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@Grav Velocity just a question from me. In general, how is "gravitational time dilation" defined?
Grav Velocity said:"Static" space time involves only one massive body
Grav Velocity said:Non-static space time involves at least two source (massive) objects that are gravitationally interacting with one another and therefore moving.
Grav Velocity said:This movement changes the shape of space time as time passes.
Grav Velocity said:The most obvious example of this would be two objects orbiting one another and the resulting space time distortions or gravity waves….
Grav Velocity said:These gravity waves would create a fluctuating time dilation (and length) and any given point in space time.
Grav Velocity said:The space time distortions created by the orbiting planets in non-static space time causes a time dilation at a particular location that does not match the corresponding gravitational potential (velocity) at that same point.
Grav Velocity said:this difference between gravitational potential and time dilation breaks the waterfall model.
Grav Velocity said:I can say the math for gravitational potential and time dilation for two massive object affecting a single point in space time seems to work out without any problems for various positions of two objects orbiting one another (just some simple vector additions)
No, that is not right. Some of the underlying problem here is that you still don't understand what time dilation is, and that is confusing you. In post #7 of this thread @Dale described time dilation as a ratio between coordinate time and proper time, and I have suggested that you understand the role of relativity of simultaneity in velocity-based time dilation. Until you've done these things or similar exercises, you will find it very difficult to construct a workable mental model.Grav Velocity said:The space time distortions created by the orbiting planets in non-static space time causes a time dilation...
It's not that it "does not match", the issue is that the concept of gravitational potential is not meaningful here. Talking about the potential at a point in one of these spacetimes is like talking about the color and weight of an emotion - a grammatically correct but meaningless string of words.at a particular location that does not match the corresponding gravitational potential (velocity) at that same point