Kicking the Sacred Cow

by James P. Hogan

  Or is there?

  Maybe there's some kind of a Freudian slip at work when the cardinals of the modern Church of Cosmology make repeated allusions to "glimpsing the mind of God" in their writings, and christen one of their exotic theoretical creations the "God Particle."

  The servant, Mathematics, who was turned into a god, created the modern cosmos and reveals Truth in an arcane language of symbols accessible only to the chosen, promising ultimate fulfillment with the enlightenment to come with the promised day of the Theory of Everything.

  To be told that if they looked through the telescope at what's really out there, they'd see that the creator they had deified really wasn't necessary, would make the professors very edgy and angry indeed.

  THREE

  Drifting in the Ether

  Did Relativity Take A Wrong Turn?

  Nature and Nature's laws lay hid in night: God said Let Newton be! And all was light.

  — Alexander Pope. Epitaph intended for Sir Isaac Newton

  It did not last. The Devil, shouting, Ho! Let Einstein be! restored the status quo.

  — Unknown

  It is generally held that few things could be more solidly grounded than Einstein's theory of relativity which, along with quantum mechanics, is usually cited as one of the twin pillars supporting modern physics. Questioning is a risky business, since it's a subject that attracts cranks in swarms. Nevertheless, a sizeable body of well-qualified, far-from-crankish opinion exists which feels that the edifice may have serious cracks in its foundations. So, carried forth by the touch of recklessness that comes with Irish genes, and not having any prestigious academic or professional image to anguish about, I'll risk being branded as of the swarms by sharing some of the things that my wanderings have led me to in connection with the subject.

  The objections are not so much to the effect that relativity is "wrong." As we're endlessly being reminded, the results of countless experiments are in accord with the predictions of its equations, and that's a difficult thing to argue with. But neither was Ptolemy's model of the planetary system "wrong," in the sense that if you want to make the Earth the center of everything you're free to, and the resulting concoction of epicycles within epicycles correctly describes the heavenly motions as seen from that vantage point. Coming up with a manageable force law to account for them, however, would be monumentally close to an impossibility. 63 Put the Sun at the center, however, and the confusion reduces to a simplicity that reveals Keplerian order in a form that Newton was able to explain concisely in a way that was intuitively satisfying, and three hundred years of dazzlingly fruitful scientific unification followed.

  In the same kind of way, critics of relativity maintain that the premises relativity is founded on, although enabling procedures to be formulated that correctly predict experimental results, nevertheless involve needlessly complicated interpretations of the way things are. At best this can only impede understanding of the kind that would lead to another explosion of enlightenment reminiscent of that following the Newtonian revolution. In other words, while the experimental results obtained to date are consistent with relativity, they do not prove relativity in the way we are constantly being assured, because they are not unique to the system that follows from relativity's assumptions. Other interpretations have been proposed that are compatible with all the cited observations, but which are conceptually and mathematically simpler. Moreover, in some cases they turn out to be more powerful predictively, able to derive from basic principles quantities that relativity can only accept as givens. According to the criteria that textbooks and advocates for the scientific method tell us are the things to go by, these should be the distinguishing features of a preferred theory.

  However, when the subject has become enshrined as a doctrine founded by a canonized saint, it's not quite that simple. The heliocentric ideas of Copernicus had the same thing going for them too, but he circulated them only among a few trusted friends until he was persuaded to publish in 1543, after which he became ill and died. What might have happened otherwise is sobering to speculate. Giordano Bruno was burned at the stake in 1600 for combining similar thoughts with indiscreet politics. The Copernican theory was opposed by Protestant leaders as being contrary to Scriptural teachings and declared erroneous by the Roman Inquisition in 1616. Galileo was still being silenced as late as 1633, although by then heliocentricism was already implicit in Kepler's laws, enunciated between 1609 and 1619. It wasn't until 1687, almost a century and a half after Copernicus's death, that the simpler yet more-embracing explanation, unburdened of dogma and preconceptions, was recognized openly with the acceptance of Newton's Principia.

  Fortunately, the passions loosed in such issues seem to have abated somewhat since those earlier times. I experienced a case personally at a conference some years ago, when I asked a well-known physicist if he'd gotten around to looking at a book I'd referred him to on an alternative interpretation to relativity, written by the late Czech professor of electrical engineering Petr Beckmann 64 (of whom, more later). Although a friend of many years, his face hardened and changed before my eyes. "I have not read the book," he replied tightly. "I have no intention of reading the book. Einstein cannot be wrong, and that's the end of the matter."

  Some Basics

  Reference Frames and Transforms

  The principle of relativity is not in itself new or something strange and unfamiliar, but goes back to the physics of Galileo and Newton. It expresses the common experience that some aspects of the world look different to observers who are in motion relative to each other. Thus, somebody on the ground following a bomb released from an aircraft will watch it describe a steepening curve (in fact, part of an ellipse) in response to gravity, while the bomb aimer in the plane (ignoring air resistance) sees it as accelerating on a straight line vertically downward. Similarly, they will perceive different forms for the path followed by a shell fired upward at the plane and measure different values for the shell's velocity at a given point along it.

