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#61
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Ranging and Pioneer
John (Liberty) Bell wrote: wrote: .. The anomaly was observed for 20 years, thus giving an accumulated round trip difference of ~ 400,000 km hence time difference of 1second. The first report I have seen of the anomaly is gr-qc/9808081 and their last contact was in January 2003. If they had tried your method as soon as the anomaly was seen as being real and not just a flaw in the analysis, the best they could get was less than 5 years and the last decent signal was April 2002. This makes the timing constraint somewhat more relaxed than you suggest here. Furthermore, although an accurate figure for this distance discrepancy would be ideal, it is only necessary to establish whether there is any unambiguous distance discrepancy or not, within the available timing uncertainties, in order to answer the question of whether the apparent anomalous acceleration had real consequences or not. This, I suggest, makes any total timing uncertainty of 1 second adequate for answering that question. They would need at least three readings (at best 2.5 years apart) to separate a real acceleration from an error in the initial vector, and timings in the 10s of ms or better would be needed. and remember that signal was being sent from one station, say Madrid, and the loss of signal detected at another, for example Canberra, and millisecond accuracy would have been needed at both ends. Why? Why two stations? Because the Earth rotated during the signal flight time. Why millisecond accuracy - see above. Finally you have perhaps the biggest problem of measuring the switch-off of the signal with millisecond accuracy through a receiver chain with a bandwidth of less than 1 Hz which is what was needed to hold lock on the carrier. That applies whichever method of timing you use at the transmitter. A 1 Hz bandwidth allows a signal to pass from maximum to zero and back again in 1 second. This suggests that detecting a change from maximum to zero in ~ half a second is, in fact, perfectly feasible with such a receiver chain. The problem isn't the speed as such, with a perfect signal you can set the threshold at say 50% and know the timing quite accurately. The problem is that there is noise present too. You are hitting the time-domain equivalent of Shannon's Theorem. (Possible phase shifts implicit this close to the bandwidth limit are not a problem since a Pioneer response can be mocked up on Earth, and tested through that receiver chain to determine in advance what that phase shift will be.) Phase shift isn't a problem you are looking at the output of an rms power detector for a "sudden" reduction in (signal+noise) level. Thanks for your additional comments. Pleasure. I'm not really knocking your idea but rather trying to show the problems that need to be worked round. If you find a solution to the bandwidth problem I would love to know it, it's a frequently encountered limitation in my line of work ;-) regards George |
#62
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Ranging and Pioneer
Oh No wrote: Thus spake "John (Liberty) Bell" 2) I have yet to see an adequately satisfactory explanation of how that proposed effect can produce a red shift on one side of a galaxy, and a blue shift on the opposite side, whilst still giving the observed Pioneer blue shift, on both sides of the Solar System. What is measured is a shift in the wavefunction corresponding to an eigenstate of acceleration. What, precisely, do you mean by this? For a general motion in radial coordinates a Newtonian acceleration toward the origin is given by -r^dotdot + r w^2, where r is radial distance and w is angular velocity. Quite so, when we are dealing with Newtonian gravitational physics. However, you have already said under previous discussions that Newtonian physics remains unaltered in your theory (hence MOND compatibility), and have indicated your effect is just due to your predicted changes in frequency of the emitter relative to the observer, which does not represent a real change in velocity or acceleration. Are you now saying that your predicted effect is dependent on the Newtonian state of motion of the emitter relative to the observer or not? If so, how, precisely? In the case of Pioneer the motion is principally radial and the first term dominates; the result is an illusory radial acceleration. Fine, provided your predicted effect is _independent of_: a) distance from centre of gravity b) radial velocity relative to observer c) gravitational field For a star in orbit the motion is approximately circular, so the second term dominates. The actual calculation is a little more complicated, but the net result for a star in orbit is an apparent increase in orbital velocity, or rather a shift in the wave function equivalent to such an increase. Not fine if you are claiming to explain galaxy rotation curves without dark matter or modifications to Newtonian physics, unless your predicted effect is _dependent on_: a) distance from centre of gravity b) radial velocity relative to observer c) gravitational field Requirements abc and ABC appear to be mutually contradictory. John (Liberty) Bell http://global.accelerators.co.uk (Change John to Liberty to respond by email) |
#63
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Ranging and Pioneer
Thus spake "John (Liberty) Bell"
Oh No wrote: Thus spake "John (Liberty) Bell" 2) I have yet to see an adequately satisfactory explanation of how that proposed effect can produce a red shift on one side of a galaxy, and a blue shift on the opposite side, whilst still giving the observed Pioneer blue shift, on both sides of the Solar System. What is measured is a shift in the wavefunction corresponding to an eigenstate of acceleration. What, precisely, do you mean by this? In quantum theory a general state is not measured and it is not possible to discuss values of measurable properties in such a state. When a measurement is done the measured property acquires an exact value and the state is said to be in an eigenstate for the corresponding observable operator. Corresponding to any state there is a wave function. In standard quantum theory in flat space the wavelength of the wave function corresponds to momentum in inverse proportion. I am suggesting that in curved space this proportionality is broken. That the wavelength is shifted but the classical momentum of an orbiting body is not altered. For a general motion in radial coordinates a Newtonian acceleration toward the origin is given by -r^dotdot + r w^2, where r is radial distance and w is angular velocity. Quite so, when we are dealing with Newtonian gravitational physics. However, you have already said under previous discussions that Newtonian physics remains unaltered in your theory (hence MOND compatibility), and have indicated your effect is just due to your predicted changes in frequency of the emitter relative to the observer, which does not represent a real change in velocity or acceleration. yes Are you now saying that your predicted effect is dependent on the Newtonian state of motion of the emitter relative to the observer or not? If so, how, precisely? If motion is, as for pioneer, essentially radial, acceleration determined is determined by r^dotdot. In this case the effect appears as a Doppler drift. For an orbital motion acceleration is r w^2. In this case constant acceleration corresponds to a fixed Doppler shift. In the case of Pioneer the motion is principally radial and the first term dominates; the result is an illusory radial acceleration. Fine, provided your predicted effect is _independent of_: a) distance from centre of gravity b) radial velocity relative to observer c) gravitational field yes For a star in orbit the motion is approximately circular, so the second term dominates. The actual calculation is a little more complicated, but the net result for a star in orbit is an apparent increase in orbital velocity, or rather a shift in the wave function equivalent to such an increase. Not fine if you are claiming to explain galaxy rotation curves without dark matter or modifications to Newtonian physics, unless your predicted effect is _dependent on_: a) distance from centre of gravity b) radial velocity relative to observer c) gravitational field Requirements abc and ABC appear to be mutually contradictory. Very briefly, to show how this works, and without going into gory detail: At any time we actually measure velocity, not acceleration. Inward acceleration for a body in a circular orbit is v^2/r. If the true orbital velocity of a star in orbit about a mass M due to gravity is v_g = sqrt(GM/r) and the apparent orbital velocity due to a constant inward acceleration is v_P = sqrt(Hcr/32) (the factor 32 comes in because of a weird stretching needed for quantum coordinates) then the net observed apparent orbital velocity is v = v_g + v_P As you say, this satisfies requirements abc. But the apparent acceleration is v^2/r = (v_g + v_P)^2/r = GM/r^2 + sqrt(GMHc/8)/r + Hc/32 The first term is standard Newtonian gravity, the second is the apparent MONDian acceleration. The third is a term which comes from taking the centre of the galaxy as the origin of coordinates, while actually we are looking at light from a star. It is actually a mathematical artefact and cannot be directly observed. Regards -- Charles Francis substitute charles for NotI to email |
#64
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Ranging and Pioneer
Oh No writes:
Thus spake "John (Liberty) Bell" Oh No wrote: Thus spake "John (Liberty) Bell" 2) I have yet to see an adequately satisfactory explanation of how that proposed effect can produce a red shift on one side of a galaxy, and a blue shift on the opposite side, whilst still giving the observed Pioneer blue shift, on both sides of the Solar System. What is measured is a shift in the wavefunction corresponding to an eigenstate of acceleration. What, precisely, do you mean by this? In quantum theory a general state is not measured and it is not possible to discuss values of measurable properties in such a state. When a measurement is done the measured property acquires an exact value and the state is said to be in an eigenstate for the corresponding observable operator. Corresponding to any state there is a wave function. In standard quantum theory in flat space the wavelength of the wave function corresponds to momentum in inverse proportion. I am suggesting that in curved space this proportionality is broken. That the wavelength is shifted but the classical momentum of an orbiting body is not altered. The obvious problem with your above claim is that, even if one assumes that one _can_ construct a self-adjoint "acceleration operator," an "eigenstate of acceleration" would almost certainly be unphysical and non-normalizable, for the same reasons that eigenstates of position or momentum are unphysical and non-normalizable. In particular, one may expect that an "eigenstate of acceleration" would be _completely delocalized_, much as an eigenstate of momentum is completely delocalized --- leaving one with absolutely no information about position. By contrast, in "Real World" measurements, one would only be able to observe position, velocity, and acceleration to _finite precision_, and hence, even if one believes that "wave function collapse" is a "physical process" rather than an artifact of the observer's revised knowledge about the state of the quantum system, the result of a finite precision "acceleration measurement" will =NOT= in fact be an "eigenstate of acceleration," but rather an incoherent _MIXTURE_ of eigenstates of acceleration, with an uncertainty determined by the precision of the "acceleration measurement"... -- Gordon D. Pusch perl -e '$_ = \n"; s/NO\.//; s/SPAM\.//; print;' |
#65
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Ranging and Pioneer
Thus spake "John (Liberty) Bell"
Oh No wrote: Thus spake "John (Liberty) Bell" 2) I have yet to see an adequately satisfactory explanation of how that proposed effect can produce a red shift on one side of a galaxy, and a blue shift on the opposite side, whilst still giving the observed Pioneer blue shift, on both sides of the Solar System. What is measured is a shift in the wavefunction corresponding to an eigenstate of acceleration. What, precisely, do you mean by this? In quantum theory a general state is not measured and it is not possible to discuss values of measurable properties in such a state. When a measurement is done the measured property acquires an exact value and the state is said to be in an eigenstate for the corresponding observable operator. Corresponding to any state there is a wave function. In standard quantum theory in flat space the wavelength of the wave function corresponds to momentum in inverse proportion. I am suggesting that in curved space this proportionality is broken. That the wavelength is shifted but the classical momentum of an orbiting body is not altered. For a general motion in radial coordinates a Newtonian acceleration toward the origin is given by -r^dotdot + r w^2, where r is radial distance and w is angular velocity. Quite so, when we are dealing with Newtonian gravitational physics. However, you have already said under previous discussions that Newtonian physics remains unaltered in your theory (hence MOND compatibility), and have indicated your effect is just due to your predicted changes in frequency of the emitter relative to the observer, which does not represent a real change in velocity or acceleration. yes Are you now saying that your predicted effect is dependent on the Newtonian state of motion of the emitter relative to the observer or not? If so, how, precisely? If motion is, as for pioneer, essentially radial, acceleration determined is determined by r^dotdot. In this case the effect appears as a Doppler drift. For an orbital motion acceleration is r w^2. In this case constant acceleration corresponds to a fixed Doppler shift. In the case of Pioneer the motion is principally radial and the first term dominates; the result is an illusory radial acceleration. Fine, provided your predicted effect is _independent of_: a) distance from centre of gravity b) radial velocity relative to observer c) gravitational field yes For a star in orbit the motion is approximately circular, so the second term dominates. The actual calculation is a little more complicated, but the net result for a star in orbit is an apparent increase in orbital velocity, or rather a shift in the wave function equivalent to such an increase. Not fine if you are claiming to explain galaxy rotation curves without dark matter or modifications to Newtonian physics, unless your predicted effect is _dependent on_: a) distance from centre of gravity b) radial velocity relative to observer c) gravitational field Requirements abc and ABC appear to be mutually contradictory. Very briefly, to show how this works, and without going into gory detail: At any time we actually measure velocity, not acceleration. Inward acceleration for a body in a circular orbit is v^2/r. If the true orbital velocity of a star in orbit about a mass M due to gravity is v_g = sqrt(GM/r) and the apparent orbital velocity due to a constant inward acceleration is v_P = sqrt(Hcr/32) (the factor 32 comes in because of a weird stretching needed for quantum coordinates) then the net observed apparent orbital velocity is v = v_g + v_P As you say, this satisfies requirements abc. But the apparent acceleration is v^2/r = (v_g + v_P)^2/r = GM/r^2 + sqrt(GMHc/8)/r + Hc/32 The first term is standard Newtonian gravity, the second is the apparent MONDian acceleration. The third is a term which comes from taking the centre of the galaxy as the origin of coordinates, while actually we are looking at light from a star. It is actually a mathematical artefact and cannot be directly observed. Regards -- Charles Francis substitute charles for NotI to email |
#66
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Ranging and Pioneer
Oh No wrote: For an orbital motion acceleration is r w^2. In this case constant acceleration corresponds to a fixed Doppler shift. But this is clearly wrong! For a spiral galaxy viewed from above or below, no such Doppler shift is observed (beyond second order relativistic effects). For a spiral galaxy observed edge on, with its nearest part moving from left to right, extremities on the left hand side of the galaxy are observed to be blue shifted (far more than predicted by Newtonian theory without dark matter), whilst extremities on the right hand side of the galaxy are observed to be red shifted (far more than predicted by Newtonian theory without dark matter). For observers in different directions, the Doppler shifts of all the stars change! This is why your thesis doesn't make any sense. John (Liberty) Bell http://global.accelerators.co.uk (Change John to Liberty to respond by email) |
#68
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Ranging and Pioneer
John (Liberty) Bell wrote: wrote: ... I refer you to section 2.1 of gr-qc/9903024 v2 which confirms that the anomaly was first noticed in 1980. I previously read this as saying that in 1987, they identified the anomaly which showed an effect on the craft from 1980 onwards. It would be reasonable to take it your way as well. If my arithmetic is correct, this makes 22 years elapsed from first observation to the last decent signal, and 26 years to the present. If they had realised the measurement was needed and had done it straight away in 1980 then yes about 20 years might have been available. The SNR in 2002 might not have allowed an accurate measure but a year or two earlier should have provided an adequate signal. They would need at least three readings (at best 2.5 years apart) to separate a real acceleration from an error in the initial vector You are mistaken. There is no ambiguity over where or when Pioneer 10 was launched. Over 20 years the anomaly produces a displacement of about 174000 km. An error in inital speed of just 0.276 m/s would produce the same displacement in the same time. There is similarly no ambiguity over the Doppler figures monitored thereafter. On the contrary, the usefulness of the range measurements would be to distinguish whether the frequency was shifted due to motion of the craft via the Doppler effect or whether the frequency was being directly affected in some manner without matching displacement. George |
#69
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Ranging and Pioneer
"John (Liberty) Bell" writes: Craig Markwardt wrote: .... The fact that such _off_ control was only used by NASA/JPL to provide extra power for manoeuvres, does not restrict humanity to blindly following that precise procedure in perpetuity. My point was that we might potentially exploit our own intelligence and originality to perform an experiment which was not part of the original Pioneer plan. One of the top rules of spacecraft operations is: "don't turn anything off unless you absolutely must." There is a finite chance that whatever is turned off won't be recoverable. The communications system is vitally important to the mission, so there is no reason to ever turn it off.[*] [*] ... except in the case when power is low and maneuvers must be performed to preserve communications of course! .... The traveling wave tube amplifier, the device that is turned off and then on again after the maneuver, is a macroscopic device with elements that must warm up and stabilize. That is also irrelevant, if the proposed measured action is a switch _off_, not switch on, as I suggested, originally to overcome the signal lock time uncertainty. Still, given the various elements inside of the device, it's likely that it will not just "switch off" quickly. [ For example, if there is an heated cathode electron gun in the amplifier, it will not be possible to cool it instantly. ] .... The spacecraft and ground receiver have acquisition and tracking loops which are not totally deterministic (and take at least several seconds to acquire). Such a technique would also only produce one estimate of the light travel time. Thus, your proposed technique is totally unreliable for precision navigation. You seem to have misunderstood the purpose of the proposal. It was not to provide precise navigation. It was to establish whether the apparent anomalous acceleration was demonstrably real, in the sense of resulting in a different elapsed distance, or illusory, as suggested by Charles Francis. I think that is a distinction without a difference. Nobody would believe one or two round trip travel times. To be believable and robust, many ranges would be needed, and they would need to be placed in context of a trajectory model. I.e. a full navigation solution would be needed. .... CM |
#70
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Ranging and Pioneer
wrote: John (Liberty) Bell wrote: wrote: .. I refer you to section 2.1 of gr-qc/9903024 v2 which confirms that the anomaly was first noticed in 1980. I previously read this as saying that in 1987, they identified the anomaly which showed an effect on the craft from 1980 onwards. It would be reasonable to take it your way as well. If my arithmetic is correct, this makes 22 years elapsed from first observation to the last decent signal, and 26 years to the present. If they had realised the measurement was needed and had done it straight away in 1980 then yes about 20 years might have been available. The SNR in 2002 might not have allowed an accurate measure but a year or two earlier should have provided an adequate signal. They would need at least three readings (at best 2.5 years apart) to separate a real acceleration from an error in the initial vector You are mistaken. There is no ambiguity over where or when Pioneer 10 was launched. Over 20 years the anomaly produces a displacement of about 174000 km. An error in inital speed of just 0.276 m/s would produce the same displacement in the same time. There is similarly no ambiguity over the Doppler figures monitored thereafter. On the contrary, the usefulness of the range measurements would be to distinguish whether the frequency was shifted due to motion of the craft via the Doppler effect or whether the frequency was being directly affected in some manner without matching displacement. That was precisely my point in the first place. However, I still maintain that a single direct ranging observation (the later the better) would have sufficed (and still might suffice) to answer that question. As I understand it, the basic principle of ranging using Doppler data is as follows: Measuring the Doppler shift gives an accurate figure of the radial velocity of the probe relative to the observer, at any given time. Integrating that data over time gives an accurate figure for the total radial distance travelled by the probe relative to that observer. Looked at another way, the total difference between the number of signal oscillations since launch, and the total number that would have been observed in the same time if the probe remained on Earth, provides a direct (Doppler) measure of the total radial distance travelled by the probe, in that time. Yes, we can jiggle our model of the exact trajectory somewhat to modify both tangential relativistic corrections to Doppler shifts and the predicted decelerations of our model due to gravity. However, the reported anomaly is the _minimum_ anomaly that remains after all such adjustments are taken into account, given e.g. the tight constraints provided by observations performed during planetary catapaulting. Such data indicates a) that the probe has travelled less far than predicted b) that the probe is travelling slower than predicted c) that the probe is continuing to decelerate faster than predicted. Consequently, all we need to do to test if the conclusions reached by Doppler observations are physically meaningful is to test if the total distance travelled is greater than the distance admitted by Doppler ranging. The _minimum_ additional distance required for a round trip signal (if Doppler conclusions are illusory) would already have been greater than 1 light second (using your own figure for 1980 to the last good signal), and would have been even larger if that Pioneer Doppler effect was present (but unrecognised) prior to 1980. It is thus completely irrelevant when the effect was first noticed, for the purpose of testing that hypothesis. John Bell http://global.accelerators.co.uk (Change John to Liberty to respond by email) |
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