Borderlands of Science

by Charles Sheffield

  THE NEW PHYSICS: THE SPEED OF

  LIGHTNESS, CURVED SPACE,

  AND OTHER HERESIES

  Listwolme is a small world with a thin but permanently cloudy atmosphere. The inhabitants have never seen the stars, nor become aware of anything beyond their own planet. There is one main center of civilization which confined itself to a small region of the surface until about a hundred years ago, when an industrial revolution took place. For the first time, rapid transportation over substantial areas of the planet became possible.

  Orbital velocity at the surface of Listwolme is less than two kilometers a second. The meetings of the Listwolme Scientific Academy following the development of highvelocity surface vehicles are chronicled below. The highlights of those meetings were undoubtedly the famous exchanges between Professor Nessitor and Professor Spottipon.

  The first debate: In which Professor Nessitor reveals the curious results of his experiments with high-speed vehicles, and proposes a daring hypothesis.

  Nessitor: As Members of the Academy will recall, a few months ago I began to install sensitive measuring devices aboard the Tristee Two, the first vehicle to move at a speed more than ten times that of a running schmitzpoof. The work was not easy, because it was first necessary to suppress all vibration induced by the car's contact with the surface.

  One month ago we achieved the right combination of smooth suspension and vibration damping. It was with some excitement that I placed one of our instruments, a sensitive spring balance, within the vehicle and we began steadily to increase our speed. As you may have heard, there have been reports of "feeling light" from the drivers of these cars when they go at maximum velocity.

  Fellow scientists, those feelings are no illusion! Our instruments showed a definite decrease in load on the balance as our speed was increased. There is a relationship between weight and motion!

  (As Nessitor paused, there was a murmur of surprise and incredulity around the great hall. Professor Spottipon rose to his feet.)

  Spottipon: Professor Nessitor, your reputation is beyond question. What would arouse skepticism from another in your case is treated with great respect. But your statement is so amazing that we would like to hear more of these experiments. For example, I have heard of this "lightening" effect at high speeds, but seen no quantitative results. Were your balances sensitive enough to measure some relation between the lightness and the speed?

  Nessitor (triumphantly): With great precision. We measured the weight shown on the balance at a wide variety of speeds, and from this I have been able to deduce a precise formula between the measured weight, the original weight when the vehicle was at rest, and the speed of movement. It is as follows.

  Here Professor Nessitor went to the central display screen and sketched on it the controversial formula. It is believed that this was the first time it had ever appeared to public view. In the form that Nessitor used, it reads:

  (Weight at speed v)=(Rest weight)x(1-v2/c2)

  When the formula was exhibited there was a silence, while the others examined its implications.

  Spottipon (thoughtfully): I think I can follow the significance of most of this. But what is the constant, c, that appears in your equation?

  Nessitor: It is a velocity, a new constant of nature. Since it measures the degree to which an object is lightened when it moves with velocity v, I suggest that the basic constant, c, should be termed the "speed of lightness."

  Spottipon (incredulously): You assert that this holds anywhere on Listwolme? That your formula does not depend on the position where the experiment is conducted?

  Nessitor: That is indeed my contention. In a series of experiments at many places on the surface, the same result was obtained everywhere, with the same velocity, "c." It is almost four times as fast as our fastest car.

  (There was a long pause, during which Professor Spottipon was seen to be scribbling rapidly on a scribe pad. When he had finished his face bore a look of profound inspiration.)

  Spottipon: Professor Nessitor, the formula you have written has some strange implications. You assert that there is a lightening of weight with speed across the surface. This we might accept, but you have not taken your formula to its logical limit. Do you realize that there must be a speed when the weight vanishes? When v=c, you have a situation where an object does not push at all on the balance! Worse than that, if v exceeds your "speed of lightness" you would calculate a negative weight. If that were true, a car moving at such a speed would fly completely off the surface. You would have created the long-discussed and arguably impossible "flying machine."

