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Can the Pioneer Anomaly Be Explained by Inertia Modification?

by Richard Obousy

Physicist Richard Obousy here takes a look at an intriguing new paper by Mike McCulloch, a researcher at Plymouth University. In addition to his work in theoretical physics and warp drive possibilities, Obousy is current project leader and primary propulsion design lead for Project Icarus, a joint venture between the British Interplanetary Society and the Tau Zero Foundation to re-think the original Project Daedalus starship design. In the review below, Obousy places McCulloch’s work on the Pioneer anomaly in the context of current thinking on dark matter, dark energy and the nature of mass. Does the Higgs field explain inertial mass, or are there alternatives? Read on.

Few areas of research have garnered as much attention from both the public and scientific communities as those of dark energy and dark matter – and for good reason. Both terms stem from observations of the physical universe that, simply put, don’t belong within the well-understood framework of known physics. Another phenomenon discovered in the nineties concerns an anomalous acceleration of the Pioneer probes. These ostensibly unrelated observations may, in fact, be connected to each other by an intriguing line of research currently being investigated by Mike McCulloch, a researcher at the University of Exeter. Before exploring McCulloch’s research, a brief review of dark energy, dark matter, and the anomalous Pioneer acceleration will be presented.

Dark matter is a proposal put forward to explain the observations first made by Zwicky in 1933 that galaxies were too energetic to be held together by observable matter. Zwicky originally proposed the existence of an unseen form of baryonic matter that provided the necessary gravitational force to hold the galaxies together. Due to constraints imposed by modern cosmology, the idea has evolved to assume this form of matter is non-baryonic (not made of quarks); however, the fundamental idea has remained unchanged. After decades of searching for dark matter, none has been directly detected, but a number of experiments are ongoing.

Dark energy stems from the truly astounding observation made originally by Riese and Perlmutter in the late 90’s that the rate of cosmological expansion, long thought to be either static or decelerating, is actually accelerating. For this to be happening, it is commonly believed that the universe is filled with a ubiquitous and exotic negative pressure field that drives the accelerated expansion. Although we can give this energy a name, and predict what it will do, dark energy as a ‘real’ physical field has never actually been measured in the lab, and today, dark energy remains somewhat of an enigma.

As if dark energy and dark matter haven’t dealt theoreticians enough of a blow, cracks began to appear in our understanding of gravity due to the observation made by Anderson et al in 1996 that both Pioneer 10 and 11 are experiencing an anomalous acceleration of 8.74±1.33×10-10 m/s2 directed approximately towards the sun. It is precisely this anomaly that is studied by Mike McCulloch in his recent publication in Europhysics Letters called Minimum Accelerations from Quantized Inertia (reference below). McCulloch’s work addresses the Pioneer anomaly, and within the framework of his model, one could perhaps come to a deeper understanding of dark matter and dark energy thanks to a novel idea known as MOND, or Modified Newtonian Gravity.

The basic idea that McCulloch explores is the nature of mass, and the possibility that inertial mass, in fact, changes slightly under certain conditions. It has been known since the time of Newton that all bodies attract all other bodies in the universe with a force that is proportional to their mass. This type of mass is what is known as gravitational mass. It is also known that when one applies a force to an object, it accelerates at a magnitude that is proportional to its mass. This type of mass is known as inertial mass. It is commonly assumed that gravitational and inertial mass are identical, and this has been verified by our highest precision instruments to date.

The fundamental nature of inertial mass is not precisely known and is an issue that has been pondered at least since the time of Mach. Recent efforts to codify inertial mass into the Standard Model (SM) of particle physics have resulted in the famous Higgs field, which is a ubiquitous field that bestows mass upon matter via a process known as spontaneous symmetry breaking. Although the Higgs field has not been experimentally detected, many physicists are confident that it will be found at the Large Hadron Collider.

Despite the widespread acceptance in the existence of the Higgs field, there have been alternative attempts to uncover the nature of inertial mass. One paper, Inertia as a Zero Point Lorentz Force, written in 1994 by Rueda, Puthoff and Haisch (RPH), represents a stalwart effort to model inertia as a back-reaction of matter to the quantum vacuum similar to the Unruh field. Despite not gaining widespread acceptance in the theoretical community, the paper galvanized interest in the possibility that the quantum vacuum and inertial mass may be related. The basic premise of the paper was that matter, modeled as a ‘Parton’, interacts with the quantum vacuum in such a way that any acceleration generates a Lorentz-type back-reaction to the vacuum which manifests itself macroscopically as a resistance to acceleration or, more simply, as inertial mass.

The RPH paper was not the first to suggest that accelerated matter is effected by the quantum vacuum. In 1976, Unruh showed that a body undergoing an acceleration in the vacuum sees a thermal radiation of temperature T that is related to its acceleration. Wien’s displacement law tells us that, for a given temperature, there will be a dominant wavelength which, via the Unruh effect, is inversely proportional to the acceleration – namely, as the acceleration gets smaller, the radiation wavelength gets bigger. As the acceleration decreases, this wavelength reaches a limiting value: the wavelength of the observable universe. Milgrom, in 1994, speculated that at this point, there would be a ‘break in the response to the vacuum’ and the Unruh radiation would be unobservable. He further speculated that this could have an effect on inertial mass. Herein lies the crux of this line of thinking – that matter’s response to the vacuum is what generates inertia.

McCulloch further develops the idea of Milgrom by allowing for a more natural development in the Unruh radiation spectrum. In the original idea by Milgrom, only the dominant wavelength was considered. McCulloch, however, develops what he calls a Hubble-Scale Casimir effect, where a range of wavelengths are allowed based on the boundary conditions of the size of the observable universe.

“The new assumption is that this Unruh radiation is subject to a Hubble-scale Casimir effect. This means that only Unruh wavelengths that fit exactly into twice the Hubble scale (harmonics with nodes at the boundaries) are allowed, so that a greater proportion of longer Unruh waves are disallowed, reducing inertia in a new, more gradual, way for low accelerations.”

Using this model, McCulloch is able to develop an equation which illustrates the modification of inertial mass for low accelerations. Put in simpler terms, as the Pioneer probes depart our solar system they experience a force due to the gravitational attraction of the sun. This force generates an acceleration which, due to its extremely small value, modifies the inertial mass of the pioneer probe. Because of this modification, the Pioneer probes, seemingly now less massive, feel a greater acceleration due to the sun than that predicted by Newtonian mechanics, creating the anomalously large acceleration.

How does this all relate to dark energy and dark matter? The answer is in the relationship between certain natural scales that occur in physics. The basic building block is the scale that characterizes the cosmological constant. We call this scale R and it is the distance scale over which the cosmological constant curves the universe. R is about 10 billion light years and is 1040 times the size of an atomic nucleus – the scale where the standard model of particle physics is applicable). R is also 1060 times the Planck scale – the scale at which we believe in GUT’s (Grand Unified Theories), where all the forces in nature behave identically. It is therefore pragmatic to wonder whether this scale R might be indicative of some new physics.

Hints at new physics at the scale R manifest themselves in the cosmic microwave background (CMB) – thermal radiation left over from the Big Bang. This radiation has been cooling as the universe expands, and is now at a fairly uniform temperature of 2.7 degrees Kelvin. Fluctuations in this temperature exist to a level of a few parts per 100,000, and the patterns of these fluctuations provide us with clues to the physics of the early universe.

Analysis of the temperature fluctuations over the last decades illustrate how much energy is contained in this radiation as a function of wavelength. It appears that the CMB is dominated by a single large peak, followed by a number of smaller peaks. It also appears that there is very little energy in the longest wavelength. This data can be interpreted as indicative of a ‘cutoff’, above which the thermal modes are less excited. What is particularly remarkable is that this cutoff occurs on a scale R which we associate with the cosmological constant.

This cutoff is somewhat puzzling from the perspective of inflation theory, which was developed by Alan Guth of MIT and, originally, by Alexei Starobinsky of the Landau Institute for Theoretical Physics in Moscow. According to the theory of inflation, the early and rapid expansion of the universe created huge regions of the cosmos with relatively uniform properties. This region is thought to be much larger than the observable universe. The cutoff indicates that, at the scale R, inflation stopped just at the point where it created a region as large as we now currently observe. If, in fact, inflation ‘switched off’ just at the point where it created the cosmos as large as we currently observe, then some physical mechanism must have been responsible for selecting this unique time to stop. This seems incredibly improbable, since nothing in the physics of inflation says anything about scales on the order of 10 billion light years.

