- #1

- 457

- 1

## Main Question or Discussion Point

I have been working on something and I want to see if you guys get the same result. Let's say we have a hovering observer at r from a large gravitating body such as the sun. The gravitational time dilation there would be z_r = sqrt(1 - 2 G M / (r c^2)), correct? If a clock directly passes the hovering observer, then since SR is valid locally, the hovering observer will measure a kinetic time dilation on the clock of z_kinetic = sqrt(1 - (v_local / c)^2), right? To a distant observer, since there is no simultaneity difference between the two observers, the distant observer will also observe that the clock is ticking z_kinetic slower than the hovering observer's clock, and that the hovering observer's clock is ticking z_r slower than his own, so the distant observer measures a time dilation for the clock of z_r * z_kinetic, is that right so far?

Now let's say that there is another small gravitating mass at r. The hovering observer at r is far from it but there is a second hovering observer a distance of d from the smaller mass, but still at r from the first mass. Since the first and second hovering observers are both a distance of r from the first mass, there is no difference in time dilation between them due to the first mass, but the second hovering observer is time dilating by z_d due to the gravity of the second mass, right? That is according to the second hovering observer, but according to the distant observer, the time dilation of the second hovering observer is z_d slower than the first hovering observer while the first hovering observer is time dilating by a factor of z_r to the distant observer's clock, so the distant observer measures a time dilation of the second hovering observer's clock of z_d * z_r, right?

Now let's say that there is another small gravitating mass at r. The hovering observer at r is far from it but there is a second hovering observer a distance of d from the smaller mass, but still at r from the first mass. Since the first and second hovering observers are both a distance of r from the first mass, there is no difference in time dilation between them due to the first mass, but the second hovering observer is time dilating by z_d due to the gravity of the second mass, right? That is according to the second hovering observer, but according to the distant observer, the time dilation of the second hovering observer is z_d slower than the first hovering observer while the first hovering observer is time dilating by a factor of z_r to the distant observer's clock, so the distant observer measures a time dilation of the second hovering observer's clock of z_d * z_r, right?

Last edited: