Quantum God (short story)

(link to pdf version) 
(link to Italian version, translation by Erica Mannoni)

2033 AD. The entire population of the planet was watching, most of them through the eyes of the media, waiting for Lord Q to perform a miracle and save the world. Thousands of people gathered around his tent, meditating, praying, praising him, and hoping for the miracle. The asteroid was heading toward the Earth. All previous attempts to destroy the asteroid failed, because it was a black hole. It was detected only by the way it bent the light and the trajectories of other asteroids in the Solar System. So the asteroid continued undisturbed to threaten the Earth, and Quentin, named by his followers Lord Q, was the only hope.

* * *

Roxanne joined Quentin’s group one year before, not as a believer, but as one of the last skeptics alive, by now a dying species. In the previous decades, scientific and technological progress continued to hunt God into the farthest and most obscure explanatory gaps, into oblivion. Until the emergence of Lord Q three years earlier, when everything was turned upside-down. Since then, he performed the most scientifically incredible miracles, normally attributed to a deity. Roxanne, a reputed physicist with a hobby of debunking pseudoscience, received a grant from a philanthropist who asked her to either find a scientific explanation for Quentin’s miracles, or prove that they are authentic.

When she joined the group, the believers disliked her for her skepticism, which remained unchanged even now, a year later. The only reason they tolerated her was because Quentin seemed to have a strange affection for her. She was allowed to be in his proximity all the time, and this made them dislike her even more, but they had to accept her. Quentin liked her, and was continuously amused by the suspicious look in her eyes, which was visible even when she was surprised by his miracles. For a year she followed him everywhere, witnessed him healing people, stopping natural catastrophes, wars, crime, and bringing back faith. She even saw him bringing back to life the president of the United States, killed by a rare form of cancer. But she continued to say that there must be a scientific explanation for everything.

Quentin never ceased to be intrigued by her disbelief and continued to watch her reaction as he performed his miracles. Once, he started to make flowers grow up out of nowhere and blossom in seconds, covering every piece of ground where Roxanne stepped. She was surprised, she blushed, and she told him that this is harassment. He didn’t know whether she was joking, so he stopped. It would have been the easiest thing for him to make her fall in love with him or even become a believer, but he didn’t want it to be like this. He loved her for being independent, and he would have never traded the chance to see her surprised and at the same time unimpressed by his powers for having an obedient Roxanne in place, a fervent adorer like the rest of his followers.

* * *

As Roxanne was waiting, worried to see what Quentin will do about the asteroid, Tom approached her.

– He will make it, don’t worry, he said.

– I know, she replied.

Tom was the first and only friend Roxanne made among Quentin’s followers. He used to be the leader of the third group of scientists sent by the James Randi Educational Foundation. The group tried to debunk Quentin’s miracles and find mistakes in the reports of the previous two groups, which declared that this was indeed the first authentic miracle recorded by the foundation. He saw no other choice but to accept Quentin’s miracles as true. The Foundation had to award the Psychic Prize for the first time in the history. They offered Quentin one billion dollars, which was the value of the prize at that time. Quentin donated the money to charity, of course. Tom became a believer, and in fact the most ardent one, given that he really looked for the smoke and mirrors and didn’t find any.

During one of their first conversations, Tom told Roxanne that he believed that all these miracles can be explained if Quentin had the ability to control quantum probabilities.

The behavior of particles is governed by quantum mechanics, which is very different from what we observe in our day-to-day life where things behave more like in classical mechanics. According to quantum mechanics, there is always an infinitesimally small probability for something apparently impossible for us to happen even in the real life. In the quantum world, if you observe that a particle – for example an atom – is in a small region of space, at a later time there is a small, but non-zero chance to find it in any other region of space. The reason is that quantum uncertainty makes the particle you know as being in a certain place to have an undetermined velocity, and therefore be able to move anywhere. Hence, at a later time, the particle will potentially be in all places simultaneously. When you observe it again, you will find it in one of these potential places. You can never know where it will be, only know the probability to find it in a given place. This probability is given by a formula called the Born rule. The probability to find the particle in a given place is small, nearly infinitesimally small, but not zero. The same works for more particles or atoms. It’s true that the probabilities become smaller and smaller as the number of involved atoms increases, but it never truly vanishes.

So Tom told Roxanne that he thinks Quentin performs his miracles by selecting which of the potential positions of a particle becomes true. If he can make a particle be where he wants, he can move objects. He can rearrange matter at will. Roxanne remembered that the neuroscientist Adam Hobson used to entertain similar ideas some years ago, but she always considered him a crackpot. She said:

– This happens only for quantum measurements, while Quentin, through his senses, makes classical observations, just like any of us. But, given that any observation we make is eventually a quantum one, maybe your hypothesis is true. However, the probability to control like this even a grain of sand is almost zero.

Tom said:

– Well, the chances are one in a billion of billions of billions… whatever, let’s just say a chance in a gazillion – but Quentin seems to bring those odds into existence.

– But even if he could do this, how can he influence larger objects, which behave classically due to decoherence?

Tom said:

– Decoherence suppresses the probability that the object behaves in a quantum way, but that probability never becomes truly zero. So there is always a very small chance that even larger objects behave in a quantum way, and apparently Quentin has a way to make this chance happen.

Roxanne replied that quantum probabilities are just those the Born rule says they are, and she doesn’t believe anyone can really break this law even a bit. So she can’t accept Tom’s suggestion, especially since it would mean Quentin breaking them. Tom said that for him the alternative is even worse because otherwise Quentin would break other laws, which are exact.

– Forced to choose between an exact physical law and a probabilistic law, Tom said, I would choose to sacrifice the probabilistic one.

– What about the many-worlds interpretation? she asked.

According to the many-worlds interpretation, every possible alternative result of a quantum observation is realized in an alternative world. This way, all possibilities already existing before the observation continue to exist in independent worlds, as if the world splits in many alternative histories.

Roxanne continued:

– Assuming the many-worlds interpretation is true, if Quentin’s miracles are explained because he controls the probabilities, this means that in the vast majority of the alternative worlds he doesn’t control them, just like any of us. And even for us, there is a very tiny chance that the possibility we wish becomes true, but that chance is so small, that it practically never happens. And even if miracles are just very improbable but still possible events, the Born rule has to remain valid in each of the alternative worlds. So the chances that Quentin remains in a world in which he always gets to make his miracles are the same – one in a gazillion.

Tom said he wants to think about this. Next day he said:

– What if he suppresses the possibility of the other worlds when he controls the probabilities?

Roxanne said she has to think about it.

Together, Roxanne and Tom analyzed every miracle made by Quentin, and indeed found that these could be achieved if Quentin had the ability to control quantum probabilities. Healing people, levitating, moving objects, all these seemed to them plausibly explainable if he would really control the quantum probabilities for the particles constituting the objects. But she was still not satisfied, she wanted to know how he does all these, and whether he really breaks the Born rule. She was sure that there must be a better explanation.

* * *

In the last minutes before the asteroid was about to hit Earth, Quentin got out of his tent holding a TV set. He put the TV on a table as the TV anchor was reporting the most recent news about the asteroid. Quentin sat on the grass and started to meditate. After several minutes, his peaceful face, his entire body started to glow. He began to levitate. He raised his eyes to the sky, then his hand, and smiled warmly. Shortly after, the anchor reported in an explosion of joy that the black hole changed its place, and it was no longer a threat to Earth. After a worldwide celebration, life on Earth continued to exist as before. 

* * *

A few weeks later, one night, Quentin was walking with Roxanne. After a full day of prodding him with all kinds of devices, she kept asking him all sorts of questions. He told her with a comforting voice to relax and just enjoy the night. Suddenly, she saw the stars moving in the sky, until they formed the image of her face. Really terrified, she yelled:

– Why did you do that?

Confused, he asked her what the problem was. She said:

– You just moved thousands of stars to impress me by drawing my portrait!

– So what? he said.

– You probably just killed dozens of civilizations!

She looked again in the sky, and the stars were back to their usual positions. He laughed:

– It was an illusion. I didn’t rearrange the stars in the sky, apparently I just bent the light rays coming from them. Or maybe I moved them back, I’m not sure…

They laughed, but she was still frightened.

* * *

For days, Roxanne kept studying Quentin with various high-tech devices. The money was not a problem for her sponsor. She scanned him, monitored his brain activity, recorded everything, and sent the data to specialized laboratories, for more thorough analysis. She found that he had a device implanted in his brain, following a car crash that happened three years earlier. Quentin refused to talk about the implant. But the implant seemed to do nothing relevant that would explain his abilities. It was simply a device that monitored his brain activity, collecting data from a number of places on his cortex. The implant was also stimulating some regions of his brain from time to time, but nothing relevant.

She also found something that surprised her even more: everywhere in Quentin’s body, there were billions of tiny spheres. She didn’t see them initially, they were too small, but she eventually found them after a more detailed analysis of Quentin’s tissues. She collected several of them and sent them to a laboratory. Just like the implant in his brain, the spheres seemed to be useless, or at least they didn’t exchange energy or information with the body at all, so she was very curious about their role.

When the result came back, she was perplexed. The tiny spheres were nanobombs, this was their only functionality. Remote controlled nanobombs, programmed to blow if they receive a certain signal, but obviously never detonated because that signal was never sent. Why on Earth would he have an implant that collects brain activity and never does anything with it, and why have billions of nanobombs also doing nothing at all? Anyway, the presence of nanobombs prevented her from trying to disable Quentin’s brain implant to see if it was the source of his powers.

* * *

Roxanne told Quentin what she found, and insisted that he should give her more explanations. He said that he will tell her more, if she promised to keep the secret.

– I have something to confess, he said. I am not the first one with these powers. Professor Adam Hobson, my uncle, who saved me after the car crash, he used to have them as well.

– You mean Adam Hobson, the guy with that crazy theory about the quantum brain, who disappeared a few years ago and was never found? Roxanne said.

Quentin told her how he had the car accident, and Adam saved his life with his highly advanced surgical robots. He said he had to implant a device in Quentin’s brain. Then Adam personally conducted the recovery therapy, teaching Quentin how to gain control of his body again and how to control his thoughts. After the recovery, Adam revealed more to Quentin. He said that both of them had implants, and that the implants allowed their minds to control matter.

Quentin continued:

– Uncle Adam taught me how to make miracles, by wishing them and by thinking at the changes I should be observing in the world after every miracle. He told me that he can already do this, and I will soon be able to do it too, and that both of us are godlike beings. He said there is no room for two gods, and that he will soon leave this world for a better one. He also said that I will leave this world soon too, and to tell everyone who cares about me that I will go to a better world. Then Uncle Adam activated my implant, and then he vanished in a bright explosion. It was the last time I saw him. I don’t know how this device functions. I just wish for things to happen, visualize what to expect once they happen until I have that feeling that they will do, and then they happen exactly as I visualized them. I learned that this way I can do pretty much anything.

Roxanne said:

– But this doesn’t make sense. The implant doesn’t do anything, it just collects your brain activity and stimulates it to make you feel happy. I just don’t understand…

* * *

Quentin was doing his morning meditation, when Roxanne came with a desperate look on her face, yelling from afar:

– You have to stop doing any miracle right now! This is gonna kill you!

– What?! said Quentin. What do you mean? What happened?

– You know Tom’s hypothesis that the way you do your miracles is by controlling quantum probabilities? Well, you can’t control them, nobody can!

– OK… so what? Quentin said.

– I know what’s in your head, what that implant does to you, she said.

– Well, good to know you finally got it. I’m all ears. Sit down here with me…

Roxanne caught her breath, but didn’t sit on the grass near Quentin. Instead she kept circling him, explaining:

– Whenever there’s a choice between more quantum alternatives, new worlds are created, in which each of these possibilities become reality. You can’t control which world is ours, you exist in all of them. Including in those in which your miracle doesn’t work. But when you make a miracle, you visualize the desired result, and your brain implant collects this information from your brain. Then, it compares it with what you observe afterwards. If your wish becomes real, then nothing happens.

– I don’t get it, Quentin said. Nothing happens, so the device does nothing. Then how can this explain anything?

Roxanne grabbed his shoulders and looked at him frantically:

– But if your wish doesn’t come true, which is almost always the case, then the implant detonates the billions of bombs in your body. You explode into a bright light, and you die.

– I never died…

– You will always find yourself, of course, in a world in which you are not killed, hence where your wish came true. Your implant is a quantum suicide device, inspired by the quantum suicide thought experiment proposed in the eighties to test the many-worlds interpretation. Gazillions of worlds are created whenever you make a miracle, and gazillions of copies of you are killed in all of these worlds! Gazillions of copies of us are left in tears… In all worlds, except in those very, very, very rare in which your wish comes true!

Seeing her crying, Quentin dispersed the clouds in the sky and made out of thin air a rain of flower petals.

– See, nothing happened, dummy…

Cristi Stoica, May 17, 2016

The unreasonable beauty of mathematics in the natural sciences*

Imagine a man and a woman, seeing and liking each other at a party or club or so. They start talking, the mutual attraction is obvious, but they want to be casual for two minutes. So they exchange informal formalities about doesn't matter what. Then he asks her: "so, what do you do?", and she replies "I'm a poet". What if the guy would say something like "I hate poetry!", or even declare proudly "I never knew how to use letters to write words and stuff, and I don't care!". Or imagine she's a musician, and he says "I hate music!". There are two things we can say about that kind of guy. First, he is very rude, he never ever deserves a second chance with that girl or any other human being for that matter. He should be isolated, kept outside society. Second, or maybe this should be first, how on earth can he be proud for being illiterate!

You probably guessed that this story is true. OK, In my case it was about math instead of poetry, and the genders are reversed. This happened to me or to anyone in the same situation quite often. There is no political correctness when it comes about math, maybe because one tends to believe that if you like math, you have no feelings, and such a remark wouldn't hurt you. And I actually was never offended when a girl said such outrageous things like that she hates math. Because whenever a girl told me she hates math, I knew she calls math something that really is boring and ugly, and not what I actually call math. Because math as I know it is poetry, is music, and is a wonderful goddess.

The story continues, years later. You talk about physics, with people interested in physics, or even with physicists. And you say something about this being just a mathematical consequence of that, or that certain phenomenon can be better understood if we consider it as certain mathematical object. It happens sometimes that your interlocutor becomes impatient and says that this is only math, and you were discussing physics, that math has no power there, and so on. Or that math is at best just a tool, and it actually obscures the real picture, or even that it limits our power of understanding.

People got the wrong picture that math is about numbers, or letters that stand for unknown numbers, or being extremely precise and calculating a huge number of decimals, or being very rigid and limited. In fact, math is just the study of relations. You will be surprised, but this is actually the mathematical definition of math. Numbers come into math only incidentally, as they come into music, when you indicate the duration or the tempo. Math is just a qualitative description of relations, and by relations we can understand a wide rainbow of things. I will detail this another time.

Imagine you wake up and you don't remember where you are, or who you are, like you were just born. You are surrounded by noise, which hurts your ears and your brain, meaningless random violent noise. You run desperately, trying to avoid it, but it is everywhere. And you finally find a spot where everything becomes suddenly wonderful: the noise becomes music, a celestial, beautiful music, and everything starts making sense. You are in a wonderful Cathedral, and you are tempted to call what you are listening "music of the spheres". The same music played earlier, but you were in the wrong place, where the acoustics was bad, or the sounds reached your ear in the wrong order, because of the relative positions of the instruments. Or maybe your ears were not yet tuned to the music. The point is that what seemed to be ugly noise, suddenly became so wonderful.

So, when someone says "I hate math!", all I hear is "I am in the Cathedral you call wonderful, but in the wrong place, where the celestial music becomes ugly violent noise!".

If you are interested in physics, you entered the Cathedral. But if you hate math, you will not last here, and maybe it is better to get out immediately! And if you are still interested in physics, come inside slowly, carefully choosing your steps, to avoid being assaulted by the music of the spheres, to allow it gently to enter in your mind, and to open your eyes. Choose carefully what you read, what lectures you watch, and ask questions. Don't be shy, any question you will ask is the right question for your current position, and for your next step.

There are some places in the Cathedral where the music is really beautiful. If you meet people there, to share the music, to dance, you will feel wonderful. If not, you will feel lonely. So you will want to share that place, you will want to invite your friends to join you.

The reason I love physics, is that I want to find these places. The reason I read blogs and papers, is that I want them to help me find such places. The reason I write papers, and I blog about this, is that I would like to  share my places with others. I attend conferences (four so far this year) because they are like concerts, where you get the chance to listen some wonderful music, and to play your own.

But these are just words. I would like to write more posts in which I show the unreasonable beauty of math in physics, with concrete examples. Judging by the statistics, I have a few readers; judging by the number of comments, I don't really touch many of them. I know sometimes I am too serious, or too brief when I should explain more, especially when mathematical subtleties are involved. I am not very good at explaining abstract things to non-specialists, but I want to learn. I would like to write better, to be more useful, so, I would like to encourage comments and suggestions. Ask me to clarify, to explain, to detail, to simplify. Tell me what you would like to understand.

To start, I would like to write about vectors. They are so fundamentals in all areas of physics and mathematics, so I think it's a good idea to start with them. You may think they are too simple, and that you know all about them from high school, but you don't know the whole story. Later, when I will say something about quantum mechanics and relativity, they will be necessary (after all, according to quantum mechanics, the state of the universe is a vector). On the other hand, if you will understand them well, you will be around half of the way to understand some modern physics.

______________________

* You surely guessed that the title is a reference to Wigner's brilliant and insightful lecture, The unreasonable effectiveness of mathematics in the natural sciences.

Update, October 14, 2014

I just watched an episode of the Colbert Report, where the mathematician Edward Frenkel was invited in April this year. It was about Frenkel's new book and about his movie. He discusses at some point precisely the fact that it is so acceptable to hate math, as opposed to hating music or painting. Here is what he says for The Wall Street Journal:

It's like teaching an art class where they only tell you how to paint a fence but they never show you Picasso. People say 'I'm bad at math,' but what they're really saying is 'I was bad at painting the fence.'

Also see this video: