Rigilusburgh Warriors


In the old city of Rigilusburgh, as the legend says, the finest warriors were trained day and night to protect the city. Among them, and as always, there were cowardly and brave soldiers. The brave dreamt of future battles where they would fight with honour, while the coward were quite happy to stay around, showing off and pretending they were eager to go to war. The brave were calm by nature and did not need anyone to tell them what to do, but some insecure cowards came around, and the courage of the brave was such, and the energy of their speech was such, that the coward became brave just by listening to them. However, the brave lived a solitary tough life, and sometimes that was too much to bear. Over-weighed by worries and inexistent battle, they became cowards themselves, and came back to find refuge in the crowd.

One day, because of the prosperity of the city, the soldiers were forced to expand and colonize new territories. They all started together, the brave and the coward, but at the very front of the army, where there were not that many warriors, the brave found themselves alone, some of them becoming cowards, the others finding it difficult to convince others. This allowed the coward to gain advantage. However, close to the front there were still some brave soldiers who tried to call for the ones who were behind them, and made them speed up a bit, because they still could see the new territory, free of human activity, free of cowards.

Regrettably, at some point, the cowards took so much advantage, that the foremost brave soldier could not see the new territory any more, it was all full of cowards. That was a sad day. There was no point in trying to call the others to find a land he could not see. At that point, he decided to slow down and regroup with the other brave soldiers in order not to disappear completely. From that moment on, the brave advanced slowly inside the mass of cowards, trying to convince as many of them as possible, and trying not to become cowards themselves.

Suddenly, the danger came, the enemy gates were reached, and then all the cowards that had thought too much of themselves died easily at their enemies’ hands. They called for the braves, they begged for them to come, but they were far behind, and the Rigilsburgh soldiers died, and the city knew nothing about them.

It was only after some time that the brave slowly caught up and finally found the enemy. All their cowardly friends were piled up at the gates while the enemies laughed from above. That offence ought to be avenged, and it would be indeed. They were brave soldiers from Rigilsburgh after all. They grouped, they fought, they took their bows and arrows, their shields and swords, and the heads of the enemies were rolling down the walls before the night came. The brave soldiers took the wall and saw what laid in front of them. A land infested with enemies, a land for the braves to conquer, and endless battle to fight.

As the braves defeated the enemy, a few cowards joined them after the wall, but most of the territory was still dangerous, and the bodies at the wall put most of them off, so it was only a few of them that were not coward enough to join the brave, and waited there for the moment to become brave themselves, to live in this land of endless battle.

The Science behind the Story

This story, and part of the following explanation, are included in my PhD thesis, published by the University of Edinburgh in 2013. Only a few minor corrections have been added.

I worked on a project that involved the propagation of bacteria that were either susceptible to an antibiotic (coward) or resistant to it (brave). There is a mechanism by which this resistance can be transferred from a resistant bacteria to a susceptible one. It is called horizontal gene transfer, and it involves an exchange of genetic material between individuals of the same generation. In the story this process is represented by the brave convincing the coward.

Sometimes the resistance to the antibiotics is lost, or a brave soldier becomes a coward. This process happen without interaction with other cowards (when the soldiers feel alone). The motion of the warriors correspond to the diffusion of the bacteria, while the growth in the new territory corresponds to bacteria multiplication.

At the very front of the army, the process of brave soldiers becoming cowardly is more intense than the convincing of cowards, and as a result the cowards win advantage. However, there are some brave soldiers in front of the coward mass, and that is why they pull the rest of the brave population, calling for them. Or in scientific terms, the resistant bacteria drag the others forward so long as they are not overtaken by the majority of the susceptible ones.

Nevertheless, the moment the braves are overcome by the cowards front, they slow down and all the brave population goes at a slower speed. This corresponds to the propagation of resistant and susceptible bacteria without any antibiotics barrier.

Finally, when the antibiotic barrier/the enemy is reached, it is only the braves who can continue, and now expand at a much larger speed, happy to fight and live in the new environment, free of cowards. However, there are some cowards who still join them in a small quantity. The susceptible bacteria or the cowardly soldiers would not be able to live in this dangerous environment by themselves, but a few of them survive on the shadow of the braves.

