I don't know what you are referring to. I commented on the latest post you made prior to mine.Regretfully you did not comment on the correction to the erroneous statement.
Yes, they do. See below.Light signals in the other direction don't add information for this question
Fine. Now tell me what "clock rate is reduced in a gravitational field" actually means, in terms of direct observables. See below.it is generally acknowledged that clock rate is reduced in a gravitational field.
You missed the key phrase "local inertial frame". You are not even addressing what I'm actually saying.As you see above, the interpretation that you advocate does not match all the observations
Once again, it doesn't seem like you are reading my posts. I specifically talked about a local inertial frame. The GPS satellite clock scenario (which I assume is what you are referring to) obviously cannot be covered by a single local inertial frame. Also, an orbiting satellite is a bad example because it is not at rest relative to an observer on the Earth's surface; it would be better to talk about an observer at rest on Earth's surface, compared to an observer at rest on, say, a platform high above the first observer.Satellite clocks are typically slowed down in order to run at the correct clock rate in space around the Earth; Doppler effects can only explain that by pretending that the Earth is exploding at almost 10 m/s2.
We agree on this; but I don't think we agree on what the bug is. Let me re-state the key points from my perspective.I think that this is probably a permanent bug
We want to compare two scenarios:
Scenario #1: A rocket accelerating in flat spacetime. Observer 1R is at the rear of the rocket; observer 1F is at the front.
Scenario #2: At rest in a gravitational field. Observer 2R is at rest at some altitude in the field; observer 2F is at rest at some higher altitude.
We stipulate that observers 1R and 2R feel the same proper acceleration, and observers 1F and 2F feel the same proper acceleration. We stipulate that the proper distance between observers 1R and 1F is the same as the proper distance between observers 2R and 2F, and that both proper distances are unchanging.
We have observer 1R send a light signal to observer 1F, and observer 2R send a light signal to observer 2F. Both light signals are redshifted when they are received. Why is this? We have two ways of analyzing it:
Local Inertial Frame Analysis: Pick a local inertial frame in which the R observer is at rest at the instant the light signal is emitted. Because both the R and F observers are accelerating in this frame, the F observer will be moving away from the light signal when it is received; so there will be a Doppler redshift.
Non-Inertial Frame Analysis: Construct a non-inertial frame in which the observers are at rest. For scenario #1, this will be Rindler coordinates; for scenario #2, it will be Schwarzschild coordinates. In this frame, there will be a "gravitational redshift"--or, if you don't like the term "gravitational" in the flat spacetime case, you can simply look at the timelike Killing vector field with respect to which the R and F observers are both following integral curves--both coordinate charts are adapted to this KVF, so that the KVF corresponds to the timelike basis vector and its integral curves are curves of constant spatial position. The invariant length of the KVF is different for the R and F observers--it is "shorter" for the R observer than for the F observer. This causes observer F to see light signals from observer R as redshifted (the math is simple and applies to any stationary spacetime).
So both analyses give the same answer. The advantage of the second analysis is that it can be extended beyond a single local inertial frame, so if you want to say you prefer it for that reason, that's fine. But that doesn't make the first analysis invalid; it just restricts its scope. If we're talking about the equivalence principle, the scope is restricted to a single LIF anyway.
However, there is another issue. You had claimed, in the post I originally responded to that started this subthread, that
"(to first order) the apparent difference in clock rates in an accelerating rocket is an artefact of using accelerating coordinates"
and I had responded that we can look at repeated round-trip light signals to verify that the difference in clock rates is not an artefact. You apparently still do not understand how that works. The scenario is simple: the R and F observers send repeated round-trip light signals back and forth, and each measures his own elapsed proper time between successive signals. The R observer finds less elapsed proper time than the F observer does from signal to signal. This is a direct observable that shows the difference in clock rates.
It is true that this result is simplest to derive in the non-inertial coordinates of the second analysis above, but that doesn't make it an "artefact" of using accelerating coordinates. Elapsed proper time along a given worldline between two given events is an invariant, independent of coordinate choice. So I am entirely unable to understand how you can justify your claim that I quoted above.