As we said at the beginning, it's not so much a case of being "wrong." When a theory's predictions accord with the facts as far as can be experimentally determined, it obviously can't be rejected as an invalid way of looking at things. But that isn't enough to make it the only valid way. And if other ways that can be shown to be equally valid by according with the same facts are able to do so more simply, they deserve consideration. The objection is more to the confident assurances that we now have all the answers, no way of doing better is conceivable, and the book is closed. When claims to a revelation of final Truth are heard, with all moves toward criticism being censured, ridiculed, or dismissed out of hand, then what's going is drifting toward becoming intolerant dogmatism rather than science. Einstein would probably have been one of the first to agree. One of his more endearing quotes was that "I only had two original ideas in my life, and one of them was wrong." I don't think he would object at all to our taking a long, hard look at the other one too.
Not everyone is as enamored that the disappearance of such fundamental concepts as space and time into abstractions of mathematical formalism helps our understanding of anything or sees it as necessary. Traditionally, length, time, and mass have constituted the elements of physics from which all other quantities, such as acceleration, force, energy, momentum, and so on, are derived. Elevating a velocity (length divided by time) to a privileged position as Nature's fundamental reality, and then having to distort space and time to preserve its constancy, just has the feel about it, to many, of somehow getting things the wrong way around. This isn't to say that what's familiar and apparently self-evident can always be relied upon as the better guide. But a physics of comprehension built on a foundation of intuition that can be trusted is surely preferable to one of mere description that results from applying formalized procedures that have lost all physical meaning. We live in a world inhabited not by four-dimensional tensors but by people and things, and events that happen in places and at times. A map and a clock are of more use to us than being told that an expression couched in terms of components having an obscure nature is invariant. If other interpretations of the facts that relativity addresses can be offered that integrate more readily with existing understanding, they deserve serious consideration.
A good place to start might be with Lorentz's ether theory (LET). Recall that it was compatible with all the electromagnetic results that SRT accounts for but postulated a fixed ether as the propagating medium, which is what the c in Maxwell's equations referred to. In another reference frame the velocity of light will be c plus or minus that frame's velocity relative to the privileged frame defined by the ether. "But measurements don't show c plus or minus anything. They show c." Which was where all the trouble started. Well, yes, that's what measurements show. But measurements are based on standards like meter-rules and clocks. While SRT was willing to give up the Lorentzian assumptions of space and time being immutably what they had always been, the proponents of an LET interpretation point out that SRT itself carries an assumption that would seem far closer to home and more readily open to question, namely that the measuring standards themselves are immutable. Before consigning the entire structure of the universe to deformities that it hasn't recovered from since, wouldn't it be a good idea to make sure that it wasn't the rules and clocks that were being altered?
If this should be so, then the rest frame of the ether is the one the electromagnetic laws are correct in, which the c in Maxwell's equations refers to. In frames that are moving relative to it, the speed of light will be different. However, motion through the ether alters physical structures in such a way that the standards used will still measure it as c. So nobody can detect their motion with respect to the ether frame, and the same experimental results as are derived from SRT follow. But space and time remain what they've always been, and light retains the same property as every other wave phenomenon in physics in that its velocity is a constant with respect to the medium that it's traveling through.
If motion relative to the ether frame could be established, the notion of absolute simultaneity would be restored. The velocity of light within that frame is known, and it would be meaningful to say, for example, that signals sent from the ends of a measured distance arrive at the midpoint at the same time. Velocities in other frames could then be corrected with respect to that standard. The situation would be similar to using sound signals to synchronize a clock on the ground with one carried on a moving vehicle.
It might seem a remarkable coincidence that the distortions induced in the measuring standards should be of just the right amount to keep the apparent value of c at that given by Maxwell's equations. But it isn't really, since the Lorentz Transforms that yield the distortions were constructed to account for those experimental results in the first place.
Lorentz himself conducted theoretical investigations of the flattening of electrons, assumed to be normally symmetrical, in their direction of motion through the ether. If basic particles can be affected, the notion of physical objects being distorted becomes less difficult to accept. After all, "matter" comprises a volume of mostly empty spaceor ether in the context of the present discussiondefined by a highly dispersed configuration of electrical entities linked by forces. (Think of those models made up from balls connected by webs of springs that you see in science displays in museums and high-school laboratories to represent molecules.) Maybe the idea that objects moving fast through the ether could ever not be distorted is what really needs explaining.
Such distortions would perturb the energy dynamics of electron shell structures and atomic nuclei, with consequent modifications to emitted frequencies and other time-dependent processes, and hence any measuring techniques based on them. So the assumption of immutable clocks stands or falls on the same ground.
An introduction to the arguments favoring an LET model, and to the philosophical considerations supporting it is given concisely by Dr. George Marklin. 68 The LET interpretation can also be extended to include gravitational effects by allowing the ether to move differentially. Such a general ether theory has been developed by Ilja Schmelzer. 69 It is mathematically equivalent to GRT but uses Euclidean space and absolute time. Schmelzer gives the ether a density, velocity and pressure tensor and satisfies all the appropriate conservation equations, but it's a fairly recent development and there are still unresolved issues.
A comprehensive treatment that covers all the ground of SRT and GRT as well as addressing the controversial experimental issues that are argued both ways, such as the interpretation of results from rotating frames, transporting of atomic clocks around the world, and the calibrating of GPS satellite ranging is Ronald Hatch's "modified Lorentz ether theory," MLET. 70 The "modified" part comes from its extension of using the same ether to account for material particles in the form of standing waves. The theory and its ramifications are explored in detail in Hatch's book Escape from Einstein. 71
The concept of a fixed ether pervading all of space uniformly like a placid ocean was perhaps something of an idealization that owed more to Aristotlean notions of perfection than the messy, turbulent world we find ourselves living in. The Michelson-Morely result showed that no motion through such an ether can be detectedat least not by present methodsfrom which one conclusion is that it might as well not be there, and therefore to all practical purposes it doesn't exist. This is the path that SRT develops. However, the same result would be obtained if the ether in the vicinity of the Earth moved with it in its orbit around the Sun, accompanying it as a kind of "bubble" inside which the Earth and the local ether remain at rest relative to each other. Such an "entrained ether" interpretation was in fact favored by Michelson himself, who never accepted the SRT explanation. The general consensus, however, was it was incompatible with the aberration effect on starlight described earlier, and it was rejected accordingly.
But aberration turns out, on closer examination, to be a more complex business than is often acknowledged. The typical SRT textbook explanation attributes the effect to relative velocity, for example: " . . . the direction of a light ray depends essentially on the velocity of the light source relative to the observer. . . . This apparent motion is simply due to the fact that the observed direction of the light ray coming from the star depends on the velocity of the earth relative to the star." 72
This can't be so, however, since stars in general possess velocities that vary wildly with respect to the Earth. Pointing a telescope at any patch of sky constrained sufficiently to signify direction should still capture a representative sample of them, which should display a spread of aberration displacements accordingly. But that isn't what's found. They turn out to be all the same.
Then again, let's consider what are known as spectroscopic binary stars, that is, double stars too close together to be resolved separately but which can be distinguished by their Doppler-shifted spectra. If aberration depended on velocity, the very difference in velocities that produces the Doppler shifts would be sufficient to separate the images resolvablyin which case they would no longer be spectroscopic binaries!
And further, even for a star that was not moving with respect to the Earth at all, the atoms in the star's photosphere that do the actual emitting of light, and which therefore constitute its true sources, will be moving thermally in all directions randomly. If aberration were due to their velocities, the compound effect would be sufficient to expand the points seen in the sky to a size that could be discerned with a good pair of binoculars.
There is an apparent displacement of planets, also called aberration, unfortunately, that results from the delay of light in reaching the Earth. It does depend on source velocity, but this isn't the quantity that we're talking about. Its effect reduces with distance and is effectively zero for things like stars. According to Thomas E. Phipps Jr., Einstein used the wrong one. 73 Howard Hayden, professor emeritus of physics at the University of Connecticut, Storrs, arrives at the same conclusion. 74
Stellar aberration affects all stars in a locally surveyed region equally and varies systematically with an annual cycle. The velocity that it depends on is clearly the orbital velocity of the Earth, which would seem to imply velocity with respect to the Sun's frame. But there's a difficulty. Suppose there was a streetlamp beyond the telescope, directly in line with the star being observed. If some kind of motion through an ether were responsible, you'd think that light from one would follow the same path as the light from the other, and the same aberration should be observed. It isn't. No measurable effect occurs at all. Relativists chuckle and say, "We told you so. It's because there's no relative motion between the street light and the observer." But the considerations above are enough to say that can't be true either. It's more as if different ethers were involved, one containing the Earth and the streetlamp, inside which there is no aberration, the other extending out to somewhere less than the Sun's distance such that its annual motion within the Sun's frame produces the effect on starlight. There are further complications too, such as why long-baseline radio telescope arrays should detect aberration when there's no tube for photons to move sideways in, and the theories and arguments currently doing the rounds to try and account for them could bog us down for the rest of this book. I've dwelt on it this far to show that the whole subject of aberration is a lot more involved than the standard treatments that dismiss it in a few lines would lead one to believe.