  Nessitor (calmly): As Professor Spottipon has observed with his usual profound insight, the speed of lightness is a most fundamental constant. My interpretation is as follows: since it is clearly ridiculous that an object should have negative weight, the formula is trying to tell us something very deep. It is pointing out that there is no way that an object can ever exceed the speed of lightness. The speed that we can deduce from these experiments, c, represents the ultimate limit of speed that can ever be attained.

  (Sensation. The assembled scientists began to talk among themselves, some frankly disbelieving, others pulling forth their scribe pads and writing their own calculations. At last a loud voice was heard above the general hubbub.)

  Voice: Professor Nessitor! Do you have any name for this new theory of yours?

  Nessitor (shouting to be heard): I do. Since the effects depend only on the motion relative to the ground, I suggest the new results should be termed the principle of relativity. I think that . . .

  (Professor Nessitor's next comments were unfortunately lost in the general noise of the excited assembly.)

  Six months passed before Professor Nessitor appeared again at a meeting of the Academy. In those months, there had been much speculation and heated argument, with calls for more experiments. It was to an expectant but still skeptical audience that the Professor made his second address.

  Nessitor: Distinguished colleagues, last time that I was here there were calls for proof, for some fundamental basis for the formula I presented to you then. It was to answer those calls that I embarked, four months ago, on a new set of experiments with the Tristee Two vehicle. We had installed a new instrument on board our car. It measures distances very accurately, and permits the car's course to be controlled to an absolutely straight line. For it had occurred to me to ask the question, if velocity and weight are so closely linked, could it be that distance itself depends on some unknown factors?

  Spottipon (somewhat irritably): With all due respect, Nessitor, I have no idea what you mean by such a statement. Distance is distance, no matter how fast you traverse it. What could you hope to find? I hoped that you would have repeated the experiments on speed and weight.

  Nessitor: My esteemed colleague, please have patience. Permit me to tell you what happened. We set the Tristee Two to travel a long distance at various speeds. And indeed, we confirmed the speed-weight relation. At the same time, we were measuring the distance traveled. But in performing this experiment we were moving longer linear distances over the surface of Listwolme than any other scientific group had ever done.

  I therefore decided to conduct an experiment. We traveled a long distance in a certain direction, accurately measuring this with our new instrument. Then we made a half turn and proceeded far along this new line, again measuring distance all the way. Finally, we headed straight back to our original starting point, following the hypotenuse of the triangle and measuring this distance also.

  Now, we are all familiar with the Sharog-Paty Theorem that relates the lengths of the sides of a right-angled triangle.

  (Nessitor went to the central display panel and scribed the famous Sharog-Paty relation: c2=a2+b2. There was a mutter of comments from behind him.)

  Impatient voice from the audience: Why are you wasting our time with such trivia? This relation is known to every unfledged child!

  Nessitor: Exactly. But it is not what we found from ou
r measurements! On long trips—and we made many such—the Sharog-Paty relation does not hold. The further we went in our movements, the worse the fit between theory and observation.

  After some experiment, I was able to find a formula that expresses the true relation between the distances a, b, and c. It is as follows.

  (Nessitor stepped again to the display panel and wrote the second of his famous relations, in the form:

  cos(c/R)=cos(a/R)xcos(b/R)

  There was more intense study and excited scribbling in the audience. Professor Spottipon alone did not seem to share in the general stir. His thin face had gone pale, and he seemed to be in the grip of some strong private emotion. At last he rose again to his feet.)

  Spottipon: Professor, old friend and distinguished colleague. What is "R" in your equation?

  Nessitor: It is a new fundamental constant, a distance that I calculate to be about three million paces.

  Spottipon (haltingly): I have trouble saying these words, but they must be said. In some of my own work I have looked at the geometry of other surfaces than the plane. Professor Nessitor, the formula you have written there already occurs in the literature. It is the formula that governs the distance relations for the surface of a sphere. A sphere of radius R.

