Speed of light - with observer experiencing gravity

rcgldr

This is related to time dilation effect due to strength of gravity, basically GR effect on calculated speed of light.

Two observers, observer#1 on a very large non-rotating sphere, experiencing 1.0g of gravity, observer#2 is a large distance from the sphere, experiencing 0.1g of gravity. Both observers have identical clocks, and it is known that #1's clock's rate is slower than #2's clock's rate. There are two distant spheres sphere#2, and sphere#3, a large and known distance apart (as measured at 0g while between the two spheres).

A beam of light travels from sphere#2 to sphere#3. If the two observers caclculate the velocity of light based on the known distance versus their local time, they will calculate different velocities.

It seems the only solution to this dilema is if the observed distance between sphere#2 and sphere#3 differs depending on the amount of gravity experienced by an observer, so that observer#1, experiencing 1.0g of gravity, observes a shorter distance between the two distant spheres than observer #2, experincing 0.1g of gravity.

jonmtkisco

Hi Jeff,
I don't know if it's relevant to the answer, but I'll point out that the transverse light beam can't be viewed directly by the observers. Instead, at best they can observe a reflection of the beam, once at the time of emission from sphere #2 and again at the time of arrival at sphere #3. So their perception of sphere #2 - sphere #3 travel time is affected by the additional leg of the trip between each sphere and the observer's location. Observer #1 will see images which are blueshifted compared to what Observer #2 sees although for both observers that will be offset by some redshift depending on the relative masses of the 3 spheres.

Neither observer is in the inertial frame of any portion of the transverse leg of the lightbeam, so I wouldn't think they would have to agree on what they remotely measure to be the speed of light in any such transverse inertial frame.

Jon

rcgldr

Assume sphere #2 and sphere #3 have very little mass, and are equal distances from both observers.