Helgoland: Making Sense of the Quantum Revolution

by Carlo Rovelli

It has destroyed the image of reality as made up of particles that move along defined trajectories—without, however, clarifying how we should think of the world instead. Its mathematics does not describe reality. Distant objects seem magically connected. Matter is replaced by ghostly waves of probability.

If the strangeness of quantum theory confuses us, it also opens new perspectives with which to understand reality. A reality that is more subtle than the simplistic materialism of particles in space. A reality made up of relations rather than objects.

What Born understands is that the value of Schrödinger’s ψ wave at a point in space is related to the probability of observing the electron at this point.

Schrödinger’s ψ is therefore not a representation of a real entity: it is an instrument of calculation that gives the probability that something real will occur. It is like the weather forecasts telling us what could happen tomorrow. The same—it soon becomes clear—is true of Göttingen matrix mechanics: the mathematics gives predictions that are probabilistic, not exact. Quantum theory, just as much in Heisenberg’s version as in Schrödinger’s, predicts probability, and not certainty.

I have told the story of how quantum theory was born between 1925 and 1926, and have introduced two ideas: the peculiar idea, found by Heisenberg, of describing only observables, and the fact that the theory predicts only probabilities, understood by Born.

The name “quantum theory” comes, indeed, from “quanta,” which is to say “grains.” “Quantum” phenomena reveal the granular aspect of the world, at a very small scale.

Granularity is the third idea of quantum theory, next to probability and observations. The rows and columns of Heisenberg’s matrices correspond directly to the individual discrete values that the energy can take.

Before concluding, here are a few words about the single equation that quantum theory adds to classical physics. It is a strange equation. It states that multiplying the position by the velocity is different from multiplying the velocity by the position. If position and velocity were numbers, there could be no difference, because 7 × 9 is the same as 9 × 7. But position and velocity are now tables of numbers, and when you multiply two tables, the order counts.

X P – P X = i ħ

about the new quantum theory and explains how to use it.32 In 1930, Dirac writes a book in which the formal structure of the new theory is beautifully elucidated.33 It is still today the best book to learn it from.

Remaining faithful to Werner Heisenberg’s seminal insight on Helgoland, the theory doesn’t tell us where to find any one particle of matter when we are not looking at it. It only speaks about the probability of finding it at one point if we observe it.

But we need to be careful here: 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.

The wave function “collapses,” that is to say it leaps, converging in one point, the moment we observe it.

The Hidden Variables interpretation brings quantum physics back into the same logical realm as classical physics: everything is deterministic and predictable. If we knew the position of the electron and the value of the wave, we could predict everything. But it’s not really as simple as this. As it happens, we cannot ever know the wave, because we never see it: we only see the electron.45 Hence the behavior of the electron is determined by variables (the wave) that for us remain hidden. The variables are hidden in principle: we can never determine them. This is how the theory gets the name Hidden Variables.

What quantum theory describes, then, is the way in which one part of nature manifests itself to any other single part of nature.

interactions. Individual objects are the way in which they interact.

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.

I hope that I have not lost my reader in the last few subtle but essential paragraphs. The gist is that the properties of objects exist only in the moment of their interactions, and they can be real with respect to one object and not with respect to another.

Properties do not reside in objects, they are bridges between objects. Objects are such only with respect to other objects, they are nodes where bridges meet. The world is a perspectival game, a play of mirrors that exist only as reflections of and in each other.

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.

To say that a physical variable “has information” on another physical variable in this sense is simply to say that there is a tie of some kind (a common history, a physical link, the glue on the plastic sheet) due to which the value of one variable implies something about the value of the other.68 This is the meaning of the word “information” that I am using here.

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.

His most radical suggestion is to stop thinking of phenomena as manifestations of objects and to think, instead, of objects as nodes between phenomena.

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.

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.

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.

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

Whereas in classical physics the interactions between an object and the measuring apparatus can be overlooked—or if necessary can be taken into account and compensated for—in quantum physics this interaction is an inseparable part of the phenomenon.

An isolated object, taken in itself, independent of every interaction, has no particular state. At most we can attribute to it a kind of probabilistic disposition to manifest itself in one way or another.102 But even this is only an anticipation of future phenomena, a reflection of phenomena past, and only and always relative to another object. The conclusion is revolutionary. It leaps beyond the idea that the world is made up of a substance that has attributes, and forces us to think about everything in terms of relations.103

In analytic philosophy, structural realism is based on the idea that relations come before objects.

Even this very incomplete overview is sufficient to show how recurrent is the idea that the world is woven by relations and interactions more than by objects.

There are no elementary entities that we can describe except in the context of their interaction with something else.

What really interests us about ancient texts is not what the author initially intended to say: it is how the work can speak to us now, and what it can suggest today.

The central thesis of Nāgārjuna’s book is simply that there is nothing that exists in itself independently from something else.

But it is a world of interdependence and contingencies, not a world we should trouble ourselves attempting to derive from an Absolute.

The search for knowledge is not nourished by certainty: it is nourished by a radical absence of certainty.

In the information theory of Claude Shannon, information is only counting the number of possible states of something.

Shannon also defines the notion of relative information, which is the one I used in the previous chapters: a measure of the physical correlation between two variables. 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.

Relative information between two objects means that if I observe the two objects, I find correlations: “You have information about the color of the sky today” means that if I ask you about the color of the sky, I find that what you tell me fits with what I see; there is a correlation between you and the sky. That two objects (the sky and you) have relative information is hence, in the final analysis, something that regards a third object (me observing you). Relative information, remember, is a dance for three, like entanglement.

The cosmos is change, life is discourse—as

If I look at a forest from afar, I see a dark green velvet. As I move toward it, the velvet breaks up into trunks, branches and leaves: the bark of the trunks, the moss, the insects, the teeming complexity. In every eye of every ladybug, there is an extremely elaborate structure of cells connected to neurons that guide and enable them to live. Every cell is a city, every protein a castle of atoms; in each atomic nucleus an inferno of quantum dynamics is stirring, quarks and gluons swirl, excitations of quantum fields. This is only a small wood on a small planet that revolves around a little star, among one hundred billion stars in one of the thousand billion galaxies constellated with dazzling cosmic events. In every corner of the universe we find vertiginous wells of layers of reality.

It turns out, however, that the brain does not work like this at all. It functions, in fact, in an opposite way. Many, if not most, of the signals do not travel from the eyes to the brain; they go the other way, from the brain to the eyes.132 What happens is that the brain expects to see something, on the basis of what it knows and has previously occurred. The brain elaborates an image of what it predicts the eyes should see. This information is conveyed from the brain to the eyes, through intermediate stages. If a discrepancy is revealed between what the brain expects and the light arriving into the eyes, only then do the neural circuits send signals toward the brain. So images from around us do not travel from the eyes to the brain—only news of discrepancies regarding what the brain expects do.

The implications for the relationship between what we see and the world, however, are remarkable. When we look around ourselves, we are not truly “observing”: we are instead dreaming an image of the world based on what we know (including bias and misconception) and unconsciously scrutinizing the world to reveal any discrepancies, which, if necessary, we will try to correct. What I see, in other words, is not a reproduction of the external world. It is what I expect, corrected by what I can grasp.

In the model known as PCM (projective consciousness model), for example, the hypothesis is that consciousness is the activity of the brain constantly attempting to predict the input that constantly varies because of the variability of the world and the change of our position. Representations are techniques to minimize mistakes in predictions using observed discrepancies.133 In the words of the nineteenth-century French philosopher Hippolyte Taine, we can say that “external perception is an internal dream which proves to be in harmony with external things; and instead of calling ‘hallucination’ a false perception, we must call external perception ‘a confirmed hallucination.’”134

The best description of reality that we have found is in terms of events that weave a web of interactions. “Entities” are nothing other than ephemeral nodes in this web. Their properties are not determined until the moment of these interactions; they exist only in relation to something else. Everything is what it is only with respect to something else. Every vision is partial. There is no way of seeing reality that is not dependent on a perspective—no point of view that is absolute and universal.