  Nessitor: I know. I have made a deduction from this—

  Spottipon: I beg you, do not say it!

  Nessitor: I must, although I know its danger. I understand the teachings of our church, that we live on the Great Plain of the World, in God's glorious flatness. At the same time I cannot ignore the evidence of my experiments.

  (The Great Hall had fallen completely silent. One of the recording scribes dropped a scribe pin in his excitement and received quick glares of censure. It was a few seconds before Nessitor felt able to continue. He stood there with head bowed.)

  Nessitor: Colleagues, I must say to you what Professor Spottipon with his great insight realized at once. The distance formula is identical with that for distances on a sphere. My experiments suggest that space is curved. We live not on a plane, but on the surface of an immense sphere.

  (The tension crackled around the hall. The penalty for heresy—smothering in live toads—was known to all. At last Professor Spottipon moved to Nessitor's side and placed one hand on his shoulder.)

  Spottipon: My old friend, you have been overworking. On behalf of all of us, I beg you to take a rest. This "curved space" fancy of yours is absurd—we would slide down the sides and fall off!

  (The hall rang with relieved laughter.)

  Spottipon: Even if our minds could grasp the concept of a curved space, the teachings of the Church must predominate. Go home, now, and rest until your mind is clearer.

  (Professor Nessitor was helped from the stage by kind hands. He looked dazed).

  For almost a year, the Academy met without Nessitor's presence. There were rumors of new theories, of work conducted at white heat in total seclusion. When news came that he would again attend a meeting, the community buzzed with speculation. Rumors of his heresy had spread. When he again stood before the assembly, representatives of the Church were in the audience. Professor Spottipon cast an anxious look at the Churchmen as he made Nessitor's introduction.

  Spottipon: Let me say how pleased we are, Professor Nessitor, to welcome you again to this company. I must add my personal pleasure that you have abandoned the novel but misguided ideas that you presented to us on earlier occasions. Welcome to the Academy!

  Nessitor (rising to prolonged applause, he looked nervous but determined): Thank you. I am glad to be again before this group, an assembly that has been central to my whole working life. As Professor Spottipon says, I have offered you some new ideas over the past couple of years, ideas without fundamental supporting theory. I am now in a position to offer a new and far more basic approach. Space is curved, and we live on the surface of a sphere! I can now prove it.

  Spottipon (motioning to other scientists on the stage): Quick, help me to get him out of here before it's too late.

  Nessitor (speaking quickly): The curvature of space is real, and the speed of lightness is real. But the two theories are not independent! The fundamental constants c and R are related to a third one. You know that falling bodies move with a rate of change of speed, g, the "gravitational constant." I can now prove that there is an exact relation between these things, that c2=gxR. To prove this, consider the motion of a particle around the perimeter of a circle . . .

  (The audience was groaning in dismay. Before Nessitor could speak further, friends were removing him gently but firmly from the stage. But the representatives of the church were already moving forward.)

  At his trial, two months later, Professor Nessitor recanted all his heretical views, admitting that the new theories of space and time were deluded and nonsensical. His provisional sentence of toad-smothering was commuted to a revocation of all leaping privileges. He has settled quietly to work at his home, where he is writing a book that will be published only after his death.

  And there were those present at his trial who will tell you that as Nessitor stepped down from the trial box he whispered to himself—so softly that the words may have been imagined rather than heard—"But it is round."

  CHAPTER 14

  The End of Science

  Maybe it is because we are at the turn of the century, facing the new millennium. Maybe it is because there has been no obvious big breakthrough for a couple of decades. Maybe global pessimism is the current fad. For whatever reason, several recent books have suggested that the "end of science" may be in sight.

  Their titles betray the direction of their thinking: Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature (Weinberg, 1992); The End of Physics: The Myth of a Unified Theory (Lindley, 1993); The End of Science: Facing the Limits of Knowledge and the Twilight of the Scientific Age (Horgan, 1996).

  These all suggest, in the case of the last book with considerable relish, that the great moments of science have all occurred; that scientists are now on a road of diminishing returns; and that the next hundred years will offer nothing remotely comparable to the discoveries of the last few centuries.

  Steven Weinberg is a physicist, and a great one. He would very much like to see a "theory of everything" in his lifetime. That does not mean that everything will then have been explained, only that the most basic underpinnings of everything, which he sees as the laws of fundamental physics, will have been established. He recognizes that there will be more questions to be answered, and perhaps many discoveries in other branches of science that will come to be regarded as absolutely radical and basic. But physics is nearing its final form.

  David Lindley and John Horgan are both editors, at Science magazine and Scientific American respectively. Lindley, after a careful review of the development of physics since the end of the last century, disagrees with Weinberg. He concludes that the "theory of everything will be, in precise terms, a myth. A myth is a story that makes sense within in its own terms . . . but can neither be proved nor disproved." Scientists in pursuit of a final theory are then like dogs chasing an automobile. What will they do with it if they catch it?

  Horgan takes a broader approach. He interviewed scores of eminent scientists who have made major contributions in their diverse fields. In the end, his conclusion is that, whether or not we are approaching a final theory, we are at any rate at the end of all discoveries of the most fundamental kind. The scientists of future generations will mainly be engaged in mopping-up operations.

  This tune may sound familiar. It has been heard before, notably at the end of the nineteenth century. Here is Max Planck, recalling in 1924 the advice given to him by his teacher, Philipp von Jolly, in 1874: "He portrayed to me physics as a highly developed, almost fully matured science . . . Possibly in one or another nook there would perhaps be a dust particle or a small bubble to be examined and classified, but the system as a whole stood there fairly secured, and theoretical physics approached visibly that deg
ree of perfection which, for example, geometry has had already for centuries."

  Is it more plausible now than it was then, that the end of science is in sight? And if so, what does it mean for the future of science fiction?

  As Sherlock Holmes remarked, it is a capital mistake to theorize before one has data. Let us examine the evidence.

  First, let us note that because Horgan's scientists are already recognized major figures, most of them are over sixty. None is under forty, many are over seventy, a few are well into their eighties, and several have died in the two years since the book was published. Although everyone interviewed seems as sharp as ever, there is an element of human nature at work which Horgan himself recognizes and in fact points out. Gregory Chaitin, in a discussion with Richard Feynman, said he thought that science was just beginning. Feynman, a legend for open-mindedness on all subjects, said that we already know the physics of practically everything, and anything that's left over is not going to be relevant.

  Chaitin later learned that at the time Feynman was dying of cancer. He said, "At the end of his life, when the poor guy knows he doesn't have long to live, then I can understand why he has this view. If a guy is dying he doesn't want to miss out on all the fun. He doesn't want to feel that there's some wonderful theory, some wonderful knowledge of the physical world, that he has no idea of, and he's never going to see it."

  We are all dying, and anyone over seventy is likely to be more aware of that than someone twenty-five years old. But the latter is the age, particularly in science, where truly groundbreaking ideas enter the mind. If we accept the validity of Chaitin's comments, Horgan's interviews were foreordained to produce the result they did. Science, as perceived by elderly scientists, will always be close to an end.

  As Arthur Clarke has pointed out, when elderly and distinguished scientists say that something can be done, they are almost always right; when they say that something cannot be done, they are almost always wrong. Fundamental breakthroughs, carrying us far from the scientific mainland, are, before they take place, of necessity unthought if not unthinkable. That is the philosophical argument in favor of the idea that we are not close to the end of progress. There is also a more empirical argument. Let us make a list of dates that correspond to major scientific events. Lists like this tend to be personal; the reader may choose to substitute or add milestones to the ones given here, or correct the dates to those of discovery rather than publication.