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The Casimir Effect

Léo’s Cottage

Certain complex mental operations, involving large regions of the brain, are nevertheless vulnerable to localized disturbances. Patients suffering from temporal-lobe epilepsy often develop hyperreligiosity, a tendency to colour every event, great or small, with cosmic significance. They are also prone to hypergraphia, a compulsion to express their visions in an undisciplined stream of poems, letters or stories.[^1]

Marthe puts down her book and watches the fire emit long, exponentially rising whistles as though calling for help. She has not yet decided its fate. The afternoon is already warmer, and there will probably be no need to heat the house.

The clock strikes three. She closes her eyes and allows the three chimes time to dissipate and merge with the ordinary sounds of the house. When she opens them again, her gaze lingers on a spider calmly going about its business in a corner of the ceiling. The house no longer has the rectory-like cleanliness she once demanded. Things are slowly beginning to come apart, a little like autumn in its early days, when August persists in preserving summer while the trees quietly relinquish their first weary leaves. She thinks again of Armand. As with autumn, she could not see it coming. Or, like most people, she chose not to.

Bruz and Katou have settled near the hearth, curled around each other in the alchemy of their dreams. She rises and goes to the window overlooking the river. The trees around Léo’s cottage sway with the gusts, illuminated from time to time by stronger rays of sunlight. She scans the sky; there are not that many clouds. Why, then, so much variation in the light?

Her past could be summed up by this cottage, which housed Léo for thirty-five years. Her body remembers; her old skin asks for him again. Léo’s storms, his fits of desire, of physical possession, all alien to Marthe’s cerebral nature. She shudders, her body deceived by memory, her forehead against the window. What is being woven through the convolutions of her brain? she wonders. Which neurotransmitters are acting at this moment to remind her that she has become white flour, hulled, stripped of its nourishing husk? What chemical components make her believe she still loves the same man? That she would have wanted to die like this, replete? She is not sure. The best thing to do is cauterize this wound. She tells herself so endlessly, though the thought of doing it frightens her. Nothing new under the sun.

The fire seems to beg her one last time to come to its rescue before it goes out for good. The nights are cool in August beside the river. She leaves the window and adds logs to the hearth. The embers immediately set upon the dry bark. One flame appears as if by magic, then another. Before long, they have already blackened the wood’s surface. Bruz watches the flames’ intriguing movements through one weary eye, then falls asleep again. She examines the stones of the fireplace and touches a few; their surfaces have been polished by the heat flowing from the hearth. Between them, the mortar has kept its roughness. A sad and bitter distance, like the collisions between human beings.

She rises, returns to the window, and the reflex is the same: she looks at Léo’s cottage. The fire has resumed its cruising speed, burning full steam through the archaeological sap of the logs. The intensity of the combustion produces a soft, persistent whistle. A moment of vertigo, a brief loss of balance. She braces her hands against the window frame. A long spell of weariness, a languorous sadness, the kind that accompanies time in its work of erosion.

She takes her shawl, passes before the mirror, adjusts a few locks of hair without lingering unduly, takes a ring of keys hanging beside the door, opens it and looks at the two cats. They understand the signal, though they still take the time to stretch slowly. Marthe smiles. Katou licks one paw.

“Are you coming out, Katou?”

The cat continues licking herself while Bruz waits beside his mistress. Less patient than Marthe, he calls plaintively to his companion. She obeys and leaves the house with her tail held high. Marthe closes the door.

The outdoor air floods into her, good air, wholesome and unpretentious, perfect and honest. The sun, already perched high above, distributes its light somewhat listlessly.

The cats play with the fallen leaves, watching those that move too much and trying to bring them quickly to order with a swat of the paw. But there are too many, and the cats grow a little wild themselves, eventually battling the leaves, hypnotized by all that motion. Bruz suddenly races off towards nowhere, stops short, lies down and waits for Katou to come near before pouncing on her playfully. Marthe soon loses sight of them and has no fear that they will run away; they always return.