Said another way, if inflation produced a largely uniform universe, then it likely produced uniformity on scales much larger than we observe. Thus, the patterns produced by inflation, the small fluctuations, should be visible beyond the present size of the universe. Instead – what the data indicate is that these fluctuations stop above the scale R.

Another indication that new physics may occur at scales on the order of R is an apparent asymmetry in the distribution of hot and cold spots in the CMB dubbed the ‘Axis of Evil’. This observation was first made in 2005 by Kate Land and Joao Magueijo of Imperial College London. A number of independent studies have confirmed this apparent alignment of anisotropies in the CMB.

There are additional phenomena associated with the scale R that are worth discussing. One way we can explore R is to combine it with additional constants of nature. An interesting place to start is to combine it with the speed of light, c, to give us R/c. Dimensionally, R/c gives us a time, and that time corresponds to the present age of the universe. Taking the reciprocal of this, c/R, gives a frequency, a profoundly low ‘note’ which has completed one oscillation in the entire lifetime of the universe.

Going one step further, we can explore c2/R which, dimensionally, gives us the units of acceleration. Remarkably, this number is the acceleration produced by the cosmological constant. This is the same acceleration that we currently believe dark energy is responsible for and is on the order of 10-10 m/s. This also happens to be the roughly the same anomalous acceleration that the Pioneer probes are currently experiencing!

The c2/R also crops up when we examine rotational velocity of orbiting stars in galaxies. Recall that stars are seen to rotate at a velocity that would, according to Newtonian Mechanics, be too fast for them to be held in a stable orbit. The contemporary fix for this problem is to introduce dark matter. This is not the only fix, however. For spiral galaxies, in which stars move in circular orbits, anomalous velocities (orbital velocities that, according to Newtonian Mechanics, should not be possible) are only apparent beyond a certain orbit. Within this ‘special’ orbital distance Newtonian gravity works perfectly. Because stars move in a circular orbit they experience an angular acceleration which is related to their velocity (a=v2/r). The breakdown of Newtonian gravity occurring at this ‘special’ orbital distance occurs when the stars are rotating with an angular acceleration of 1.2×10-10 m/s2, almost identical to the scale c2/R. This is thoroughly fascinating, and this string of relationships which appear to be related to the scale R represent tantalizing hints at physics beyond what is currently studied and practiced within the mainstream academic community.

Today, nobody knows for certain what this new physics is (if it really is new physics), and nobody has written down a theory codifying its behavior. Mike McCulloch, however, is arguably helping to increase momentum within this curious and remarkable area of research.

The paper is McCulloch, “Minimum accelerations from quantised inertia,” Europhysics Letters Vol. 90, No. 2 (20 May, 2010). An abstract is available, with full text here. The paper by Rueda, Haisch and Puthoff is “Inertia as a Zero Point Lorentz Force,” Physical Review A, Vol 49, No 2 (February 1994), pp.678-694.


Comments on this entry are closed.

  • Paul Titze July 30, 2010, 12:02

    Hi Paul/Richard,

    Interesting paper. I recently finished reading Christoph Schiller’s Motion Moutnain (all 6 volumes) http://www.motionmountain.net/ ,the last volume where he outlines his strand model was particularly interesting and comes up with several explanations for various items in the Millenium list of unsolved physics problems and several testable predictions.

    I’d suggest reading p295 of Vol6 which is relevant to the issues mentioned in the article however here’s the interesting bit:

    “there is nothing to be discovered about nature outside general relativity and the standard model of particle physics. There is no hidden aspect of nature. The strand model predicts a so-called high-energy desert: it predicts the lack of the Higgs boson and of any other new elementary particle. In short, there is no room for discoveries at the Large Hadron Collider in Geneva, nor at
    the various dark matter searches.”

    So far I haven’t seen anything in current Physics that contradicts his model so it would be worth keeping an eye on, although if his strand model is incorrect (ie they do find a Higgs at the LHC) I would be relieved as we can still have Science Fiction ;-)

    Cheers, Paul.

  • Volucris July 30, 2010, 12:36

    Since gravitational constant is around 6.7e-11 in SI units, we should be seeing accelerations of ~1e-10 m*s^-2 between masses around ~1kg at about distance of ~1m. So if gravity acts funny at those scales, could we be able to devise some experiment to catch the anomaly in action? Have there been any experiments probing gravity between such small masses?

