Kicking the Sacred Cow

by James P. Hogan

  Another thought was that whenever light was transmitted through a material medium, this medium provided the local privileged frame in which c applied. Within the atmosphere of the Earth, therefore, the speed of light should be constant with respect to the Earth-centered frame. But this runs into logical problems. For suppose that light were to go from one medium into another moving relative to the first. The speeds in the two domains are different, each being determined by the type of medium and their relative motion. Now imagine that the two media are progressively rarified to the point of becoming a vacuum. The interaction between matter and radiation would become less and less, shown as a steady reduction of such effects as refraction and scattering to the point of vanishing, but the sudden jump in velocity would still remain without apparent cause, which is surely untenable.

  Once again, experimental evidence proved negative. For one thing, there was the phenomenon of stellar aberration, known since James Bradley's report to Newton's friend Edmond Halley, in 1728. Bradley found that in the course of a year the apparent position of a distant star describes an ellipse around a fixed point denoting where it "really" is. The effect results from the Earth's velocity in its orbit around the Sun, which makes it necessary to offset the telescope angle slightly from the correct direction to the star in order to allow for the telescope's forward movement while the light is traveling down its length. It's the same as having to tilt an umbrella when running, and the vertically falling rain appears to be coming down at a slant. If the incoming light were swept along with the atmosphere as it entered (analogous to the rain cloud moving with us), the effect wouldn't be observed. This was greeted by some as vindicating the corpuscular theory, but it turns out that the same result can be derived from wave considerations too, although not as simply. And in similar vein, experiments such as that of Armand Fizeau (1851), which measured the speed of light through fast-flowing liquid in a pipe, and Sir George Airy (1871), who repeated Bradley's experiment using a telescope filled with water and showed aberration didn't arise in the telescope tube, demonstrated that the velocity of light in a moving medium could not be obtained by simple addition in the way of airplanes and machine-gun bullets or as a consequence of being dragged by the medium.

  Relativity is able to provide interpretations of these results—indeed, the theory would have had a short life if it couldn't. But the claim that relativity is thereby "proved" isn't justified. As the Dutch astronomer M. Hoek showed as early as 1868, attempts at using a moving material medium to measure a change in the velocity of light are defeated by the effect of refraction, which cancels out the effects of the motion. 66

  Michelson, Morely, and the Ether That Wasn't

  These factors suggested that the speed of light was independent of the motion of the radiation source and of the transmitting medium. It seemed, then, that the only recourse was to abandon the relativity principle and conclude that there was after all a privileged, universal, inertial reference frame in which the speed of light was the same in all directions as the simplest form of the laws required, and that the laws derived in all other frames would show a departure from this ideal. The Earth itself cannot be this privileged frame, since it is under constant gravitational acceleration by the Sun (circular motion, even at constant speed, involves a continual change of direction, which constitutes an acceleration) and thus is not an inertial frame. And even if at some point its motion coincided with the privileged frame, six months later its orbit would have carried it around to a point where it was moving with double its orbital speed with respect to it. In any case, whichever inertial frame was the privileged one, sensitive enough measurements of the speed of light in orthogonal directions in space, continued over six months, should be capable of detecting the Earth's motion with respect to it.

  Many interpreted this universal frame as the hypothetical "ether" that had been speculated about long before Maxwell's electromagnetic theory, when experiments began revealing the wave nature of light. If light consisted of waves, it seemed there needed to be something present to be doing the "waving"—analogous to the water that carries ocean waves, the air that conducts sound waves, and so on. The eighteenth to early nineteenth centuries saw great progress in the development of mathematics that dealt with deformation and stresses in continuous solids, and early notions of the ether sought an interpretation in mechanical terms. It was visualized as a substance pervading all space, being highly rigid in order to propagate waves at such enormous velocity, yet tenuous enough not to impede the motions of planets. Maxwell's investigations began with models of fields impressed upon a mechanical ether, but the analogy proved cumbersome and he subsequently dispensed with it to regard the field itself as the underlying physical reality. Nevertheless, that didn't rule out the possibility that an "ether" of some peculiar nature might still exist. Perhaps, some concluded, the universal frame was none other than that within which the ether was at rest. So detection of motion with respect to it could be thought of as measuring the "ether wind" created by the Earth's passage through it in its movement through space.

  The famous experiment that put this to the test, repeated and refined in innumerable forms since, was performed in 1887 by Albert Michelson and Edward Morley. The principle, essentially, was the same as comparing the round-trip times for a swimmer first crossing a river and back, in each case having to aim upstream of the destination in order to compensate for the current, and second covering the same distance against the current and then returning with it. The times will not be the same, and from the differences the speed of the current can be calculated. The outcome was one of the most famous null results in history. No motion through an ether was detected. No preferred inertial reference frame could be identified that singled itself out from all the others in any way.

  So now we have a conundrum. The elaborate experimental attempts to detect a preferred reference frame indicated an acceptance that the relativity principle might have to be abandoned for electromagnetism. But the experimental results failed to identify the absolute reference frame that this willingness allowed. The laws of electromagnetism themselves had proved strikingly successful in predicting the existence of propagating waves, their velocity and other quantities, and appeared to be on solid ground. And yet an incompatibility existed in that they were not covariant under the classical transforms of space and time coordinates between inertial frames. The only thing left to question, therefore, was the process involving the transformations themselves.

  Lorentz's Transforms for Electromagnetics

  Around the turn of the twentieth century the Dutch theoretical physicist Hendrick Lorentz followed the path of seeking alternative transformation laws that would do for electromagnetics what the classical transforms had done for mechanics. Two assumptions that few people would question were implicit in the form of the Galilean transforms: (1) that observers in all frames will measure time the same, as if by some universal clock that ticks the same everywhere; and (2) while the space coordinates assigned to points on a rigid body such as a measuring rod might differ, the distance between them would not. In other words, time intervals and lengths were invariant.

  In the Lorentz Transforms, as they came to be called, this was no longer so. Time intervals and lengths measured by an observer in one inertial frame, when transformed to another frame, needed to be modified by a factor that depended on the relative motion between them. Lorentz's system retained the notion of an absolute frame in which the ether is at rest. But the new transforms resulted in distances being reduced in the direction of motion relative to it, and it was this fact which, through an unfortunate coincidence of effects, made detection of the motion unobservable. As a matter of fact, an actual physical shrinkage of precisely this form—the "Fitzgerald Contraction"—had been proposed to explain the Michelson-Morley result as due to a shortening of the interferometer arms in the affected direction. Some textbook writers are of the opinion that Lorentz himself took the contractions as real; others, that he used them simply
as mathematical formalisms, symbolizing, as it were, some fictitious realm of space and time that applied to electromagnetic phenomena. I don't claim to know what Lorentz thought. But here was a system which acknowledged a preferred frame as required by Maxwell's equations (defined by the constancy of c), yet at the same time observed the relativity that the optical experiment seemed to demand. Okay, maybe things were a bit messy in that a different system applied to mechanics. But everything more or less worked, and maybe that was just the way things from now on would have to be.

  Except that somebody called Albert Einstein wasn't happy with it.

  The New Relativity

  Einstein: Transforming All of Physics

  Neither mechanics nor—regardless of the constant in Maxwell's equations— electromagnetics had revealed an absolute frame of reference. All experiments seemed to indicate that any inertial frame was as good as another. What this suggested to Einstein was that some kind of relativity principle was in evidence that applied across the whole of science, according to which physics should be the same for all observers. Or putting it another way, the equations expressing all physical laws should be covariant between inertial frames. Following Lorentz, but with an aim that was general and not restricted to a subset of physics, Einstein set out to discover a system of transforms that would make this true. Two postulates formed his starting point. (1) The relativity principle applies for all of physics across all inertial frames, which was what the intuitively satisfying solution he was searching for required. (2) The velocity of light, c, is the same for observers in all inertial frames regardless of their state of motion relative to each other. For that's what Maxwell's equations said, and being a physical law, it had to apply in all frames for (1) to be true.

  And what he did in his paper on special relativity, published in 1905, was rediscover the Lorentz Transforms. This was hardly surprising, since they gave the right answers for electromagnetism—hence anything saying otherwise would have been wrong. But there was a crucial difference. Whereas Lorentz's application of them had been restricted to the special area of electromagnetism, Einstein maintained that they applied to everything—mechanics as well.

  But, wait a minute. If the relativity principle was to be observed, and the new transforms applied, how could they still be compatible with Newton's long-established mechanics, which was enthroned as being consistent with the classical Galilean transforms, not with the new Lorentzian ones?

  The only answer could be that Newtonian mechanics wasn't as invincibly established as everyone thought it was. Recall the two assumptions we mentioned earlier that the Galilean transforms imply: that space and time intervals are invariant. What Einstein proposed was that the velocity-dependencies deduced by Lorentz were not part of some fudge-factor needed for electromagnetism, but that they expressed fundamental properties of the nature of space and time that were true universally, and hence called for a revision of mechanics. However, the new mechanics could hardly render invalid the classical results that centuries of experimenting had so strongly supported. And indeed, this turned out to be so; at the low velocities that classical science had been confined to, and which shape the common sense of everyday experience, the equations of the new mechanics merged into and became indistinguishable for all practical purposes from the Newtonian ones.

  Relativity's Weird Results

  Where the two systems began departing significantly was when very high velocities were involved—of the order of those encountered in electromagnetism and late-nineteenth-century experiments on fast-moving particles, where it had already become clear that classical mechanics couldn't be correct. Space and time were no longer fixed and unchanging but behaved weirdly at extremes of velocity that everyday experience provided no schooling for, with consequences that Newtonian mechanics hadn't anticipated. These are well-enough known now to require no more than that they be listed. All have been verified by experiment.

