Tag: wavefunction

• From the Heisenberg cut to the Copenhagen interpretation

  The following post was motivated by this exchange (on X.com), which prompted me to write out my understanding of the Copenhagen interpretation of quantum mechanics and the part the Heisenberg cut plays in it. I haven’t gone into the variants of the interpretation that Maria Violaris brings up; I only focus on understanding what the interpretation does and doesn’t say to begin with, and its history.

  There are many interpretations of what quantum mechanics says about reality. This is unlike classical physics, where theory and reality converge almost perfectly. If using Newton’s laws of motion you determine that a ball flying through the air will have some speed at some point, you’ll find that to be the case when you take measurements. Quantum mechanics on the other hand has some uncertainty baked into the outcomes of certain measurements; there’s no escaping it. That means the mathematical formalism describes only the probability of the outcomes of measurement rather than the event itself, creating a fundamental gap between the theory and observations that different interpretations have tried to bridge with competing philosophical explanations.

  Perhaps the most popular among them is the Copenhagen interpretation: a small 2016 survey found it enjoys the most agreement among physicists; it also holds sway in the popular imagination thanks to Erwin Schrödinger’s thought experiment involving a cat that’s both dead and alive. However, Schrödinger came up with that idea to illustrate his belief that the Copenhagen interpretation of quantum mechanics paints an absurd picture of reality. The interpretation has been refined over time and is more complicated than that, and certainly not absurd.

  In Schrödinger’s thought experiment, the cat is a metaphor for an observable property of a quantum system. That the cat is both dead and alive — a statement that the wavefunction of the property is in a superposition of two (or more) states. When you open the box to see if the cat is dead or alive (but not both) in the metaphor, the description of the system updates from a superposition to a single outcome.

  Note that this is a simplified picture. For a more thoroughgoing account, I recommend Jim Baggott’s post ‘The Copenhagen Confusion’. Here’s a line from the operative passage: “The ‘collapse of the wavefunction’ was never part of the Copenhagen interpretation because the wavefunction isn’t interpreted realistically. The only thing that happens when an electron is detected on a screen in the context of Copenhagen is that we gain knowledge of the position of the electron.” In this post, however, I’m going to flatten these details for simplicity’s sake where necessary.

  

  A useful entry point to the interpretation is the Heisenberg cut, which is a conceptual boundary within the interpretation. It draws the line between the quantum system, i.e. the wavefunction and probabilistic laws, and the measuring apparatus or the observer, described by classical mechanics and deterministic laws. And these two parts of the overall system share a foundational relationship: the Copenhagen interpretation uses this cut to bridge the gap between the mathematical formalism of quantum mechanics and the empirical reality of what scientists observe in a lab.

  In Niels Bohr’s view, the cut is required because humans are macroscopic entities who communicate using classical language. (“It’s very hard to talk quantum using a language originally designed to tell other monkeys where the ripe fruit is”: Terry Pratchett.) Bohr argued that we don’t have a choice but to describe experiments in terms of everyday physics, including positions, momenta, and times, because these concepts also define our cognitive and linguistic capabilities. This means even though the subatomic world is quantum mechanical, the instruments we use to measure it, like photographic plates and our eyes, must be treated as classical objects. The Heisenberg cut is an imaginary boundary in our description of experiments where we stop using quantum concepts and start using classical ones.

  An important feature of the cut is its mobility, i.e. that a person can draw it anywhere in their description of the thought experiment: when a photon of light hits the cat, when a photon reflected by the cat reaches your eye, when you first open the box or somewhere else. According to the Copenhagen interpretation, the physical predictions of quantum mechanics don’t change based on where you make the cut, as long as it is placed somewhere along the chain of measurement. And the cut must exist if you’re to be able to ‘measure’ the system.

  The Heisenberg cut is also intimately tied to the measurement problem. On the quantum side of the cut, the system will evolve according to the Schrödinger equation, which is deterministic and preserves superpositions, i.e. it allows a particle to be in two states at once. On the classical side of the cut, you observe definite outcomes: the particle is either here or there.

  In effect the cut marks the point where multiple possible outcomes give way to a single recorded result. And in the Copenhagen interpretation, this transition isn’t a physical process that can be derived from the Schrödinger equation itself; instead it’s a non-dynamical event that occurs whenever a quantum system interacts with a classical measuring device. This leads to the somewhat paradoxical conclusion that quantum mechanics is a complete theory of the microscopic universe yet it banks on classical concepts (that it can’t make sense of) to make sense of its predictions.

  While both Bohr and Werner Heisenberg, for whom the cut is named, agreed that this cut should exist, they arrived at it for different reasons. Heisenberg treated the cut as a moveable mathematical boundary that separated the object from the subject, highlighting the subjective nature of observation. He was interested in how the observer’s knowledge changed the state of the system. Bohr on the other hand viewed the cut as an epistemological necessity fixed by the experimental arrangement. In other words for Bohr the cut wasn’t about a subjective observer disrupting nature but about the objective impossibility of separating the observer from the observed in the quantum realm (a.k.a. the uncertainty implicit to quantum mechanics).

  Second, let’s look at how the Copenhagen interpretation treats the maths of quantum mechanics. The theory postulates that a quantum system evolves according to the Schrödinger equation. However, our human experience is obviously discontinuous: we see definite outcomes, not superpositions. The ‘collapse’ is the instant when the system switches from its smooth quantum evolution to a single, definite state.

  Without the Heisenberg cut, on the other hand, there’s no logical place for the wavefunction to collapse. If you treated the entire universe — including a subatomic particle, a microscope, a scientist, and the scientist’s brain — as one giant quantum system, everything would just keep evolving according to the Schrödinger equation forever. Eventually you’d end up with a universe in a massive, complex superposition but you’d never arrive at a specific measurement or result. This is actually the premise of the many-worlds interpretation of quantum mechanics, which removes the collapse and thus removes the need for a cut.

  In the Copenhagen interpretation, however, because you eventually arrive at a definite result (and which you need to do for science to be science), you’re forced to draw a line: “Everything on this side is quantum and describes probabilities and everything on that side is classical and describes facts”. The wavefunction ‘collapse’ is defined as the point at which the quantum description gives way to a single, definite experimental outcome. When the quantum system crosses the Heisenberg cut and interacts with the classical side, the wavefunction is said to have collapsed.

  Thus to discuss the Heisenberg cut is essentially to discuss the mechanism of collapse and highlights the implicit dualism of the Copenhagen interpretation: the universe is divided into the observer and the observed. The wavefunction describes what’s being observed and the collapse ensures the observed entity matches the observer’s reality.

  The concept of the cut originated in a few intense months leading up to Heisenberg’s publication of a paper in March 1927. At the time, Heisenberg had been working at Bohr’s institute in Copenhagen on rescuing the concept of particle trajectories, e.g. the tracks of particles recorded in a cloud chamber, which seemed to contradict the (then) new quantum mechanics.

  In 1925, Heisenberg formulated matrix mechanics, the first logically consistent mathematical framework for quantum mechanics. (This invention was an important first step of the ‘new’ quantum mechanics, whose centenary physicists celebrated worldwide last year.) Among other things, matrix mechanics predicted that certain physical quantities, such as energy, take on discrete values. However, this raised questions about reconciling the theory with physicists observing apparently smooth, continuous particle tracks in cloud chambers.

  

  Heisenberg resolved this contradiction by redefining what a ‘path’ actually is in a cloud chamber. This is a device filled with alcohol vapour that’s supersaturated, meaning it’s cooled to the point where it’s just about ready to turn into liquid. When a charged particle moves through this gas, it knocks electrons out of the alcohol molecules, creating a trail of ions. The vapour rapidly turns into liquid droplets around these ions, forming a visible white track that traces the exact path of the subatomic particle through the chamber.

  But Heisenberg argued that we never actually see a continuous path in a cloud chamber — only the sequence of individual droplets formed by ionisation. Solving the problem of the particle’s trajectory in matrix mechanics would never spit out a continuous path but it could determine the probability of an electron’s state transitioning from one discrete droplet to the next.

  When we say an object transitions from point A to point B in everyday life, we mean it moved through the space in between them. But in matrix mechanics, an electron state transitioning between droplets means a discontinuous update of reality rather than movement. In the context of this post, the state of the electron is a mathematical list of properties the electron possesses at the exact moment it hits a gas molecule and creates a droplet.

  So say when it hits droplet 1, the electron has energy E_high, momentum P₁, and is roughly at position X₁. At droplet 2, scientists find the same electron has energy E_low (because it lost some energy when it smashed into the first atom), momentum P₂, and is roughly at position X₂. In Heisenberg’s telling, the laws of physics don’t describe this journey so much as the probability of state 2 happening given state 1 just happened.

  This description resolved Heisenberg’s problem because his maths only handled the energy levels and transitions; it had no variable for the particle’s location at each instant in time. In other words by looking at the cloud chamber and saying, “Aha! This track is just a pile of separate water droplets”, he could claim that the physical world also works like his maths. Which means the path we see in the cloud chamber is just our human brains drawing a line between the dots. The electron itself only becomes classically describable when it hits something.

  In other words, in classical physics, the particle has a path regardless of whether we look at it, and the droplets merely reveal it. In Heisenberg’s view, the particle has no defined position or path in the empty space between the droplets. Instead a path as such comes into view only because the cloud chamber is performing a rapid series of measurements: each droplet represents an observation that forces the electron to take a stand on its position while the eventual smooth line is a mental construct we create by connecting these dots.

  Continuing from this idea, in a famous letter to Wolfgang Pauli and subsequently in his March 1927 paper, The Actual Content of Quantum Theoretical Kinematics and Mechanics, Heisenberg introduced a thought experiment involving a gamma-ray microscope. He argued that to observe an electron, one must hit it with a photon. This interaction would disturb the electron. He initially framed the measurement problem as a physical interaction between the electron (the system) and the photon (the probe), where the act of measurement mechanically disturbed the system.

  Bohr’s critique of Heisenberg’s draft then reforged the cut as a central tenet of the Copenhagen interpretation. When Heisenberg showed Bohr his paper, Bohr tore into it arguing that Heisenberg was wrong to focus on the disturbance because he assumed the electron had a definite position and momentum before the measurement and which the measurement then messed up. Bohr insisted on the more radical view that the properties of the electron aren’t well-defined until the experimental arrangement itself is fixed. For Bohr, the cut wasn’t just where a disturbance happened but the line where the observer switched from using quantum concepts to classical concepts to describe the experiment.

  The conversations on this point between the two men in February and March 1927 were intense, protracted, and emotionally exhausting. Heisenberg was 25 years old at the time and convinced he had solved the riddle of quantum mechanics with his paper whereas Bohr was relentless in his criticism, insisting Heisenberg’s fundamental premise was logically flawed.

  According to historical accounts, including Heisenberg’s own recollections later in life, the discussions would go on for hours, often late into the night. At one point, the combination of mental exhaustion and Bohr’s stubborn refusal to accept Heisenberg’s interpretation caused Heisenberg to break down in tears of frustration. But Heisenberg eventually capitulated, though not entirely: he didn’t rewrite the entire body of his paper but he did add a postscript to the end of the published version where he acknowledged that his explanation of the gamma-ray microscope had been too simplistic and that Bohr’s view regarding the electron’s indefiniteness was the deeper truth.

  The tears were the physical manifestation of the painful process of aligning the two different viewpoints into what became the Copenhagen interpretation. In fact, and at the risk of repetition, let’s treat this interpretation as the peace treaty that reconciled Heisenberg’s idea of uncertainty with Bohr’s idea of complementarity. Heisenberg’s view was initially very mechanical and focused on the observer’s limitations; he held that the fuzziness of the quantum world was a result of our clumsiness: i.e. the reality existed but our clumsy hands destroyed the data every time we tried to touch it. To him the Heisenberg cut was the place where this mechanical disturbance happened.

  Bohr however worked with the concept of complementarity: that the electron has a dual nature, wave and particle, and that these two natures are mutually exclusive, meaning we can’t see both at the same time. And the uncertainty isn’t because we hit the particle but because the electron literally doesn’t have a defined position and momentum at the same time. If you build an experiment to measure its position, the wave nature would vanish, and vice versa. He was saying in effect that the experiment itself defined what reality was allowed to exist at all in that moment.

  The Copenhagen interpretation loosely synthesised these two views, though it leaned heavily toward Bohr’s. It stated that we must accept two contradictory truths: the mathematical formalism (Heisenberg’s matrix mechanics and the Schrödinger equation) that predicts probabilities and the classical world of our measuring devices. The interpretation is the agreement that we can’t speak about what the electron is doing when we aren’t looking. We can only speak about the results of the interaction between the electron and the machine.

  In effect, the Copenhagen interpretation asserts that physics isn’t about the ontological nature of the electron, i.e. what it is, but about the epistemological nature of our knowledge, or what we can say. And the Heisenberg cut is the necessary border where the indefinite, contradictory quantum world based on Bohr’s idea of complementarity is forced to collapse into a single, definite fact.

  If Bohr and Heisenberg provided the philosophical foundation for the Copenhagen interpretation, the Hungarian-American physicist John von Neumann gave it its formal mathematical form in his 1932 book Mathematical Foundations of Quantum Mechanics. Von Neumann was also the one to show that the mathematics of quantum mechanics allowed the cut to be placed anywhere in this chain without changing the final calculated probabilities.

  Where’s Schrödinger’s cat in all of this, then? As it happens, the famous thought experiment in which the cat is both dead and alive is often misunderstood as a quirk of quantum physics; it was actually a scathing piece of satire Schrödinger designed to show that the Copenhagen interpretation was absurd. Schrödinger in fact didn’t believe a cat could be simultaneously dead and alive. His point was that if you followed Bohr and Heisenberg’s logic to its ultimate conclusion, you’d end up with such a nonsensical reality.

  In fact, the thought experiment, published in 1935, targeted the concept of the Heisenberg cut. In the Copenhagen view, a quantum particle like an atom doesn’t have a defined state: it exists in a superposition of all possible states until an observer measures. Schrödinger could accept this for atoms but couldn’t digest the prospect of applying the idea to macroscopic objects.

  In his mental argument, Schrödinger described a radioactive atom placed in a sealed steel box. If the atom decays in a random quantum event, a Geiger counter nearby would push a hammer, which would smash a vial of cyanide and kill a cat. If the atom doesn’t decay, the cat would live. According to the strict logic of the Copenhagen interpretation, this system remains in a superposition until an observer opens the box to check the cat’s existential status. But until the measurement itself, because the atom is both decayed and not decayed, the Geiger counter is both triggered and not triggered, and the cat is simultaneously dead and alive. Schrödinger’s question was about where the quantum ends and the classical world begins. In other words, where’s the Heisenberg cut?

  

  If we make the cut at the Geiger counter, the cat would be a classical object and thus either dead or alive, not both. However, Bohr, Heisenberg, and von Neumann had shown that the cut was mobile. If we moved it to the human observer opening the box, the cat itself would become part of the system’s overall wavefunction — and Schrödinger had contended that treating a living organism as a probability wave was ridiculous. He used the cat to argue that there must be something missing in the theory, some hidden variables or physical reality, that would determine the state of the cat before an observer looks at it.

  For Schrödinger, the cat proved that the Copenhagen interpretation’s refusal to define objective reality between measurements was a philosophical failure. It showed that while the cut could work mathematically, as von Neumann had proved, it led to macroscopic impossibilities in the physical domain.

  The Copenhagen interpretation in turn didn’t surmount Schrödinger’s critique by answering the riddle but by dismissing Schrödinger’s question as unscientific. Bohr argued that Schrödinger was ‘illegally’ extending quantum concepts beyond the point where a classical description would be required. In his view a Geiger counter is a macroscopic measuring device so the cut between the quantum and classical worlds would occur the moment the particle interacts with the Geiger counter. And by the time the signal reaches the hammer, let alone the cat, the quantum description would already have yielded a definite outcome at the measuring device, so the cat would never have had to be described as being in superposition.

  There was also a powerful sociological narrative at the time that painted Schrödinger and Albert Einstein as an ‘old guard’ that was too stuck in classical determinism to accept the radical new truths quantum mechanics was throwing up. By 1935, the Copenhagen interpretation was the dominant orthodoxy among the younger, more productive generation of physicists like Pauli and (to a lesser extent) Paul Dirac, who viewed the cat and the Einstein-Podolsky-Rosen paradox not as genuine physical problems but as the confusion of men who couldn’t let go of the past. The proponents of the interpretation essentially declared that if the theory predicted the results of experiments correctly, then any philosophical discomfort about cats that were both dead and alive was the philosopher’s problem, not the physicist’s. And quantum mechanics perfectly predicted the results of experiments.

  Historical timing also played an important part in cementing the Copenhagen interpretation’s dominance. Shortly after Schrödinger published his paper, physics shifted dramatically from the philosophical debates of the 1920s to the pragmatic urgency of the 1930s and 1940s. The rise of fascism and World War II turned the focus of the community towards nuclear energy and The Bomb. In this environment, the “shut up and calculate” approach — a phrase coined later to describe this attitude — took over and physicists shelved questions about the reality of the cat as irrelevant metaphysics.

  The interpretation was also shielded by von Neumann’s mathematical authority. His 1932 book also claimed to show that ‘hidden variable’ theories, i.e. which would restore a specific reality to the cat independent of observation, were mathematically impossible. While Grete Hermann and John Bell later found this proof to be circular, for decades it served as a brick wall that convinced the physics community that there was literally no alternative to the Copenhagen interpretation.

  2026.01.31

• What does it mean to interpret quantum physics?

  The United Nations has designated 2025 the International Year of Quantum Science and Technology. Many physics magazines and journals have taken the opportunity to publish more articles on quantum physics than they usually do, and that has meant quantum physics research has often been on my mind. Nirmalya Kajuri, an occasional collaborator, an assistant professor at IIT Mandi, and an excellent science communicator, recently asked other physics teachers on X.com how much time they spend teaching the interpretations of quantum physics. His question and the articles I’ve been reading inspired me to write the following post. I hope it’s useful in particular to people like me, who are interested in physics but didn’t formally train to study it.

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  Quantum physics is often described as the most successful theory in science. It explains how atoms bond, how light interacts with matter, how semiconductors and lasers work, and even how the sun produces energy. With its equations, scientists can predict experimental results with astonishing precision — up to 10 decimal places in the case of the electron’s magnetic moment.

  In spite of this extraordinary success, quantum physics is unusual compared to other scientific theories because it doesn’t tell us a single, clear story about what reality is like. The mathematics yields predictions that have never been contradicted within their tested domain, yet it leaves open the question of what the world is actually doing behind those numbers. This is what physicists mean when they speak of the ‘interpretations’ of quantum mechanics.

  In classical physics, the situation is more straightforward. Newton’s laws describe how forces act on bodies, leading them to move along definite paths. Maxwell’s theory of electromagnetism describes electric and magnetic fields filling space and interacting with charges. Einstein’s relativity shows space and time are flexible and curve under the influence of matter and energy. These theories predict outcomes and provide a coherent picture of the world: objects have locations, fields have values, and spacetime has shape. In quantum mechanics, the mathematics works perfectly — but the corresponding picture of reality is still unclear.

  The central concept in quantum theory is the wavefunction. This is a mathematical object that contains all the information about a system, such as an electron moving through space. The wavefunction evolves smoothly in time according to the Schrödinger equation. If you know the wavefunction at one moment, you can calculate it at any later moment using the equation. But when a measurement is made, the rules of the theory change. Instead of continuing smoothly, the wavefunction is used to calculate probabilities for different possible outcomes, and then one of those outcomes occurs.

  For instance, if an electron has a 50% chance of being detected on the left and a 50% chance of being detected on the right, the experiment will yield either left or right, never both at once. The mathematics says that before the measurement, the electron exists in a superposition of left and right, but after the measurement only one is found. This peculiar structure, where the wavefunction evolves deterministically between measurements but then seems to collapse into a definite outcome when observed, has no counterpart in classical physics.

  The puzzles arise because it’s not clear what the wavefunction really represents. Is it a real physical wave that somehow ‘collapses’? Is it merely a tool for calculating probabilities, with no independent existence? Is it information in the mind of an observer rather than a feature of the external world? The mathematics doesn’t say.

  The measurement problem asks why the wavefunction collapses at all and what exactly counts as a measurement. Superposition raises the question of whether a system can truly be in several states at once or whether the mathematics is only a convenient shorthand. Entanglement, where two particles remain linked in ways that seem to defy distance, forces us to wonder whether reality itself is nonlocal in some deep sense. Each of these problems points to the fact that while the predictive rules of quantum theory are clear, their meaning is not.

  Over the past century, physicists and philosophers have proposed many interpretations of quantum mechanics. The most traditional is often called the Copenhagen interpretation, illustrated by the Schrödinger’s cat thought experiment. In this view, the wavefunction is not real but only a computational tool. In many Copenhagen-style readings, the wavefunction is a device for organising expectations while measurement is taken as a primitive, irreducible step. The many-worlds interpretation offers a different view that denies the wavefunction ever collapses. Instead, all possible outcomes occur, each in its own branch of reality. When you measure the electron, there is one version of you that sees it on the left and another version that sees it on the right.

  In Bohmian mechanics, particles always have definite positions guided by a pilot wave that’s represented by the wavefunction. In this view, the randomness of measurement outcomes arises because we can’t know the precise initial positions of the particles. There are also objective collapse theories that take the wavefunction as real but argue that it undergoes genuine, physical collapse triggered randomly or by specific conditions. Finally, an informational approach called QBism says the wavefunction isn’t about the world at all but about an observer’s expectations for experiences upon acting on the world.

  Most interpretations reproduce the same experimental predictions (objective-collapse models predict small, testable deviations) but tell different stories about what the world is really like.

  It’s natural to ask why interpretations are needed at all if they don’t change the predictions. Indeed, many physicists work happily without worrying about them. To build a transistor, calculate the energy of a molecule or design a quantum computer, the rules of standard quantum mechanics suffice. Yet interpretations matter for several reasons, but especially because they shape our philosophical understanding of what kind of universe we live in.

  They also influence scientific creativity because some interpretations suggest directions for new experiments. For example, objective collapse theories predict small deviations from the usual quantum rules that can, at least in principle, be tested. Interpretations also matter in education. Students taught only the Copenhagen interpretation may come away thinking quantum physics is inherently mysterious and that reality only crystallises when it’s observed. Students introduced to many-worlds alone may instead think of the universe as an endlessly branching tree. The choice of interpretation moulds the intuition of future physicists. At the frontiers of physics, in efforts to unify quantum theory with gravity or to describe the universe as a whole, questions about what the wavefunction really is become unavoidable.

  In research fields that apply quantum mechanics to practical problems, many physicists don’t think about interpretation at all. A condensed-matter physicist studying superconductors uses the standard formalism without worrying about whether electrons are splitting into multiple worlds. But at the edges of theory, interpretation plays a major role. In quantum cosmology, where there are no external observers to perform measurements, one needs to decide what the wavefunction of the universe means. How we interpret entanglement, i.e. as a real physical relation versus as a representational device, colours how technologists imagine the future of quantum computing. In quantum gravity, the question of whether spacetime itself can exist in superposition renders interpretation crucial.

  Interpretations also matter in teaching. Instructors make choices, sometimes unconsciously, about how to present the theory. One professor may stick to the Copenhagen view and tell students that measurement collapses the wavefunction and that that’s the end of the story. Another may prefer many-worlds and suggest that collapse never occurs, only branching universes. A third may highlight information-based views, stressing that quantum mechanics is really about knowledge and prediction rather than about what exists independently. These different approaches shape the way students can understand quantum mechanics as a tool as well as as a worldview. For some, quantum physics will always appear mysterious and paradoxical. For others, it will seem strange but logical once its hidden assumptions are made clear.