For more on the science of the story, see also the original research paper.


Drawing by Iantresman at en.wikipedia [Public domain], via Wikimedia Commons. PD-US.Source: William Howitt, John Cassell, John Cassell’s Illustrated History of England: From the earliest period to the reign of Edward the Fourth., Editor: John Frederick Smith, Publisher W. Kent and Co., 1857. Page 6.


Quantum Break-up



Two weeks ago at this time I was still with Naomi. There was surprise, anger, sadness, and now all I’m left with are questions. When did the whole thing go bad? When did love turn to hate? When was I wrong? When was I right? The more I think about it, the more I blame the whole thing on her. It was all her fault, yet something bugs me.

“What the hell are you worrying about? She was a bitch!” said Rachel, who had always been on my side, even when she shouldn’t have.

“You really think so?”, I asked hopeful.

“She slapped you, for God’s sake! You know what I’d do if a guy slapped me?”

“She saw me kissing Mary.”

“She saw Mary kissing you.”

“I’m not sure any more. Every time I think of that night-”

“I was there! One second and you pushed her away, how’s that your fault?”

“I know.”

“What’s wrong with you? She shouts at you, she leaves you outside waiting in the rain, and she slaps you. Don’t spend one more second thinking of her”.

Everything Rachel said was true, and so was everything I’d ever told her. Yet, it wasn’t the first time I had that feeling I couldn’t articulate something. Right as she was, Rachel hadn’t been there all the time. She hadn’t seen us in private. She had missed so many inexplicable intimacies, and those unspoken details were now dancing inside my head.

Tony had been a good friend these past weeks. He was playing the neutral game, meeting both of us, but he was Naomi’s friend long before I met him. We all knew he was going to stick with her.

“Just apologise” was his first conclusion.

“Excuse me?” was my reply.

“Apologise to her. Text her or something. Say you’re sorry and then forget the whole thing”.

I wondered if he just wanted to finish our friendship fast, or if he also wanted to date her in the near future.

“Sure. Here it goes. -Naomi, I’m sorry you slapped me. Your hand must really hurt after that. Also, staying in your warm flat at 2 am must have been a pain. You could have been down at the door with me feeling the rain on your skin-.”, I said.

“Who started all this? Who was the one not texting, the one saying I’m too busy?”, he replied.

“Are you really comparing these things?”

“I’m just saying she was lovely to you before you started not returning her calls.”

“You’re telling me everything would have been alright if I had picked up the phone?”

“Yes! That’s exactly what I’m telling you.”

“And she wouldn’t have slapped me, either.”

“Can you really blame her after kissing Mary?”

“She kissed me!”

“So what? You’d been talking to her for an hour leaving your girlfriend alone in a party where she didn’t know anyone else.”

I had to leave the room. This is the kind of bullshit I don’t need to listen to. If it was something I could really blame myself for, I’d take it. I really would. But not this crap. My friend Rachel was right, my soon to be ex-friend Tony wasn’t. That was it. Yet why was there something inside my head still wondering? In these moments of confusion Claire always helped.

Claire’s days were perfectly planned from 8.00 am to 11.59 pm. She wouldn’t waste any time, but she would spend it with me every time I called her. I met her at her lab.

“I don’t know, Claire, I just feel I’m missing something.”

She pointed at her experiment.

“This is a quantum system. Before I send light to take the measurement, it’s in a mixed state. Let’s say it’s not red, or blue, or green. It’s all of it at the same time.”

“Claire, I appreciate you-”

“When I send the light, I can see it with clarity. It’s only blue. Yet, if somebody else had repeated the experiment in the same circumstances, it would be only red.”


“The thing is that once I see it blue, I can’t stop seeing it blue.”

“Claire! I’m not in the mood today. I don’t want to learn all this shit.”

“I’m just trying to help.”

“I know you are, I’m just, ah, forget it.”

I got up from there and left the room. Claire was my last hope to understand, and she was just telling me all this crap about the mixed state, and seeing it blue and somebody else seeing it red, and this, oh, shit. I turned on my feet and came back to the lab. She was already knee-deep in calculations.

“When you said quantum system, you meant relationship?”, I asked.

“Yup”, she replied, still looking at her papers.

“And when you said light, you meant break-up?”


“Was I being a moron?”

“You’re starting to get it.”

“So if I see it blue, could I stop seeing it blue?”

“No, you’ve lost that mixed state. The break-up made it disappear.”

“And another person would see it red?”

“They would.”


“So you learn. If you repeat the experiment with identical systems, sometimes you see it red, others blue, others green. You find out the quantity of them in the total mix.”

“But there are no identical Naomis. All I can see it’s blue.”

“You’d better learn from the blue, then.”

I’d better.

The science behind the story

This story is slightly different to previous ones, as the concept is itself explained in the story through Claire. To put it all in a nutshell, a quantum measurement makes the system go into one defined state. However, before we take that measurement, the system could be in several possible states. That’s why Schrödinger’s cat is often used as a metaphor, as it could be alive and dead inside its box before we look at it. In the story the break-up of a couple is used as an irreversible separation of perspectives. For a comprehensive approach to quantum measurements, see the Wikipedia page.


Photo from Pixabay, used with license CC0 Public Domain.

The Force of Love


Once upon a time there were seven physicist brothers with seven inquisitive minds. As young men, they were very interested in love; as good physicists, they were all trying to figure it out.

Isaac, the oldest brother, would look at someone and see how much they had in common, how deep inside all people were the same. That recognition created a soft but unbreakable attraction that dragged him close to everyone. He moved through life without any fixed agenda and always giving his full attention to people around him. It was not a strong passionate love what he felt for others, but a universal connection to everybody.

Peaceful as he was, Isaac still lived many adventures. If there happened to be two people around, as he was able to connect with both, he wouldn’t mind jumping into an unusual relationship. It was a bit chaotic, for sure, but he would give it a go. Other times, some people would come close to him but never dare to speak. They would move around him at a safe distance, feeling the attraction but not coming closer. Isaac wanted to get to them, but no matter how much he moved, the others still would be too far, and eventually they would walk out of his life.

James, the second brother, partied hard every night, looking for girls and guys around him without knowing what was going on. He would wake up in the afternoon surrounded by friends and strangers. Some people came into his life, some people went away. Some would stick around without making a move, as it happened with Isaac. Others would move with him accompanying in his path.

When James finally took his time to breath he learned he was like Isaac, just more passionate and more selective. He decided he liked women, just women, and he would push away guys just to get rid of the competition. He would see a woman and just fly to her without thinking of the consequences. A look was enough as long as the girl and himself took their time and didn’t mess around.

Hideki, the third brother, was clearly into women, but was so anxious about them that the only happy moments he experienced happened when love was out of his mind. Every time he played football with his mates and love was off the table, he experienced a friendship stronger than the love Isaac or James had ever felt. This partnership, this “I love you, bro”-moments were something else.

There was of course the odd moment when a goal celebration kiss landed on somebody’s lips. Then, an instant separation, a look saying “No shit, bro” and another look replying “Of course not, bro” fixed it all. Hideki recognised this feeling of companionship as a reflection of something stronger inside him. A true love and respect for himself that everybody felt in the team. It was natural than when they saw each other, this inner love would come out to form a solid team.

Enrico, the fourth brother, liked the challenged. He would go after women with partners just to prove he was able to break them apart, and he was. When women saw Enrico, they were taken by his aura of mystery. He was the promise of things they’d never felt before. They would leave their partners in the middle of an engaging conversation or a passionate kiss just to meet this stranger.

Every time the woman got close however, something inexplicable happened. All her sudden passion was gone the moment they got close to Enrico. His shy smile suddenly removed all the mystery. The woman felt cheated, confused, and Enrico never knew how to react and ended up saying something inappropriate. She ran back to her partner, but by that time, the boyfriend would feel used and ignored, and he would break up with her. Enrico was a master breaking couples, not creating them.

Sheldon, the fifth brother, rather than creating new strategies, learned from his brothers. He liked the variety of James relationships, but also recognised the indisputable talent of Enrico getting rid of the competition. If only he could combine both. He normally behaved as James, but if he had to break up partners from time to time, he didn’t mind. He was a bit more subtle than Enrico, though.

One day Sheldon was with a friend at the pub and they saw the most gorgeous woman coming in. “Oh my God, she’s hot”, said Sheldon. And then it didn’t matter. It didn’t matter that she had a boyfriend, it didn’t matter whether he had to behave like James or Enrico, it just didn’t matter at all. He flew to her and did all he knew at once, started at her, at her boyfriend, and ended up telling him “You’re so hot”. The girl laughed so much it hurt, almost as much as the punch Sheldon received from the guy. It took a bit longer than the usual, but Sheldon got the girl in the end.

Peter, the sixth brother, quite liked the combined approach of Sheldon. However, he also thought Hideki knew what he was doing, and he learned to integrate it all. For him romantic and fraternal love were all part of the same thing. He analysed everything, broke apart every little feeling and sensation until he understood what was attractive to him. Sometimes he needed to switch from one approach to the other, but it all made sense to him, and with that careful analysis he was so far the most successful of the brothers.

Albert, the youngest one, was naturally closest to Peter, and learned a lot from him. He saw his brother was successful with any person he fancied. However, Albert also appreciated the graceful acceptance of Isaac. His oldest brother was not needy or without standards, as some people said. He genuinely wanted to be close to people and enjoy everyone’s unique beauty. Albert liked that, and he wanted to combine it with Peter’s success.

He struggled to put it all together, though. When unconditional love carried him away, he missed the nuances Peter saw. When he focused too much on the details, he was picky and did not accept the other person. Peter had put together a lot already, but still none of the brothers was getting what the oldest one had, that unconditional happiness. Albert studied the matter for ages, experimenting, perfecting his theory and scribbling endlessly on papers. Finally, after much work, Albert put his notes aside and went down to the pub.

Five pints later he came out held by a woman. “You’re hilarious when you drink, Albert!”, said she. “It’s the ethanol, my dear”, said he, and pointed his right index up to the sky. “Ha! Ethanol has taken me further than all my physics research. You know what that means, my dear?”. “What’s that?”, asked she, half intrigued, half drunk. “Love is, after all, a question of chemistry”.

They got married a year later.


The science behind the story

As usually stated, the characters here are purely fictional and any similarity with real people is unintended. However, the name of every character stands for a physicist, in particular a physicist who studied forces that behaved in the same way the characters do in the story. There are four basic forces in nature and there are theories that combine then. Let’s see this in detail.

Isaac behaves himself as if following the gravitational interaction (studied of course, by Sir Isaac Newton). This force or interaction is universal, that is, every body is attracted to all the others. The strength of this force is inversely proportional to the distance. That’s why Isaac focuses more on whoever is closer to him.

This universal attraction doesn’t result in everything collapsing together. As we see in the story and in real life, gravitational interaction leads for example to closed orbits like the ones described by Isaac’s lovers that never dare to talk to him, or like the Earth revolving around the Sun. Gravitational interactions between three bodies can easily be chaotic. It’s up to the reader to decide how this last statement compares to love affairs.

James behaves as if experiencing electromagnetic forces, that were unified by James Clerk Maxwell. Motion under these forces includes all type of trajectories: ellipses, hyperbolas, helices, and that’s why James experiences all kind of relationships and crazy adventures.

When charged particles (the only ones that experience electromagnetic forces) are at rest, the situation is much more simple, and there’s simply attraction between the opposite charges and repulsion between the charges of the same sign. That’s why James flies into women and repels men. In general, the idea of opposites attracting each other is extrapolated to many descriptions of love.

Hideki stands for Hideki Yukawa, the first Japanese Nobel Laureate. He characterised what is the third type of force in nature: the strong force, or strong nuclear interaction. This force holds the protons together in the nucleus despite the electric repulsion. That’s why it’s said that Hideki’s love is stronger than Isaac’s or James’, because the strong interaction is much more intense than gravity or electromagnetic interactions. This attraction between protons becomes repulsion when these particles are too close together. That’s why the guys in the story separate quickly they moment they get too close.

It’s important to state that this attraction between the protons is a side effect of the much stronger interactions between the quarks, elementary particles that form the protons and neutrons, among other particles. That’s why Hideki recognises his bond with his team mates as something that reflects something much stronger inside him.

Enrico represents the weak force, first modelled by Enrico Fermi. The weak force is responsible for the radioactive desintegration of subatomic particles (hence the break-ups), but produces no bound state. That’s why the Enrico of the story can never get a girl, he only separates them from their partners.

The character of Sheldon is a tribute to Sheldon Glashow who, along with Abdus Salam  and Steven Weinberg, contributed massively to the unification of electromagnetic and weak interactions theory. This unified description receives the name of Electroweak interaction. That’s why the Sheldon in the story tries to combine James and Enrico’s approach. It’s important to state that if the temperature is high enough, then the electromagnetic and the weak interactions combine into the same force. So when Sheldon spots a really hot girl, he just throws everything he has at once.

Peter follows the standard model, that gained even more strength recently when the Higgs Boson, postulated by Peter Higgs and others, was detected. This model unifies three of the four forces types in physics: electromagnetic, weak and strong. It is based on a systematic classification of subatomic particles to explain all these forces, and that’s why in the story Peter deconstructs, equally successfully, each of his complex feelings.

Finally, Albert’s approach is actually the one that Albert Einstein followed in real life (apart from the drinking in the end). It was his dream, and many other physicists’, to unify the four basic forces of nature into a single theory, sometimes called a Theory of everything. Einstein did improve Newton’s work wonderfully with his general theory of relativity, which is to date the most accurate description of gravity. However, it’s incompatible with the Standard Model and with any quantum description of reality. This unification of forces, along with a physical understanding of love, remains still an unsolved mystery.

Photo: La palabra amor en la arena.  License: Public Domain.

The origin of this idea comes from my first feature film in which the main character, a physicist, describes love using the four types of forces (LVOE, from 41:42 to 42:47).

Platonic Spectrum


“The world’s full of light!”, they shout at your side, and the voices don’t let you think. You look for a corner of silence, a refuge of solitude from which to look before speaking. There the light looks almost like darkness. Something is missing in this cavern. Something else must be outside. But the others only see what the light shows, and it’s only you feel the chains.

You pull once, and again, and once more until the shackles break. The unknown noise draws some attention, and now shouts of rejection turn towards you. Your tremulous body rises and takes the first step. Your lethargic legs stumble upon the chains, and you fall down towards the voices. But nobody grabs you. They would have to move by themselves to do that. You rise again, and new steps follow the first one. The shouts are now echoes in the distance.

The exterior opens in front of you. You’re blinded, yet you see more than ever. The light is only a piece of a whole spectrum that before remained invisible: there are rays that darken your skin in plain sunlight, twinkles that blind you without ever being seen. The light was not enough before, now the spectrum is too much. You try to understand blindly, reaching for a glimpse of clarity. Your own thoughts exhaust you. You have one breath left, and you go back with it to the cavern.

“There is something else out there. What we see is not everything”, you say, but the outraged whispering becomes a howl, louder than your clam voice. “Madman!”, they shout, because you don’t shout with them. That word resonates inside your head with echoes of doubt, and for a moment you look for comfort in the dark light of the cavern. But you saw more, you still see more, and slowly hear less and less those who shout.

The spectrum speaks louder than the crowd, and holds you up when you rise. The second time is easier to go outside, and the third one even easier. Several trips make you understand the spectrum. It is nothing but an extension of light, some of it more vibrating, some of it less. As easy as changing colour, as difficult as listening in silence.

You’ve realised how the outside influences the cavern, how the latter is a part of the former. There is something you’ve understood, and there are things you can change. You use the invisible energy to improve life inside the cavern. A little invention here, a little adjustment there, and now the cavern is a more comfortable place. You celebrate your achievement, and you almost hope to find acceptance, even admiration.

People use your inventions, yet despise, in a louder or lower voice, your madness. Some of them admire you without understanding you, while others completely forget you. They all now wait for the next novelty without caring where it comes from. You don’t find the strength, not even inside you, to make the next trip. The noise grows in your head and pierces your eardrums. Maybe you should leave it all, maybe you should shout with the rest. It looks liberating somehow.

With the energy you no longer have you look around one last time, and finally, you see something different. Something shines in the darkness. Where the shouts almost don’t let you see, a mirror returns your gaze. In the distance another madman listens, another madman waits. He also was blinded by the spectrum outside, he also thought impossible colours. It is a madness of another kind, sure, but a madness after all.

When you see this light the cavern becomes mute. The chains fall at your side and cease to exist. The way out is now easier knowing someone else waits. You find each other beyond the voices, and your silence introduce you. You don’t walk, you run at each other’s side towards those invisible lights. Far too well you know that at the end of the day you’ll have to go back to the cavern, but now the way out will always be open.

The Science behind the Story

The story is an extension of Plato’s Cave myth that illustrates the Electromagnetic Spectrum. The original story describes a cavern where people only see shadows of real objects, while the true world waits outside.

Scientists and engineers see light as a part of a whole spectrum. The only difference between the sections of the spectrum is the frequency of vibration. Apart from visible light, there are many other electromagnetic waves. For example, UV light are the “rays that darken your skin in plain sunlight”, while the gamma rays are the “twinkles that blind you without ever being seen”. Microwaves, X-rays, infrared and radio waves complete the spectrum.

Picture: Public Domain Images – Cave Red Rocks Light Beam Cavern


El Espectro Platónico (Spanish version)


“¡El mundo está lleno de luz!” gritan a tu lado, y las voces no te dejan pensar. Buscas un rincón de silencio, un refugio de soledad desde donde mirar antes de hablar. Allí la luz casi parece oscuridad. Algo falta en esta caverna, algo más debe existir afuera. Pero los demás sólo ven lo que la luz enseña, y sólo tú pareces sentir las cadenas.

Tiras una vez, otra, otra más, hasta que saltan las argollas. Ese ruido desconocido atrae la atención, y ahora gritos de rechazo se giran hacia ti. Consigues alzar tu cuerpo tembloroso para dar el primer paso. Tus piernas aletargadas tropiezan con las cadenas, y caes hacia las voces. Pero nadie te retiene, para eso tendrían que moverse por sí mismos. Te levantas una vez más, y a un paso le siguen otros. Los gritos son ya ecos en la lejanía.

El exterior se abre ante ti. Cegado, ves más que nunca. Reconoces la luz como un pedazo de todo un espectro antes invisible: rayos que oscurecen tu piel a plena luz del día, destellos que te dejarían ciego sin ser vistos. Si antes la luz no era suficiente, ahora el espectro te satura. Buscas entender a ciegas, arañando una fibra de entendimiento. Tu propio pensamiento te agota. Te queda sólo un último aliento, y vuelves con él a la caverna.

“Hay algo más ahí fuera. Lo visible no lo es todo”, dices, pero ya el murmullo indignado se convierte en un aullido más alto que tu voz calmada. “¡Loco!” te gritan, pues no gritas con ellos. Esa palabra resuena en tu interior con ecos de duda, y por momentos buscas cobijo en la oscura luz de la caverna. Pero tú viste más, aún ves más, y poco a poco oyes menos a los que gritan.

La luz habla más alto que la multitud, y te sostiene cuando te levantas. La segunda vez cuesta menos salir al exterior, y menos aún la tercera. Tras varios viajes entendiste el espectro. No es más que una extensión de la luz, alguna más vibrante, otra menos. Tan fácil como cambiar de color, tan difícil como escuchar en silencio.

Ahora ves cómo el exterior influye en la caverna, cómo la una es parte del otro. Algo has entendido, y algo puedes cambiar. Puedes incluso aprovechar esa energía invisible para mejorar la caverna. Una pequeña invención aquí, un pequeño ajuste allá, y la caverna es ahora un lugar más cómodo. Celebras tanto tu logro, que casi esperas encontrar aceptación ahí dentro, admiración incluso.

Y aunque la gente utiliza tus invenciones, a la vez desprecia, en voz más o menos baja, tu locura. Unos pocos te admiran sin comprenderte, mientras los demás olvidan que eres tú quien trajo las mejoras. Ya todos esperan las siguientes novedades sin preocuparse de dónde vienen. Y ya no encuentras fuerzas, ni fuera ni dentro de ti, para el próximo viaje. El ruido vuelve a crecer en tus oídos y te perfora los tímpanos. Quizá deberías dejarlo, quizá deberías gritar con los demás. Parece liberador de alguna forma.

Con la energía que ya no queda miras a tu alrededor una vez más, y al fin, ves algo diferente. Algo brilla allí en la oscuridad. Donde los gritos casi no te dejan ver, un espejo te devuelve la mirada. A lo lejos otro loco calla, otro loco mira. Él también quedó cegado con la luz de afuera, él también pensó colores imposibles. Una locura tal vez distinta a la tuya, sí, pero una locura al fin y al cabo.

Al ver esta luz la caverna queda muda. Las cadenas caen a vuestro lado y no parecen existir. El camino a la salida es más fácil sabiendo ahora que alguien espera. Os encontráis más allá de las voces, y vuestro silencio basta para presentaros. Y no andáis, corréis el uno al lado del otro hacia esas luces invisibles. Demasiado bien sabéis que al final del día habrá que volver a la caverna, pero para vosotros el camino de vuelta al exterior estará ya siempre abierto.

La ciencia detrás de la historia

Este relato es una ampliación del mito de la Caverna de Platón para explicar el Espectro Electromagnético. En la historia original los habitantes de la caverna sólo ven sombras de los objetos reales, mientras todo un mundo real espera fuera de la caverna.

Para los científicos e ingenieros la luz que todos vemos es sólo una parte de todo un espectro, cuyas regiones se caracterizan por tener distinta frecuencia de vibración. Así, además de la luz visible, existen otras ondas electromagnéticas. Por ejemplo, los conocidos rayos UVA son los que “oscurecen tu piel a plena luz del día y los rayos gamma son los “destellos que te dejarían ciego sin ser vistos”. Las microondas, los rayos X, los infrarrojos y las ondas de radio completan el espectro.

Foto: Public Domain Images – Cave Red Rocks Light Beam Cavern



Mirembe had married Jabari two years ago. She had renounced her inheritance to marry the man she loved. She never had been poorer, or happier. Their little house at the end of the street stood proudly as a refuge for peace and love. For some reason she never fully understood, the houses in her street were less and less opulent as she walked along it. The first one was occupied by her friend Abimbola and her husband, and it had everything one could wish for; the last one was occupied by Mirembe and Jabari, and it only had everything they could wish for.

With one young couple in every house, it was the liveliest street in the small village. People would dance around and wander among the crowd with no direction. Money made the world go round and the people go around, and it was no wonder that the richest neighbours went out to the city more often. Mirembe, on the other hand, had to work all day long, and stayed home after sunset. But a night in was never a bad night for her.

One morning Mirembe went out and felt unnaturally cold for that time of the year. The warmth of people had disappeared from the streets. She knocked on her neighbours’ door, but only a nervous noise came out from the inside. Suddenly a rifle clicked behind her. A bunch of helmets and uniforms walked towards her, shouting threats in a language she did not understand. She put her hands up. Among all the incomprehensible shouting she could only make out the friendly “Go home” coming out one of the houses. The guns pushed her back home, and finally she collapsed on the floor by the door, embracing it in search of support.

Jabari woke her up and Mirembe looked at him, happy to let go of her bad dream. Suddenly someone knocked on the door, and the shouting from her dream echoed back into reality. Jabari helped her up, and opened the door with caution. There they were again: the guns and the angry shouting. They took them to the square at the end of the street, where more guns were waiting. They took their money and their colourful clothes, and covered them with grey one-piece uniforms. A soldier wielding a razor shaved Mirembe’s head, then Jabari’s, then everyone else’s. By the end of the day, those long hairs and dresses were gone.

Mirembe hadn’t seen Abimbola on the square. Soldiers had settled into her house, and she was nowhere to be seen. “She left the moment she smelled danger”, said someone in the crowd. She was not the only one gone. The neighbours from the richest houses had all evaporated. The military had occupied their houses, and they threatened to expand further. Mirembe and Jabari made it back home, and held each other for an eternity that didn’t last nowhere enough. Another couple came knocking on their door, homeless and hopeless. As hours went by, more couples joined them in their poor house. What would have normally been a reason for celebration felt now like a cold isolation.

Jabari, a quiet and peaceful man, was screaming inside his squeezed mind. He needed to go out, and soon. Others in the house wanted to fight back, to steal the soldiers’ guns. Mirembe didn’t want to hear any of this, and just hoped for things to pass. She had seen what soldiers were capable of, and she did not even dare to go out. This would end some day. It had to.

The discussion about what to do and what not to do went on and on for days. There was no plan or agreement, only shouting as incomprehensible as the one outside. Desperate, unable to hold the pain inside him any longer, Jabari stormed out of the room. He just wanted to go out and shout. And he did go out, but he did not get to shout. A bullet pierced his head and ended his pain in a split second. Mirembe wanted to cry, to shout, to hurt herself, but above all she wanted to hug her husband one last time. Prudence held her back through her neighbours’ arms.

She cried until her eyes were empty, and all meaning had abandoned life. She could not move, and she would not have if other neighbours had stopped coming into her house, but they did not. Out of options, out of space, there was nowhere to go, but outside. She would not go very far on her own, but talking to others would end up in endless wandering. So she did not talk. She stood in the middle of the room, grabbed her friend’s hand at her side, and walked the first step. Other hands joined the chain, and other feet joined the march. Only crossing the door was left.

It was a cold dark night outside. What came out of Mirembe’s house was a bunch of people so close together you could not tell them apart any more. The first soldier who saw it ran scared at the image of the crowd, moving together with one goal in mind. He ran to a second soldier, and the second one to a lieutenant, and after ten minutes they had nowhere to run, no one to run to.

That was not the end of it. It took many neighbourhoods in the city, many sacrifices to get the soldiers out for good. But when those people with their shaven heads and their grey uniforms moved as one, their clothes, their hair, their city was theirs to claim.

The Physics behind the Story

At the beginning, people in the neighbourhood are all different, and we can tell them apart by the house they occupy and their sex. I’m going to assume, strictly for the sake of the analogy, that all couples are made up of a woman and a man. There is a type of subatomic particles in physics that behave in a similar manner; they are called fermions. There may be many identical fermions in a system (e.g. many electrons in an atom), that are distinguishable by the level of energy (that would be the house in this story) and their spin (their sex). Mirembe’s and Jabari’s house is at the bottom, at the lowest energy level, while Abimbola’s one is at the top. It is important to remember that energy is quantised at the subatomic scale, that is, one may live in a house or another, but not between houses.

The moment the soldiers occupy the neighbourhood, people drastically change their behaviour and now behave as a group of bosons. The difference with fermions is that an unlimited number of bosons can occupy the same level of energy and have the same spin. This is portrayed in the story by making people of both sexes look alike by shaving their heads (that would be the same spin) and later occupying the same house (same level of energy). It is important to remark that in real life fermions do not turn into bosons, and this change of particle type is done in the story to illustrate the difference between these two types of particles and their associated behaviours.

The whole process of people moving into Mirembe’s house is analogous to the forming of a Bose-Einstein condensation (see also this link). First of all, the richest people like Abimbola or the bosons in the highest levels of energy disappear from the system, or in real life, they evaporate (metaphor here). Then, the temperature (money in the story) is reduced so the mobility of all people/bosons is limited. They all end up concentrating in the poorest house or in the state of smallest possible speed. Actually the temperature is so low that Bose-Einstein condensates are sometimes referred to as the “coldest place in the Universe”.

At the very end of the process, the Bose-Einstein condensate is properly formed. The number of people allowed to live in other houses is limited by the soldiers, and they are all pushed down to Mirembe’s and Jabari’s house, the lowest level of energy. When the number of people is high enough, as it happens at the end of the story, they behave as a group rather than a collection of separated bosons. This is the moment when they all march as one and get rid of their enemies. It is important to remark that all bosons in a Bose-Einstein condensate are in the same level of energy (Mirembe’s house) but in real life that does not necessarily mean that they are close together in space, even if people are close in the analogy.

Bose-Einstein condensate behaves in a way that is fundamentally different from solids, liquids or gases, and therefore is considered to be a different state of matter. It is not only of theoretical interest, but it can be applied to create new technology, including quantum computers.

Other metaphors

Other analogies have been offered before for the Bose-Einstein condensation. For example, the Science magazine designed a cover with bosons portrayed as soldiers, being the role of soldiers completely different to the one in the story above. Other metaphors describe the process in terms of dancers and cars.

Image from absfreepic.com, used with license CC0 Public Domain.