Petr Beckmann, a Czech professor of electrical engineering at the University of Colorado, developed an alternative theory in which the second of SRT's two founding premisesthat the speed of light is constant with respect to all observers everywhereis replaced by its speed being constant with respect to the dominant local force field through which it propagates. (SRT's first premise was the relativity principle, by which the same laws of physics apply everywhere.) For most of the macroscopic universe in which observers and laboratories are located, this means the gravitational field that happens to dominate wherever one happens to be. On the surface of the Earth it means the Earth's field, but beyond some distance that gives way to the Sun's field, outside which the field of the local part of the galactic realm dominates, and so on. This gives a more tangible form to the notion of embedded "ether bubbles," with light propagating at its characteristic speed within fields that move relative to each otherlike the currents and drifts and doldrums that make up a real ocean, as opposed to a universally static, glassy abstraction. And since, as with any conservative vector field (one in which energy potentials can be defined), any point of a gravity field is described by a line of force and the equipotential passing through it, the field coordinate system can serve as a local standard of rest.
Does this mean, then, that the gravitational field is, in fact, the long sought-for "ether"? Beckmann asks, in effect, who cares? since the answers come out the same. Marklin is more of a purist, insisting on philosophical grounds that whatever its nature finally turns out to be, a physically real medium must exist. A "field," he pointed out when I visited him at his home in Houston while researching this book, is simply a mathematical construct describing what a medium does. The smile can't exist without the Cheshire cat. I'm not going to attempt to sit in judgment on heavyweights like Petr and George. The purpose of this essay is simply to inform interested readers on some of the ideas that are out there.
The cause of all the confusion, Beckmann argues, is that what experiments have been telling us about motion relative to the field has been mistakenly interpreted as meaning motion relative to observers who have always been attached to it. Since every experiment cited to date as supporting or "proving" relativity has been performed in a laboratory solidly at rest on the Earth's surface, the same experiments are consistent with either theory. Both theories account equally well for the same results. Except that doing the accounting can be a far more involved business in one case than in the other. As an example of how the same result is explained simply and straightforwardly by one theory but requires elaborate footwork from the other, let's consider the Michelson-Gale experiment of 1925, which rarely finds its way into the textbooks. 75
Michelson-Morley had failed to detect any motion of the Earth relative to an ether in its orbit around the Sun. This could be because there is no ether (SRT), or there is but the distortion of measuring standards obscures it (LET), or because the local ether moves with the Earth (Beckmann-type field-referred theories). Does the local ether bubble rotate with the Earth also, or does the Earth spin inside it?
Michelson and Gale set up an experiment to try to answer this at Clearing, Ilinois, using a rectangular interferometer large enough to detect the difference in velocity between the north and south arms due to the southern one's being slightly nearer the equator and hence moving slightly faster. It was a magnificent affair measuring over 2,000 feet east-west and 1,100 feet north-south, with evacuated pipes 12 inches across to carry the beams, and concrete boxes for the mirrors, lenses, and beam splitters. Two hundred sixty-nine measurements were taken in sets representing various conditions.
And fringe shifts were observednot only of a magnitude consistent with the "hypothesis of a fixed ether" (Michelson's words) within the limits of observational error, but from which the experimenters were able accurately to calculate the rotation speed of the Earth.
Beckmann's theory predicts this on the theoretical argument that if the gravitational field describes an outward propagation, the effect would "decouple" from the source as soon as it leaves, somewhat like bullets from a rotating machine gun still radiating outward in straight lines. In other words, the field's effects shouldn't share the source's rotation, and hence the speeds of the light beams in the two arms of the interferometer will be different. This doesn't contradict Einstein, though, where the General Theory is invoked to arrive at the same result on the grounds that each beam has its own idea of time. But whereas Beckmann's conclusion follows from Galilean principles and a few lines of high-school algebra, GRT requires multidimensional tensors in spacetime and non-Euclidian geometry.