  Interpretations also play a role in experiment design. Objective collapse theories, for example, predict that superpositions of large objects should spontaneously collapse. Experimental physicists are now testing whether quantum superpositions survive for increasingly massive molecules or for diminutive mechanical devices, precisely to check whether collapse really happens. Interpretations have also motivated tests of Bell’s inequalities, an idea that shows no local theory with “hidden variables” can reproduce the correlations predicted by quantum mechanics. The scientists who conducted these experiments confirmed entanglement is a genuine feature of the world, not a residue of the mathematical tools we use to study it — and won the Nobel Prize for physics in 2022. Today, entanglement is exploited in technologies such as quantum cryptography. Without the interpretative debates that forced physicists to take these puzzles seriously, such developments may never have been pursued.

  The fact that some physicists care deeply about interpretation while others don’t reflects different goals. Those who work on applied problems or who need to build devices don’t have to care much. The maths provides the answers they need. Those who are concerned with the foundations of physics, with the philosophy of science or with the unification of physical theories care very much, because interpretation guides their thinking about what’s possible and what’s not. Many physicists switch back and forth, ignoring interpretation when calculating in the lab but discussing many-worlds or informational views over chai.

  Quantum mechanics is unique among physical theories in this way. Few chemists or engineers spend time worrying about the ‘interpretation’ of Newtonian mechanics or thermodynamics because these theories present straightforward pictures of the world. Quantum mechanics instead gives flawless predictions but an under-determined picture. The search for interpretation is the search for a coherent story that links the extraordinary success of the mathematics to a clear vision of what the world is like.

  To interpret quantum physics is therefore to move beyond the bare equations and ask what they mean. Unlike classical theories, quantum mechanics doesn’t supply a single picture of reality along with its predictions. It leaves us with probabilities, superpositions, and entanglement, and it remains ambiguous about what these things really are. Some physicists insist interpretation is unnecessary; to others it’s essential. Some interpretations depict reality as a branching multiverse, others as a set of hidden particles, yet others as information alone. None has won final acceptance, but all try to close the gap between predictive success and conceptual clarity.

  In daily practice, many physicists calculate without worrying, but in teaching, in probing the limits of the theory, and in searching for new physics, interpretations matter. They shape not only what we understand about the quantum world but also how we imagine the universe we live in.

  2025.09.03

• The Hyperion dispute and chaos in space

  When reading around for my piece yesterday on the wavefunctions of quantum mechanics, I stumbled across an old and fascinating debate about Saturn’s moon Hyperion.

  The question of how the smooth, classical world around us emerges from the rules of quantum mechanics has haunted physicists for a century. Most of the time the divide seems easy: quantum laws govern atoms and electrons while planets, chairs, and cats are governed by the laws of Newton and Einstein. Yet there are cases where this distinction is not so easy to draw. One of the most surprising examples comes not from a laboratory experiment but from the cosmos.

  In the 1990s, Hyperion became the focus of a deep debate about the nature of classicality, one that quickly snowballed into the so-called Hyperion dispute. It showed how different interpretations of quantum theory could lead to apparently contradictory claims, and how those claims can be settled by making their underlying assumptions clear.

  Hyperion is not one of Saturn’s best-known moons but it is among the most unusual. Unlike round bodies such as Titan or Enceladus, Hyperion has an irregular shape, resembling a potato more than a sphere. Its surface is pocked by craters and its interior appears porous, almost like a sponge. But the feature that caught physicists’ attention was its rotation. Hyperion does not spin in a steady, predictable way. Instead, it tumbles chaotically. Its orientation changes in an irregular fashion as it orbits Saturn, influenced by the gravitational pulls of Saturn and Titan, which is a moon larger than Mercury.

  In physics, chaos does not mean complete disorder. It means a system is sensitive to its initial conditions. For instance, imagine two weather models that start with almost the same initial data: one says the temperature in your locality at 9:00 am is 20.000º C, the other says it’s 20.001º C. That seems like a meaningless difference. But because the atmosphere is chaotic, this difference can grow rapidly. After a few days, the two models may predict very different outcomes: one may show a sunny afternoon and the other, thunderstorms.

  This sensitivity to initial conditions is often called the butterfly effect — it’s the idea that the flap of a butterfly’s wings in Brazil might, through a chain of amplifications, eventually influence the formation of a tornado in Canada.

  Hyperion behaves in a similar way. A minuscule difference in its initial spin angle or speed grows exponentially with time, making its future orientation unpredictable beyond a few months. In classical mechanics this is chaos; in quantum mechanics, those tiny initial uncertainties are built in by the uncertainty principle, and chaos amplifies them dramatically. As a result, predicting its orientation more than a few months ahead is impossible, even with precise initial data.

  To astronomers, this was a striking case of classical chaos. But to a quantum theorist, it raised a deeper question: how does quantum mechanics describe such a macroscopic, chaotic system?

  Why Hyperion interested quantum physicists is rooted in that core feature of quantum theory: the wavefunction. A quantum particle is described by a wavefunction, which encodes the probabilities of finding it in different places or states. A key property of wavefunctions is that they spread over time. A sharply localised particle will gradually smear out, with a nonzero probability of it being found over an expanding region of space.

  For microscopic particles such as electrons, this spreading occurs very rapidly. For macroscopic objects, like a chair, an orange or you, the spread is usually negligible. The large mass of everyday objects makes the quantum uncertainty in their motion astronomically small. This is why you don’t have to be worried about your chai mug being in two places at once.

  Hyperion is a macroscopic moon, so you might think it falls clearly on the classical side. But this is where chaos changes the picture. In a chaotic system, small uncertainties get amplified exponentially fast. A variable called the Lyapunov exponent measures this sensitivity. If Hyperion begins with an orientation with a minuscule uncertainty, chaos will magnify that uncertainty at an exponential rate. In quantum terms, this means the wavefunction describing Hyperion’s orientation will not spread slowly, as for most macroscopic bodies, but at full tilt.

  In 1998, the Polish-American theoretical physicist Wojciech Zurek calculated that within about 20 years, the quantum state of Hyperion should evolve into a superposition of macroscopically distinct orientations. In other words, if you took quantum mechanics seriously, Hyperion would be “pointing this way and that way at once”, just like Schrödinger’s famous cat that is alive and dead at once.

  This startling conclusion raised the question: why do we not observe such superpositions in the real Solar System?

  Zurek’s answer to this question was decoherence. Say you’re blowing a soap bubble in a dark room. If no light touches it, the bubble is just there, invisible to you. Now shine a torchlight on it. Photons from the bulb will scatter off the bubble and enter your eyes, letting you see its position and color. But here’s the catch: every photon that bounces off the bubble also carries away a little bit of information about it. In quantum terms, the bubble’s wavefunction becomes entangled with all those photons.

  If the bubble were treated purely quantum mechanically, you could imagine a strange state where it was simultaneously in many places in the room — a giant superposition. But once trillions of photons have scattered off it, each carrying “which path?” information, the superposition is effectively destroyed. What remains is an apparent mixture of “bubble here” or “bubble there”, and to any observer the bubble looks like a localised classical object. This is decoherence in action: the environment (the sea of photons here) acts like a constant measuring device, preventing large objects from showing quantum weirdness.

  For Hyperion, decoherence would be rapid. Interactions with sunlight, Saturn’s magnetospheric particles, and cosmic dust would constantly ‘measure’ Hyperion’s orientation. Any coherent superposition of orientations would be suppressed almost instantly, long before it could ever be observed. Thus, although pure quantum theory predicts Hyperion’s wavefunction would spread into cat-like superpositions, decoherence explains why we only ever see Hyperion in a definite orientation.

  Thus Zurek argued that decoherence is essential to understand how the classical world emerges from its quantum substrate. To him, Hyperion provided an astronomical example of how chaotic dynamics could, in principle, generate macroscopic superpositions, and how decoherence ensures these superpositions remain invisible to us.

  Not everyone agreed with Zurek’s conclusion, however. In 2005, physicists Nathan Wiebe and Leslie Ballentine revisited the problem. They wanted to know: if we treat Hyperion using the rules of quantum mechanics, do we really need the idea of decoherence to explain why it looks classical? Or would Hyperion look classical even without bringing the environment into the picture?

  To answer this, they did something quite concrete. Instead of trying to describe every possible property of Hyperion, they focused on one specific and measurable feature: the part of its spin that pointed along a fixed axis, perpendicular to Hyperion’s orbit. This quantity — essentially the up-and-down component of Hyperion’s tumbling spin — was a natural choice because it can be defined both in classical mechanics and in quantum mechanics. By looking at the same feature in both worlds, they could make a direct comparison.

  Wiebe and Ballentine then built a detailed model of Hyperion’s chaotic motion and ran numerical simulations. They asked: if we look at this component of Hyperion’s spin, how does the distribution of outcomes predicted by classical physics compare with the distribution predicted by quantum mechanics?

  The result was striking. The two sets of predictions matched extremely well. Even though Hyperion’s quantum state was spreading in complicated ways, the actual probabilities for this chosen feature of its spin lined up with the classical expectations. In other words, for this observable, Hyperion looked just as classical in the quantum description as it did in the classical one.

  From this, Wiebe and Ballentine drew a bold conclusion: that Hyperion doesn’t require decoherence to appear classical. The agreement between quantum and classical predictions was already enough. They went further and suggested that this might be true more broadly: perhaps decoherence is not essential to explain why macroscopic bodies, the large objects we see around us, behave classically.

  This conclusion went directly against the prevailing view of quantum physics as a whole. By the early 2000s, many physicists believed that decoherence was the central mechanism that bridged the quantum and classical worlds. Zurek and others had spent years showing how environmental interactions suppress the quantum superpositions that would otherwise appear in macroscopic systems. To suggest that decoherence was not essential was to challenge the very foundation of that programme.

  The debate quickly gained attention. On one side stood Wiebe and Ballentine, arguing that simple agreement between quantum and classical predictions for certain observables was enough to resolve the issue. On the other stood Zurek and the decoherence community, insisting that the real puzzle was more fundamental: why we never observe interference between large-scale quantum states.

  At this time, the Hyperion dispute wasn’t just about a chaotic moon. It was about how we could define ‘classical behavior’ in the first place. For Wiebe and Ballentine, classical meant “quantum predictions match classical ones”. For Zurek et al., classical meant “no detectable superpositions of macroscopically distinct states”. The difference in definitions made the two sides seem to clash.

  But then, in 2008, physicist Maximilian Schlosshauer carefully analysed the issue and showed that the two sides were not actually talking about the same problem. The apparent clash arose because Zurek and Wiebe-Ballentine had started from essentially different assumptions.

  Specifically, Wiebe and Ballentine had adopted the ensemble interpretation of quantum mechanics. In everyday terms, the ensemble interpretation says, “Don’t take the quantum wavefunction too literally.” That is, it does not describe the “real state” of a single object. Instead, it’s a tool to calculate the probabilities of what we will see if we repeat an experiment many times on many identical systems. It’s like rolling dice. If I say the probability of rolling a 6 is 1/6, that probability does not describe the dice themselves as being in a strange mixture of outcomes. It simply summarises what will happen if I roll a large collection of dice.

  Applied to quantum mechanics, the ensemble interpretation works the same way. If an electron is described by a wavefunction that seems to say it is “spread out” over many positions, the ensemble interpretation insists this does not mean the electron is literally smeared across space. Rather, the wavefunction encodes the probabilities for where the electron would be found if we prepared many electrons in the same way and measured them. The apparent superposition is not a weird physical reality, just a statistical recipe.

  Wiebe and Ballentine carried this outlook over to Hyperion. When Zurek described Hyperion’s chaotic motion as evolving into a superposition of many distinct orientations, he meant this as a literal statement: without decoherence, the moon’s quantum state really would be in a giant blend of “pointing this way” and “pointing that way”. From his perspective, there was a crisis because no one ever observes moons or chai mugs in such states. Decoherence, he argued, was the missing mechanism that explained why these superpositions never show up.

  But under the ensemble interpretation, the situation looks entirely different. For Wiebe and Ballentine, Hyperion’s wavefunction was never a literal “moon in superposition”. It was always just a probability tool, telling us the likelihood of finding Hyperion with one orientation or another if we made a measurement. Their job, then, was simply to check: do these quantum probabilities match the probabilities that classical physics would give us? If they do, then Hyperion behaves classically by definition. There is no puzzle to be solved and no role for decoherence to play.

  This explains why Wiebe and Ballentine concentrated on comparing the probability distributions for a single observable, namely the component of Hyperion’s spin along a chosen axis. If the quantum and classical results lined up — as their calculations showed — then from the ensemble point of view Hyperion’s classicality was secured. The apparent superpositions that worried Zurek were never taken as physically real in the first place.

  Zurek, on the other hand, was addressing the measurement problem. In standard quantum mechanics, superpositions are physically real. Without decoherence, there is always some observable that could reveal the coherence between different macroscopic orientations. The puzzle is why we never see such observables registering superpositions. Decoherence provided the answer: the environment prevents us from ever detecting those delicate quantum correlations.

  In other words, Zurek and Wiebe-Ballentine were tackling different notions of classicality. For Wiebe and Ballentine, classicality meant the match between quantum and classical statistical distributions for certain observables. For Zurek, classicality meant the suppression of interference between macroscopically distinct states.

  Once Schlosshauer spotted this difference, the apparent dispute went away. His resolution showed that the clash was less over data than over perspectives. If you adopt the ensemble interpretation, then decoherence indeed seems unnecessary, because you never take the superposition as a real physical state in the first place. If you are interested in solving the measurement problem, then decoherence is crucial, because it explains why macroscopic superpositions never manifest.

  The overarching takeaway is that, from the quantum point of view, there is no single definition of what constitutes “classical behaviour”. The Hyperion dispute forced physicists to articulate what they meant by classicality and to recognise the assumptions embedded in different interpretations. Depending on your personal stance, you may emphasise the agreement of statistical distributions or you may emphasise the absence of observable superpositions. Both approaches can be internally consistent — but they  also answer different questions.

  For school students that are reading this story, the Hyperion dispute may seem obscure. Why should we care about whether a distant moon’s tumbling motion demands decoherence or not? The reason is that the moon provides a vivid example of a deep issue: how do we reconcile the strange predictions of quantum theory with the ordinary world we see?

  In the laboratory, decoherence is an everyday reality. Quantum computers, for example, must be carefully shielded from their environments to prevent decoherence from destroying fragile quantum information. In cosmology, decoherence plays a role in explaining how quantum fluctuations in the early universe influenced the structure of galaxies. Hyperion showed that even an astronomical body can, in principle, highlight the same foundational issues.

  2025.08.24

• What on earth is a wavefunction?

  If you drop a pebble into a pond, ripples spread outward in gentle circles. We all know this sight, and it feels natural to call them waves. Now imagine being told that everything — from an electron to an atom to a speck of dust — can also behave like a wave, even though they are made of matter and not water or air. That is the bold claim of quantum mechanics. The waves in this case are not ripples in a material substance. Instead, they are mathematical entities known as wavefunctions.

  At first, this sounds like nothing more than fancy maths. But the wavefunction is central to how the quantum world works. It carries the information that tells us where a particle might be found, what momentum it might have, and how it might interact. In place of neat certainties, the quantum world offers a blur of possibilities. The wavefunction is the map of that blur. The peculiar thing is, experiments show that this ‘blur’ behaves as though it is real. Electrons fired through two slits make interference patterns as though each one went through both slits at once. Molecules too large to see under a microscope can act the same way, spreading out in space like waves until they are detected.

  So what exactly is a wavefunction, and how should we think about it? That question has haunted physicists since the early 20th century and it remains unsettled to this day.

  In classical life, you can say with confidence, “The cricket ball is here, moving at this speed.” If you can’t measure it, that’s your problem, not nature’s. In quantum mechanics, it is not so simple. Until a measurement is made, a particle does not have a definite position in the classical sense. Instead, the wavefunction stretches out and describes a range of possibilities. If the wavefunction is sharply peaked, the particle is most likely near a particular spot. If it is wide, the particle is spread out. Squaring the wavefunction’s magnitude gives the probability distribution you would see in many repeated experiments.

  If this sounds abstract, remember that the predictions are tangible. Interference patterns, tunnelling, superpositions, entanglement — all of these quantum phenomena flow from the properties of the wavefunction. It is the script that the universe seems to follow at its smallest scales.

  To make sense of this, many physicists use analogies. Some compare the wavefunction to a musical chord. A chord is not just one note but several at once. When you play it, the sound is rich and full. Similarly, a particle’s wavefunction contains many possible positions (or momenta) simultaneously. Only when you press down with measurement do you “pick out” a single note from the chord.

  Others have compared it to a weather forecast. Meteorologists don’t say, “It will rain here at exactly 3:07 pm.” They say, “There’s a 60% chance of showers in this region.” The wavefunction is like nature’s own forecast, except it is more fundamental: it is not our ignorance that makes it probabilistic, but the way the universe itself behaves.

  Mathematically, the wavefunction is found by solving the Schrödinger equation, which is a central law of quantum physics. This equation describes how the wavefunction changes in time. It is to quantum mechanics what Newton’s second law (F = ma) is to classical mechanics. But unlike Newton’s law, which predicts a single trajectory, the Schrödinger equation predicts the evolving shape of probabilities. For example, it can show how a sharply localised wavefunction naturally spreads over time, just like a drop of ink disperses in water. The difference is that the spreading is not caused by random mixing but by the fundamental rules of the quantum world.

  But does that mean the wavefunction is real, like a water wave you can touch, or is it just a clever mathematical fiction?

  There are two broad camps. One camp, sometimes called the instrumentalists, argues the wavefunction is only a tool for making predictions. In this view, nothing actually waves in space. The particle is simply somewhere, and the wavefunction is our best way to calculate the odds of finding it. When we measure, we discover the position, and the wavefunction ‘collapses’ because our information has been updated, not because the world itself has changed.

  The other camp, the realists, argues that the wavefunction is as real as any energy field. If the mathematics says a particle is spread out across two slits, then until you measure it, the particle really is spread out, occupying both paths in a superposed state. Measurement then forces the possibilities into a single outcome, but before that moment, the wavefunction’s broad reach isn’t just bookkeeping: it’s physical.

  This isn’t an idle philosophical spat. It has consequences for how we interpret famous paradoxes like Schrödinger’s cat — supposedly “alive and dead at once until observed” — and for how we understand the limits of quantum mechanics itself. If the wavefunction is real, then perhaps macroscopic objects like cats, tables or even ourselves can exist in superpositions in the right conditions. If it is not real, then quantum mechanics is only a calculating device, and the world remains classical at larger scales.

  The ability of a wavefunction to remain spread out is tied to what physicists call coherence. A coherent state is one where the different parts of the wavefunction stay in step with each other, like musicians in an orchestra keeping perfect time. If even a few instruments go off-beat, the harmony collapses into noise. In the same way, when coherence is lost, the wavefunction’s delicate correlations vanish.

  Physicists measure this ‘togetherness’ with a parameter called the coherence length. You can think of it as the distance over which the wavefunction’s rhythm remains intact. A laser pointer offers a good everyday example: its light is coherent, so the waves line up across long distances, allowing a sharp red dot to appear even all the way across a lecture hall. By contrast, the light from a torch is incoherent: the waves quickly fall out of step, producing only a fuzzy glow. In the quantum world, a longer coherence length means the particle’s wavefunction can stay spread out and in tune across a larger stretch of space, making the object more thoroughly delocalised.

  However, coherence is fragile. The world outside — the air, the light, the random hustle of molecules — constantly disturbs the system. Each poke causes the system to ‘leak’ information, collapsing the wavefunction’s delicate superposition. This process is called decoherence, and it explains why we don’t see cats or chairs spread out in superpositions in daily life. The environment ‘measures’ them constantly, destroying their quantum fuzziness.

  One frontier of modern physics is to see how far coherence can be pushed before decoherence wins. For electrons and atoms, the answer is “very far”. Physicists have found their wavefunctions can stretch across micrometres or more. They have also demonstrated coherence with molecules with thousands of atoms, but keeping them coherent has been much more difficult. For larger solid objects, it’s harder still.

  Physicists often talk about expanding a wavefunction. What they mean is deliberately increasing the spatial extent of the quantum state, making the fuzziness spread wider, while still keeping it coherent. Imagine a violin string: if it vibrates softly, the motion is narrow; if it vibrates with larger amplitude, it spreads. In quantum mechanics, expansion is more subtle but the analogy holds: you want the wavefunction to cover more ground not through noise or randomness but through genuine quantum uncertainty.

  Another way to picture it is as a drop of ink released into clear water. At first, the drop is tight and dark. Over time, it spreads outward, thinning and covering more space. Expanding a quantum wavefunction is like speeding up this spreading process, but with a twist: the cloud must remain coherent. The ink can’t become blotchy or disturbed by outside currents. Instead, it must preserve its smooth, wave-like character, where all parts of the spread remain correlated.

  How can this be done? One way is to relax the trap that’s being used to hold the particle in place. In physics, the trap is described by a potential, which is just a way of talking about how strong the forces are that pull the particle back towards the centre. Imagine a ball sitting in a bowl. The shape of the bowl represents the potential. A deep, steep bowl means strong restoring forces, which prevent the ball from moving around. A shallow bowl means the forces are weaker. That is, if you suddenly make the bowl shallower, the ball is less tightly confined and can explore more space. In the quantum picture, reducing the stiffness of the potential is like flattening the bowl, which allows the wavefunction to swell outward. If you later return the bowl to its steep form, you can catch the now-broader state and measure its properties.

  The challenge is to do this fast and cleanly, before decoherence destroys the quantum character. And you must measure in ways that reveal quantum behaviour rather than just classical blur.

  This brings us to an experiment reported on August 19 in Physical Review Letters, conducted by researchers at ETH Zürich and their collaborators. It seems the researchers have achieved something unprecedented: they prepared a small silica sphere, only about 100 nm across, in a nearly pure quantum state and then expanded its wavefunction beyond the natural zero-point limit. This means they coherently stretched the particle’s quantum fuzziness farther than the smallest quantum wiggle that nature usually allows, while still keeping the state coherent.

  To appreciate why this matters, let’s consider the numbers. The zero-point motion of their nanoparticle — the smallest possible movement even at absolute zero — is about 17 picometres (one picometre is a trillionth of a meter). Before expansion, the coherence length was about 21 pm. After the expansion protocol, it reached roughly 73 pm, more than tripling the initial reach and surpassing the ground-state value. For something as massive as a nanoparticle, this is a big step.

  The team began by levitating a silica nanoparticle in an optical tweezer, created by a tightly focused laser beam. The particle floated in an ultra-high vacuum at a temperature of just 7 K (-266º C). These conditions reduced outside disturbances to almost nothing.

  Next, they cooled the particle’s motion close to its ground state using feedback control. By monitoring its position and applying gentle electrical forces through the surrounding electrodes, they damped its jostling until only a fraction of a quantum of motion remained. At this point, the particle was quiet enough for quantum effects to dominate.

  The core step was the two-pulse expansion protocol. First, the researchers switched off the cooling and briefly lowered the trap’s stiffness by reducing the laser power. This allowed the wavefunction to spread. Then, after a carefully timed delay, they applied a second softening pulse. This sequence cancelled out unwanted drifts caused by stray forces while letting the wavefunction expand even further.

  Finally, they restored the trap to full strength and measured the particle’s motion by studying how they scattered light. Repeating this process hundreds of times gave them a statistical view of the expanded state.

  The results showed that the nanoparticle’s wavefunction expanded far beyond its zero-point motion while still remaining coherent. The coherence length grew more than threefold, reaching 73 ± 34 pm. Per the team, this wasn’t just noisy spread but genuine quantum delocalisation.

  More strikingly, the momentum of the nanoparticle had become ‘squeezed’ below its zero-point value. In other words, while uncertainty over the particle’s position increased, that over its momentum decreased, in keeping with Heisenberg’s uncertainty principle. This kind of squeezed state is useful because it’s especially sensitive to feeble external forces.