  • NS July 31, 2010, 1:50

    “there is nothing to be discovered about nature outside general relativity and the standard model of particle physics. There is no hidden aspect of nature.”

    I have no qualifications to judge this, other than to note that statements of this sort have often been wrong.

  • Mike Lorrey July 31, 2010, 3:32

    You should look at Jim Woodwards recent paper about the Mach Effect, that c^2/R …..

  • James M. Essig July 31, 2010, 9:52

    Hi Folks;

    One possibility for explaining the Pioneer Anomaly is a general unification of Special and General Relativity in the sense that say, special relativistic reference frame distortion and shape changing would alter the general relativistic space time curvature produced by the space craft. If such space time relativistic reference frame distortion was of the proper shape, perhaps gravitational radiation emmitted by the space craft would be enhanced thereby bleeding off space craft kinetic energy. Depending on the velocity vector profile of the craft, perhaps the radiation emitted by the space craft would be gravatic or anti-gravatic. Even if gravatic, the space craft might experience a positive acceleration due to a gravitational radiation rocket like effect.

    If only ordinary 4-D Einsteinian space time is considered, perhaps the effect would be insignificant in the sense that any arbitrary shaped space craft has an arbitrary space time distortion wherein one shape is as good as another for producing space time curvature, being that the degree of general relativistic curvature of a Newtonian velocity space craft is very small no matter what its shape.

    However, since special relativistic distortion also effects time, via the Lorentz transformation factor of gamma, perhaps even at Keplerian velocities, there exist a general relativistic space time distortion produced by the space craft that goes beyond what would occur for a space craft at rest or with respect to its own reference frame.

    We might not notice any such general relativistic space time distortion based kinetic energy bleed off or gain of particles in our particle accellerators perhaps because of the spherical symmetry or the rotationally symmetric like pan cake configuration of the high gamma factor accelerated particles, just as a rotating uniform density toriodal ring would not emit gravitational waves, at least while its rotational velocity remains constant.

    Another possibility is that any higher Kaluza Klein like hyperspatial extension of the space craft and/or its gravitational field may be special relativistically distorted in a manner that might alter its velocity through 3-D space such as might occur for the case that some of the space time strain energy produced by such distortion is bled off into higher dimensional space via gravitational radiation or perhaps by some other mechanism. Once again, depending on the velocity vector profile of the craft, perhaps the radiation emitted by the space craft would be gravatic or anti-gravatic. Even if gravatic, the space craft might experience a positive acceleration due to a gravitational radiation rocket like effect.

    Regardless, the Pioneer Anomaly requires us to consider what caused it, and this observation along with many other anomalies that have been observed over the past decade, seem to indicate that the there is something wrong with the Standard Model, and that Special and General Relativity and Quantum Theory are not complete.

  • Gregory Benford July 31, 2010, 20:18

    Riley Newman at UCI Physics has set limits on such kg masses at 1 m distance, and sees no nonNewtonian effects, so far.

  • Paul Titze July 31, 2010, 21:10

    Hi Paul,

    Remember now where in Motion Mountain the Pioneer Anomaly is mentioned (Vol2 p185):

    “For a long time, people have speculated why the Pioneer 10 and 11 artificial satellites, which are now over 70 astronomical units away from the Sun, are subject to a constant deceleration of 8 ⋅ 10−10 m/s2 (towards the Sun) since they passed the orbit of Saturn.This effect is called the Pioneer anomaly.The origin is not clear and still a subject of research. But several investigations have shown that the reason is not a deviation from the inverse square dependence of gravitation, as is sometimes proposed. In other words, the effect must be electromagnetic. There are many hints that point to an asymmetry in heat radiation emission. Indeed, an front-to-back asymmetry of only 80W is sufficient to explain the effect. (The on-board generators produce 2.5 kW.) But the source of the asymmetry has not been understood yet. Finding the asymmetry – or another explanation for the deceleration – is one of the
    challenges of modern space physics. Test yourself: could the light mill effect, namely that impinging light pulls the object towards the source, be the reason for the effect?”

    I’d go for the simpler explanation first before gettting into models that start to modify the Standard Model and General Relativity.

    Cheers, Paul.

  • James M. Essig July 31, 2010, 22:27

    Hi Folks;

    I was thinking about the Pioneer Anomaly all day today and had the following additional thoughts to share regarding a potential special-general relativistic effect that might be producing the anomalous acceleration. My guess is that if MOND is not the causal mechanism, then perhaps some not yet understood special and/or general relativistic effect is at work which may or may not be the below summarized mechanism.

    Regarding a theory of Special General Relativity, it is not only the gravitational field of a relativistic space craft that can experience special relativistic reference frame distortion and shape change, but also electric fields, magnetic fields, electromagnetic fields, weak force boson neutral fields, Quantum-Chromo-Dynamics flavor fields, Aka, gluon fields, Standard Model Higgs Field, potentially Minimally Supersymmetric Standard Model (MSSM) fields, and the like may also come into to play. Each or any combinations of these non-gravatic fields might be used to produce novel space-time distortion effects that are special relativistic and/or general relativistic.

    Another consideration of special – general relativistic gravatic effects, involves the notion of a space craft traveling at such a high relativistic gamma factor that its relativistic mass approaches that of a black hole having the same mass as that of the space craft.

    Regarding special general relativistic space-time distortion based on extreme gamma factor space craft, it seems likely that the interaction of the special relativistic reference frame distortion effects and those due to general relativistic distortion would be non-linear. To understand why, consider the onset of general relativistic reference frame distortion at near black hole craft relativistic densities. As the craft general relativistically distorted, that distortion would be subject to special relativistic distortion: a process that would result in yet further distortion of general relativistic forms, which would be self amplified which the result being a further co-occurring special relativistic reference frame distortion. Through in values of extreme space craft acceleration and the mathematics to untangle all of this could become a mess but have profound implications for space craft traveling at utterly extreme relativistic gamma factors (gamma generally in the range of 10 EXP 12 to 10 EXP 18 or greater for a one million metric ton rest mass space craft due to the Lorentz contraction of the gravitational fields produced by the craft, surface area density increases along the direction of the craft velocity vector, and the general relativistic energy increase of the craft with respect the space it passes through).

    We usually consider general relativistic effects in the context of gravitation. We now consider analogues based on electromagnetic fields as a mechanism for space time topology manipulation, as well as analogues based on QCD gluon fields, weak force boson fields, and other mechanisms.

    If a space craft would have a small degree of extension into higher dimensional Kaluza Klein hyperspace, then we can consider the hyper-spatial deformation of the space craft due to special relativistic and/or general relativistic reference frame distortion.

    For cases where any small degree of hyper-spatial extension of the space craft is thermodynamically, topologically, and/or general relativistically partitioned at least in part from the 3-D spatial characteristics of the space craft, it may be the case that the hyper-spatial volumetric mass distribution for extremely relativistic space craft would general relativistically effect the 3-D spatial characteristics wherein both the hyper-spatial mass distribution pattern and the 3-D mass distribution pattern of the space craft would interact in a more or less modular manner commensurate with the degree of separation or non-immediate coupling between these two spatial mass distribution aspects of the space craft.

    If the special and/or general relativistic distortion of the space craft in terms of its hyper-spatial extension could be made extreme enough, perhaps the hyper-spatial portion of the space craft and/or its hyper-spatial extension could somehow pull on or tug on the 3-D Newtonian spatial aspects and composition of the space craft wherein the entire 3-D Newtonian aspects of the space craft would be tugged into the fourth, and/or fifth, and/or sixth, etc spatial dimensions thus enabling the space craft to completely enter hyperspace and perhaps take any short cuts to remote regions in space-time, past, present, or future, within our universe, another universe, a parallel universe, another multiverse, a parallel multiverse, another forest, a parallel forest, another biosphere, a parallel biosphere, and the like. The bi-modular effects described in the previous paragraph might conceivably be brought about by higher dimensional gravatic, electromagnetic, electric, magnetic, QCD field or gluonic, weak force, Higgs Field, or MSSM field, etc or any combination of two or more of the preceding fields, inter-continuum coupling.

    Any such 3-D spatially and hyper-spatially coupled distortions might special relativistically and/or general relativistically reinforce or modify each other in a linear, non-linear, or highly non-linear manner depending perhaps on the nature of the field coupling, the relativistic gamma factor of the craft, the degree of space craft acceleration, the orientation between the craft velocity vector and acceleration vector, and the like.

  • Ron S August 1, 2010, 16:03

    Many novel physics theories have been crushed to death between the implacable jaws of increasingly-tighter error bars of experiment. I expect to see the same outcome in the present case.