She adjusts her shawl and walks hesitantly towards Léo’s cottage. She hears her breathing grow heavier and, for a few moments, forgets the river, autumn and the ravenous wind. The closer she comes, the more she senses the strange immobility of the past within this place, or the quiet vacancy of a mausoleum.

Like the other buildings, the front of the small house, encircled by a narrow veranda, faces the river. Marthe stops at the foot of the steps, turns and searches the river for some kind of encouragement. There is a pale speck in the middle. A boat? She examines the oak to her left. Léo used to fasten a canvas to it and rub it with a grease pencil. If not the tree, then the river stones, Marthe’s hair, the feet of a stranger he stopped on the village street, as though he did not believe himself capable of creating ex nihilo forms he had nevertheless already conceived clearly in his mind.

The white speck is indeed a small craft. People here are reckless; they play with the river as though it were an ordinary stream. She watches attentively, making certain there is no sign of distress from the boat. An old coastal reflex inherited from her father. Her eyes blur, her sight betrays her. She cannot tell. Two people are aboard; navigating such waters is an act of carelessness all the same.

From time to time, she hears the sound of an outboard motor. Everything seems fine. She climbs the steps and looks at the cottage door. She used to come here often when Léo was in Europe during the winter. She liked to sleep in his bed, light the fire, warm the rooms and tend the house. Since he gave almost no sign of life throughout the season he hated, she made do with the unused furniture, the dusty brushes and a few unfinished canvases awaiting the master’s return, either to receive their final touches or to be brutally put to death.

She cannot bring herself to go any farther and prefers to sit on the steps.

She surveys her property. Her paradise. Once again, she can only rejoice in her good fortune. And her happiness. And her sadness. And her passion. She looks at the ground. On this very grass some thirty years ago, they made love beneath the stars, rather like the Adam and Eve of the Bible, but with orgasm tucked between the iotas of the commandments. “In any case, you’re too old now to love that way.” She pouts. That goes without saying.

Armand’s cottage, visible a little farther away, is the smallest of the lot. Léo had accepted the new tenants without complaint. He behaved like the reclusive artist he had always been, leaving his studio only to eat, make love to Marthe and laugh with Lucienne, then gradually becoming friends above all with Armand, with whom he could talk for hours. He also enjoyed playing cards with Armand and Gustave. His relationship with Hélène was more distant, but nothing more.

Marthe had left him free. He had done the same for her. Two trees intertwined in their canopy, certainly, and no doubt subtly joined at the roots. That had not prevented him from uprooting himself, from tearing himself violently out of the soil of their past. She rises, shaking her head to drive away both the light and the shadow of her memories.

She unlocks the door. The noisy wind cannot distract her from the deathly silence inside. She hesitates again, closes the door, feels ridiculous, opens it once more and enters the cottage resolutely, closing it behind her. Silence resumes its ancient right.

Sacrilege. She closes her eyes, partly to quiet her anguish. She knows the place by heart and walks by feel without holding out her hands to avoid obstacles. The sofa is here; she brushes it with one finger to make certain. The bedroom is to the right. She can sense its pull and its darkness, almost a tomb, a hole in an abandoned vault. She makes her way towards the studio at the back, beyond the kitchenette that had never really been used. Her eyes still tightly sealed, she wants to wait until she is seated in that studio, to find the passionate Léo again. She gets there without knocking into anything and is amused.

She sits in the armchair near the window and feels the sun’s warmth through her eyelids. It smells very strongly of dust, but also of filaments of mould and old fabrics absorbing the acid of time. What else is there?

She knows what is before her and decides to look, only to be disappointed at once. She had forgotten that the canvas was covered by a tarpaulin. Numerous paintings stand against two walls of the room, protected by scattered, dusty sheets. Léo had taken nothing with him. He had left as though he meant to return, or simply because he knew he was capable of starting over.

