RETHINKING RELATIVITY

No one has paid attention yet, but a well-respected physics journal just published an article whose conclusion, if generally accepted, will undermine the foundations of modern physics -- Einstein's Theory of Relativity in particular. Published in Physics Letters A (December 21, 1998), the article claims that the speed with which the force of gravity propagates must be at least twenty billion times faster than the speed of light. This would contradict the Special Theory of Relativity of 1905, which asserts that nothing can go faster than light. This claim about the special status of the speed of light has become part of the world view of educated laymen in the twentieth century.

Special Relativity, as opposed to the General Theory (1916), is considered by experts to be above criticism, because it has been confirmed "over and over again." But several dissident physicists believe that there is a simpler way of looking at the facts, a way that avoids the mind-bending complications of Relativity. Their arguments can be understood by laymen. I wrote about one of these dissidents, Peter Beckmann, over five years ago (TAS, August 1993, and Correspondence, TAS, October 1993). The present article introduces new people and arguments. The subject is important because if Special Relativity is supplanted, much of twentieth-century physics, including quantum theory, will have to be reconsidered in that light.

The article in Physics Letters A was written by Tom Van Flandern, a research associate in the physics department at the University of Maryland. He also publishes Meta Research Bulletin which supports "promising but unpopular alternative ideas in astronomy." In the 1990's, he worked as a special consultant to the Global Positioning System (GPS), a set of satellites whose atomic clocks allow ground observers to determine their position to within about a foot. Van Flandern reports that an intriguing controversy arose before GPS was even launched. Special Relativity gave Einsteinians reason to doubt whether it would work at all. In fact, it works fine (But more on that later).

The publication of his article is a breakthrough of sorts. For years, most editors of mainstream physics journals have automatically rejected articles arguing against Special Relativity. This policy was informally adopted in the wake of the Herbert Dingle controversy. A professor of science at the University of London, Dingle had written a book popularizing Special Relativity, but by the 1960's he had become convinced that it couldn't be true. So he wrote another book, Science at the Crossroads (1972), contradicting the first. Scientific journals, especially Nature, were bombarded with his (and others') letters.

An editor of Physics Letters A promised Van Flandern that reviewers would not be allowed to reject his article simply because it conflicted with received wisdom. Van Flandern begins with the "most amazing thing" he learned as a graduate student of celestial mechanics at Yale: that all gravitational interactions must be taken as instantaneous. At the same time, students were also taught that Einstein's Special Relativity proved that nothing could propagate faster than light in a vacuum. The disagreement "sat there like an irritant," Van Flandern told me. He determined that one day he would find its resolution. Today, he thinks that a new interpretation of Relativity may be needed.

The argument that gravity must travel faster than light goes like this. If its speed limit is that of light, there must be an appreciable delay in its action. By the time the Sun's "pull" reaches us, the Earth will have "moved on" for another 8.3 minutes (the time of light travel). But by then the Sun's pull on the Earth will not be in the same straight line as the Earth's pull on the Sun. The effect of these misaligned forces "would be to double the Earth's distance from the Sun in 1200 years." Obviously, this is not happening. The stability of planetary orbits tells us that gravity must propagate much faster than light. Accepting this reasoning, Isaac Newton assumed that the force of gravity must be instantaneous.

Astronomical data support this conclusion. We know, for example, that the Earth accelerates toward a point 20 arc-seconds in front of the visible Sun -- that is, toward the true, instantaneous direction of the Sun. Its light comes to us from one direction, its "pull" from a slightly different direction. This implies different propagation speeds for light and gravity.

It might seem strange that something so fundamental to our understanding of physics can still be a matter of debate. But that in itself should encourage us to wonder how much we really know about the physical world. In certain Internet discussion groups, "the most frequently asked question and debated topic is 'What is the speed of gravity?,'" Van Flandern writes. It is heard less often in the classroom, but only "because many teachers and most textbooks head off the question." They understand the argument that it must go very fast indeed, but they also have been trained not to let anything exceed Einstein's speed limit.

