Is relativity reciprocal or directional?

• SpiderET

SpiderET

I was wondering whether is there some real evidence for directional relativity in this article or is this rather a pure speculation. Actually it sounds as common sense for me, that the relativity effects are taking place on the moving object and not on both objects reciprocally.

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I was wondering whether is there some real evidence for directional relativity in this article or is this rather a pure speculation. Actually it sounds as common sense for me, that the relativity effects are taking place on the moving object and not on both objects reciprocally.
Time Dilation is reciprocal only between two inertial observers. It doesn't apply between one in orbit around another or for gravitational Time Dilation.

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Time Dilation is reciprocal only between two inertial observers. It doesn't apply between one in orbit around another or for gravitational Time Dilation.
So you mean that GPS satellite is not inertial and time dilation is directional and it is in line with mainstream explanation of Special relativity?

So you mean that GPS satellite is not inertial and time dilation is directional and it is in line with mainstream explanation of Special relativity?

GPS satellites are "inertial" in the sense that they are in free fall; but a frame in which a particular GPS satellite is always at rest is not an "inertial frame" except over a very short time and distance. Treating such a frame as inertial without restriction is one of the key errors in the paper referenced in the article.

The relative time dilation between GPS satellites and Earth-bound observers includes both "SR" effects (relative motion) and "GR" effects (gravitational time dilation due to difference in altitude). Whether the SR effect is "directional" or "reciprocal" depends on what simultaneity convention you adopt (the GR effect is always directional). For the standard simultaneity convention used in GPS, that of the "Earth-centered inertial" (ECI) frame (see below for why this frame can be considered inertial for this scenario while the GPS satellite "rest frame" can't), the effect is directional.

The reason the ECI frame can be considered "inertial" for this scenario, while the GPS satellite rest frame can't, is that, while all inertial frames are only local in curved spacetime, the meaning of "local" depends on the frame and what object is at rest in it. For a body in free-fall orbit about another body, a local inertial frame can only cover a range of time and space that is small compared to the orbital dimensions (period and radius). So a frame in which a given GPS satellite is at rest is only inertial over a time span small compared to one satellite orbit, and a spatial range small compared to the orbital radius; that's certainly not enough to cover a complete orbit or to cover an Earth-bound observer as well as the satellite, so such a frame can't be used to compare clock rates over a complete orbit. However, the ECI frame is inertial over a time span small compared to a year, and a spatial range small compared to the Earth's distance from the Sun; that is still plenty of room to cover many GPS satellite orbits, so it's more than enough to compare clock rates as required for this scenario.

(Note that the ECI frame is still not completely "inertial" because the effects of altitude have to be considered; but that can be modeled as a simple adjustment to clock rates based on altitude, without changing anything else, so it doesn't preclude treating the ECI frame as inertial for the purpose of modeling relative motion.)

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