She pulls the painting before her out of its covering. Her face saddens, her eyes marvel; she suffers. So much detail in a work still unfinished: an exacerbated mannerism, red waves in profusion, routed purple clouds and, on the right, a white silhouette rooted in uncertain ground, a still ill-defined form that one senses to be a woman, clinging to a rock like seaweed and receiving without a moan the waves’ salty tongues, the bluish spines of the wind, her head touching clouds that seem to issue from her as if they were nightmares. At the bottom, in what appears to be a region half ocean, half clay, are traced letters, covered with violent patterns so that they can only be guessed at, though the capitals themselves are straight, almost implacable: MARTHE.

She must close her eyes, catch her breath, calm the great upheavals of the past and restore order to her thoughts. Yet the painting’s intricate lines remain imprinted on the inner surface of her eyelids.

She quickly replaces the tarpaulin over the painting, resolved to take inventory of the place. All this artist’s clutter would have to be removed, the unfinished canvases gathered, the unused materials burned or given to a school. The cottage existed only for painting. Though Léo lived in it, he had never made it his home.

Would she have the right to sell the paintings, since Léo is still alive? Send them to him? Where does he live now? Is he still as nomadic? So many things she no longer knows already. She circles the studio with a connoisseur’s step, lifting the sheets to appraise the sleeping works.

At the back of the room, apart from the other paintings, stands a canvas she knows by heart, buried beneath a soiled sheet. She pulls at the sheet, which seems to have been held in place only by the dust accumulated upon it.

Its fall raises a cloud that chokes her. She smiles and shivers. Two trees on a hill, almost identical, silvered and velvety. A sky curled like a Greek statue and a pastel light recalling the milt of fish. A celestial yet aquatic universe. Marthe had it framed with old planks found on the strand, long polished by the water. Léo had inscribed them with graffiti, half African, half Brazilian, as well as the title at the bottom: The Casimir Effect.

As is her habit when she wishes to calm herself, she runs a finger over an object, perhaps to trace the source of her anguish or carve its remedy there. Léo had scored the wood in an attempt to imitate the work of water. Her hands tense, jealous.

She blows on the dusty canvas. Wherever the air passes, the colours revive. She lifts the painting slightly and feels behind it with her fingers. There, the pages are still present, wedged between frame and canvas. She takes them, carefully unfolds them, recognizes the imprint of her old typewriter and brushes her fingers against the title’s minute furrows: The Casimir Effect. A Short Introduction. She smiles. The text must be thirty years old. They liked to draw from scientific literature explanations they meant to run parallel to their own experiences, a kind of mystical appeal grounded in strange terms they managed to understand only intuitively.

She returns to the armchair by the window. The text is in English, another of their whims, preferring to read already abstruse explanations in a foreign language. They were young. Her smile fades, allowing itself to be kneaded by memory. It had all been almost too beautiful; it had already been very complicated, as mysterious as the Casimir effect or the explanations in English. Then, from reading so much in that language, the mystery had evaporated of its own accord, like mist weary of the morning. She places her glasses on her nose:

The Casimir Effect. A Short Introduction.

The Casimir effect is a small attractive force which acts between two close parallel uncharged conducting plates. It is due to quantum vacuum fluctuations of the electromagnetic field.

The effect was predicted by the Dutch physicist Hendrik Casimir in 1948. According to the quantum theory, the vacuum contains virtual particles which are in a continuous state of fluctuation. Casimir realised that between two plates, only those virtual photons whose wavelengths fit a whole number of times into the gap should be counted when calculating the vacuum energy. The energy density decreases as the plates are moved closer which implies there is a small force drawing them together.

The tiny force was measured by Steven Lamoreaux. His results were in agreement with the theory to within 5%.

Particles other than the photon also contribute a small effect but only the photon force is measurable. All Bosons such as photons produce an attractive Casimir force while Fermions make a repulsive contribution. If electromagnetism were supersymmetric there would be fermionic photinos whose contribution would exactly cancel that of the photons and there would be no Casimir effect. The fact that the Casimir effect exists shows that if supersymmetry exists in nature it must be a broken symmetry.

According to the theory the total zero point energy in the vacuum is infinite when summed over all the possible photon modes. The Casimir effect comes from a difference of energies in which the infinities cancel. The energy of the vacuum is a puzzle in theories of quantum gravity since it should act gravitationally and produce a large cosmological constant which would cause space-time to curl up. The solution to the inconsistency is expected to be found in a theory of quantum gravity.

She still does not understand most of the terms used and, just as thirty years ago when she had Léo read it, retains only that an enigmatic force connects objects if they are placed close enough to one another for long enough.

She smiles. They were naked in the large bed in her room one autumn afternoon, probably a Sunday. They ate grapes dipped in wine. They had just moved into this large house. Léo had already achieved considerable renown and was particularly joyful then. His painting was voluptuous, his intentions clear and forthright. After reading the article, he had made her sit cross-legged facing him, then asked her to hold her hands out before her. He placed his own parallel to hers without touching. They closed their eyes, trying to feel this invisible force.

How long did it last? She cannot remember. She felt that force and identified it not with Casimir but with desire; she smiled, arms extended before her, Léo’s magnetic force drawing her towards him. Then she opened her eyes and realized that Léo was observing her with a certain sadness.

“What did you feel?” he asked.

“Desire.”

He pouted.

“I didn’t detect anything.”

He said it almost maliciously. She opened her mouth, partly in surprise, partly in anger, but his eyes signalled for her to look towards his sex. He was erect.

“But my cock did…”

She burst out laughing as he toppled her onto the bed.

She laughs again at his way of turning situations to his advantage, making them comic, serious or inconsequential as he chose. He controlled the relationship; she knew that well, but allowed herself to be swept along. The next day, he began painting The Casimir Effect.

She rises and returns to the canvas, running a finger over the ageing paint. Léo had made it the central theme of his work. Obsessively braided scrolls, coloured lace both diffuse and compact, traced over large canvases until they induced vertigo, until they told stories. A sky painted this way resembled water; a tree so coloured looked like gills, and the water appeared dead, wrinkled by some prehistoric molecular churning. Waves took on the appearance of obsessive tresses, and skin that of volcanoes held within the mesh of desire.

For her part, Marthe did not hesitate to invoke the same effect during sessions with her patients. By dint of being near each other, do things and beings not eventually come to possess a common soul? Might valleys not possess a memory and gentleness identical to the water that shaped them? Do lovers, old couples and eternal enemies not arrive at a divinatory understanding? Since the world became the world, since the Earth became the Earth, has there not emerged a resemblance, a shared rhythm?

In the anticipated boredom of daily life, someone catches our eye and smiles at us. The best encounters… the best sighs, the same movements, as though we all drew sustenance from one and the same river. Chance is there, and yet coincidence takes on the colour of destiny, flows in a single turbulent direction. Some sail, others drown; the waves bring some together, bring others together, save one, lose another… The friends of our friends are our friends, sometimes become our lovers; our boats draw alongside, depart again or remain forever joined to one another.

She looks through the window at the river’s imposing mass, crawling for centuries towards the same horizon. She also observes the trees, the rocks, the invisible far shore, then examines the cottage’s interior, all these objects she recognizes and the history attached to them. She closes her eyes and listens to her body and its many rhythms and rivers. She thinks of her friends, her former patients, her parents, adding these sensations together before pouring them into a river more turbulent and hypnotic still, the one upon which she and Léo sailed.

She has to sit again. On the table beside her are dusty brushes and yellowed sketches. With a sudden gesture, she sweeps them all to the floor. The dust makes her cough. She takes the time to recover her breath as the echo of the fall fades. Silence, like water that has been cleaved, resumes its place.

Before fleeing, Léo had left only a note that explained nothing. He never justified his actions and permitted himself every insolence. People forgave him because he was brilliant. Marthe alone took offence, but with no more success.

She suddenly feels too agitated, wants to rise, cannot. Spontaneity has deserted her muscles. She resists the urge to cry and looks at the brushes on the floor. He did not clean them before leaving. She stands and slowly tours the rooms.

She bumps into a lamp, which falls to the floor and shatters. She stops, astounded, and understands that this is what she should have done from the beginning: smash everything. There, on the kitchen counter, are glasses. She resolutely hurls them to the floor. She is seized by hysterical laughter that quickly turns to coughing and tears. No, this is not right; this is not how she usually behaves. Each reckless gesture reminds her of her age. She makes her way to the bedroom. The sheets are still unmade. Five years they have lain like this, abandoned, no longer covering the night with any dream. Five years her life has orbited this empty tomb, visited many times at first so she could moan in solitude while her friends waited patiently for her to calm down. She cannot understand this inertia, this black hole in her will. Is it another dirty trick of chance, or the natural consequence of time, the weight of expectation’s sedimentation suddenly tipping the hourglass in the opposite direction without warning?

Her heart is beating too hard. What if it stopped here, before she could burn a single stone of this past frozen in permafrost? She rushes from the cottage, prepares to flee, changes her mind and instead collapses onto a bench on the veranda. Mechanically, she checks that her hair remains intact. The sun has already sunk low on the horizon. The shadows have lengthened, announcing with their slender black lines that the day wants to sleep. The telephone in the cottage—an old extension of the line from the main house—rings. She starts. It must be Armand. She goes in and picks up the receiver just inside the entrance.

“Hello?”

“It’s me.”

She tries to sound warm.

“How are you?”

He does not answer at once; she hears him panting.

“Not too bad. They’ve already injected me with all kinds of things for tomorrow’s tests.”

She listens as he describes the various tests he will undergo to determine the extent of the damage. She makes a mental note of the room number and senses that he is deeply confused, anxious to get it over with.

“I was calling about Katou… I didn’t think of her.”

She reassures him, confirms that Katou has already made herself at home in the house, then pinches her lips at her clumsiness, but Armand does not appear to notice the implication. He thanks her and hangs up rather abruptly.

She replaces the receiver, disappointed that she was not equal to the moment, then becomes conscious of her surroundings again and looks at the objects she broke. She will have to ask Lucienne to clean. She will have to contact Léo’s agent to learn his intentions regarding the paintings. No! She will have to write to Léo. That is it: write to him through his agent, explain what she is preparing to do, threaten in some fashion to empty the place, to clean out the past.

She lowers her eyes; he will surely laugh at this belated letter, telling himself she has not changed. But no, he will be surprised and disconcerted if she chooses the right words. She returns to the red canvas, which at this hour of day is beginning to take on dark violet tones. The colours of his canvases have always been Léo’s great strength, endowed with a life that follows the hours, yielding to the passage of day and closing like flowers at nightfall.

She sits on the sofa again, searches for calm, braves the past and tells it that it must die—or rather, be reborn. She plunges back into her memories and watches them parade one by one before her. The canvas turns blue. She lights a lamp and continues reading the loose-leaf novel of her life. Outside, river and sky have become a single shifting black curtain. The moon appears. Marthe is neither thirsty nor hungry and almost falls asleep. Her heart beats more slowly than the wind.

She hears a car park, then the laughing voices of Hélène and Gustave. She hears them approach and remark that there is a light in Léo’s cottage. They climb the steps.

“Marthe?”

“Come in,” she says.

“What are you doing here?” Hélène asks, coming to kiss her.

“Sit down, please.”

Gustave glances around.

“It’s dismal in here!”

“You’re quite right. Tomorrow, I’ll ask Lucienne to come and give the place a thorough cleaning.”

“Still determined to rent it out?” he asks coldly.

“I don’t know…”

She hesitates.

“I have to tell you about Armand.”

She falls silent, making certain they absorb the blow.

“He’s in the hospital.”

[^1]: Edward O. Wilson, Consilience: The Unity of Knowledge (New York: Alfred A. Knopf, 1998). The French manuscript identifies the passage as the author’s translation.