  So who's correct? It doesn't take much to see that they both are when speaking in terms of their own particular viewpoint. Just as the inhabitants of Seattle and Los Angeles are both correct in stating that San Francisco lies to the south and north respectively, the observers on the ground and in the plane arrive at different but equally valid conclusions relative to their own frame of reference. A frame of reference is simply a system of x, y, and z coordinates and a clock for measuring where and when an event happens. In the above case, the first frame rests with the ground; the other moves with the plane. Given the mathematical equation that describes the bomb's motion in one frame, it's a straightforward process to express it in the form it would take in the other frame. Procedures for transforming events from the coordinates of one reference frame to the coordinates of another are called, logically enough, coordinate transforms.

  On the other hand, there are some quantities about which the two observers will agree. They will both infer the same size and weight for the bomb, for example, and the times at which it was released and impacted. Quantities that remain unvarying when a transform is applied are said to be "invariant" with respect to the transform in question.

  Actually, in saying that the bomb aimer in the above example would see the bomb falling in a straight line, I sneaked in an assumption (apart from ignoring air resistance) that needs to be made explicit. I assumed the plane to be moving in a straight line and at constant speed with respect to the ground. If the plane were pulling out of a dive or turning to evade ground fire, the part-ellipse that the ground observer sees would transform into something very different when measured within the reference frame gyrating with the aircraft, and the bomb aimer would have to come up with something more elaborate than a simple accelerating force due to gravity to account for it.

  But provided the condition is satisfied in which the plane moves smoothly along a straight line when referred to the ground, the two observers will agree on another thing too. Although their interpreta
tions of the precise motion of the bomb differ, they will still conclude that it results from a constant force acting in a fixed direction on a given mass. Hence, the laws governing the motions of bodies will still be the same. In fact they will be Newton's familiar Laws of Motion. This is another way of saying that the equations that express the laws remain in the same form, even though the terms contained in them (specific coordinate readings and times) are not themselves invariant. Equations preserved in this way are said to be covariant with respect to the transformation in question. Thus, Newton's Laws of Motion are covariant with respect to transforms between two reference frames moving relative to one another uniformly in a straight line. And since any airplane's frame is as good as another's, we can generalize this to all frames moving uniformly in straight lines relative to each other. There's nothing special about the frame that's attached to the ground. We're accustomed to thinking of the ground frame as having zero velocity, but that's just a convention. The bomb aimer would be equally justified in considering his own frame at rest and the ground moving in the opposite direction.

  Inertial Frames

  Out of all the orbiting, spinning, oscillating, tumbling frames we can conceive as moving with the various objects, real and imaginable, that fill the universe, what we've done is identify a particular set of frames within which all observers will deduce the same laws of motion, expressed in their simplest form. (Even so, it took two thousand years after Aristotle to figure them out.) The reason this is so follows from one crucial factor that all of the observers will agree on: Bodies not acted upon by a force of any kind will continue to exist in a state of rest or uniform motion in a straight line—even though what constitutes "rest," and which particular straight line we're talking about, may differ from one observer to another. In fact, this is a statement of Newton's first law, known as the law of inertia. Frames in which it holds true are called, accordingly, "inertial frames," or "Galilean frames." What distinguishes them is that there is no relative acceleration or rotation between them. To an observer situated in one of them, very distant objects such as the stars appear to be at rest (unlike from the rotating Earth, for example). The procedures for converting equations of motion from one inertial frame to another are known as Galilean transforms. Newton's laws of motion are covariant with respect to Galilean transforms.

  And, indeed, far more than just the laws of motion. For as the science of the eighteenth and nineteenth centuries progressed, the mechanics of point masses was extended to describe gravitation, electrostatics, the behavior of rigid bodies, then of continuous deformable media, and so to fluids and things like kinetic theories of heat. Laws derived from mechanics, such as the conservation of energy, momentum, and angular momentum, were found to be covariant with respect to Galilean transforms and afforded the mechanistic foundations of classical science. Since the laws formulated in any Galilean frame came out the same, it followed that no mechanical experiment could differentiate one frame from another or single out one of them as "preferred" by being at rest in absolute space. This expresses the principle of "Galilean-Newtonian Relativity." With the classical laws of mechanics, the Galilean transformations, and the principle of Newtonian relativity mutually consistent, the whole of science seemed at last to have been integrated into a common understanding that was intellectually satisfying and complete.

