Helgoland: Making Sense of the Quantum Revolution

by Carlo Rovelli

Quantum theory has clarified the 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.

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.

The abyss of what we do not know is always magnetic and vertiginous. But to take quantum mechanics seriously, reflecting on its implications, is an almost psychedelic experience: it asks us to renounce, in one way or another, something that we cherished as solid and untouchable in our understanding of the world. We are asked to accept that reality may be profoundly other than we had imagined: to look into the abyss, without fear of sinking into the unfathomable.

Niels Bohr was already a renowned scientist. He had written formulas, simple but strange, that predicted the properties of chemical elements even before measuring them. They predicted, for instance, the frequency of light emitted by elements when heated: the color they assume.

Einstein had shown that even our most rooted convictions can be wrong. What seems most obvious to us now might turn out not to be correct. Abandoning assumptions that seem self-evident can lead to greater understanding. Einstein had taught that everything should be based on what we see, not on what we assume to exist.

We cannot find new laws of motion to account for Bohr’s orbits and his “leaps”? Fine, let’s stick with the laws of motion that we’re familiar with, without altering them. Let’s change, instead, our way of thinking about the electron. Let’s give up describing its movement. Let’s describe only what we can observe: the light it emits. Let’s base everything on quantities that are observable. This is the idea.

Bohr, the master, will recall years later: “We had at the time only a vague hope of [being able to arrive at] a reformulation of the theory in which every inappropriate use of classical ideas would be gradually eliminated. Daunted by the difficulty of such a program, we all felt great admiration for Heisenberg when, at just twenty-three, he managed it in one swoop.”11 Except for Born, who is in his forties, Heisenberg, Jordan, Dirac and Pauli are all twentysomethings. In Göttingen they call their physics Knabenphysik, or “boys’ physics.”

The calculation scheme by Heisenberg, Born, Jordan and Dirac, the strange idea of “limiting yourself to only what’s observable,” and to substituting physical variables with matrices,12 has never yet been wrong. It is the only fundamental theory about the world that until now has never been found wrong—and whose limits we still do not know.

What does it mean that “everything is still very vague and unclear to me, but it seems that electrons no longer move in orbits”? His friend Pauli wrote of Heisenberg: “He reasoned in a terrible way, he was all about intuition; he did not pay any attention to elaborating clearly the fundamental assumptions and their relation to existing theories.”

Years later, Schrödinger, who will nevertheless become one of the most acute thinkers on questions about quanta, recognized his defeat. “There was a moment,” he writes, “when the creators of wave mechanics [that is, himself; who else?] nurtured the illusion of having eliminated the discontinuities in quantum theory. But the discontinuities eliminated from the equations of the theory reappear the moment the theory is confronted with what we observed.”

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.

In 1900, twenty-five years before Heisenberg’s journey to Helgoland, the German physicist Max Planck had discovered a formula that reproduced well the way that the energy of heat, measured in a laboratory, distributed among waves of different frequency.27 He derived this formula from general rules, but added a curious hypothesis: the energy could be transmitted to the waves only in integer multiples of elementary energies. In discrete packets.

Five years later, Einstein suggests that light and all the other electromagnetic waves are actually made up of elementary grains.29 These are the first “quanta.” Today we call them “photons,” the quanta of light.

Einstein has provided the inspiration for quantum mechanics in numerous ways. He begins to realize, already in 1905, that the issues raised by these phenomena were serious enough to require a complete revision of mechanics. Born learns from him the idea that mechanics needs to be revised in depth. Einstein’s idea that light is a wave but also a cloud of photons inspires de Broglie to think that all the elementary particles could be waves, and that leads Schrödinger to introduce the ψ wave. Heisenberg is inspired by Einstein to restrict his attention to quantities that are measurable. There is more: Einstein is also the first to study atomic phenomena using probability, opening the path that leads Born to understand that the meaning of the ψ wave is to be found in probability. Quantum physics owes much to Einstein.

These phenomena—photons, the photoelectric effect, the distribution of energy among electromagnetic waves, Bohr’s orbits, the discreteness of rotation—are all regulated by the Planck constant ħ.

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.

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 what does a particle care if we are observing it or not? The most effective and powerful scientific theory is an enigma.

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.

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)

Not to fear rethinking the world is the power of science: ever since Anaximander removed the foundations on which the Earth rested, Copernicus launched it to rotate in the sky, Einstein dissolved the rigidity of space and of time, and Darwin demolished the separateness of humanity . . . reality is constantly being redrawn in images that are increasingly effective.

The discovery of quantum theory, I believe, is the discovery that the properties of any entity are nothing other than the way in which that entity influences others. It exists only through its interactions. Quantum theory is the theory of how things influence each other. And this is the best description of nature that we have.

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.

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

Entanglement is not a dance for two partners, it is a dance for three.

You look at a butterfly and see the color of its wings. In relation to me, a relation is established between you and the butterfly: the butterfly and you are now in an entangled state. Even if the butterfly moves away from you, the fact remains that if I look at the color of its wings and ask you which color you have seen, I will find that our answers match . . . even if it is not impossible that there will be subtle interference phenomena with the configuration whereby the butterfly is a different color. 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 reads: “Delta X times Delta P is always greater than or equal to h-bar divided by two.” This general property of reality is called “Heisenberg’s uncertainty principle.” It applies to everything. 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.

Furthermore, when we observe the world at our scale, we do not see its granularity. We cannot see single molecules: we see the whole cat. With many variables, fluctuations become irrelevant, and probability nears certainty.79 Billions of discontinuous events of the agitated and fluctuating quantum world are reduced by us to the few continuous and well-defined variables of our everyday experience. At our scale, the world is like the wave-agitated surface of the ocean seen from the moon: the smooth surface of a blue marble.

Mach is not a systematic philosopher; his work at times lacks clarity. And yet I believe that the extent and depth of his influence on contemporary culture has been undervalued.83 Mach inspired the beginning of both of the great twentieth-century revolutions in physics: relativity and quantum theory. He played a direct role in the birth of the scientific study of perception. He was at the center of the politico-philosophical debate that led to the Russian Revolution. He had a determining influence on the founders of the Vienna Circle (the official name of which was Verein Ernst Mach, or the Ernst Mach Society), the philosophical environment that proved to be fertile ground for logical positivism, which directly inherits from Mach its “anti-metaphysical” rhetoric and is the root of so much contemporary philosophy of science. His direct influence reaches to American pragmatism, another root of today’s analytic philosophy.

If only “sensations” are real, argues Lenin, then external reality is assumed not to exist: we live in a solipsistic world where there is only myself and my sensations. I take myself, the subject, as the only reality. This idealism, for Lenin, is the ideological manifestation of the enemy: it is pure bourgeois-ism. Against idealism, Lenin poses a materialism that sees the human being—human consciousness, human spirit—as an aspect of a concrete world that is objective, knowable, and comprising solely matter in motion in space.

Even more impressive is Bogdanov’s political reply to Lenin. Lenin speaks of absolute certainties. He presents the historical materialism of Marx and Engels as if it were timelessly valid. Bogdanov points out that this ideological dogmatism not only fails to accord with the dynamic of scientific thought, it also leads to calcified political dogmatism.

A doctor, an economist, a philosopher, a natural scientist, a science-fiction novelist, a poet, teacher, politician, progenitor of cybernetics and of the science of organization, a pioneer of blood transfusion and a lifelong revolutionary, Aleksandr Bogdanov, prodigiously talented,97 is one of the most complex and fascinating figures of the intellectual world at the beginning of the twentieth century.

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.

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.

Niels Bohr was the spiritual father of the young Turks who built quantum theory. He pushed Heisenberg to preoccupy himself with the problem and accompanied him on his delvings into the mysteries of atoms. He mediated the argument between Heisenberg and Schrödinger, his two overly brilliant bickering children. It was he who formulated the way of thinking about the theory that has ended up in physics books all over the world. He was the scientist who perhaps strained more than any other to understand what it all meant. His discussion with Einstein on the plausibility of the theory lasted for years, forcing both these giants to clarify their positions, and to compromise.

What we need to add to Bohr’s paragraph is the awareness, which has grown in the course of a century of successes for the theory, of the fact that all nature is quantum, and that there is nothing special about a physics laboratory containing measuring apparatus. There are not quantum phenomena only in laboratories and non-quantum phenomena elsewhere: all phenomena are quantum phenomena.

The discovery that quantities we had thought of as absolute are, in fact, relative instead is a theme that runs throughout the history of physics. Beyond physics, relational thinking can be found in all the sciences. In biology, the characteristics of living systems are comprehensible in relation to their environment formed by other living beings. In chemistry, the properties of elements consist of the way in which they interact with other elements. In economics, we speak of economic relations. In psychology, the individual personality exists within a relational context. In these and many other cases, we understand things (organisms, chemicals, psychological life) through their being in relation to other things.

There is nothing mysterious about this: the world is not divided into stand-alone entities. It is we who divide it into objects for our convenience. A mountain chain is not divided into individual mountains: it is we who divide it up into parts that strike us as in some way separate. A countless number of our definitions, perhaps all of them, are relational: a mother is a mother because she has a child; a planet is a planet because it orbits a star; a predator is such because it hunts prey; a position in space is there only in relation to something else. Even time exists only as a set of relations.

The history of Western philosophy is to a large extent an attempt to provide an answer to the question as to what is fundamental. It is a search for the point of departure from which everything else follows: matter, God, the spirit, the atoms and the void, Platonic Forms, a priori forms of intuition, the subject, Absolute Spirit, elementary moments of consciousness, phenomena, energy, experience, sensations, language, verifiable propositions, scientific data, falsifiable theories, the existence of the being for whom being matters, hermeneutic circles, structures . . . A long list of candidates, not one of which ever managed to achieve a universal acceptance as ultimate foundation.

The central thesis of Nāgārjuna’s book is simply that there is nothing that exists in itself independently from something else. The resonance with quantum mechanics is immediate. Obviously, Nāgārjuna knew nothing, and could not have imagined anything, about quanta—that is not the point. The point is that philosophers offer original ways of rethinking the world, and we can employ them if they turn out to be useful. The perspective offered by Nāgārjuna may perhaps make it a little easier to think about the quantum world.

I believe that one of the greatest mistakes made by human beings is to want certainties when trying to understand something. The search for knowledge is not nourished by certainty: it is nourished by a radical absence of certainty. Thanks to the acute awareness of our ignorance, we are open to doubt and can continue to learn and to learn better. This has always been the strength of scientific thinking—thinking born of curiosity, revolt, change. There is no cardinal or final fixed point, philosophical or methodological, with which to anchor the adventure of knowledge.

This is the meaning of culture: an endless dialogue that enriches us by feeding on experiences, knowledge and, above all, exchanges.

But there is no need to attribute proto-consciousness to elementary systems in order to get around a frozen “simple matter.” It is enough to have observed how the world is better described by relative variables and their correlations. This allows us to be released from the prison of a blunt opposition between the objectivity of matter and mental life. The rigid distinction between a mental world and a physical one fades. It is possible to think of both mental and physical phenomena as natural phenomena: both products of interactions between parts of the physical world.

In the information theory of Claude Shannon, information is only counting the number of possible states of something. A USB memory stick has a quantity of information, expressed in bits or gigabytes, which indicates how many different ways its memory can be arranged. The number of bits does not know the meaning of what is in the memory; it does not even know whether the content of the memory means something or is just noise.

The discovery of biological evolution, on the other hand, has allowed us to build some bridges between concepts that we use when speaking about animate things and concepts that we use for the rest of nature. In particular, it has clarified the biological—and in the final analysis, physical—origin of such notions as utility and relevance.

The biosphere is formed by structures and processes that are useful for the continuation of life: we have lungs in order to breathe; eyes with which to see. Darwin’s discovery is that we understand why there are these structures by reversing the order of cause and effect between their utility and their existence: their function (to see, to eat, to breathe, to digest . . . to contribute to life) is not the purpose of these structures. It is the other way around: living beings survive because these structures are there. We do not love in order to live: we live because we love.

Life is a biochemical process that unfolds across the surface of the Earth and dissipates the abundant “free energy,” or “low entropy,” with whic...

But structures and processes are not there so that the organisms may survive and reproduce. It is the other way around: organisms survive and reproduce because these structures have happened to gradually develop. They reproduce and populate the Earth because they are functional.

Darwin clarified the crucial importance of the variability of biological structures that allows the continuous exploration of a space of endless possibilities; and of natural selection, which allows access to gradually more extensive regions of that space, where structures and processes are found even more capable, together, of persisting.