects of special relativity occur instantaneously, independed of the distance between the observing and the observed frame of reference?