  Extending Classical Relativity

  Problems with Electrodynamics

  As the quotation at the beginning of this section says, it couldn't last. To begin with, the new science of electrostatics appeared to be an analog of gravitation, with the added feature that electrical charges could repel as well as attract. The equations for electrical force were of the same form as Newton's gravitational law, known to be covariant under Galilean transform, and it was expected that the same would apply. However, as the work of people like André-Marie Ampère, Michael Faraday, and Hans Christian Oersted progressed from electrostatics to electrodynamics, the study of electrical entities in motion, it became apparent that the situation was more complicated. Interactions between magnetic fields and electric charges produced forces acting in directions other than the straight connecting line between the sources, and which, unlike the case in gravitation and electrostatics, depended on the velocity of the charged body as well as its position. Since a velocity in one inertial frame can always be made zero in a different frame, this seemed to imply that under the classical transformations a force would exist in one that didn't exist in the other. And since force causes mass to accelerate, an acceleration could be produced in one frame but not in the other when the frames themselves were not accelerating relative to each other—which made no sense. The solution adopted initially was simply to exclude electrodynamics from the principle of classical relativity until the phenomena were better understood.

  But things got worse, not better. James Clerk Maxwell's celebrated equations, developed in the period 1860–64, express concisely yet comprehensively the connection between electric and magnetic quantities that the various experiments up to that time had established, and the manner in which they affect each other across intervening space. (Actually, Wilhelm Weber and Neumann derived a version of the same laws somewhat earlier, but their work was considered suspect on grounds, later shown to be erroneous, that it violated the principle of conservation of energy, and it's Maxwell who is remembered.) In Maxwell's treatment, electrical and magnetic effects appear as aspects of a combined "electromagnetic field"—the concept of a field pervading the space around a charged or magnetized object having been introduced by Faraday—and it was by means of disturbances propagated through this field that electrically interacting objects influenced each other.

  An electron is an example of a charged object. A moving charge constitutes an electric current, which gives rise to a magnetic field. An accelerating charge produces a changing magnetic field, which in turn creates an electric field, and the combined electromagnetic disturbance radiating out across space would produce forces on other charges that it encountered, setting them in motion—a bit like jiggling a floating cork up and down in the water and creating ripples that spread out and jiggle other corks floating some distance away. A way of achieving this would be by using a tuned electrical circuit to make electrons surge back and forth along an antenna wire, causing sympathetic charge movements (i.e., currents) in a receiving antenna, which of course is the basis of radio. Another example is light, where the frequencies involved are much higher, resulting from the transitions of electrons between orbits within atoms rather than oscillations in an electrical circuit.

  Maxwell's Constant Velocity

  The difficulty that marred the comforting picture of science that had been coming together up until then was that the equations gave a velocity of propagation that depended only on the electrical properties of the medium through which the disturbance traveled, and was the same in every direction. In the absence of matter, i.e., in empty space, this came out at 300,000 kilometers per second and was designated by c, now known to be the velocity of light. But the appearance of this value in the laws of electromagnetism meant that the laws were not covariant under Galilean transforms between inertial frames. For under the transformation rules, in the same way that our airplane's velocity earlier would reduce to zero if measured in the bomb aimer's reference frame, or double if measured in the frame of another plane going the opposite way, the same constant velocity (depending only on electrical constants pertaining to the medium) couldn't be true in all of them. If Maxwell's equations were to be accepted, it seemed there could only exist one "absolute" frame of reference in which the laws took their standard, simplest form. Any frame moving with respect to it, even an inertial frame, would have to be considered "less privileged."

  Putting it another way, the laws of electromagnetism, the classical Galilean transforms of space and time coordinates, and the principle of Newtonian relativity, were not compatible. Hence the elegance and aesthetic appeal that had been found to apply for mechanics d
idn't extend to the whole of science. The sense of completeness that science had been seeking for centuries seemed to have evaporated practically as soon as it was found. This was not very intellectually satisfying at all.

  One attempt at a way out, the "ballistic theory," hypothesized the speed of light (from now on taken as representing electromagnetic radiation in general) as constant with respect to the source. Its speed as measured in other frames would then appear greater or less in the same way as that of bullets fired from a moving airplane. Such a notion was incompatible with a field theory of light, in which disturbances propagate at a characteristic rate that has nothing to do with the movement of their sources, and was reminiscent of the corpuscular theory that interference experiments were thought to have laid to rest. But it was consistent with the relativity principle: Light speed would transform from one inertial frame, that of the source, to any other just like the velocity of a regular material body.

  However, observations ruled it out. In binary star systems, for example, where one star is approaching and the other receding, the light emitted would arrive at different times, resulting in distortions that should have been unmistakable but which were not observed. A series of laboratory experiments 65 also told against a ballistic explanation. The decisive one was probably one with revolving mirrors conducted by A. A. Michelson in 1913, which also effectively negated an ingenious suggestion that lenses and mirrors might reradiate incident light at velocity c with respect to themselves—a possibility that the more orthodox experiments hadn't taken into account.