The law of inertia says that a mass tends to keep its momentum constant, i.e., it resists external forces that try to change that momentum. That's what the definition of mass is. The same is true of an electromagnetic field. A steady electric current produces a steady magnetic field. If the field is changed by changing the current, it will, by Faraday's law, induce an electric field that will seek to restore the current and its field to its original valueall familiar to electrical engineers as Lenz's laws of self-inductance, mutual inductance, and so forth. Similarly, a steady electric field is produced by a steady distribution of charge. If the charge sources are moved to change the field, the resulting "displacement current" gives rise to a magnetic field, and the changing magnetic field induces an electric field that opposes the movement of the charges. This is sometimes known as the "inertia" of the electromagnetic field, manifesting an "electromagnetic momentum."
It turns out that the electromagnetic counterpart to momentum also carries precisely its counterpart to mass. The electromagnetic mass of a charged body is an additional factor by which it resists physical acceleration beyond the resistance normally exhibited by the uncharged mechanical mass. This was known to the classical physicists of the nineteenth century. It comes out as a constant that multiplies velocity to add a further parcel of momentum in the same way that regular Newtonian mass does.
At least, it does when the electric (Coulomb) field carried by the charged body is spherically symmetrical, as would be the case when it's at restand near enough when it isn't moving very fast. The direction of the electric field at any point around a charged bodythe line of voltage gradientlies perpendicular (orthogonal) to the surfaces of equipotential. For a charge at rest the equipotential surfaces are concentric spheres like the skins of an onion, across which the field lines radiate straight and symmetrically in all directions like sea-anemone spikes.
However, Maxwell's equations and the relativity principleand nothing moreindicate that when the body moves, the charge distribution will change as the charge begins to partly "catch up" with its own equipotentials, causing them to bunch up ahead and spread out behind. The result is that the orthogonal field lines are no longer straight but become curves. (This was what prompted Lorentz to conclude that electrons contract in the direction in which they move.)
Now it gets interesting. The expression for the electromagnetic mass of a body depends on the distribution of its electric field in space. When the rearrangement that takes place with increasing velocity is taken into account, the electromagnetic mass increases from its value at rest. The formula that the classical physicists of the nineteeth century derived to describe it is the same as the SRT equation for mass increase. The difference is that instead of rearranging the field distribution, SRT rearranged space and time, then applied the result to all masses, electromagnetic or mechanical, charged or neutral. It would appear that SRT's way of getting there wasn't necessary.
Page, for example showed in 1912 76 that Coulomb's law of electrostatic attraction and the Lorentz transforms are sufficient to derive Maxwell's equationsfrom which everything supporting SRT follows. But Coulomb's law is formally identical with Newton's law of gravitation. Hence, Page's method must lead to formally identical resultsa "Maxwell" law that holds for mechanical, electrically neutral mass. By this argument all mass is shown to be velocity-dependent from classical principles, invoking none of the observer-dependence of SRT. (Objection. "But it's right there in the textbooks. Force equals mass times acceleration. F = mždv/dt. Mass is a constant. You can't get away from it." Answer: "True, that's what most textbooks show. But Newton never said it. His force was always given by the change in momentum: d(mžv)/dt. It allowed for the possibility of mass being velocity dependent. Mark of a careful scientist.") And since both masses, neutral and electromagnetic, respond to velocity in the same way, they can be combined into a single inertial reactiona force that resists changes in momentumincreasing with velocity. There's nothing especially remarkable about velocity-dependent forces. Hydraulic friction and aerodynamic drag are everyday examples.
When the mass expressed as a function of c is used to calculate the work done in accelerating a body from rest to velocity v, the resulting expression for kinetic energy reduces to the familiar 1/2mv2 when v is small. At rest, a residual energy E0 remains that's related to the mass m0 by, yes, you've guessed, E0 = m0žc2. You can do it without Einstein.
In his book Einstein Plus Two Beckmann goes on to show that all of the experiments usually cited as confirming the Einsteinian formulas for mass, energy, and momentum are equally consistent with the field-referred theory. Similar arguments were presented following the publication of Einstein's original SRT paper in 1905see, for example, Lewis, 1908, which derives the velocity-dependent relationships showing mass tending to infinity as its velocity approaches that of light, from considerations of conservation when a mass is accelerated by radiation pressure.
From the theory based on the real, physical deformation of forces in motion through the locally dominant field, Beckmann is also able to derive from first principles the line spacing of the spectrum of the hydrogen atom, a first approximation to the Schrödinger equation of quantum mechanics, and the Titius-Bode series giving the distances between planetary orbits, which relativity must simply accept as given. Doesn't this make it a more powerful candidate predictively? In the latter connection, Beckmann also correctly deduces the precession of the perihelion of Mercury's orbit, usually cited as one of the decisive tests for GRT, and shows that a German by the name of Paul Gerber was able to do so using purely classical considerations in 1898, seventeen years before publication of the Einstein General Theory in 1915.
In fact, it was more in connection with the General Theory that the word "relativity" caught the world's attention. SRT didn't really create that much of a stiras mentioned earlier, Einstein's Nobel Prize was awarded for a different paper also published in 1905, on the photoelectric effect. But in 1919 it was announced that observations of the solar eclipse in the western Pacific by a team headed by the British physicist Sir Arthur Eddington had confirmed the GRT prediction of the bending of rays of starlight passing close to the Sun, which elevated Einstein to instant fame and retroactively the SRT, too, by association. Whether it was really a triumph of the magnitude popularly depicted has been questioned. Ian McCausland, for example, 77 shows that the measurements were not particularly accurate, the standard error being about 30 percent, while the various displacements ranged from half to twice what the theory predicted, and a lot of fudging went on to come up with an average of the order that was needed. But in any case, if the local gravitational field is effectively the propagating ether, the speed of a traveling disturbance will vary with its density, and the same result can be arrived at by treating it as a refractive medium in uncurved space. 78
Why have we been postulating the local gravitational field as the possible propagating medium, when everything we've been talking about refers to electromagnetics? Well, the reference frame that Beckmann's theory actually postulates is the dominant local force field. For most practical purposes it reduces to the same thing. The magnetic force between moving charges is so small compared to the electric force between them (one of those relationships like that of mass with energy, involving c2) that it can't even be measured unless the electric field is neutralized.
The example Beckmann gives to illustrate this is two lines of negative chargeselectrons, saymoving past a stationary observer like parallel columns of soldiers. The moving charges constitute currents moving in the same direction, which accordingly generate a magnetic attraction between them. But this attractive force will be completely overshadowed by the electrostatic repulsion of the charges. To reveal the magnetic effect, it's first necessary to neutralize this repulsion, which could be achieved by adding a row of stationary positive charges like fence posts along the line of march of at least one of the columns. This is exactly what happens with the ionized atoms inside a conductor. What this says is that to demonstrate a magnetic force, at least one of the currents must flow in a normally neutral conductor such as a wire.
In the macroscopic world of neutral matter that we live in and build instruments out of for investigating electromagnetic phenomena, therefore, the dominant force field that's left after the electric fields have been eliminated by positive and negative charges that neutralize each other is that of gravitation. Or perhaps we should say "almost neutralize each other." Some fascinating work is going on that interprets the gravitational force as a residual effect of electromagnetismsee, for example, Assis, 1992 and 1995. So certainly it might be the case that in other parts of the universe not dominated by neutral matter, some other definition of the local reference frame should apply.
Dr. Carl Zapffe in his A Reminder on E = mc2 interprets the phenomena usually cited as relativistic in a field-referred theory using the magnetosphere, which also defines the local frame moving with the Earthand in the process he provides three derivations using classical physics of the sanctified formula contained in the title. Plots derived from space probe data and other sources show the Earth's magnetopausethe boundary of the magnetosphereas a huge, teardrop-shaped bubble compressed to a bowshock front on the sunward side and extending outward more than ten Earth radii, around which the solar wind streams like the airflow around the body of a plane. On our planet deep inside this bubble, we've been trying assiduously for over a century to measure our airspeed with our instruments inside the cabin. Zapffe offers a model of
successively embedded domains in which the terrestrial magnetosphere riding with the Earth inside a "heliosphere," similarly formed by its motion through the larger "galactosphere," and so on.
We can conduct a conversation effortlessly with another passenger in a plane because our entire acoustic environment is moving with us. Trying it sitting out on the wing would be a different matter, swiftly disposing of any notions we might have formed that air doesn't exist. It might be revealing to perform experiments along the lines of Michelson-Morley on a space platform outside the Earth's magnetosphere, under conditions that have never been tested before, in motion relative to the local frame as defined by the Sun.
When we're assured of something to the effect that "relativity is confirmed routinely in laboratories all around the world thousands of times every day," one of the instances usually cited is the verifying of time dilation. The example given earlier was of muon decay, where more muons from the upper atmosphere survive long enough to reach the ground than should be able to. According to relativity, it's because time in the muon's moving frame runs slower than the time in the observer's frame, which includes the ground, the atmosphere, and the whole of the path followed in the particle's flight down. But a crucial question isn't being asked about another possible state of affairs that would produce the same result.
Is some semi-abstract quantity called "time" actually being dilated? Or is it simply that a difference in the internal dynamics (increased mass, for example) of moving clocksmeaning time-varying processes in generalmakes them run slower? What's the difference? The difference is fundamental if by "moving" we mean with respect to some privileged reference frame such as a general Lorentzian ether, the local gravity field, or whatever. Simply put, a clock moving in that frame runs slowera physical reality, not some trick of appearances or mathematical acrobaticsthan a clock that's at rest in it. The laboratory is at rest in the Earth's frame while the muon isn't, and so the muon's clock actually runs slower.
As an illustration of the principle (one which has nothing to do with relativity), consider an ordinary pendulum clock being flown around the world in an eastbound direction. The rate of a pendulum clock depends on g, the acceleration due to gravity. The Earth's rotation generates an upward centrifugal force that acts against g, reducing it slightly. Since an eastbound clock is adding to the Earth's rotation speed, this effect will be increased, causing the airborne clock to run marginally slower. This isn't due to time in the aircraft "dilating," but a real, physical effect arising from its motion. Hayden discusses this distinction and provides references to relevant experiments. 79
This is also the answer that LET or field-referred-type theories give to the famous "twins paradox," where two young twins are separated by a motion that can be regarded as symmetrical and then reunited, upon which one or the other or neither is found to be older, depending which argument you buy.
"One's frame had to be accelerated somehow in order to bring them back together again, and therein lies the difference," runs one line. Response: "But the difference in ages increases with the time that the traveling one has been traveling. Yet exactly the same process of stopping and reversing will eventually return him whatever the duration of the trip. How can the same acceleration sequence cause different results?"
"It's the reversal of direction of one of them that does it. Even with the ingenious arrangements that have been proposed for effectively synchronizing oppositely moving, constant-speed conveyors." 80 Response: "But the SRT equations don't anything about direction. They only involve velocity."
"Acceleration is involved one way or the other, so SRT doesn't apply. You need to go to GRT." Response: "So why was it given as an example of an SRT effect in the first place?"
And so it goes. The debate has gone on for as long as the theory of relativity has existed. Careers have been toppled by it. 81 According to LET and its equivalents, the twin who does the most moving through the preferred reference frame (or the local preferred frames at the places he passed through) will age more, and that's the end of it.
In principle there is a way to resolve this. Going back to the muon, relativity says that only the velocity with respect to the observer matters, so the muon is just as entitled to argue that it's the laboratory that's moving. Thus, by the muon's frame of reckoning, the laboratory's time should be running slower. What we need is an observer sitting on the muon as it passes through the lab to tell us once and for all if the laboratory clock runs faster (Lorentz, Beckmann, field-referred) or slower (Einstein). This has never been done, of course. But eventually the ingenuity of experimenters will no doubt come up with an equivalent.
Perhaps the closest that anyone has come to actually testing this is the Hafele-Keating experiment in 1972, where cesium atomic clocks were transported east and west in commercial jets and their rates compared to a standard on the ground at the U.S. Naval Observatory in Washington, D.C. It's not uncommon to hear the result dismissed blandly with, "The moving clocks ran slower, just as relativity says they should." And it's true that they didreferred to a fictitious standard that didn't figure anywhere in the experiment. And they did so at different rates. The fact was that relative to the stated ground reference in Washington, D.C., the westbound clock ran faster, gaining 273 nanoseconds, whereas the eastbound one lost 59 nanoseconds. In a fast-foot shuffle to accommodate this awkward state of affairs, the relativists decided that everything should be referred to a nonrotating Earth-centered frame, relative to which everything was moving east, and hence it was possible to describe the three clocks as moving "slow" (westbound), "slower" (Washington, D.C.), and "slowest" (eastbound). But that still doesn't rescue the theory, which says, clearly, that as far as Washington, D.C., is concerned, as with any observer, lightspeed is constant and moving clocks are slowed irrespective of direction. Those who regard the clocks as moving with regard to an absolute local reference have no problem. Apparently, R. L. Keating himself was surprised by the result 82 but accepted the explanation that astronomers always use the Earth's frame for local phenomena. But they use a solar barycentric frame for other planetary phenomena in order to get results that agree with relativity. Interesting, eh?