So maybe there is something wrong with Special Relativity after all. In The ABC of Relativity (1925), Bertrand Russell said that just as the Copernican system once seemed impossible and now seems obvious, so, one day, Einstein's Relativity theory "will seem easy." But it remains as "difficult" as ever, not because the math is easy or difficult (Special Relativity requires only high-school math, General Relativity really is difficult), but because elementary logic must be abandoned. "Easy Einstein" books remain baffling to almost all. The sun-centered solar system, on the other hand, has all along been easy to grasp.

Nonetheless, Special Relativity (which deals with motion in a straight line) is thought to be beyond reproach. General Relativity (which deals with gravity, and accelerated motion in general) is not regarded with the same awe. Stanford's Francis Everitt, the director of an experimental test of General Relativity due for space-launch next year, has summarized the standing of the two theories in this way: "I would not be at all surprised if Einstein's General Theory of Relativity were to break down," he wrote. "Einstein himself recognized some serious shortcomings in it, and we know on general grounds that it is very difficult to reconcile with other parts of modern physics. With regard to Special Relativity, on the other hand, I would be much more surprised. The experimental foundations do seem to be much more compelling." This is the consensus view.

Dissent from Special Relativity is small and scattered. But it is there, and it is growing. Van Flandern's article is only the latest manifestation. In 1987, Peter Beckmann, who taught at the University of Colorado, published Einstein Plus Two, pointing out that the observations that led to Relativity can be more simply reinterpreted in a way that preserves universal time. The journal he founded, Galilean Electrodynamics was taken over by Howard Hayden of the University of Connecticut (Physics), and is now edited by Cynthia Kolb Whitney of the Electro-Optics Technology Center at Tufts. Hayden held colloquia on Beckmann's ideas at several New England universities, but could find no physicist who even tried to put up an argument.

A brief note on Einstein's most famous contribution to physics -- the formula that everyone knows. When they hear that heresy is in the air, some people come to the defense of Relativity with this question: "Atom bombs work, don't they?" They reason as follows: The equation E = mc2 was discovered as a byproduct of Einstein's Special Theory of Relativity (True). Relativity, they conclude, is indispensable to our understanding of the way the world works. But that does not follow. Alternative derivations of the famous equation dispense with Relativity. One such was provided by Einstein himself in 1946. And it is simpler than the relativistic rigmarole. But few Einstein books or biographies mention the alternative. They admire complexity, and cling to it.

Consider Clifford M. Will of Washington University, a leading proponent of Relativity today. "It is difficult to imagine life without Special Relativity," he says in Was Einstein Right? "Just think of all the phenomena or features of our world in which Special Relativity plays a role. Atomic energy, both the explosive and the controlled kind. The famous equation E = mc2 tells how mass can be converted into extraordinary amounts of energy." Note the misleading predicate, "plays a role." He knows that the stronger claim, "is indispensable," would be pounced on as inaccurate.

Is there an alternative way of looking at all the facts that supposedly would be orphaned without Relativity? Is there a simpler way? A criterion of simplicity has frequently been used as a court of appeal in deciding between theories. If it is made complex enough, the Ptolemaic system can predict planetary positions correctly. But the Sun-centered system is much simpler, and ultimately we prefer it for that reason.

Tom Van Flandern says the problem is that the Einstein experts who have grown accustomed to "Minkowski diagrams and real relativistic thinking" find the alternative of universal time and "Galilean space" actually more puzzling than their own mathematical ingenuities. Once relativists have been thoroughly trained, he says, it's as difficult for them to rethink the subject in classical terms as it is for laymen to grasp time dilation and space contraction. For laymen, however, and for those physicists who have not specialized in Relativity, which is to say the vast majority of physicists, there's no doubt that the Galilean way is far simpler than the Einsteinian. Special Relativity was first proposed as a way of sidestepping the great difficulty that arose in physics as a result of the Michelson-Morley experiment (1887). Clerk Maxwell had shown that light and radio waves share the same electromagnetic spectrum, differing only in wave length. Sea waves require water, sound waves air, so, it was argued, electromagnetic waves must have their own medium to travel in. It was called the ether. "There can be no doubt that the interplanetary and interstellar spaces are not empty," Maxwell wrote, "but are occupied by a material substance or body, which is certainly the largest, and probably the most uniform body of which we have any knowledge." As today's dissidents see things, it was Maxwell's assumption of uniformity that was misleading.

The experiment of Michelson and Morley tried to detect this ether. Since the Earth in its orbital motion must plow through it, an "ether wind" should be detectable, just as a breeze can be felt outside the window of a moving car. Despite repeated attempts, however, no ethereal breeze could be felt. A pattern of interference fringes was supposed to shift when Michelson's instrument was rotated. But there was no fringe shift.

Einstein explained this result in radical fashion. There is no need of an ether, he said. And there was no fringe shift because the speed of an approaching light wave is unaffected by the observer's motion. But if the speed of light always remains the same, time itself would have to slow down, and space contract to just the amount needed to ensure that the one divided by the other -- space divided by time -- always gave the same value: the unvarying speed of light. The formula that achieved this result was quite simple, and mathematically everything worked out nicely and agreed with observation.

The skeptical, meanwhile, were placated with this formula: "I know it seems odd that time slows down and space contracts when things move, but don't worry, a measurable effect only occurs at high velocities -- much higher than anything we find in everyday life. So for all practical purposes we can go on thinking in the same old way." (Meanwhile, space and time have been subordinated to velocity. Get used to it.)

Now we come to some modern experimental findings. Today we have very accurate clocks, accurate to a billionth of a second a day. The tiny differentials predicted by Einstein are now measurable. And the interesting thing is this: Experiments have shown that atomic clocks really do slow down when they move, and atomic particles really do live longer. Does this mean that time itself slows down? Or is there a simpler explanation?

The dissident physicists I have mentioned disagree about various things, but they are beginning to unite behind this proposition: There really is an ether, in which electromagnetic waves travel, but it is not the all-encompassing, uniform ether proposed by Maxwell. Instead, it corresponds to the gravitational field that all celestial bodies carry about with them. Close to the surface (of sun, planet, or star) the field, or ether, is relatively more dense. As you move out into space it becomes more attenuated. Beckmann's Einstein Plus Two introduces this hypothesis, I believe for the first time, and he told me it was first suggested to him in the 1950's by one of his graduate students, Jiri Pokorny, at the Institute of Radio Engineering and Electronics in Prague. Pokorny later joined the department of physics at Prague's Charles University, and today is retired.

I believe that all the facts that seem to require special or General Relativity can be more simply explained by assuming an ether that corresponds to the local gravitational field. Michelson found no "ether wind," or fringe shift, because of course the Earth's gravitational field moves forward with the Earth. As for the bending of starlight near the Sun, the confirmation of General Relativity that made Einstein world-famous, it is easily explained given a non-uniform light medium. It is a well known law of physics that wave fronts do change direction when they enter a denser medium. According to Howard Hayden, refracted starlight can be derived this way "with a few lines of high school algebra.? And derived exactly. The tensor calculus and Riemannian geometry of General Relativity gives only an approximation. Likewise the "Shapiro Time-Delay," observed when radar beams pass close to the Sun and bounce back from Mercury. Some may prefer to try to understand all this in terms of the "curvature of Space-Time," to use the Einstein formulation (unintelligible to laymen, I believe). But they should know that a far simpler alternative exists.

The advance of the perihelion of Mercury's orbit, another famous confirmation of General Relativity, is worth a closer look (the perihelion is the point in the orbit closest to a sun). Graduate theses may one day be written about this peculiar episode in the history of science. In his book, Subtle Is the Lord, Abraham Pais reports that when Einstein saw that his calculations agreed with Mercury's orbit, "he had the feeling that something actually snapped in him ... This experience was, I believe, by far the strongest emotional experience in Einstein's scientific life, perhaps in all his life. Nature had spoken to him."

Fact: The equation that accounted for Mercury's orbit had been published 17 years earlier, before Relativity was invented. The author, Paul Gerber, used the assumption that gravity is not instantaneous, but propagates with the speed of light. After Einstein published his General Relativity derivation, arriving at the same equation, Gerber's article was reprinted in *Annalen der Physik* (the journal that had published Einstein's Relativity papers). The editors felt that Einstein should have acknowledged Gerber's priority. Although Einstein said he had been in the dark, it was pointed out that Gerber's formula had been published in Mach's Science of Mechanics, a book that Einstein was known to have studied. So how did they both arrive at the same formula?

Tom Van Flandern was convinced that Gerber's assumption (gravity propagates with the speed of light) was wrong. So he studied the question. He points out that the formula in question is well known in celestial mechanics. Consequently, it could be used as a "target" for calculations that were intended to arrive at it. He saw that Gerber's method "made no sense, in terms of the principles of celestial mechanics." Einstein had also said (in a 1920 newspaper article) that Gerber's derivation was "wrong through and through."

So how did Einstein get the same formula? Van Flandern went through his calculations, and found to his amazement that they had "three separate contributions to the perihelion; two of which add, and one of which cancels part of the other two; and you wind up with just the right multiplier." So he asked a colleague at the University of Maryland, who as a young man had overlapped with Einstein at Princeton's Institute for Advanced Study, how in his opinion Einstein had arrived at the correct multiplier. This man said it was his impression that, "knowing the answer," Einstein had "jiggered the arguments until they came out with the right value."

If the General Relativity method is correct, it ought to apply everywhere, not just in the solar system. But Van Flandern points to a conflict outside it: binary stars with highly unequal masses. Their orbits behave in ways that the Einstein formula did not predict. "Physicists know about it and shrug their shoulders," Van Flandern says. They say there must be "something peculiar about these stars, such as an oblateness, or tidal effects." Another possibility is that Einstein saw to it that he got the result needed to "explain" Mercury's orbit, but that it doesn't apply elsewhere.

The simplest way to understand all this "without going crazy," Van Flandern says, is to discard Einsteinian Relativity and to assume that "there is a light-carrying medium." When a clock moves through this medium "it takes longer for each electron in the atomic clock to complete its orbit." Therefore, it makes fewer "ticks" in a given time than a stationary clock. Moving clocks slow down, in short, because they are "ploughing through this medium and working more slowly." It's not time that slows down. It's the clocks. All the experiments that supposedly "confirm" Special Relativity do so because all have been conducted in laboratories on the Earth's surface, where every single moving particle, or moving atomic clock, is in fact "ploughing through" the Earth's gravitational field, and therefore slowing down.

Both theories, Einsteinian and local field, would yield the same results. So far. Now let's turn back to the Global Positioning System. At high altitude, where the GPS clocks orbit the Earth, it is known that the clocks run roughly 46,000 nanoseconds (one-billionth of a second) a day faster than at ground level, because the gravitational field is thinner 20,000 kilometers above the Earth. The orbiting clocks also pass through that field at a rate of three kilometers per second -- their orbital speed. For that reason, they tick 7,000 nanoseconds a day slower than stationary clocks.

To offset these two effects, the GPS engineers reset the clock rates, slowing them down before launch by 39,000 nanoseconds a day. They then proceed to tick in orbit at the same rate as ground clocks, and the system "works." Ground observers can indeed pin-point their position to a high degree of precision. In (Einstein) theory, however, it was expected that because the orbiting clocks all move rapidly and with varying speeds relative to any ground observer (who may be anywhere on the Earth's surface), and since in Einstein's theory the relevant speed is always speed relative to the observer, it was expected that continuously varying relativistic corrections would have to be made to clock rates. This in turn would have introduced an unworkable complexity into the GPS. But these corrections were not made. Yet "the system manages to work, even though they use no relativistic corrections after launch," Van Flandern said. "They have basically blown off Einstein."

The latest findings are not in agreement with relativistic expectations. To accommodate these findings, Einsteinians are proving adept at arguing that if you look at things from a different "reference frame," everything still works out fine. But they have to do the equivalent of standing on their heads, and it's not convincing. A simpler theory that accounts for all the facts will sooner or later supplant one that looks increasingly Rube Goldberg-like. I believe that is now beginning to happen.

University of London Professor Herbert Dingle showed why Special Relativity will always conflict with logic, no matter when we first learn it. According to the theory, if two observers are equipped with clocks, and one moves in relation to the other, the moving clock runs slower than the non-moving clock. But the Relativity principle itself (an integral part of the theory) makes the claim that if one thing is moving in a straight line in relation to another, either one is entitled to be regarded as moving. It follows that if there are two clocks, A and B, and one of them is moved, clock A runs slower than B, and clock B runs slower than A. Which is absurd.

Dingle's Question was this: Which clock runs slow? Physicists could not agree on an answer. As the debate raged on, a Canadian physicist wrote to Nature in July 1973: "Maybe the time has come for all of those who want to answer to get together and to come up with one official answer. Otherwise the plain man, when he hears of this matter, may exercise his right to remark that when the experts disagree they cannot all be right, but they can all be wrong."

The problem has not gone away. Alan Lightman of MIT offers an unsatisfactory solution in his Great Ideas in Physics (1992). "The fact that each observer sees the other clock ticking more slowly than his own clock does not lead to a contradiction. A contradiction could arise only if the two clocks could be put back together side by side at two different times." But clocks in constant relative motion in a straight line "can be brought together only once, at the moment they pass." So the theory is protected from its own internal logic by the impossibility of putting it to a test. Can such a theory be said to be scientific? --TB

Tom Van Flandern's Meta Research Bulletin ($15) and his book, Dark Matter, Missing Planets ($24.50), may be obtained from P.O. Box 15186, Chevy Chase, MD 20825; Peter Beckmann's Einstein Plus Two ($40) from Golem Press, P.O. Box 1342, Boulder, CO 80306. Beckmann's book is highly technical; Van Flandern's is mostly accessible to laymen.

Tom Bethell is TAS's Washington correspondent. His new book, The Noblest Triumph, was recently published by St. Martin's Press.

I already told you why I reject Relativity - it goes against common sense. Same reason I don't accept evolution and the Big Bang.

I see. Believe me, I understand. I've been waaaay down that road.

When I studied physics in college, they made sure to take us down it. The Newton/Laplace clockwork universe was made very clear to us, as were the laws of thermodynamics, and Maxwell's electromagnetism. We got very good at manipulating them, too. It all made sense--common sense--and it all worked perfectly. Or so they made us believe.

Then, in our junior year, they started to introduce us to certain uncomfortable facts. Experimental facts. Facts that couldn't be made to fit into the commonsense framework that we'd just spent two years and thousands of dollars building in our own heads. Clocks slow down when they move. Rulers get shorter when they move. Light waves arrive in tiny lumps of energy. A small bit of matter takes multiple paths to get from one place to another. Outcomes of certain events are apparently changed retroactively.

The demonstrable behavior of the universe is different from what very well-trained common sense would expect.

I've never witnessed it myself, but many professors who teach junior physics have stories of students who have become emotionally distraught at this. But it's important that every professional physicist, at least once, undergo the experience of having a perfectly coherent physical worldview smashed irretrievably by experimental fact.

The cold reality is that nature, at its core, does not conform to man's common sense. Mathematics contradicts it, experimental fact contradicts it, and the two of them agree with each other. It takes humility to yield to this, but the universe is the way that it is, and not how we would wish it to be.

I already told you why I reject Relativity - it goes against common sense. Same reason I don't accept evolution and the Big Bang.

From here: http://math.ucr.edu/home/baez/RelWWW/tests.html

"The Classical Tests

Anyone who has taken a first course in general relativity will be aware of the so-called "classical solar system tests":

light bending: according to gtr, the images of stars near a foreground isolated massive object such as the Sun should be displaced outwards from their usual positions by an amount first computed by Einstein in 1915. This effect could be consider the simplest kind of gravitational lensing effect. As is well known, a team of astronomers, including Arthur Stanley Eddington, confirmed Einstein's prediction that a stellar image which according to Newtonian gravitation would just graze the limb of the Sun would be displaced outwards by 1.75 seconds of arc during the solar eclipse of 1919. Many further observations of other exclipses have since been made, but these observations were too uncertain to provide very accurate tests. However, the effect should be the same for any frequency of EM radiation, including radio waves, and in recent years the Very Long Baseline Array Interferometer (VBLI) array has been used to confirm the prediction of gtr to within 0.1%, Most recently, the Hipparchos star mapping mission confirmed the effect for occultations by the major planets such as Jupiter, as well as our Sun.

Shapiro time delay: according to gtr, the travel time of a radar signal should be longer if the radar beam travels near an isolated massive object such as the Sun, by an amount first computed by Shapiro. Radar ranging experiments using the Viking and Voyager spacecraft (whose position is known with great accuracy) have confirmed this effect to within about 1% of the value predicted by gtr, and observations of the Pulsar PSR 1937+21 have provided an independent verification that this effect works as advertised (to within about 5% of the value predicted by gtr) elsewhere in the Universe, not just in our own solar system!

Time delay and light bending observations are actually measuring the same PPN parameter, gamma. The percentage accuracies quoted above are the percentage to which gamma conforms to the value it has according to gtr; this is far more physically relevant than reporting the percentage accuracy of individual predictions, because it shows that if gtr is not the correct classical field theory limit of the presumed quantum theory of gravitation, then this limit must be a good mimic of gtr, at least in so far as the amount of spacetime curvature caused by a given amount of mass-energy is concerned. Here is a graph, taken from this paper by Clifford Will, of various measurements of gamma.

gravitational red shift: according to gtr, static clocks held close to an isolated massive object run more slowly than static clocks which are further away, in the sense that radio signals and other EM radiation "climbing away" from a massive object are red-shifted, as recieved by a distant static observer, by an amount first computed by Einstein as early as 1913. Today, this effect would be considered a test of principle of local position invariance, and thus a test of a large class of "metric gravitation theories", not just a test of gtr. The effect has been verified by progressively more accurate experiments since the classic experiment of Pound and Rebka in 1961, and the best current experimental results confirm the effect to within about 0.02% of the value predicted by assuming LPI.
In addition, careful observations of a very rapidly rotating pulsar (neutron star) have confirmed to within a few percent. that this effect also works as advertised elsewhere in the universe. Futhermore, the ASCA X-ray satellite has observed very strongly gravitationally redshifted light emitted from the inner edge of the accretion disk a supermassive black hole in the galaxy MCG-6-30-15. This light appears to come from r = 10m to r = 3m; note that the inner edge of the accretion disk is located at r = 6m, so these observations appear to confirm that very hot material is leaving the disk and plunging into the event horizon, effectively disappearing at about r= 3m, just as gtr predicts!

Last but not least, the clocks aboard the Global Positioning System satellites in effect test every day both the gravitational red shift effect and the kinematical red shift predicted by str to within 50 nanoseconds per day (the str effects and gtr effects account for a comparable amount of the rate by which the satellite clocks differ from the rate of comparable clocks on the Earth's surface), and if either of those predictions were not correct, the clocks would drift by 40 microseconds per day, which would immediately render the GPS system completely useless!

Recall from the above that gravitational redshift is actually a measure of the post-PPN parameter alpha; here again is the graph from the paper by Will summarizing various measurements of alpha.

precession of periastrion of objects such as a planet orbiting a more massive object such as a star: according to gtr, non-circular orbits of planets around a star (or of satellites around the Earth) are not exact Keplerian ellipses, but are more like ellipses which slowly "rotate" so that their point of closest approach (periastrion) slowly "precesses" in the direction of motion of the orbiting object. The precession predicted by gtr was first computed by Einstein in 1915, who found that it precisely accounted for an unexplained "extra-Newtonian" precession of the planet Mercury in its orbit around the sun, in the amount of about 43 seconds of arc per century. (The total precession is much larger, about 5600 seconds per century, but almost all of this is explained by perturbations of the orbit of Mercury due to Jupiter and other Newtonian astrodynamical effects. Because in the limit of weak fields and slow motion (the motion of Mercury around the Sun falls into this category), gtr behaves pretty much like Newtonian gravitation, the previously known explanations for all but the ``extra-Newtonian'' 43 seconds also apply in gtr, but gtr's first great success was that it also explained the "extra" precession which could not be explained by Newtonian astrodynamics. Since 1915, progressively more accurate observations have tested the effect using the orbits of all the inner planets (specifically: the ``extra-Newtonian'' precession of Venus is observed to be 8 seconds of arc per century, and the ``extra-Newtonian'' precession of Earth is observed to be 5 seconds of arc per century, both also in perfect agreement with the prediction of gtr), the orbits of various asteroids, and the orbits of various spacecraft.

The PPN parameter which controls this precession is betabar; the above mentioned observations show that betabar agrees to 0.1% with the gtr value. The main source of uncertainty in these measurements is the value of the quadrupole moment of the Sun; helioseismology suggests that this moment is less than 10^(-7), but if it were larger, the estimated value of betabar might be affected.

In addition to the above mentioned classical solar-system tests, since 1969, when the Apollo astronauts placed a laser reflector on the surface of the Moon, the Earth-Moon distance has been tracked continuously with an accuracy of 15 cm (!). This LURE data shows that the PPN parameter alpha1 is within 0.1% of the gtr value, and that the PPN parameter zeta3 is within 10^(-8) of the gtr value. According to gtr, the spin axis of a spinning gyroscope in orbit about a massive object should precess; this effect was first noticed by de Sitter, and is called geodetic precession (if the massive object is itself spinning, there is an additional, much smaller, gravitomagnetic precession of the spin axis). The LURE data has confirmed this prediction to within 0.7 % of the predicted value for the Earth-Moon system, considered as a ``gryoscope'' in orbit about the Sun. In addition, measurements of the Sun's alignment with the ecliptic shows that the PPN parameter alpha2 is within 10^(-6) of the gtr value, and measurments of Earth tides show that the PPN parameter xi is within 0.1% of the gtr value.

As we'll see below, the remaining PPN parameters are constrained by strong-field measurements coming from observations of binary pulsars; at present, all the PPN parameters are known to agree with the gtr values to between 10^(-3) and 10^(-20) (!). Actually, these figures do not by themselves do justice to the actual known contraints upon the PPN parameters. In fact, when we combine deductions from several different types of measurements, we find not only that the resulting estimates are consistent with one another, but that they ``trap'' the space of metric theories which are in agreement with all known data to within a very small neighborhood of the gtr PPN values. For example, here is a graph, taken from this paper by Esposito-Farese, showing the constraints on the PPN parameters gamma = 1 + gammabar and beta = 1 + betabar, given by combining

- the observed ``extra-Newtonian'' precession of the perihelia of Mercury,
- tracking of the Earth-Mars distance, using a radar reflector placed on Mars as part of the Viking mission,
- Very Long Baseline Array (VLBI) interferometry measurements "

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