Helgoland: Making Sense of the Quantum Revolution

by Carlo Rovelli

foundations of chemistry, the functioning of atoms, of solids, of plasmas, of the color of the sky, the dynamics of the stars, the origins of galaxies . . . a thousand aspects of the world. It is at the basis of the latest technologies: from computers to nuclear power. Engineers, astrophysicists, cosmologists, chemists and biologists all use it daily; the rudiments of the theory are included in high school curricula. It has never been wrong. It is the beating heart of today’s science. Yet it remains profoundly mysterious, subtly disturbing.

At first, I was deeply alarmed. I had the feeling that I had gone beyond the surface of things and was beginning to see a strangely beautiful interior, and felt dizzy at the thought that now I had to investigate this wealth of mathematical structures that Nature had so generously spread out before me.

Nothing is like the emotion of seeing a mathematical law behind the disorder of appearances.

The phenomenon from which the strangeness of quanta derives is called “quantum superposition.” A quantum superposition is when two contradictory properties are, in a certain sense, present together. An object could be here but at the same time elsewhere. It is what Heisenberg means by saying that “the electron no longer has a trajectory”: the electron is found not to be only in one place or another. In a sense it is in both places. In the jargon, we say that an object can be in a “superposition” of positions. Dirac called this bizarre behavior the “principle of superposition.” For him it was the theory’s conceptual foundation.

we never see a quantum superposition. What we see are consequences of the superposition. These consequences are called “quantum interference.” It is the interference that we see, not the superposition.

If you find all this confusing, if you cannot make head or tail of it, you are not alone. It is why Richard Feynman wrote that nobody understands quanta. (If instead what I have described seems perfectly clear, then it means that I have not been clear enough about it. For as Niels Bohr once said, you should “never express yourself more clearly than you are able to think.”37)

the keystone of the ideas in this book, is the simple observation that scientists, and their measuring instruments as well, are all part of nature. What quantum theory describes, then, is the way in which one part of nature manifests itself to any other single part of nature.

At the heart of the “relational” interpretation of quantum theory is the idea that the theory does not describe the way in which quantum objects manifest themselves to us (or to special entities that do something special denoted “observing”). It describes how every physical object manifests itself to any other physical object. How any physical entity acts on any other physical entity.

To understand nature, we must focus on these interactions rather than on isolated objects.

Quantum theory is the theory of how things influence each other. And this is the best description of nature that we have.52

The properties of an object are the way in which it acts upon other objects; reality is this web of interactions. Instead of seeing the physical world as a collection of objects with definite properties, quantum theory invites us to see the physical world as a net of relations. Objects are its nodes.

This is the significance of Heisenberg’s original intuition: to ask what the orbit of an electron is when it is not interacting with anything is an empty question. The electron does not follow an orbit because its physical properties are only those that determine how it affects something else, for instance, the light that it emits when it is interacting. If the electron is not interacting, there are no properties. This is a radical leap. It is equivalent to saying that everything consists solely of the way in which it affects something else. When the electron does not interact with anything, it has no physical properties. It has no position; it has no velocity.

Is it possible that a fact might be real with respect to you and not real with respect to me? Quantum theory, I believe, is the discovery that the answer is yes. Facts that are real with respect to an object are not necessarily so with respect to another.* A property may be real with respect to a stone, and not real with respect to another stone.55

Einstein’s special relativity is the discovery that the notion of simultaneity is relative, and so on. The discovery of quantum theory is only slightly more radical: it is the discovery that all the properties (variables) of all objects are relational, just as in the case of speed.

Physical variables do not describe things: they describe the way in which things manifest themselves to each other. There is no sense in attributing a value to them if it is not in the course of an interaction.

The ψ wave is the probabilistic calculation of where and how an event relative to us might occur.56 The wave as well is therefore a perspectival quantity. An object does not have one ψ wave, it has one with respect to every other object with which it interacts. Events that take place in relation to one thing do not influence the probability of ev...

The world is the network of relative facts: relations realized when physical entities interact. A stone collides with another stone. The light from the ...

The life of an electron is not a line in space: it is a dotted manifestation of events, one here and another there. Events are punctiform, discontinuous, probabilistic, relative.

definitely other than how we had conceived of it. Even if we know all that can be predicted about one object and another object, we still cannot predict everything about the two objects together.64 The relationship between two objects is not something contained in one or the other of them: it is something more besides.65

an exchange of signals is an interaction, where new elements of reality come about.

The joint properties of two objects exist only in relation to a third. To say that two objects are correlated means to articulate something with regard to a third object: the correlation manifests itself when the two correlated objects both interact with this third object, which can check. The apparent incongruity raised by what seemed like communication at a distance between two entangled objects was due to neglect of this fact: the existence of a third object that interacts with both the systems is necessary to give reality to the correlations. Everything that manifests itself does so in relation to something. A correlation between two objects is a property of the two objects—like all properties, it exists only in relation to a further, third object. Entanglement is not a dance for two partners, it is a dance for three.

Entanglement is therefore far from being a rare phenomenon that occurs only in particular situations: it is what happens, generically, in an interaction when this interaction is considered in relation to a system external to it. From an external perspective, any manifestation of one object to another, which is to say any property, is a correlation; it is an entanglement between an object and another. Entanglement, in sum, is none other than the external perspective on the very relations that weave reality: the manifestation of one object to another, in the course of an interaction, in which the properties of the objects become actual.

All the information that we have about the world, considered externally, is in these correlations. Since all properties are relative properties, everything in the world does not exist other than in this web of entanglement.

this language allows us to pinpoint the difference between classical and quantum physics. This can be summarized in two general facts that radically differentiate quantum physics from classical physics, encapsulating the novelty of the quanta:69 The maximal amount of relevant information about an object70 is finite. It is always possible to acquire new relevant information about any object.

If we could know with infinite precision all the physical variables that describe a thing, we would have infinite information. But this is impossible. The limit is determined by the Planck constant ħ.73 This is the meaning of Planck’s constant. It is the limit up to which we can determine physical variables.

An immediate consequence is granularity. Light, for instance, is made of photons or grains of light, because portions of energy that were even more minute than this would violate this principle: the electric field and the magnetic field (that are like X and P, for light) would both be too determined and would violate the first postulate.

The delicate phenomena of interference between the cat awake and the cat sleeping are lost in the noise of the world that surrounds us. When interference is lost, we can take facts as stable, that is, we can forget that they are only true relative to something else.78

Our everyday experience is thus compatible with the quantum world: quantum theory incorporates classical mechanics and our usual vision of the world—as approximations. We understand it as a man with good sight can understand the experience of a myopic person. But at the molecular scale, the cutting edge of a sharp knife is as fluctuating and imprecise as the edge of an ocean in a storm, fraying upon the white sand of its shore. The solidity of the classical vision of the world is nothing other than our own myopia. The certainties of classical physics are just probabilities. The well-defined and solid picture of the world given by the old physics is an illusion.

Knowledge is possessed, for Mach, not by the abstract “subject” of idealism: it is instead the concrete human activity, in the concrete course of history, that learns to better and better organize the facts of the world with which it interacts.

The key concept of Bogdanov’s theoretical work is the notion of organization. Social life is the organization of collective work. Knowledge is the organization of experience and of concepts. It is possible to understand the whole of reality as organization, structure. The picture of the world that Bogdanov proposes is based on a spectrum of kinds of organization that become gradually more complex: from minimal elements that interact directly, through the organization of matter in the living, the biological development of individual experience organized in individuals, up to scientific knowledge, which, for Bogdanov, is collectively organized experience. Through the cybernetics of Norbert Wiener and the system theory of Ludwig von Bertalanffy, these ideas will have a little-recognized but profound influence on modern thought, on the birth of cybernetics, on the science of complex systems, down to contemporary structural realism.

The “anti-metaphysical” spirit that Mach promoted is an attitude of openness: We should not seek to teach the world how it should be. Let’s listen to the world instead, in order to learn from it how to think about it.

When Einstein objected to quantum mechanics by remarking that “God does not play dice,” Bohr responded by admonishing him, “Stop telling God what to do.” Which means: Nature is richer than our metaphysical prejudices. It has more imagination than we do.

We must expect to have to modify our provincial metaphysical perspectives just as soon as we learn something new. We must take seriously the new things we learn about the world, even if they clash with our preconceptions about how reality is constituted. This seems to me an attitude that renounces the arrogance of possessing knowledge, while keeping faith with reason and our capacity to learn. Science is not a Depository of Truth, it is based on the awareness that there are no Depositories of Truth. The best way to learn is to interact with the world while seeking to understand it, readjusting our mental schemes to what we encounter and find. This respect for science as the source of our knowledge nurtures the naturalism of philosophers such as Willard Quine, for whom our knowledge itself is one of many natural processes and can be studied as such.

I believe that we need to adapt our philosophy to our science, and not our science to our philosophy.

There is no ultimate or mysterious essence to understand—that is the true essence of our being. “I” is nothing other than the vast and interconnected set of phenomena that constitute it, each one dependent on something else. Centuries of Western speculation on the subject, and on the nature of consciousness, vanish like morning mist.

If every metaphysics seeks a primary substance, an essence on which everything may depend, the point of departure from which everything follows, Nāgārjuna suggests that the ultimate substance, the point of departure . . . does not exist.

Conventional, everyday existence is not negated; on the contrary, it is taken into account in all of its complexity, with its levels and facets. It can be studied, explored, analyzed, reduced to more elementary terms. But there is no sense, Nāgārjuna argues, in looking for an ultimate substratum.

Two variables have “relative information” if they can be in fewer states than the product of the number of states that each can be in.

Information plays several roles in biology. Structures and processes reproduce equal to themselves for hundreds of millions, perhaps billions of years, altered only by the slow drift of evolution. The principal means of this stability are the molecules of DNA, which remain more or less similar to their ancestors. This implies that there are correlations, that is to say relative information, across eons of time. The molecules of DNA codify and transmit information. This informational stability is perhaps the most characteristic aspect of living matter.

The existence of such relevant correlations reveals the physical foundation of the notion of meaning: relevant relative information. Relative information in the (physical) sense given by Shannon—which is relevant in the (biological, therefore ultimately also physical) sense clarified by Darwin. This is a precise way in which we can say that its information on the concentration of sugar has meaning for the bacterium. Or that the thought of the tiger in my brain, that is, the corresponding neuronal configuration, actually signifies the tiger, an existential threat. It is correlation that matters: about which the organism “cares.”

In order to be coherent, a vision of the world—a theory of the world—must be able to justify and give an account of the ways in which the inhabitants of that world arrive at that vision, at that theory.

The double meaning of “information” gives it its ambiguous character. The basis that we have for understanding the world is our information about the world, which is effectively a (useful) correlation between us and the world. We know the world from within it.

If we imagine the totality of things, we are imagining being outside the universe, looking at it from out there. But there is no “outside” to the totality of things. The external point of view is a point of view that does not exist.128 Every description of the world is from inside it. The externally observed world does not exist; what exists are only internal perspectives on the world which are partial and reflect one another. The world is this reciprocal reflection of perspectives.

Who is the “I” that has the sensation of feeling, if not the integrated set of our mental processes? We have an intuition of unity when we think about ourselves, but this is justified by the integration of our body and by the ways our mental processes work, of which the part we call conscious does one thing at a time. The first term of the problem, the “I,” is the residue of a metaphysical error: the result of the common mistake of mistaking a process for an entity. (Mach is categorical: “Das Ego ist unrettbar”: the “I” cannot be saved. Bogdanov is said to have put it in political terms: “The individual is a bourgeois fetish.”130) To ask what consciousness is, after having unraveled the neural processes, is like asking what a storm is after having understood its physics: it is a question that makes no sense. To add in a “possessor” of sensations is like adding Jove to the phenomenon of the thunderstorm. It is like saying, after having understood the physics of the storm, that there still remains, as Chalmers would put it, the “hard question” of connecting it with the anger of Jove.

It is true that we have the “intuition” of an independent entity that is the “I.” But we also once had the “intuition” that behind a storm there was Jove. And that the Earth was flat. It is not through uncritical “intuitions” that we construct an effective comprehension of reality. Introspection is the worst instrument of inquiry if we are interested in the nature of mind: it is tantamount to looking for our own prejudices and wallowing in them.

Even worse is the second term of the question, “matter.” It is, as well, the residue of an incorrect metaphysics based on too naive a conception of matter as a universal substance defined only by mass and motion. This is erroneous metaphysics because it is contradicted by quantum physics. If we think in terms of processes, events, in terms of relative properties, of a world of relations, the hiatus between physical phenomena and mental phenomena is muc...

The relational perspective distances us from subject/object and matter/spirit dualisms, and from the apparent irreducibility of the reality/thought or brain/consciousness dualism. If we come to untangle the processes that take place in our bodies and their relations with the external world, what is left to understand? What is the phenomenology of our consciousness if not the name that these processes assign to themselves in the game of mirrors of relevant information contained in the signals carried by our neurons?

Bell’s argument is subtle, very technical, but solid. An interested reader can find it, with extensive detail, in Stanford Encyclopedia of Philosophy: https://plato.stanford.edu/entries/bell-theorem/.

written with the two ψ1 and ψ2 waves alone. Formally, the state of two systems does not live in the tensor sum of two Hilbert H1 ⊗ H2, but rather in their tensor product H1 ⊗ H2.

no degree of freedom of any physical system can have its state localized in its phase space with precision greater than ħ (the constant ħ has the dimensions of a volume in phase space).