In SRT, Minkowski's four-dimensional spacetime is considered to be "flat"—uncurved, like the classical Euclidian space of Newton. An object's "world-line"—the path showing its history in spacetime—will be a straight line when the object is in a state of rest or uniform motion. What differentiates accelerating frames is that their world-lines become curved. In developing his general theory of relativity (GRT), Einstein sought to remove the restriction of inertial frames and extend the principle to frames in general. In doing so he proposed that a region of space subject to gravitation is really no different from a reference frame undergoing acceleration. Inside an elevator, for example, there's no way of telling if a pen falling to the floor does so because the elevator is accelerating upward or because the floor is attracting it downward. 67
If a gravitational field is equivalent to acceleration, motions associated with it will also be represented by curved world-lines in spacetime. Hence, in GRT gravitation is interpreted geometrically. Instead of somehow attracting bodies like planets to move in curved paths through flat space, the presence of the Sun's mass itself warps the geometry of spacetime such that the paths they naturally follow become curved. An analogy often used to illustrate this is a stretched rubber sheet, representing undeformed space. Placing a heavy object like a bowling ball on the sheet creates a "well," with sides steepening toward the center, that the ball sits in, but which would be indiscernible to a viewer vertically above who had no knowledge of a dimension extending in that direction. If a marble is now rolled across the sheet, its trajectory will be deflected exactly as if the sheet were flat and the ball exerted an attraction. In the absence of any friction, the marble could be trapped in a closed path where the tendencies to fall down the well and to be lifted out of it by centrifugal force balance, causing it to orbit the bowling ball endlessly.
If spacetime itself is curved in the vicinity of masses, then not just massive objects but anything that moves through space will also follow paths determined by the nonflat geometry. So stars, for instance, should "attract" light, not just material bodies. That this is so is verified by the observed deflection of starlight passing close to the Sun. So once again, all forms of energy exhibit the equivalence to a property of mass.
Finally we're back to a situation where we have the principle of relativity, a universal statement of the laws of physics (the new mechanics, which subsumes electrodynamics), and a system of transformations that are mutually consistent. Science has been integrated into a common understanding that's found to be intellectually satisfying and complete. Its successes are celebrated practically universally as the crowning achievement of twentieth-century science. So what are some people saying is wrong with it?
Dissident Viewpoints
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.
Elegant, Yes. But Is It Really Useful?
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.
Lorentz's Ether Revisited
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 space—or ether in the context of the present discussion�
�defined 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
Entraining the Ether
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 detected—at least not by present methods—from 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 resolvably—in 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.
Field-Referred Theories
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 premises—that the speed of light is constant with respect to all observers everywhere—is 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 other—like 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.
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