  • Erik Anderson August 2, 2010, 13:30

    For once I agree with Ron S. :-D

    Too bad that NASA did not see fit to configure New Horizons in a way that’s conducive to further testing of the Pioneer Anomaly.

  • Ron S August 2, 2010, 14:39

    Erik, I agree, but it may be enough to perform the acceleration test for New Horizons in the same manner. If the anomalous acceleration is different from that for Voyager that will add credence for a mundane cause, where the different spacecraft design results in a different thermally-driven acceleration (assuming this continues as the top candidate).

    If the acceleration is exactly the same, that will be *very* interesting. Unfortunately we’ll have to wait a while yet for the data.

  • stephen August 2, 2010, 15:20

    Didn’t anybody detect any similar anomalies with the Voyager 1 and Voyager 2 probes? If they didn’t, that would be significant, wouldn’t it?

  • Ron S August 2, 2010, 17:17

    Oops! I meant Pioneer, not Voyager, in my previous comment.

  • James Jason Wentworth August 3, 2010, 5:05

    If the Pioneer Anomaly is caused by asymmetrical emission of thermal photons, then the effect may also be detectable among spin-stabilized spacecraft in solar orbit. (The maneuvers of 3-axis stabilized sun-orbiting probes such as the Mariners and Veneras would have wiped out the fine-scale orbital motion tracking data that would be required to make a determination for their motions.)

    Pioneers 6, 7, 8, and 9 and the two West German Helios solar orbiters were all spin-stabilized spacecraft. Detailed studies of their orbital motions made by reviewing the tracking data for them (taking into account the Yarkovsky Effect and the effects of sunlight pressure on the spacecraft) might yield an inner solar system version of the Pioneer Anomaly.

  • Erik Anderson August 3, 2010, 10:12

    To Ron S:

    Well, unless the thermal component has no part whatsoever in the anomaly, then of course the precise results will differ. My understanding is that New Horizon’s radioisotope thermoelectric generator is mounted so close to the spacecraft body that it will heat the spacecraft in unpredictable ways. Pioneer’s RTG, by contrast, was mounted on a boom. This is the most important variable needs to be controlled for.

  • ljk September 29, 2010, 0:21

    On the vacuum fluctuations, Pioneer Anomaly and Modified Newtonian Dynamics

    Authors: Dragan Slavkov Hajdukovic

    (Submitted on 17 Sep 2010)

    Abstract: We argue that the so-called “Pioneer Anomaly” is related to the quantum vacuum fluctuations. Our approach is based on the hypothesis of the gravitational repulsion between matter and antimatter, what allows considering, the virtual particle-antiparticle pairs in the physical vacuum, as gravitational dipoles.

    Our simplified calculations indicate that the anomalous deceleration of the Pioneer spacecrafts could be a consequence of the vacuum polarization in the gravitational field of the Sun. At the large distances, the vacuum polarization by baryonic matter could mimic dark matter what opens possibility that dark matter do not exist, as advocated by the Modified Newtonian Dynamics (MOND).

    Comments: Accepted for publication in Astrophysics and Space Science

    Subjects: General Physics (physics.gen-ph)

    DOI: 10.1007/s10509-010-0467-y

    Cite as: arXiv:1009.3333v1 [physics.gen-ph]

    Submission history

    From: Dragan Hajdukovic [view email]

    [v1] Fri, 17 Sep 2010 04:44:42 GMT (401kb)


  • ljk March 12, 2011, 3:09

    The Planetary Society Blog

    By Emily Lakdawalla

    LPSC 2011: Wanted: Pioneer 10 & 11 digital data

    Mar. 11, 2011 | 12:39 PST | 20:39 UTC

    Weblog Archive

    This is both a Lunar and Planetary Science Conference (LPSC) update and a public service announcement. Ted Stryk posted a blog entry yesterday summarizing the work that he presented at the LPSC poster session on Tuesday, March 8. He’s been working for years to locate the original Pioneer 10 and 11 image data from the Jupiter and Saturn encounters.

    He doesn’t mean photos that were produced from the data, which are more widely available; he means numerical data, which, for Pioneer, would most likely be in the form of a matrix of numbers printed out on some yellowed paper sitting in some institution’s library or some scientist’s personal files.

    Full article here: