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A Principle of Matter

by Geoff Hart

The keynote speaker's choice of a title for his speech at the twentieth meeting of the Society for the Interaction of Nuclei, Chemical reactions: a misunderstood process, had been guaranteed to attract—and provoke—a good crowd. Sure enough, the meeting hall was awash with noise as we awaited the speaker, a Danish grad student by the name of Kettu. Kettu had caused the greatest stir in physics since his countryman, Bohr, described the inner workings of the hydrogen atom and earned himself Denmark’s last pre-war Nobel prize something like a century earlier; indeed, it had taken the considerable resources and reputation of the University of Copenhagen to persuade Science to over-rule the journal’s referees and establish a special committee to adjudicate Kettu’s manuscript. Details of the paper had circumnavigated the globe via e-mail several times within an hour, generating a greater storm of electrons than that created by the average particle accelerator. Subsequent investigations by seasoned, skeptical researchers had borne out Kettu’s claims, and within hours of that confirmation, drafts of the paper were again speeding around the world on electronic wings.

I was present at the conference by purest chance. Peter, our lab’s senior grad student, had been the logical choice, but he’d been stricken by a nasty case of food poisoning after his farewell dinner at my apartment and right before he was due to fly to Denmark. This unfortunate occurrence, abetted by the fact that Kettu’s discovery had invalidated three hard years of my own research, persuaded my supervisor to send me to Denmark in search of a means of salvaging my thesis. My parents would certainly never have funded the trip; they’d adamantly refused to understand why I'd abandoned the prospect of a career in banking to waste my life chasing subatomic particles. When the arguments had grown too acrimonious, I suggested rather abruptly they do something no banker would contemplate doing with a client’s money, and slipped away, leaving them apoplectically groping for a suitable response.

If there were things worse than facing their knowing smiles should I return without at least a doctorate appended to the family name, I didn’t want to contemplate them. That left Denmark my only option, and the serendipity of poor Peter’s mishap came not a moment too soon. If I couldn’t save my thesis, perhaps I could at least get some satisfaction out of the bastard who’d ruined it for me.

While we waited for the session to begin, I’d been glancing over the crowd from my vantage point off to the left of the stage—it would have been presumptuous to have stolen a seat from my seniors, and since I still hoped to someday find a postdoc position, it was wiser to avoid stepping on any toes. Instead, I occupied myself with putting names to faces, and sorting out those who might deign to accept my résumé. The sharp rap of a gavel on the lectern cut short my survey, simultaneously stilling the buzz of conversation. The conference chairman, Dr. Fries, spoke into the anticipatory silence, his eagerness betrayed by the slight Danish accent that crept into his otherwise impeccable English.

“Ladies and Gentlemen, colleagues, I confess to an excitement as great as any among you. Let me skip the introductions: Welcome to our hallowed halls. I shall now introduce our keynote speaker.”

With commendable brevity, he summarized Kettu's unremarkable background—nothing you've not already heard a hundred times in the media, apart perhaps from Kettu’s little-known prowess at soccer. Fries ended with a flourish as his subject strode forth onto the platform with his laptop tucked under an arm, and set about his preparations with none of the fumbling you'd expect of a grad student making his first speech before such an august gathering. I'd hated him before, but this self-confidence only added fire to my detestation. Kettu was shorter than I’d expected, not much over five feet, and had glossy black hair that fell to his shoulders. He was cleanshaven, with angular Nordic cheekbones, and moved with the controlled grace of a dancer before a performance. Particle physicists like me tending to fall at the low end of the athletic bell curve, I hated him even more.

His computer having been whipped into shape, Kettu cleared his throat ostentatiously and took the light pen from the lectern. Turning his back on the audience, he strode to the large screen at the back of the stage. The directional mikes above my head whirred quietly as they panned to follow him. He began sketching on the screen without so much as a glance back. “My fellow physicists, today we find ourselves at about the same stage the alchemists attained when they first realized their old science was about to be replaced by the new one we call chemistry.” His rich tenor held not the slightest quaver, and his pronunciation and diction were better than my own. The man was a born speaker, and despite myself, he held my full attention.

The graph that took form on the screen became the traditional schematic of a chemical reaction, with the total energy of the system along the vertical axis and the horizontal axis labeled with the progress of the reaction, reactants on the left and products on the right. Between the two axes, Kettu sketched a horizontal line that became a rising diagonal, climbed sharply to a peak, then became a descending diagonal that sank sharply towards the line’s original level, ending as a horizontal line above the word “products”, at the same level as the original horizontal line. The result, minus the labels, resembled a child’s drawing of a witch’s hat.

“I'm well aware that this is obvious, but I crave your indulgence; we need some context.” He still hadn’t turned to face us, and an impatient murmur arose from the crowd. He highlighted the ascending diagonal line with the pointer, and it brightened. “Classical reaction kinetics states that as two reactants approach each other, the system’s total energy increases. When the two reactants finally come together, they form an unstable intermediary, and the sum of their energy is high compared with that of the reactants.” He tapped the sharp peak of the curve, highlighting it and letting the first diagonal line fade back to its former color. “Furthermore, theory states that the atoms in the reaction complex now undergo certain realignments as they seek a more stable configuration. If the atoms cannot find that configuration, with a lower energy than at the peak of the graph, the reactants fall apart and return to their original conditions... they slide back down the first slope of the curve, if you will. Conversely, if the rearrangement leads to less energetic products, the reaction proceeds onwards to those products." He tapped the descending diagonal line, and as the graph's peak faded, that line brightened.

"If sufficient energy remains within the system to push the products back up that slope, some of the product spontaneously turns itself once more into the reactants, but the majority of the reactants have lost enough energy to produce a stable product. This is a straightforward consequence of the law of entropy.

“For the moment, let’s ignore whether the reaction would be endothermic or exothermic, and instead focus on the portion of the graph to the left of the peak. Reaction dynamics tells us that random motion brings the reactants close enough to react; it’s the combination of their motion that provides the increased energy represented by the peak. Without some push, the reactants would never make it far enough uphill for the reaction to occur. I like to think of this as analogous to Sisyphus pushing his boulder up the hill, never quite able to reach the top without external aid. In this metaphor, Sisyphus is a reaction that never proceeds to completion, since the gods have decreed he shall never succeed at his task without assistance, and few are sufficiently unwise to challenge the gods. What we physicists haven’t understood until recently was the mechanism by which the reactants make it up and over the top.” He tapped the peak of the graph, highlighting it again.

There arose a buzz as the better-read in the audience whispered an explanation of the Sisyphus myth to their colleagues. Kettu patiently waited for the hubbub die down before continuing. “By analogy, modern physicists are in somewhat the same state as poor Sisyphus, in need of a helping hand. My serendipitous discovery of a means of producing the long-sought fuson particle has let us provided that helping hand.” He turned to the audience for the first time and smiled enigmatically.

Most Danes learn English in school, and speak it more fluently than many North Americans. The way he’d used the present tense to refer to Sisyphus, a Greek mythological figure, was an odd choice. Moreover, the "serendipity" of his discovery sounded increasingly at odds with his evident self-confidence. I frowned, but Kettu had begun talking again.

“The real clue lies in this peak. What causes the chemical reaction to occur? After all, the energy attained as the reactants first merge is so much higher than that of the reactants, and the reactants should roll back down that hill, like poor Sisyphus’s rock. Could it be that perhaps we had the graph just the slightest bit wrong? Could this trivial misunderstanding have misled us for so many years?”

He inverted the stylus and neatly erased the tip of the peak, then replaced it with a horizontal line. The graph now resembled a child’s drawing of a flat-topped hat with the peak just slightly above the brim. “What really happens, as I have recently demonstrated, is that the energy of the system does not in fact rise. Rather, it remains roughly constant.” He erased the remainder of the peak, then drew a dashed line to connect the two horizontal lines that were all that remained of the original witch's hat. “If we consider the reaction from this perspective, the two reactants clearly react without ever differing from the products in their energy level. In consequence, we moderns need no longer concern ourselves with poor Sisyphus and his hill, since there is no hill. All that remains is to explain the energy changes we have observed for generations, for it is a matter of record that every reaction we have studied shows a clear change in the energy status of the reactants and their products. Sometimes we must pump energy into the system, other times energy emerges, and any alternative theory must provide a testable explanation for these irrefutable observations. Where does this energy come from, or where does it go?” He turned to gaze once more upon the crowd of breathless physicists, his eyes gleaming.

“As it turns out, the energy is used to manipulate fusons, and the creation of these fundamental particles accounts for the increased energy you had formerly attributed to the peak of the graph. The fusons, in turn, tie the reaction complex together long enough for the atomic rearrangements that characterize the reaction to take place.” I wasn’t the only one in the audience to catch the switch from we to you; some grumbling became apparent as Kettu went on.

“I hypothesize, from certain experimental data, that further research will demonstrate, as is required by symmetry, that fusons have counterpart particles I have named fissons, which force the subatomic particles apart once more. The balance between fusons and fissons depends on the reaction geometry, the energy inputs, and the substrate conditions—if any—and it is this balance that determines which products will form, if any. This hypothesis is necessary to explain the force that overcomes the attraction of the fusons and causes dissociation of the reaction complex. I rather like this notion, because it has the symmetry you physicists so love.

“Where do the fusons and fissons come from? Until you developed the ten-dimensional mathematical model of the universe that supports the current version of the grand unified theorem, you would have had to say they came from nowhere. In reality, if I may misuse that word, the fusons and fissons have always been there, but masked by the measured energy changes that occur during a reaction. It's as if they are caught between the onrushing reactants and are crushed together by the force of that impact. In practice, at least four of the ten space-time parameters of the individual fusons and fissons must take on the same values as those of the reactants and all share the same parameters for the duration of the reaction. All that is required is a simple mathematical transformation—one that absorbs the energy generated by the reactants coming together: the result is the transformation of what was once perceived as the reaction’s peak into the flat line I’ve drawn here.” He gestured carelessly back at the screen, and the dashed line flared briefly as his pointer swept across it.

“How the fusons know which atoms to connect together remains a mystery to science.” His smile implied it was no longer a mystery to him, and there was puzzled silence for a moment. Egotism is an occupational hazard of the great physicists, but this was something else again. “Inevitably, however, it will be understood, and a new age of nuclear alchemy will begin. In effect, with a reaction chamber full of atoms, a little electrical energy, and the right geometric transformations, one could control any common reaction with extreme precision. Only slightly more ingenuity would be required to transform complex atoms—lead into gold, for instance—by judicious addition and subtraction of fusons and fissons. For that matter, you could transmute any material into any other material you desired, perhaps even animate matter, with a little practice. It’s fortunate that atoms are atoms, and their origin is largely irrelevant.”

The speaker sighed and smiled benevolently upon the frowning faces before him. “Of course, as Heinlein said more than half a century ago, ‘There ain’t no such thing as a free lunch.’ The laws of conservation of mass and energy clearly indicate that all those fusons and fissons must come from somewhere, and it would be particularly unfortunate if whoever or whatever lives in that particular corner of tenfold space-time resented such an intrusion.” He paused, and the silence became heavy and anticipatory as a black hole. “In fact, I may have erred when I mentioned poor, dear Sisyphus. Prometheus might be the better analogy, or Lucifer as you once called him, who was caught stealing light or fire from the gods. And we all remember what happened to Lucifer, don’t we?” His smile widened, a cat in possession of the keys to the aviary.

“Vait a minute,” called an outraged Germanic voice from the back of the auditorium. “Chust who do you think you are? A vet behind-the-ears grad shtudent, I say. Vhat you claim is pure, fantashtic shpeculation, backed by no fact or evidence. Vhat is to shtop us from taking all the fusons ve vant and forching a new golden age for mankind? An age in vich any substance can be qvickly and easily synthesized from any raw material?”

“Absolutely nothing,” chuckled Kettu. “Absolutely nothing. Just ask Lucifer. And let me leave you with a small lagniappe for your courtesy in hearing me out. Those multidimensional mathematical transformations I mentioned can be applied on a far broader scale, to macroscopic objects and not just atoms. Allow me to demonstrate.” The chill that fell upon the room as Kettu vanished was more than psychological—it was demonstrably endothermic.

The part of me that thought in terms of endothermic reactions and ten-dimensional space time was no longer so sure. As the crowd’s outrage reached an uncomfortable number of decibels, a quiet voice in my head began whispering that no matter how much crow I'd have to eat with my parents, a career in banking would be a far less risky—not to mention safer and more ethical—choice.

Author's notes

Before you ask: yes, I'd use "reagent" rather than "reactant" in my own writing. That's just a little bit of fun with word choice by someone speaking a language different from their birth language. It's been a long time since I've read Asimov, but this strikes me as precisely the kind of thing he might have written (cf. thiotimoline). The science is basically solid if you don't look too closely; the conclusion is anything but. The promethean moral is just plain fun, and hopefully not too preachy. Mammalogy trivia note: Kettu is Finnish for "fox", and that's all I'm going to say about the matter and Kettu's choice of name.

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