Hidden Variables (19 page)

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 our 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) X cos(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, that c
²
= g x R. 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."

AFTERWORD: THE NEW PHYSICS.

Sir Arthur Eddington, who will be quoted elsewhere in this collection, once remarked that one mystery of the universe is the way that everything in it seems to
rotate
—planets, stars, galaxies, they all do it. Surely Listwolme too would rotate on its axis.

This is a worrying thought. What would it do to Nessitor's observations? Well, he would have found that his "speed of lightness" was a function of direction; it would be lower if he travelled in the same direction as the planet's spin, higher if he went opposite to it. From this he would have concluded that his universe lacked perfect symmetry—there was a preferred direction to it, the direction of the spin axis of the planet.

That seems to ruin the analogy between his physics and ours, since our universe appears to exhibit no preferred direction. It is assumed to be isotropic, the same in all directions. Except that . . .

In 1949, Kurt Gödel published a strange solution of the Einstein field equations of general relativity. It describes a universe in which there
is
a preferred direction, an "axis of rotation" for the entire cosmos. People usually reject Gödel's model by saying it is "non-physical" and does not represent anything in physical reality. But one other way to look at it is to say that we happen, by accident, to live in a non-rotating universe.
Most
universes, like most other objects, may rotate—we are the odd man out. Or perhaps, as our observational methods become more and more sensitive, we will conclude that this universe is not perfectly isotropic. Maybe with better instruments we and Nessitor would both find evidence of a slow overall rotation.

FROM NATURAL CAUSES

Like droplets of acid, envy had eaten slowly into the soul of John Laker. On the day that the shell of his soul was completely eroded he killed Alan Gifford; and on that day the time of true suffering began.

The murder occurred in late September but the first taste of acid had come on a perfect June day more than twenty years earlier. Laker saw the world then through a dark haze. Tight bands of pain were closing about his chest as he went round the final bend and on into the straight, clenching his jaws and pushing towards the finishing tape. As he passed it his senses could record only one thing. Alan Gifford, on his right—and half a pace ahead. The friendly arm that held his panting body after the race was Gifford's.

That scene set the pattern for the school years. Alan Gifford and John Laker, track stars—but always in that order. It didn't help Laker to know his times easily beat those of champions of previous years. Somehow that made it worse. In the single year when Laker swept the board in track events, the sight of Gifford in the crowd, weak from an appendicitis operation but cheering Laker on, turned victory to ashes. Next year Gifford was again an agonizing half stride ahead.

College brought no relief. John Laker was a good engineering student and he did well, very well. But Gifford was an engineer too, and seemed always to win the top design prize or get extra credit for originality. By the time they left college John Laker was an obsessed and tormented man.

"What next, John?" asked Gifford on the last day of school.

"Probably a government job. Aec maybe. That's my strongest suit. How about you?"

"Still not sure. I've had a good offer from the Bureau of Standards. See you in Washington, by the look of things." He slapped Laker on the back and headed off across the noisy campus.

In the years that followed the two men ran across each other about every couple of months. Alan Gifford had no idea how closely John Laker followed his career—raises, promotions, new responsibilities. He didn't know there was an unannounced and one-sided competition. Laker resented every success Gifford achieved, was wounded by each sign of his progress. Each year the burn went a little deeper.

The murder when it came was unplanned, almost an accident. Laker, walking from the bus stop to his house, met Gifford in the street. On an impulse he asked him in for a drink.

"This your place?" said Gifford in surprise as they turned into the driveway. "I'd no idea you lived in such luxury. How much land do you have, a couple of acres?"

"A bit more." Laker looked at Gifford, hoping at last to see a sign of envy. There was only simple pleasure at the beauty of the handsome red brick Colonial and well-kept garden.

They went on into the house. Laker saw their reflection in the full-length mirror by the hall coat stand. Grey-haired, lined with bitterness, he looked the older man by ten years. Envy and grinding work had taken their toll. Gifford went to the living-room window and stood looking out over the smooth lawn and carefully tended flower beds.

"You do a first-rate job out there, John," he said. "Wish I could get my garden to look like that."

Laker came over to the window and looked out absently. "That's my gardener. He comes in every day. I don't seem to find the time to do much there myself." He had forgotten the breadth of Gifford's interests. Gifford was an enthusiastic amateur gardener, as he seemed to be an enthusiastic everything else. "What are you doing over this side of town, Alan? I thought you were still living in Arlington."

Gifford nodded. "I am. Right on the approach path to National Airport, I think. I came over here to see Don Thomson at the Arboretum. Remember him from the University? He was mad about plants even then. Has the ideal job and spends all day playing about with new varieties of flowers."

Laker smiled. "Sure, I remember him. All teeth and top-soil." He poured their drinks and shrugged. "Should get over mere myself, but you know how it is—something's only half a mile away, you figure you can see it anytime—so you never do."

"You should. There's no place like it for plant collections. Don would love to show you round."

As he spoke, Gifford was strolling slowly round the room, sipping his drink and admiring the furniture and elegant china. He shook his head ruefully. "You've got taste
and
money. You know, Jean's illness used up most of my reserves."

His wife had died three years before after a long illness. Gifford had cared for her until the end, giving his days and nights to the struggle. Childless, he lived alone. Laker, driven from within, had never married and also lived by himself. The furnishings of the house had been decided by his married sister, indulging a taste beyond her own means.

Gifford looked at his watch. "Better begin the trek home. No, I won't have another, I've got to fight the Beltway traffic. But I'd like to take a look at your garden on the way out."

"Sure. Pity the gardener's not here. He could tell you what everything is a lot better than I can."

In the big front garden they walked slowly from one flower bed to another in the early evening sunshine. Gifford kept up a running commentary.

"That's going to be a great show of chrysanthemums in another couple of months. These dahlias are show standard. Ah, now. Here's the sign of a real professional." He stopped before a flower bed set back about fifteen yards from the front double gates. "He's double digging there. Must be two feet deep, that trench. I always swear I'll do that but I never get round to it. It makes all the difference to the soil."

As they approached the hot-house Laker felt a lump in his chest. When they paused before a tray of seedlings the truth hit him like a hammer blow. He had bought the house to compete with Gifford, to show the world he was richer, more successful. But Gifford was finding more pleasure there in one evening than Laker had ever found.

The world turned red, the last drop of acid found the center of his soul. He lifted a heavy claw hammer sitting by the boxes of seedlings. Alan Gifford fell. John Laker's real torment began.

* * *

The first hours were a frenzy of activity. When darkness fell he carried Gifford's body in a wheelbarrow to the deep trench in the front garden. A crescent moon gave just enough light to drop it in and cover it with a foot and a half of topsoil. Then he went again and again over the house and garden to remove all evidence of Gifford's visit. The cleaning woman arrived at eight the next morning and found him slumped in an armchair in the living room, eyes fixed on the flowerbeds. He roused himself to call his office and explain he was sick, then call his gardener and give him a month's wages in lieu of notice. He had, he explained, a relative down on his luck who needed the job. No need to come by, he would have the gardener's tools sent over to him.