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Ranging and Pioneer
[[Mod. note -- I have snipped large chunks of quoted material from this
post in the interests of brevity. Posters, please realise that readers have generally *already* read the article you're quoting -- you don't have to quote the whole thing verbatim again! Please just quote enough to establish the context for what you want to say. -- jt]] Oh No wrote: Thus spake George Dishman ... Charles could you clarify the details of your calculation of the Pioneer effect since it is significantly larger than the cosmological redshift. [[Mod. note -- 7 lines snipped. -- jt]] The basic idea is that quantum theory can be formulated using conformally flat coordinates. I treat quantum theory as a calculational [[Mod. note -- 20 lines snipped. -- jt]] When the final state of one part of the motion is reinterpreted as the initial state for the next part of the motion, the quantum theory must be renormalised. This removes a factor of the expansion parameter from cosmological redshift, yielding the normal linear law for cosmological redshift. Thanks, I just about understood the working and the consequence is clear. When we measure classical motions local to the earth we can determine motion to great accuracy. The motion thus consists of many initial state-final state stages, and reduces to geodesic motion under the normal affine connection. Of critical importance is the timescale between initial state and final state when modelling the motion. This timescale is determined by the accuracy with which we can measure. Local distances can be measured with great accuracy, equivalent to a short timescale. Remote distances are intrinsically less accurate (e.g. radar distance measurements to mars are accurate to about 12m). I'm not familiar with the details of Mars ranging but I have looked at Pioneer in some detail. I will comment on that as it may be of interest to you but it doesn't seem to answer my original question. The signal from Pioneer uses an effective Doppler frequency of 1MHz, equivalent to a distance scale of 300m. Although the final digital analysis is done around 1MHz, the RF is heterodyned down to that against the reference. It means that the measurement resolution is still that of the 2.291GHz carrier. Further the MDA is capable of measuring phase to 1/256 of a cycle or about 0.5mm in range. While the ranging system itself wasn't available, the frequency measurements are still taken from that same hardware and have that resolution. Note the residuals from Galileo in Figure 10 of gr-qc/0104064 and the discussion to the left that indicates consistency to about 4m over a day. The actual measurements are limited to a few metres accuracy mainly due to the group delay in the somewhat unpredictable solar plasma and the unknown angle of refraction through the atmosphere and at the boundary of the ionosphere, but the resolution of the instrument which I think is the determining aspect from the QM point of view is better than 1mm. So I am predicting that when the measurement of distance is accurate to better than 300m, the period of the signal spans more than one quantum stage, and the standard general relativistic result is predicted. That would certainly apply to Pioneer whichever resolution you adopt. When measurement of distance is less accurate than 300m the Doppler signal is measured incorporating the square law for cosmological redshift. OK, so I understand those two conditions to mean either you get the conventional redshift value for low resolution measurements or you get no extra redshift locally beacause we have higher resolution measurements. In this case the anomalous Pioneer shift is found. This was the gist of my original question and where I am still puzzled. The conventional linear Hubble law if applied to Pioneer 10 predicts an apparent acceleration some 15000 times smaller than the anomaly given by the equation a_H = 2 H v. I don't understand why you think your analysis produces a result four orders of magnitude larger than the normal Hubble Law under either of the regimes you explain above. Sorry if I'm being a bit slow but it is this factor of 15000 increase that I cannot fathom. The apparent inconsistency between these two results is taken up by cycle slip, or apparent jumps in motion (it is possible that such a jump has been observed in VLBI measurements of IM Pegasi which appears to occasionally jump up to 2/3 its radius). Currently cycle slip is treated as a "blunder point" in the collection of data, and has been discarded from the analysis of the Pioneer data. If this is right it may be possible to reanalyse the pioneer archive and show that the discarded data resolves the anomaly - or it may be that there are also real blunders in the data such that the analysis becomes impossible :-( . There will be blunder points due to noise but might be distinguishable since they will always be exactly a carrier cycle at the macroscopic frequency and should occur randomly given gaussian noise in the channel. George |
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