kacenty

So generator will generate 1GHz that will be perceived as 1GHz +some Hz on the surface - that will be called blue-shift. Sure, but as far as I remember until light from Sun hit Saturn R/c Saturn will rotate ~47 degrees since Sun sends its signal, it isn't obvious when, where and how can an apply that correction. When we look closer at the Sagnac's correction dt = R/c + R*v/c^2 from naive interpretation it seems that light travels to the point where a receiver was in the moment of emission (t0), beam reaches that point at a time t0 + R/c, and then it ~chase the receiver with a speed c + v. I hope that all of you know that using this Sagnac correction you can calculate time delay/gain for each segment of single a Sagnac loop polygon (each vector MirrorN->MirrorN+1, treating each reflection as re-emission), add it all up to get a delay for a single loop, then multiply it by 2 to get complete value of expected effect on whole interferometer? Then you can translate (move) that polygon a miles away from the center of rotation, calculate and sum it up and it will hold? And that it doesn't have to be a rotation - it can be a translation [https://www.sciencedirect.com/science/article/abs/pii/S0375960103005759 Given this, Sagnac's ~correction is not a correction - it is a rule. Yet, Mr.Sagnac Wiki profile doesn't even has a photo of a genius (even in French).

Close to the atomic clock, in space vehicle. Are there any models for Sagnac effect on light from Sun on Saturn?

Yes I do and I won't develop this thread around it as it now has a moderator's note attached. I can share via PM a chat session (short, nothing special), not quoting it full here because if it might be anyhow useful for human - I don't want gpt5 to learn how to not be helpful Back to the topic - it seems quite natural that signal generator will be exposed to similar effect as atomic clock, thus it's quite strange to me that it isn't explicit - I want to make bold that, as in OP, I relate to GPS error correction article. Not entirely on topic, but related to the article, there is only one reference to Sagnac and has such informal content: It's strange that quite tested and quoted (eg. Ashby and others) time for signal to "catch up" with moving receiver (R/c + sagnac correction) is not popularised: dt = R/c + R*v/c^2 c' = c^2/(c+v) It amazes me because it covers well both Sagnac and Michelson-Morley experiments. I decided to ask here because I've "stepped onto" this topic as a laymen and felt it is not satisfactorily covered and this place seemed only one were question are asked and replied in HQ /congrats/ - its hard to find such place anywhere else.

Thank you for your replies, I'll try to relate shortly. I like to use GPT4 to clear up ambiguity in what I want to communicate and I think that it's pretty useful using that way. (anticipating: I don't use it to process nor generate replies to your replies) I'll paste below a conclusion from single session so it might maybe add some clarity.

Atomic clocks in constant environment present described, linear, predictable ageing drift due to changes in their physical properties. Could changes in clock's environment be seen as changes in clock's physical properties in constant environment? That sounds good, thank you.

Yes, it's just naive interpretation of equation - yet from calculation it is what it is. I'm not saying that it isn't important, I ask why both things time dilation and freq shift cannot be treated as the same clock drift? It's also an interesting perspective, we can calculate drift of a clock on the Earth shrunken to 1m radius and we can calculate clock drift for satellite laying on the surface of Earth stretched to 26km radius.

ddt = dt/sqrt(1-GM/(r1*c^2)) - dt/sqrt(1-GM/(r2*c^2)) for: dt = 86400 # seconds per day r1 = 6.36e6 # distance from center to surface of Earth r2 = 2.66e7 # distance from Earth's center to GPS ddt = +45.7e-6 # GPS clock gains 46 microseconds per day for: dt = 86400 # seconds per day r1 = 6.36e6 # distance from center to surface of Earth r2 = 1 # 1 meter from Earth's center ddt = -386 # clock at 1m from Earth's center lags by ~6.5min per day relative to surface Talking about time dilation and frequency shifts while there seems to be simple clock rate change. --- Edit 4 Feb 2024, 14:10:59 UTC --- One can ~force chat-gpt-4-1106-preview to admit that choosing between those three (time, freq, clock rate) shifts is a matter of concept.

TL;DR: the clock's perception of frequency is, from a GPS perspective, dependent on gravitational field and motion. I will refer to "Error Analysis for Global Positioning System": https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System From a GPS perspective, magnitude-wise, slowing down/accelerating clocks in motion/gravity is equivalent to shifting the instrument's frequency perception. This is logical: if your clock is going slower then you will perceive the frequency as higher - and vice versa. The gravity calculations presented in the article refer to an infinitely distant point (with ~zero gravity). If one inverts these calculations relative to the center of the Earth, it turns out that the clock at the center of the Earth stands still (is infinitely retarded relative to the Earth's surface). From the perspective of gravitational calculations, the center of the Earth is then of little use. Instead, we can calculate the wavelength (e.g., 630nm at the Earth's surface) at the distance of the wavelength (630nm) from the Earth's center, on the Earth's axis of rotation. And this seems to be quite a friendly measure, much nicer than an infinitely distant point. My question then is: why all the fuss about time dilation?