  The data matched theoretical models that considered photon recoil to be the main source of decoherence. Each scattered photon gave the nanoparticle a small kick, and this set a fundamental limit. The experiment confirmed that photon recoil was indeed the bottleneck, not hidden technical noise. The researchers have suggested using dark traps in future — trapping methods that use less light, such as radio-frequency fields — to reduce this recoil. With such tools, the coherence lengths can potentially be expanded to scales comparable to the particle’s size. Imagine a nanoparticle existing in a state that spans its own diameter. That would be a true macroscopic quantum object.

  This new study pushes quantum mechanics into a new regime. Thus far, large, solid objects like nanoparticles could be cooled and controlled, but their coherence lengths stayed pinned near the zero-point level. Here, the researchers were able to deliberately increase the coherence length beyond that limit, and in doing so showed that quantum fuzziness can be engineered, not just preserved.

  The implications are broad. On the practical side, delocalised nanoparticles could become extremely sensitive force sensors, able to detect faint electric or gravitational forces. On the fundamental side, the ability to hold large objects in coherent, expanded states is a step towards probing whether gravity itself has quantum features. Several theoretical proposals suggest that if two massive objects in superposition can become entangled through their mutual gravity, it would prove gravity must be quantum. To reach that stage, experiments must first learn to create and control delocalised states like this one.

  The possibilities for sensing in particular are exciting. Imagine a nanoparticle prepared in a squeezed, delocalised state being used to detect the tug of an unseen mass nearby or to measure an electric field too weak for ordinary instruments. Some physicists have speculated that such systems could help search for exotic particles such as certain dark matter candidates, which might nudge the nanoparticle ever so slightly. The extreme sensitivity arises because a delocalised quantum object is like a feather balanced on a pin: the tiniest push shifts it in measurable ways.

  There are also parallels with past breakthroughs. The Laser Interferometer Gravitational-wave Observatories, which detect gravitational waves, rely on manipulating quantum noise in light to reach unprecedented sensitivity. The ETH Zürich experiment has extended the same philosophy into the mechanical world of nanoparticles. Both cases show that pushing deeper into quantum control could yield technologies that were once unimaginable.

  But beyond the technologies also lies a more interesting philosophical edge. The experiment strengthens the case that the wavefunction behaves like something real. If it were only an abstract formula, could we stretch it, squeeze it, and measure the changes in line with theory? The fact that researchers can engineer the wavefunction of a many-atom object and watch it respond like a physical entity tilts the balance towards reality. At the least, it shows that the wavefunction is not just a mathematical ghost. It’s a structure that researchers can shape with lasers and measure with detectors.

  There are also of course the broader human questions. If nature at its core is described not by certainties but by probabilities, then philosophers must rethink determinism, the idea that everything is fixed in advance. Our everyday world looks predictable only because decoherence hides the fuzziness. But under carefully controlled conditions, that fuzziness comes back into view. Experiments like this remind us that the universe is stranger, and more flexible, than classical common sense would suggest.

  The experiment also reminds us that the line between the quantum and classical worlds is not a brick wall but a veil — thin, fragile, and possibly removable in the right conditions. And each time we lift it a little further, we don’t just see strange behaviour: we also glimpse sensors more sensitive than ever, tests of gravity’s quantum nature, and perhaps someday, direct encounters with macroscopic superpositions that will force us to rewrite what we mean by reality.

  2025.08.23

• All the science in ‘The Cloverfield Paradox’

  I watched The Cloverfield Paradox last night, the horror film that Paramount pictures had dumped with Netflix and which was then released by Netflix on February 4. It’s a dumb production: unlike H.R. Giger’s existential, visceral horrors that I so admire, The Cloverfield Paradox is all about things going bump in the dark. But what sets these things off in the film is quite interesting: a particle accelerator. However, given how bad the film was, the screenwriter seems to have used this device simply as a plot device, nothing else.

  The particle accelerator is called Shepard. We don’t know what particles it’s accelerating or up to what centre-of-mass collision energy. However, the film’s premise rests on the possibility that a particle accelerator can open up windows into other dimensions. The Cloverfield Paradox needs this because, according to its story, Earth has run out of energy sources in 2028 and countries are threatening ground invasions for the last of the oil, so scientists assemble a giant particle accelerator in space to tap into energy sources in other dimensions.

  Considering 2028 is only a decade from now – when the Sun will still be shining bright as ever in the sky – and renewable sources of energy aren’t even being discussed, the movie segues from sci-fi into fantasy right there.

  Anyway, the idea that a particle accelerator can open up ‘portals’ into other dimensions isn’t new nor entirely silly. Broadly, an accelerator’s purpose is founded on three concepts: the special theory of relativity (SR), particle decay and the wavefunction of quantum mechanics.

  According to SR, mass and energy can transform into each other as well as that objects moving closer to the speed of light will become more massive, thus more energetic. Particle decay is what happens when a heavier subatomic particle decomposes into groups of lighter particles because it’s unstable. Put these two ideas together and you have a part of the answer: accelerators accelerate particles to extremely high velocities, the particles become more massive, ergo more energetic, and the excess energy condenses out at some point as other particles.

  Next, in quantum mechanics, the wavefunction is a mathematical function: when you solve it based on what information you have available, the answer spit out by one kind of the function gives the probability that a particular particle exists at some point in the spacetime continuum. It’s called a wavefunction because the function describes a wave, and like all waves, this one also has a wavelength and an amplitude. However, the wavelength here describes the distance across which the particle will manifest. Because energy is directly proportional to frequency (E = h × ν; h is Planck’s constant) and frequency is inversely proportional to the wavelength, energy is inversely proportional to wavelength. So the more the energy a particle accelerator achieves, the smaller the part of spacetime the particles will have a chance of probing.

  Spoilers ahead

  SR, particle decay and the properties of the wavefunction together imply that if the Shepard is able to achieve a suitably high energy of acceleration, it will be able to touch upon an exceedingly small part of spacetime. But why, as it happens in The Cloverfield Paradox, would this open a window into another universe?

  Spoilers end

  Instead of directly offering a peek into alternate universes, a very-high-energy particle accelerator could offer a peek into higher dimensions. According to some theories of physics, there are many higher dimensions even though humankind may have access only to four (three of space and one of time). The reason they should even exist is to be able to solve some conundrums that have evaded explanation. For example, according to Kaluza-Klein theory (one of the precursors of string theory), the force of gravity is so much weaker than the other three fundamental forces (strong nuclear, weak nuclear and electromagnetic) because it exists in five dimensions. So when you experience it in just four dimensions, its effects are subdued.

  Where are these dimensions? Per string theory, for example, they are extremely compactified, i.e. accessible only over incredibly short distances, because they are thought to be curled up on themselves. According to Oskar Klein (one half of ‘Kaluza-Klein’, the other half being Theodore Kaluza), this region of space could be a circle of radius 10^-32 m. That’s 0.00000000000000000000000000000001 m – over five quadrillion times smaller than a proton. According to CERN, which hosts the Large Hadron Collider (LHC), a particle accelerated to 10 TeV can probe a distance of 10^-19 m. That’s still one trillion times larger than where the Kaluza-Klein fifth dimension is supposed to be curled up. The LHC has been able to accelerate particles to 8 TeV.

  The likelihood of a particle accelerator tossing us into an alternate universe entirely is a different kind of problem. For one, we have no clue where the connections between alternate universes are nor how they can be accessed. In Nolan’s Interstellar (2014), a wormhole is discovered by the protagonist to exist inside a blackhole – a hypothesis we currently don’t have any way of verifying. Moreover, though the LHC is supposed to be able to create microscopic blackholes, they have a 0% chance of growing to possess the size or potential of Interstellar‘s Gargantua.

  In all, The Cloverfield Paradox is a waste of time. In the 2016 film Spectral – also released by Netflix – the science is overwrought, stretched beyond its possibilities, but still stays close to the basic principles. For example, the antagonists in Spectral are creatures made entirely as Bose-Einstein condensates. How this was even achieved boggles the mind, but the creatures have the same physical properties that the condensates do. In The Cloverfield Paradox, however, the accelerator is a convenient insertion into a bland story, an abuse of the opportunities that physics of this complexity offers. The writers might as well have said all the characters blinked and found themselves in a different universe.

  2018.02.07

• The science in Netflix’s ‘Spectral’

  I watched Spectral, the movie that released on Netflix on December 9, 2016, after Universal Studios got cold feet about releasing it on the big screen – the same place where a previous offering, Warcraft, had been gutted. Spectral is sci-fi and has a few great moments but mostly it’s bland and begging for some tabasco. The premise: an elite group of American soldiers deployed in Moldova come upon some belligerent ghost-like creatures in a city they’re fighting in. They’ve no clue how to stop them, so they fly in an engineer to consult from DARPA, the same guy who built the goggles that detected the creatures in the first place. Together, they do things. Now, I’d like to talk about the science in the film and not the plot itself, though the former feeds the latter.

  

  

  Towards the middle of the movie, the engineer realises that the ghost-like creatures have the same limitations as – wait for it – a Bose-Einstein condensate (BEC). They can pass through walls but not ceramic or heavy metal (not the music), they rapidly freeze objects in their path, and conventional weapons, typically projectiles of some kind, can’t stop them. Frankly, it’s fabulous that Ian Fried, the film’s writer, thought to use creatures made of BECs as villains.

  A BEC is an exotic state of matter in which a group of ultra-cold particles condense into a superfluid (i.e., it flows without viscosity). Once a BEC forms, a subsection of a BEC can’t be removed from it without breaking the whole BEC state down. You’d think this makes the BEC especially fragile – because it’s susceptible to so many ‘liabilities’ – but it’s the exact opposite. In a BEC, the energy required to ‘kick’ a single particle out of its special state is equal to the energy that’s required to ‘kick’ all the particles out, making BECs as a whole that much more durable.

  This property is apparently beneficial for the creatures of Spectral, and that’s where the similarity ends because BECs have other properties that are inimical to the portrayal of the creatures. Two immediately came to mind: first, BECs are attainable only at ultra-cold temperatures; and second, the creatures can’t be seen by the naked eye but are revealed by UV light. There’s a third and relevant property but which we’ll come to later: that BECs have to be composed of bosons or bosonic particles.

  It’s not clear why Spectral‘s creatures are visible only when exposed to light of a certain kind. Clyne, the DARPA engineer, says in a scene, “If I can turn it inside out, by reversing the polarity of some of the components, I might be able to turn it from a camera [that, he earlier says, is one that “projects the right wavelength of UV light”] into a searchlight. We’ll [then] be able to see them with our own eyes.” However, the documented ability of BECs to slow down light to a great extent (5.7-million times more than lead can, in certain conditions) should make them appear extremely opaque. More specifically, while a BEC can be created that is transparent to a very narrow range of frequencies of electromagnetic radiation, it will stonewall all frequencies outside of this range on the flipside. That the BECs in Spectral are opaque to a single frequency and transparent to all others is weird.

  Obviating the need for special filters or torches to be able to see the creatures simplifies Spectral by removing one entire layer of complexity. However, it would remove the need for the DARPA engineer also, who comes up with the hyperspectral camera and, its inside-out version, the “right wavelength of UV” searchlight. Additionally, the complexity serves another purpose. Ahead of the climax, Clyne builds an energy-discharging gun whose plasma-bullets of heat can rip through the BECs (fair enough). This tech is also slightly futuristic. If the sci-fi/futurism of the rest of Spectral leading up to that moment (when he invents the gun) was absent, then the second-half of the movie would’ve become way more sci-fi than the first-half, effectively leaving Spectral split between two genres: sci-fi and wtf. Thus the need for the “right wavelength of UV” condition?

  Now, to the third property. Not all particles can be used to make BECs. Its two predictors, Satyendra Nath Bose and Albert Einstein, were working (on paper) with kinds of particles since called bosons. In nature, bosons are force-carriers, acting against matter-maker particles called fermions. A more technical distinction between them is that the behaviour of bosons is explained using Bose-Einstein statistics while the behaviour of fermions is explained using Fermi-Dirac statistics. And only Bose-Einstein statistics predicts the existence of states of matter called condensates, not Femi-Dirac statistics.

  (Aside: Clyne, when explaining what BECs are in Spectral, says its predictors are “Nath Bose and Albert Einstein”. Both ‘Nath’ and ‘Bose’ are surnames in India, so “Nath Bose” is both anyone and no one at all. Ugh. Another thing is I’ve never heard anyone refer to S.N. Bose as “Nath Bose”, only ‘Satyendranath Bose’ or, simply, ‘Satyen Bose’. Why do Clyne/Fried stick to “Nath Bose”? Was “Satyendra” too hard to pronounce?)

  All particles constitute a certain amount of energy, which under some circumstances can increase or decrease. However, the increments of energy in which this happens are well-defined and fixed (hence the ‘quantum’ of quantum mechanics). So, for an oversimplified example, a particle can be said to occupy energy levels constituting 2, 4 or 6 units but never of 1, 2.5 or 3 units. Now, when a very-low-density collection of bosons is cooled to an ultra-cold temperature (a few hundredths of kelvins or cooler), the bosons increasingly prefer occupying fewer and fewer energy levels. At one point, they will all occupy a single and common level – flouting a fundamental rule that there’s a maximum limit for the number of particles that can be in the same level at once. (In technical parlance, the wavefunctions of all the bosons will merge.)

  When this condition is achieved, a BEC will have been formed. And in this condition, even if a new boson is added to the condensate, it will be forced into occupying the same level as every other boson in the condensate. This condition is also out of limits for all fermions – except in very special circumstances, and circumstances whose exceptionalism perhaps makes way for Spectral‘s more fantastic condensate-creatures. We known one such as superconductivity.

  In a superconducting material, electrons flow without any resistance whatsoever at very low temperatures. The most widely applied theory of superconductivity interprets this flow as being that of a superfluid, and the ‘sea’ of electrons flowing as such to be a BEC. However, electrons are fermions. To overcome this barrier, Leon Cooper proposed in 1956 that the electrons didn’t form a condensate straight away but that there was an intervening state called a Cooper pair. A Cooper pair is a pair of electrons that had become bound, overcoming their like-charges repulsion because of the vibration of atoms of the superconducting metal surrounding them. The electrons in a Cooper pair also can’t easily quit their embrace because, once they become bound, the total energy they constitute as a pair is lower than the energy that would be destabilising in any other circumstances.

  Could Spectral‘s creatures have represented such superconducting states of matter? It’s definitely science fiction because it’s not too far beyond the bounds of what we know about BEC today (at least in terms of a concept). And in being science fiction, Spectral assumes the liberty to make certain leaps of reasoning – one being, for example, how a BEC-creature is able to ram against an M1 Abrams and still not dissipate. Or how a BEC-creature is able to sit on an electric transformer without blowing up. I get that these in fact are the sort of liberties a sci-fi script is indeed allowed to take, so there’s little point harping on them. However, that Clyne figured the creatures ought to be BECs prompted way more disbelief than anything else because BECs are in the here and the now – and they haven’t been known to behave anything like the creatures in Spectral do.

  For some, this information might even help decide if a movie is sci-fi or fantasy. To me, it’s sci-fi.

  

  On the more imaginative side of things, Spectral also dwells for a bit on how these creatures might have been created in the first place and how they’re conscious. Any answers to these questions, I’m pretty sure, would be closer to fantasy than to sci-fi. For example, I wonder how the computing capabilities of a very large neural network seen at the end of the movie (not a spoiler, trust me) were available to the creatures wirelessly, or where the power source was that the soldiers were actually after. Spectral does try to skip the whys and hows by having Clyne declare, “I guess science doesn’t have the answer to everything” – but you’re just going “No shit, Sherlock.”

  His character is, as this Verge review puts it, exemplarily shallow while the movie never suggests before the climax that science might indeed have all the answers. In fact, the movie as such, throughout its 108 minutes, wasn’t that great for me; it doesn’t ever live up to its billing as a “supernatural Black Hawk Down“. You think about BHD and you remember it being so emotional – Spectral has none of that. It was just obviously more fun to think about the implications of its antagonists being modelled after a phenomenon I’ve often read/written about but never thought about that way.

  2017.01.09