  Addition of velocities. In classical mechanics, a bullet fired from an airplane will hit a target on the ground ahead with a velocity equal to that of the plane relative to the ground plus that of the bullet relative to the plane. But according to relativity (henceforth the "special relativity theory," or "SRT"), what appears to be obvious isn't exactly so. The velocity in the target's frame doesn't equal the sum of the two components—although at the speeds of planes and bullets you'd never notice the difference. The higher the velocities, the greater the discrepancy, the relationship being such that the bullet's velocity in the target's frame never manages to exceed c, the speed of light. Thus even if the plane is coming in at 90% c and fires a bullet that leaves the plane at 90% c, the bullet's velocity measured by the target will be 90% c plus something, but not greater than c itself. (In fact it will be 99.45% c.) In the limit, when the bullet leaves the plane at c, the resultant, bizarre as it sounds, is still c. It has become a photon of light. Its speed is the same in both the frame of the airplane (source) and that of the target (receiver). Add two velocities—or as many as you like—each equal to c, and the result still comes out at c. And that's what all the Michelson-Morley-type experiments confirm.

  Relativity of simultaneity. The upper limit on velocity makes it impossible to devise a method for synchronizing clocks in a way that enables different frames to agree on whether two events happen simultaneously. Some arbitrary frame could be chosen as a reference, of course—such as the Sun-centered frame—and a correction applied to decide if two events were simultaneous as far as that frame was concerned, but it wouldn't mean much. One person's idea of simultaneity would still be no better or worse than any other's, and the term loses any real significance. Establishing absolute simultaneity without a privileged frame would require an infinitely fast synchronizing signal, which SRT says we don't have.

  Mass increase. Mass measures the amount of resistance that an object exhibits to being accelerated—that is, having its state of motion (speed and/or direction) changed. A cannon ball has a large mass compared to a soccer ball of the same size, as kicking or trying to stop one of each will verify. Though unobservable at everyday levels, this resistance to being accelerated increases as an object moves with higher speed. In particle accelerators, far more energy is required to nudge the velocity of a particle an additional tenth of a percent c faster when it is already moving at, say, 90% c than to accelerate it the first tenth of a percent from rest.

  Mass-energy equivalence. As the velocity of a body increases, it stores more kinetic energy. From the preceding paragraph, it also exhibits an increase in mass. This turns out to be more than just coincidence, for according to relativity mass and energy become equivalent and can be converted one into the other. This is true even of the residual mass of an object not moving at all, which still has the energy equivalent given by the famous equation E = m0 c2, where E is the energy and m0 the object's mass when at rest. All energy transitions thus involve changes in mass, but the effect is usually noticeable only in nuclear processes such as the mass deficit of particles bound into a nucleus or the yield of fission and fusion bombs; also the mass-energy balances observed in particle creation and annihilation events.

  Time dilation. Time, and hence processes that are time-dependent, runs slower in a moving frame than in one at relative rest. An example is the extended lifetimes shown by muons created by bombardment of the upper atmosphere by protons from the Sun. The muons reach the Earth's surface in numbers about nine times greater than their natural decay time (half-life 2.2 microseconds) says they should. This is explained by time in the muon's moving frame being dilated as measured from the surface, giving a longer decay period than would be experienced by a muon at rest. High-accuracy clocks on rocket sleds run slower than stationary clocks.

  The mathematician Hermann Minkowski developed the Einstein theory further by showing that it entailed a reality consisting not of the three-dimensional space and separate time that are ordinarily perceived, but of a strange, non-Euclidian, four-dimensional merging of the two known since as
spacetime. Only from the local standpoint of a particular Galilean frame do they separate out into the space and time of everyday life. But the space and time that they resolve into is different in different frames—which is what the transforms of SRT are saying.

  Unifying Physics

  Although many might remain unconvinced, this kind of thing is what scientists regard as a simplification. When phenomena that were previously thought to be distinct and independent—such as space and time in the foregoing—turn out to be just different aspects of some more fundamental entity, understanding of what's going on is deepened even if the techniques for unraveling that understanding take some work in getting used to. In the same kind of way, momentum and energy become unified in the new four-dimensional world, as do the classical concepts of force and work, and electric current and charge.

  This also throws light (pun unintended, but not bad so I'll let it stand) on the interdependence of the electric and magnetic field quantities in Maxwell's equations. In Maxwell's classical three-dimensional space the electromagnetic field is formed from the superposition of an electric field, which is a vector field, and a magnetic field, which is a tensor field. In Minkowski's spacetime these merge into a single four-dimensional tensor called the electromagnetic tensor, and the four three-dimensional equations that Maxwell needed to describe the relationships reduce to two four-dimensional ones. Hence the interdependence of electric and magnetic fields, which in the classical view had to be simply accepted as a fact of experience, becomes an immediate consequence of their being partial aspects of the same underlying electromagnetic entity.