Quantum Physics Takes Free Will into Account

Adolfo Plasencia:

Ignacio, thank you for having me.

Ignacio Cirac:

My pleasure. Thanks for coming.

A.P.:

Ignacio, you’re well aware that great expectations have been aroused by quantum physics. Some people think that Moore’s law is seeing its end days and that other alternatives have to be sought to continue our progress in computer science and information technology (IT). The ultimate alternative in this sense is quantum physics. But in addition to this, quantum physics combines with philosophy; it deals with who we are and why we exist. There is a big debate surrounding all this. For instance, in a recently published debate, some intellectuals have associated quantum mechanics with such things as human freedom, free will; with the kind of criteria more linked to metaphysics than to physics. Some people have linked quantum physics with freedom of choice and suggested they are not compatible, thereby leading to determinism.

The physicist Carlo Rovelli, leader of the Quantum Gravity Group (Équipe de gravité quantique) of the Centre de Physique Theorique de Luminy, refuted these statements in a text published by Edge: “Free Will, Determinism, Quantum Theory and Statistical Fluctuations: A Physicist's Take.”¹ There he reminded us that Democritus assumes that the movement of an atom is deterministic; that is, a different future does not happen without a different present.

Over the past century, Newton’s equations have been replaced by your and your colleagues’ equations and math—I mean those of quantum theory—which include an element of uncertainty governed by highly rigorous probabilistic dynamics. You have so many references and so much precise information that is difficult to refute. Your equations do not determine what is going to happen, but they strictly determine the probability of what is going to happen. In opposition to those who have established a link between the two, Rovelli says that free will has nothing to do with quantum physics because we are highly unpredictable as human beings, as is the case with most macroscopic systems, and there is no incompatibility between free will and microscopic determinism. In other words, people’s freedom of choice does not contradict your quantum mechanics.

Rovelli states that our idea of being free is right, but this is only a way of saying that we are ignorant about why we make decisions.

What do you think of Rovelli’s statements?

I.C.:

This is a very interesting and deep discussion. I don’t think it can be summarized in just a few words, but, even so, a few things should be highlighted. First, quantum physics gives you a new vision of nature, a new vision that perhaps has both philosophical and physical repercussions. It tells us, in a way, that the properties of objects are not defined, and we are defining them when we observe them. It’s really quite strange, a rather odd and striking theory. It’s startling that nature behaves this way.

A.P.:

Well, strange if we view it in terms of the framework that has governed physics since Newton. What do you think?

I.C.:

It’s strange from the point of view of what we are used to seeing. If somebody explains to you the principles of quantum physics, it looks like something extraordinary, a really bizarre and almost unbelievable thing. Thus, some people are looking for ways to keep our vision of nature unchanged, to preserve the vision we used to have.

And perhaps a way not to change this previously proposed vision, which I won’t go into, is to state that we do not have free will. But what would happen, you think, if we did not have free will? Could we then salvage some of nature’s properties? For instance, if, every time I do an experiment, the results conform to or don’t contradict quantum physics, it might just be that it was already programmed to turn out that way; that is, I have no power of decision and there is nothing I can do or decide about it, which would put any theory in a position of vulnerability. A few papers have been published in the last few years dealing with this issue, but I am not an expert on that.

A.P.:

However, does it make you feel obliged to be even more rigorous, to “demonstrate” and think even more?

I.C.:

These are things that cannot be demonstrated. I mean, if a robot is programmed, it’s likely that it won’t itself realize that it has been programmed, but I think very few people think about this. It is just one opinion, which is a small part of a huge range of opinions that exist, and is a very extreme one indeed.

But there are other, much more consistent possibilities, or at least they appear much more reasonable to us than the one you’ve mentioned. Quantum physics in a way takes free will into account. In itself, although maybe not in its hypotheses, it makes the assumption that we are capable of choosing and deciding how, for example, to make measurements. This is what gives rise to all the experiments and experimental arrangements that we have. But what happens with quantum physics, which is also very interesting, is that it is really different from other previous theories, which were supposed to include a description of ourselves as well. In other words, after Newton put forward his laws and Maxwell also developed his laws and equations, people thought that these principles applied to nature as a whole, which includes us, because we are made of atoms and matter. In other words, we ourselves should also follow the laws of nature. And in a way, this is what led people to think about determinism—that is, if we follow Newton’s laws and they are deterministic, that means we are determined. But some people said no, that’s not right: what is completely outside Newton’s laws and doesn’t follow them is our conscience, or whatever you want to call it. This is a real possibility until someone proves the opposite.

Quantum physics is something else. On the one hand, it states what happens with everything else, yet on the other hand it cannot define itself, which is very strange indeed. In fact, a small problem called the measurement problem arises with quantum physics precisely on this point. Why is it that this branch of physics cannot describe what we do but can describe everything else? It’s a fascinating subject. At present, various options are open to us, and none can be discarded as false until further research is undertaken.

A.P.:

The famous MIT professor Walter Lewin says in his book For the Love of Physics that the most important thing about measurement in physics is, precisely, accuracy and precision.² As Lewin says in his book, and as he also told his students, “Something which all university text books on physics always leave out when taking measurements, concerns the issue of imprecision in the measurements.”

He also kept telling his students, “Any measurement you make without knowing its imprecision is completely meaningless.”

This gives you an idea of the importance that precision has in measurements in physics. Yet, Ignacio, you quantum physicists actually make measurements that are so precise they are almost irrefutable, and everybody agrees on that.

I.C.:

Yes, what we have in quantum physics, especially in what is called quantum electrodynamics, is that its predictions are highly precise. So you can measure a physical property to twelve digits of precision. This is something that nobody imagined could be measured, but nevertheless it is measured. Therefore, it’s a very strong and sturdy theory, one that has been highly tested. Nevertheless, you always have to say that this is not the final theory. But if we go along with this line of thought, we’ll never have a final theory; there will always be experiments that we haven’t done that might have produced results leading to a different theory.

A.P.:

Have quantum physicists, like you, observed any resistance from within your field of work to your breakthroughs in the world of physics?

I.C.:

No. That happened a bit during the 1930s and 1940s, when quantum physics was under development and naturally these strange properties were found, features of nature that were so different from the classical way of thinking that there was some reluctance.

There are some examples in which there were some difficulties, but the mind of a physicist is very open, and all that most of them wanted to do was to carry out experiments and see if things were like that. As soon as the experiments were done, things started to open up. Now it is difficult to find anybody, any physicist, who does not believe in quantum physics.

A.P.:

Let’s talk a little about some of that historical opposition. Albert Einstein wrote in a letter to Max Born in 1926, “Quantum mechanics is a very serious matter, but I heard an interior voice saying, this is not the way.”³ According to Roger Penrose, Einstein didn’t like the probabilistic side of quantum mechanics. He said that this side to it was not acceptable for him because Einstein was convinced that there must be a physical world, objective in itself, even on the minute scales of quantum phenomena, which is the environment in which quantum physicists thrive.

You mentioned in an interview, “Usually, when we observe something, we see that it exists and is well defined. Whenever we see a yellow object, we think that this is an ‘objective’ property the object has, which doesn’t depend on me. That is, when I am not watching it, the object still remains yellow.”⁴ Now, quantum physics, according to you, says no; it says that some properties of the microscopic objects in movement are not defined when they aren’t being observed and only become defined when we watch them.

If I understood properly, what you have said moves away from this intrinsic “objectivity” of matter, which Einstein preferred.

Do you think it has been difficult for quantum physics to firmly contradict someone as great as Einstein?

I.C.:

I don’t think it was that difficult. In Einstein’s time, people discussed and debated at great length. Because, of course, when he says, “This theory cannot be right,” somebody wonders, what is wrong about the theory? Tell me why it’s wrong. He wasn’t able to say what was wrong. He tried to find contradictions, but he couldn’t find any. But I think there has been a process to this. On the one hand, many scientists thankfully said, “Well, it’s a strange thing, but we are going keep moving forward.” They kept working on particle theory and developed the Standard Model without worrying themselves about the issue. On the other hand, another group of physicists said, “We are going to do experiments to find out whether this is true or false.” These experiments took place, and moved forward, especially in the 1980s, and today the evidence clearly shows that nature is like this. And when you get used to it, well, I think if Einstein were alive today and had become used to it, he wouldn’t be too surprised to discover that’s how things were.

A.P.:

I don’t think he would find it strange because, in fact, I believe he did the same thing. When he’d made a number of discoveries about his theory of relativity, in a way, and in certain fields, he questioned Newton’s mechanics, which had been upheld for centuries. So could we say that you quantum physicists have done the same to him as he did to Newton?

I.C.:

Yes, in fact, they did. We haven’t done much, but they did. However, I think that the change brought about by quantum physics is much greater than that brought about by the theory of relativity. Relativity, of course, is extraordinary; it has made a huge change. But quantum physics in addition to that gives us a new vision of nature, which is not just a question of ensuring that some specific laws are observed or not, or the fact that things move and time changes when you move, and so on. Yes, it is really strange, but it tells us something else. It’s telling us that reality is stranger than what we thought. When we speak about reality, the reality of objects, it’s much more than that.

A.P.:

Much more complex?

I.C.:

Yes, reality is much more complex, has more possibilities, is more uncertain, and is beginning to provide us with more questions than answers. Well-known physicists such as Richard Feynman say that nobody understands quantum physics. Even if you try hard to think about it there is no way to relate it to any other analogy that you can find in the ordinary world. Whereas I do think that you can imagine it, that it’s easier for the imagination to grasp.

A.P.:

Ignacio, as you have put it, the change in quantum mechanics is just starting, and what you are doing is probably just the start of a huge change.

Do you have any hypothesis about which changes of scale the applications of quantum information theory might involve for our present world, which is a highly computerized and technological world, having a global network shared by more than one-third of the world’s population and with more cell phones than people?

What do you think would change if digital information being used now became quantum and networks became quantum networks?

I.C.:

We are just starting to scratch the surface of this world of quantum physics and we have just begun to be aware of the first applications, but, as happens whenever we have access to new laws of physics, the most important applications are yet undiscovered, and most likely any forecast I could make now about quantum physics applications would have nothing to do with anything that happened during the next thirty years. However, what we know now is that if we can have access to these laws of quantum physics, we will be able to build systems capable of processing and transferring information in a very different way. This allows us to envisage much faster computing, maybe not for every type of calculation or computing, but for some of them. We might also have more efficient and safer forms of communication, transmitted in such a way that nobody will be able to hack our communication. I don’t know what impact this may have, for instance, on cell phones. Smart phones already cover most of our present-day needs.

A.P.:

But also, as you know, there are already clichés about your science—something can be in two different places at the same time, the cat may be alive and dead at the same time ⁵—things that make you imagine something even stranger than you can imagine. And very often our imagination is wrong, and that is why we have your experiments. Of course, after watching Star Trek, people think that bodies can be teletransported to another galaxy.

Now, we know this cannot be true, but we can’t prevent people from imagining things that you physicists have never said, which are truly impossible, even for quantum physics.

I.C.:

Yes, that’s right. Sometimes we physicists use some unfortunate language to name phenomena, such as teletransportation—that word has a very clear meaning. Quantum teletransportation (quantum teleportation) means in a way that it is information and not matter that disappears from one place and appears in another. And this is true. But as soon as we have access, and as soon as communication systems based on quantum physics can be built into the computer, that is when ideas about how to use them will emerge, as, for instance, a huge computation power. Don’t you agree?

We already know today that such computing power might be used in drug design and new materials design. This computing is done today by supercomputers. But I guess that when we achieve it, somebody will find out what it can be used for. And the same happens with communication. We know that quantum communication is safe. As you quite rightly said, information may disappear from one place and reappear in another without going through anything on the way, and that means nobody can read it. That is an application. There may also be some talk of quantum credit cards, which no one can copy, so the information is unique and nobody can use it in your name. We already know about some of these applications, but there must be many that have not yet been exploited because we need young people with good ideas, not us, the scientists formulating and developing these phenomena, but people having ideas about how these new laws of nature should be developed.

A.P.:

That’s right, but this doesn’t mean that anything is possible. The imagination of a scripwriter may generate hypotheses that are and will always be impossible. They do, however, associate them with names as strange as the ones you have discovered, don’t they?

I.C.:

Yes, we must be careful because sometimes quantum physics seems to hide mysteries. It is even used in a wrong way, such as to insist, “This cannot happen, that can happen”—there are many instances on record. You mentioned Star Trek and physical teletransportation. We do not know how to do this today. We do not even know whether the laws of physics will allow it, but probably the answer is no. Another thing that people hear is that they can influence their future simply by—

A.P.:

By traveling into the past and changing it?

I.C.:

Well, that is another thing. I was referring to the so-called quantum superposition, that is, you can do two things at the same time, or I can use my mind to cause or make something happen. This has nothing to do with quantum physics. For this reason, there are misconceptions about the ideas of quantum physics because some people who speak about them don’t have a clear concept or understanding, or they are speaking about something completely different from quantum physics.

A.P.:

I saw you being interviewed on TV, and you said that for you there is a before and an after. Until 1994 people, even those connected to science, thought that applying quantum theory in practice was not going to be possible. But in 1995, you and the Austrian theoricist Peter Zoller together presented the first theoretical description of a quantum computer architecture.⁶ It was based on ion traps in which electrically charged atoms, cooled almost to absolute zero, were trapped by electrical fields and manipulated by lasers. Could you describe this architecture? Is there any equivalence between the description of a quantum computer architecture and that of present IT? Wired magazine referred to the computer you described in that paper as the holy grail of computer science, which has been sought by scientists since 1980.⁷ Do you find this a bit exaggerated?

But first, how is this architecture you described?

I.C.:

If we can use quantum physics to transfer information, then the first thing quantum physics says is that instead of storing and processing data in terms of bits, zeros and ones, it must be done in terms of quantum bits, or qubits, which means they have to be physical systems, such as zero and one, and also have the property of quantum + superposition. We know that this happens at an atomic level, so the only thing one has to be able to do is choose a series of atoms, in this case ions, and manipulate the properties of the electrons composing these atoms, specifically the property called electron spin, with lasers, in such a way that the electrons change from zero to one and from one to zero, and which, in addition, can also have quantum superpositions and interact with each other, in order to carry out quantum computing .

A.P.:

And in a controlled way? With an aim, I mean.

I.C.:

That’s right, with an aim. In the same way as ordinary computers handle zeros and ones in terms of logic gates, qubits can also be used to make the appropriate calculations in terms of logic gates, which we call quantum gates. And handling these quantum logic gates takes place by means of lasers—that is, by using lasers aimed at these ions, which send a little amount of light to each of them. The intensity of light sent and the time during which the light pulse is sent depend on how the program is made, based on what you want the ions to do, that is, which logic gates you want to be “executed.” This is simply what a quantum computer like those we have today does. Today’s are prototypes. They are very small, but they prove that all this works.

A.P.:

I am also very interested in the human aspect. What you were in search of, as Wired magazine says, is the holy grail of tech research, right? And for a long time, many important scientists said this was impossible. Now, all of a sudden, you present a paper and say: It is not impossible! It is possible, and that’s it. Amazing! How was that moment? Was it difficult for you and Peter?

I.C.:

Well, yes. This is a strange story. We were working in quantum physics, basically on how to cool atoms, how to cool ions, how to make them stop, and observing those strange properties produced by quantum physics, but we had hardly heard of quantum computing. We had heard about some other different things. Then, at a conference in Colorado in 1994, it was mentioned—in an abstract way, in theory—that these quantum computers might exist, but we still didn’t know whether they could be built. And as we were working on cooling these ions, we thought, perhaps this can be a way to build them, because these were the ones that we understood better, up to that moment, from the quantum point of view. So, based on this, we started to work. We had several ideas, and three months later, we concluded that, in fact, the answer was yes, this would be possible, after taking a series of steps. As we weren’t from the field of quantum computing, we wanted to know whether what we were doing was right. So we took a train to Torino to attend a conference on quantum computing theory and present our proposal before physicists working on quantum computing.⁸

A.P.:

What was the reaction? Were there any big surprises?

I.C.:

It was funny. Of course, people trusted us, more or less, because we had already predicted some experiments, which had already been tried and tested. On the other hand, their background was completely different, and they didn’t have sufficient knowledge about ions.

I particularly remember someone who was at that time working in quantum computing saying to me when I finished my speech, “This is impossible!,” and I thought: Why? “Because there is a theorem that says this is impossible!,” he said.

And I thought, but how is that possible if, mathematically, everything is correct! After the lecture I went to talk to him and I started to explain to him that we were using the qubits with two internal levels, and in order to make the logic gate we were using another internal level.

And then he told me, “No, no, but this is forbidden! You only have two levels!,” and I told him, “No, atoms have many more levels!” Then I realized what had happened. He had developed his theorems thinking that there was not another level. What we saw was that it couldn’t be done unless you added another level, so, as far as we knew, as far as we had observed, it could be done since atoms also have more possible levels.

A.P.:

So with energy, you can make an electron jump from one level to another, and, depending on the energy, it can jump to a different level, and he thought there were no intermediate levels. Is that right?

I.C.:

Yes, understanding that is a bit like understanding the difference between mathematicians and physicists. His structure was of the kind: “If I have that and that, then this is possible and this is not.” The physicist instead says: “Well, if this is impossible, what I should do is add things until it is possible, shouldn’t I?” This is a little like the way I see it. It happened to me several times during my career, experiencing the fact that we physicists try to do everything possible—in some ways breaching the a priori approaches and considerations of mathematicians—to transform things so that they stop being certain and and immovable when we want to achieve something.

A.P.:

That means not only once but many times you have come across surprised faces in the audience, haven’t you?

I.C.:

Yes, and not only with things done by me but also things done by other physicists, for example the time when some theorists predicted that Bose-Einstein condensation was practically impossible with some particular atoms. Proof of the phenomenon received the Nobel Prize in Physics in 2001; the result had been experimentally produced in 1995.⁹

The experiments were done in Colorado, where I was living at the time. I remember asking one of the experimenters, “But if it has proved impossible, why do you keep carrying out the experiment?,” and the experimenter answered, “Because I don’t follow what they mean!” Well, finally the experiment eventually worked out! And the expermentalist in question, Eric A. Cornell, was given the Nobel prize.

A.P.:

Do you mean that reality is much more open than the mathematics that claims to represent it?

I.C.:

It depends. These kinds of things have happened many times, although the opposite has also happened. Many people doing a certain experiment take a long time, and then a mathematician arrives and says, “No, you do it this way, the other way is impossible,” and if that is understood, a lot of money can be saved in research because you can see that this is not possible. So these are the two sides, but in this particular case, reality surprised them.

A.P.:

Let’s talk about another case that is happening now. In copper semiconductor technology, it is now calculated that by 2016 there will be chips with a technology of 12 nanometers. If they continue like this, physically, the specialists say, there will come a time when, for a pure physical reason, the electrical charges may jump from a copper microprofile of the chips to another, and this method will be exhausted because of the extreme reduction of its scale. From your point of view as a researcher in quantum mechanics, is it your understanding that a truly functional quantum computer will arrive before Moore’s law is exhausted?

I.C.:

I don’t think so. The first demonstration of a quantum computer, which was a basic demonstration with just one of the qubits, took place in 1995, just after we published a paper in which one of the basic parts was shown in one of the experiments. Then in 1997, experiments were done with two of the qubits. In 2000 there were four qubits; in 2004 there were eight. Today we have fifteen or sixteen, and there are people who say they have probably reached thirty. Now, if this is extrapolated to 10,000, which is what is needed, or to 100,000 or 1,000,000, which would be the optimum, there are still many years ahead.

A.P.:

What’s better right now, 10,000 or 1,000,000 qubits?

I.C.:

We know that with about 1,000 qubits, we could do some interesting calculations. The problem is that there are likely to be errors, but if we had 1,000 qubits that were perfect, we could carry out some really interesting calculations. The problem is that qubits are not perfect, and we have to perform error correction, or “debugging.” That means that the number of qubits that you have to use in practice is at least one hundred times higher than the original. Therefore, to do computing in the presence of errors, we would need about 100,000 to 1,000,000 qubits. However, to reach this figure, an important technological development is still needed, and this might come in five years or fifty. We do not know.

A.P.:

In formulating the next question, I had to consult a friend who is a wonderful physicist in the field of condensed matter, Pablo Jarillo-Herrero, and pose the question to him first. Another of your contributions, yours and Peter Zoller’s, is the quantum simulator.¹⁰ When you hear the word “simulator,” you imagine a flight simulator that simulates the outside world, with you at the controls and everything you see behaves interactively. That’s what I thought a simulator was. Pablo explained the following to me. Yours is a simulator for artificial matter with real atoms. With a simulator like this, you could work out how conducting materials behave at high temperatures, for example. In other words, it is actually a simulator of real material made artificially, but which allows the possibility of understanding how materials behave with real atoms in certain environments that are very difficult to see in nature. Is that right?

I.C.:

That’s right. The idea is somewhat similar to what I mentioned before, that it will probably take a long time for quantum computers to be constructed, and you might stop to think: Well, what do we want a quantum computer for? What applications do quantum computers have? And one of the applications, perhaps the most important one, is the one that would be capable of solving scientific problems that we cannot figure out with normal computers, problems related to materials design, perhaps with chemical reactions, the chemical composition of some materials, and so forth

So, from this analysis, we get the idea that maybe it isn’t necessary to build a quantum computer to solve these problems; maybe we can actually do it using an analogical computer in which we choose a totally different system, a system of atoms, for example, where they are made to interact in such a way that they behave like the material you want to simulate. And if you take measurements in this atomic system, you might be able to make predictions about what is going to happen with the material. We explicitly proposed that something like this should be built, and the first experiments were carried out in 2002. Today the first quantum simulations have been carried out with this equipment—simulations that we are unable to describe with normal computers. In other words, the first quantum simulator that specifically works faster than a normal computer has already been built. The problem is that there isn’t any scientific interest in this simulation, which means it is an “artificial problem.”

A.P.:

Where was this done? In Europe?

I.C.:

Yes, in Europe. In fact, the first experiment was carried out at the Max-Planck-Institut, Munich, by Immanuel Bloch’s group.¹¹ And now many experimenters are trying to replicate these simulations, and I believe that we'll soon start to see people who have worked out problems that we couldn’t solve before with normal computers using these quantum simulators.

A.P.:

But what you’re saying isn’t only physics, it’s also chemistry, isn’t it? In another conversation in this book I was told by the renowned chemist Avelino Corma, that when you work on a scale below 10 nanometers, physicists and chemists work in the same setting doing practically the same thing.¹² Would it be right to say you work in the field of physico-chemistry?

I.C.:

Yes, it would. I fully agree with Avelino on this account, to the extent that we understand each other and use the same language when we speak under these conditions.

A.P.:

There’s something else I’d like your opinion on. I’ve been asking you a lot of things about where this experiment is. You tell me “at our Institute in Germany, close to Munich,” and that it is cutting-edge experimentation. I'm interested in knowing whether the approaches have any geographic relationship, or perhaps some scientific cultural nuance. That’s why I'm asking you if there is a vision of science that characterizes and differentiates European science from what may exist in other “sciences,” for example, the United States’, even though I'm aware that science is now global, with people from all over the world working in teams. But in your opinion, is there anything that characterizes European science with respect to other scientific views?

I.C.:

I believe that European science in general is more conservative than in North America. The Americans are much more intrepid. Young people in the United States have ideas they want to put into action as soon as possible, whereas in Europe, it’s more step by step; of course, there are numerous exceptions to this rule.

A.P.:

But surely you’re not talking about scientific semantics because European science is great at inventing words and has nothing to fear from America, right?

I.C.:

No, semantically it doesn’t. But then again, it’s simply something you can see. For instance, there’s more help for young people in America. There is an idea that when you get a PhD and do a bit of postdoctoral study, what you need to do is step aside and let the ideas flow, which will probably lead to the best ideas. It’s not the same in Europe, in general. When you finish a postdoctoral course, it is possible that you might have some independence, but you always depend on somebody because they want to focus research on certain issues, which are the ones they want to be solved within many years. It is different, though. The American way is likely to be more successful on the applied research side and the European perhaps in the more theoretical domains. In fact, at the moment I think that my area of research, which is quantum computing, is on the same level or even higher than in North America.

A.P.:

I heard a scientist who was defending the European version saying it isn’t that we are more conservative, we are just more rigorous! We are more cautious about presenting results that haven’t been fully substantiated. That was how he defended the European vision. I don’t know if you agree.

I.C.:

Well, yes, I do, but the European system has its advantages and disadvantages. There are people who might think that so much rigor—as I said in the example I gave before—means it isn’t possible to do something, when perhaps they should be saying, “If it isn't possible, let's make it possible!” It was good to change experimental conditions, but even so, I think it’s difficult to differentiate European and American science except in very general terms.

A.P.:

From what you’ve told me, mathematicians are even more conservative than physicists, right?

I.C.:

Yes. The thing is that within mathematics there is also originality, people who not only figure out the problem but who also realize that some problems are more important than others, and there’s a lot of originality and art in that. There are people who find new formulas, new ways of solving problems that aren’t conservative but break away from all concepts. People used to think that to solve a problem, you had to follow a set of guidelines along the way; then someone else comes along on a completely different path that actually solves the problem in a simpler way.

A.P.:

Ignacio, thanks very much. It has been a pleasure, and I hope to see you again soon. Maybe you'll have a quantum computer up and running by then. Thanks!

I.C.:

Great! Thanks to you too!

1 Quantum Physics Takes Free Will into Account

Notes