Tag: quantum superposition

• 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

• 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

• The gap between language and quantum mechanics

  Physics World has a fantastic article about the problem with using a language invented, in Terry Pratchett’s words, “to tell other monkeys where the ripe fruit is”, to describe the peculiar but very much real possibilities created by the rules of quantum mechanics. Excerpt:

  … despite the burgeoning growth of quantum technology, one thing that hasn’t changed is the cumbersome and counterintuitive language we use to talk about all things quantum. While the reality of entanglement and superposition is beyond all reasonable doubt, it is as maddening as ever to describe them in words. Quantum phenomena are strange, but that does not mean we should be satisfied with strange language to describe them.

  From the very early days of quantum mechanics, Albert Einstein, Niels Bohr, Werner Heisenberg and others strove to understand this new-fangled non-classical physics of quantum 1.0. Their struggle concerned a gap between how we talk about phenomena and how we encounter them in the laboratory. That gap was created by the imperfect metaphorical language still largely used to characterize non-classical phenomena.

  The authors have written that the terms that writers, journalists, and scientists reach for when describing quantum phenomena to people who don’t have the mathematical awareness (for want of a better description) are probably adding to the confusion instead of clarifying quantum mechanics, and diminishing its realness. ‘Superposition’ is a good example: it’s a word that captures a particular phenomenon, but when you try to spell it out, in toto with no exceptions, to someone who doesn’t understand the math of it, you use some metaphors and approximations that either create an incomplete picture or an obscured one. And both add to quantum physics’s mystery and spookiness, which are counterproductive.

  This has been a familiar challenge in my experience covering high-energy physics as well, were the protagonists are often particles and forces that are best described using mathematical grammar (amplitudes, matrices, groups, etc.) rather than the language that facilitates everyday life. This is why I think the molasses metaphor (and minor variations of it) may well have been the most used of its kind in 2012, when the Higgs boson, and its corresponding energy field, dominated physics news: in the New York Times‘s words, “What is the Higgs field? … It has been described as a kind of cosmic molasses, dragging on particles as they move through it”. In an instructive 2013 paper, Stewart Alsop and Steven Beale wrote (emphasis in the original) about the problems with such metaphors:

  At some point, of course, all analogical thinking breaks down—the Higgs phenomena is not a crowd or molasses. Perhaps a weakness with these analogies is their reliance on a ‘medium’ as the object node mapped to the Higgs field. This is probably unavoidable, but it results in a number of points of potential confusion. The concept of a medium is generally understood to be a volume filled with a physical substance that can be manipulated and controlled. This is not the case in the standard model of the Higgs field, which is understood to be uniform and constant. The familiar conception of a medium is insufficient to fully understand the Higgs field in this respect. A medium can be entered and exited because it is localized, it can be concentrated in one location and minimized in another, and it is composed of matter and has its own mass and energy. Mapping these attributes onto the Higgs field leads to a line of reasoning reminiscent of 19th century aether theories.

  Obviously metaphors aren’t going to be perfect. That’s almost always the case. Instead, they’re handy because they capture a particularly interesting subset of something larger, more complicated, and get that across by drawing on things a person is already familiar with, like, of course, molasses. Through history, this has progressively become harder to do, and scientists themselves have taken note of it from time to time. For example, Werner Heisenberg delivered a speech in 1932, while receiving the Nobel Prize for physics, in which he pointed out the need to discard visualisation or, more accurately, visualisability as a means to unravelling the pending mysteries of atomic physics. He said it quite eloquently, so let me quote him:

  … the path so far traced by the quantum theory indicates that an understanding of those still unclarified features of atomic physics can only be acquired by foregoing visualization and objectification to an extent greater than that customary hitherto. We have probably no reason to regret this, because the thought of the great epistemological difficulties with which the visual atom concept of earlier physics had to contend gives us the hope that the abstracter atomic physics developing at present will one day fit more harmoniously into the great edifice of Science.

  This said, metaphors and analogies vis-à-vis quantum mechanics (getting quantum computing right took considerable effort, for a famous example) have become particularly problematic because this field of study has created technologies that are beginning to enter the public consciousness at large. There is now a greater price to pay by misunderstanding, for example, that quantum teleportation refers to bulk matter, as in Star Trek, rather than to information or, in fact, that entanglement is in Albert Einstein’s words “spooky action at a distance”. But it’s not spooky; it’s just something we don’t have the language for.

  But quantum mechanics and its consequent technologies don’t have a monopoly on being shortchanged by imprecise communication. Climate change is in the same boat. There is also another kind of price that has already been paid across the vast majority of science: a widespread belief among certain (sadly prevalent) groups of people that they understand science when they really don’t, leading to an inflated belief in the abilities and importance of science while overlooking our tendency to confuse faith for truly knowing something. (I have written about this before here, here, and here, among other instances.)

  Finally, the question of the gaps between language as we use it and quantum mechanics is reminiscent of a plot point in China Miéville’s Embassytown, where people designated “ambassadors” can only speak in pairs, simultaneously: each ambassador utters a different word-meaning, and their alien interlocutors combine the duo’s words-meanings to understand what they’re saying. In the book, these two word-meanings are written like a fraction – one word on top, a line in the middle, and the other at the bottom. But thanks to Miéville’s prose, we know that that’s only a partial representation of what’s really going on in the story. We come upon a relatable sensation in the film Arrival.

  Embassytown was a gratifying read that delved into the relationships between language and storytelling as much as between a language, its grammar, and its symbols. Like good fantasy fiction, it steadily yet gently dismantles the cognitive dissonance that reality sometimes foists on us – in this case, that would be cognising why English or for that matter any linear human language will always fall short of describing true simultaneity.

  One workaround, according to the Physics World article above, is that rather than trying to bend our language around the barely tractable and math-laden processes of quantum mechanics, we should describe the field in terms of its outcomes. To know more, do read the article.

  2023.04.27

• A ‘quantum consciousness’ absurdity at IIT Mandi

  As you go downward, inward, smaller and smaller, you get more vast conscious experience. This is the idea in Indian knowledge systems. At the bottom of it, or the very base of it, at the source, is Brahman. My point is that this is actually very consistent with what we’re learning about how consciousness may be produced in our brain due to quantum effects.

  The person who made this statement is Stuart Hameroff, at the 10th convocation at IIT Mandi on December 5. Hameroff is a neuroscientist and anaesthesiologist. Since 1975, he has been at the University of Arizona, where, in 1999, he became professor in the department of anaesthesiology and psychology and the director for the Center for Consciousness Studies. He became an emeritus professor in 2003. He is famous for his part in the Orch-OR hypothesis of how consciousness originates in the brain. Hameroff and Roger Penrose (who won the Nobel Prize for physics in 2020 for unrelated work) collaborated on the idea and published a few papers detailing their assumptions and conclusions.

  ‘Orch-OR’ stands for ‘orchestrated objective reduction’. Broadly speaking, the hypothesis is that the states of microtubules, which are cellular structures inside neurons, enter into a quantum superposition – becoming like the cat inside the unopened box in the Schrödinger’s cat thought-experiment. The superposition is then forced to collapse (‘the box is opened’) in favour of one state by gravity. This is taken to be the moment when consciousness comes ‘on’. One scheme of the hypothesis says that when the superposition collapses, the process should release some electromagnetic radiation – a testable prediction.

  Experiments looking for this radiation have come up empty. One experiment whose results were published in May 2022 found that the brain would have to have 1,000-times more of the cells that make up microtubules than it actually does, disfavouring the hypothesis in a range of space- and time-scales, albeit not entirely. The hypothesis is also largely controversial and doesn’t find favour among most physicists, who have been critical of Penrose’s calculations of how the gravity-mediated superposition collapse happens.

  To be sure, there has been some evidence that quantum phenomena might be going on in the human brain; what we don’t have evidence for is sophisticated hypotheses like Orch-OR that claim a precise origin of consciousness.

  So Hameroff’s statement at IIT Mandi that the concept of the ‘Brahman’ “is actually very consistent with what we’re learning about how consciousness may be produced in our brain due to quantum effects” is at best disingenuous. What we are learning is that Orch-OR is quite unlikely to be a valid explanation of the emergence of consciousness in the brain; and we are certainly not finding support for Orch-OR by shoehorning the concept of the ‘Brahman’ and spiritual ideas of consciousness into gravity’s effects on hypothetical forms of spacetime.

  But his talk gets worse. A few minutes later, Hameroff says that consciousness appears to straddle the shared border between the quantum and the classical worlds, that the phenomenon of quantum state reduction (a.k.a. superposition collapse) is akin to the emergence of the “Atman from the Brahman”, and that he wondered “whether the many faces of Krishna were a quantum superposition”. He continues:

  Under normal circumstances, the people back then didn’t see Krishna in superposition but as one, but knew in different ways that there could be this apparent superposition of many possible faces of Krishna.

  So here we have a scientist who once helped develop and support a difficult hypothesis to explain a famously intractable problem using the methods of science, but who has now gone so far as to claim that a) a Hindu deity was a real person, b) he had many heads, and c) people didn’t see these heads but d) knew that he could have many faces, and e) understood them to be in an “apparent superposition”. What are we to make of this waterfall of nonsense?

  His claims aren’t false because they’re unfalsifiable. Consider just one: Hameroff is postulating that macroscopic superposition could have been real (regarding the face of a human being, but let’s set that aside).

  Quantum computers work by manipulating qubits, the smallest units of information in these machines, using quantum phenomena like superposition and entanglement. The computer’s result is the state to which the qubits’ superposition collapses. But unlike classical bits, which are made of semiconductors, qubits are very fragile systems and must be protected against external disturbances, even small amounts of electromagnetic radiation. If a qubit is disturbed, it will lose the ability to participate in the quantum computer in a process called decoherence.

  To date, despite researchers’ best efforts, they haven’t built a quantum computer that completely eliminates errors arising out of decoherence. They also haven’t built quantum computers that can solve practical problems, like modelling stresses on a bridge or synthesising a drug with certain components either, meaning more complex machines will present more significant decoherence barriers. And quantum computers use subatomic (microscopic) particles as qubits.

  There is no evidence to date of macroscopic objects being in perfect superposition, forget an entity as complicated and ‘noisy’ as a human face or body. Hameroff’s other claims require less explanation as to their absurdity.

  There is a good chance he was invited to IIT Mandi with full knowledge of his views. Since 1994, Hameroff has been conducting a conference every year called ‘Science of Consciousness’, where some consciousness researchers present some notable ideas and results while others… Let me quote Tom Bartlett writing for The Guardian in 2018:

  While the Science of Consciousness event has, technically, three programme chairs and an advisory committee, it is more or less The Stuart Show. He decides who will and who will not present. And, to put it nicely, not everyone is in love with the choices he makes. To put it less nicely: some consciousness researchers believe that the whole shindig has gone off the rails, that it is seriously damaging the field of consciousness studies, and that it should be shut down.

  In 2012, Hameroff said,

  “Let’s say the heart stops beating, the blood stops flowing, the microtubules lose their quantum state. The quantum information within the microtubules is not destroyed, it can’t be destroyed, it just distributes and dissipates to the universe at large. … If the patient is resuscitated, revived, this quantum information can go back into the microtubules and the patient says ‘I had a near death experience’. If they’re not revived, and the patient dies, it’s possible that this quantum information can exist outside the body, perhaps indefinitely, as a soul.”

  In the Copenhagen interpretation of quantum mechanics, a superposition of states collapses into a single state when an observation is made on the system. What counts as an act of observation has been refined over the years: today, physicists understand that the collapse happens when the information required to describe the superposition is no longer locally available. In this sense, Hameroff’s delineation above seems to hew close to reality – but we have absolutely no way of saying that quantum information is the same as a soul!

  As Jim Al-Khalili, an expert in quantum biology, said in 2020 about Orch-OR:

  “There was some brief excitement about this idea initially, but I think very quickly most scientists said: ‘No, hang on a minute, just because quantum mechanics is mysterious and we don’t understand it and consciousness is mysterious and we don’t understand it, it doesn’t mean that the two have to be connected’.”

  So Hameroff has been making dubious claims for a long time, including claims for at least a decade that overlook the differences between a knowledge system concerned with verifiable truths and the elimination of bias and one that is concerned with harmonising reality and perception regardless of tests – and the pitfalls of claiming that a ‘fact’ in one system could be wholly equivalent to a ‘fact’ in the other. To quote philosophy scholar S.K. Arun Murthi:

  While [ancient Indian] systems of thought are called philosophical systems, they are unified in their aim: salvation and liberation of the soul. One question that has frequently been the topic of discussion in scholarly circles is whether Indian culture and civilisation really recognised an independent discipline called ‘philosophy’ as a discursive analytic tradition. The question arises because all its schools have been restricted to theological and soteriological concerns.

  Surendranath Dasgupta even begins his aforementioned book with a note of caution, that Indian thought always manifested itself “in an yearning after the Infinite” and that “Hindus never busied themselves about the investigation of the laws of nature except in so far as it was connected with the general philosophical speculations”.

  The other knowledge system, science, requires evidence, but Hameroff has none. Yet in May 2022 Hameroff again wrote:

  “Light is the part of the electromagnetic spectrum that can be seen by the eyes of humans and animals – visible light. … Ancient traditions characterized consciousness as light. Religious figures were often depicted with luminous ‘halos’, and/or auras. Hindu deities are portrayed with luminous blue skin. And people who have ‘near death’ and ‘out of body’ experiences described being attracted toward a ‘white light’. In many cultures, those who have ‘awakened to the truth about reality’ are ‘enlightened’.”

  (A few months earlier, Laxmidhar Behera, the director of IIT Mandi, had expressed belief and experience in exorcisms and that students should rid their friends’ parents of evil spirits using chants.)

  Armchair logicians and social-media loudmouths will now interpret Hameroff’s talk as ‘evidence’ of ancient India’s intellectual supremacy and as his tacit endorsement of the physical reality of Hindu deities and the sophisticated ideas that sages and scholars of the time contemplated. Hameroff also says that “therapies aimed at microtubule resonance e.g. with painless, safe and pleasant brain ultrasound can treat mental and cognitive disorders”, extending a handle to many quacks already using quantum-physics gobbledygook to con unsuspecting care-seekers.

  There may be some who truly believe such statements while others will wield it to further an agenda while knowing well that the claims are less than flimsy. Either way, the task in front of the debunker is much more devious: to set out not just the laws of nature and the methods of science but also the work of Hameroff and Penrose, the criticism against it, why expertise is not a carte blanche, the incommensurability of the knowledge systems involved, and the fine line between ‘absence of evidence’ and ‘evidence of absence’.

  2022.12.07

• A quantum theory of consciousness

  We seldom have occasion to think about science and religion at the same time, but the most interesting experience I have had doing that came in October 2018, when I attended a conference called ‘Science for Monks’* in Gangtok, Sikkim. More precisely, it was one edition of a series of conferences by that name, organised every year between scientists and science communicators from around the world and Tibetan Buddhist monks in the Indian subcontinent. Let me quote from the article I wrote after the conference to illustrate why such engagement could be useful:

  “When most people think about the meditative element of the practice of Buddhism, … they think only about single-point meditation, which is when a practitioner closes their eyes and focuses their mind’s eye on a single object. The less well known second kind is analytical meditation: when two monks engage in debate and question each other about their ideas, confronting them with impossibilities and contradictions in an effort to challenge their beliefs. This is also a louder form of meditation. [One monk] said that sometimes, people walk into his monastery expecting it to be a quiet environment and are surprised when they chance upon an argument. Analytical meditation is considered to be a form of evidence-sharpening and a part of proof-building.”

  As interesting as the concept of the conference is, the 2018 edition was particularly so because the field of science on the table that year was quantum physics. That quantum physics is counter-intuitive is a banal statement; it is chock-full of twists in the tale, interpretations, uncertainties and open questions. Even a conference among scientists was bound to be confusing – imagine the scope of opportunities for confusion in one between scientists and monks. As if in response to this risk, the views of the scientists and the monks were very cleanly divided throughout the event, with neither side wanting to tread on the toes of the other, and this in turn dulled the proceedings. And while this was a sensible thing to do, I was disappointed.

  This said, there were some interesting conversations outside the event halls, in the corridors, over lunch and dinner, and at the hotel where we were put up (where speakers in the common areas played ‘Om Mani Padme Hum’ 24/7). One of them centered on the rare (possibly) legitimate idea in quantum physics in which Buddhist monks, and monks of every denomination for that matter, have considerable interest: the origin of consciousness. While any sort of exposition or conversation involving the science of consciousness has more often than not been replete with bad science, this idea may be an honourable exception.

  Four years later, I only remember that there was a vigorous back-and-forth between two monks and a physicist, not the precise contents of the dialogue or who participated. The subject was the Orch OR hypothesis advanced by the physicist Roger Penrose and quantum-consciousness theorist Stuart Hameroff. According to a 2014 paper authored by the pair, “Orch OR links consciousness to processes in fundamental space-time geometry.” It traces the origin of consciousness to cellular structures inside neurons called microtubules being in a superposition of states, and which then collapse into a single state in a process induced by gravity.

  In the famous Schrödinger’s cat thought-experiment, the cat exists in a superposition of ‘alive’ and ‘dead’ states while the box is closed. When an observer opens the box and observes the cat, its state collapses into either a ‘dead’ or an ‘alive’ state. Few scientists subscribe to the Orch OR view of self-awareness; the vast majority believe that consciousness originates not within neurons but in the interactions between neurons, happening at a large scale.

  ‘Orch OR’ stands for ‘orchestrated objective reduction’, with Penrose being credited with the ‘OR’ part. That is also the part at which mathematicians and physicists have directed much of their criticism.

  It begins with Penrose’s idea of spacetime blisters. According to him, at the Planck scale (around 10^-35 m), the spacetime continuum is discrete, not continuous, and that each quantum superposition occupies a distinct piece of the spacetime fabric. These pieces are called blisters. Pernose postulated that gravity acts on each of these blisters and destabilises them, causing the superposed states to collapse into a single state.

  A quantum computer performs calculations using qubits as the fundamental units of information. The qubits interact with each other in quantum-mechanical processes like superposition and entanglement. At some point, the superposition of these qubits is forced to collapse by making an observation, and the state to which it collapses is recorded as the computer’s result. In 1989, Penrose proposed that there could be a quantum-computer-like mechanism operating in the human brain and that the OR mechanism could be the act of observation that forces it to terminate.

  One refinement of the OR hypothesis is the Diósi-Penrose scheme, with contributions from Hungarian physicist Lajos Diósi. In this scheme, spacetime blisters are unstable and the superposition collapses when the mass of the superposed states exceeds a fixed value. In the course of his calculations, Diósi found that at the moment of collapse, the system must emit some electromagnetic radiation (due to the motion of electrons).

  Hameroff made his contribution by introducing microtubules as a candidate for the location of qubit-like objects and which could collectively set up a quantum-computer-like system within the brain.

  There have been some experiments in the last two decades that have tested whether Orch OR could manifest in the brain, based on studies of electron activity. But a more recent study suggests that Orch OR may just be infeasible as an explanation for the origin of consciousness.

  Here, a team of researchers – including Lajos Diósi – first looked for the electromagnetic radiation at the instant the superposition collapsed. The researchers didn’t find any, but the parameters of their experiment (including the masses involved) allowed them to set lower limits on the scale at which Orch OR might work. That is, they had a way to figure out a way in which the distance, time and mass might be related in an Orch OR event.

  They set these calculations out in a new paper, published in the journal Physics of Life Reviews on May 17. According to their paper, they fixed the time-scale of the collapse to 0.025 to 0.5 seconds, which is comparable to the amount of time in which our brain recognises conscious experience. They found that at a spatial scale of 10^-15 m – which Penrose has expressed a preference for – a superposition that collapses in 0.025 seconds would require 1,000-times more tubulins as there are in the brain (10²⁰), an impossibility. (Tubulins polymerise to form microtubules.) But at a scale of around 1 nm, the researchers worked out that the brain would need only 10¹² tubulins for their superposition to collapse in around 0.025 seconds. This is still a very large number of tubulins and a daunting task even for the human brain. But it isn’t impossible as with the collapse over 10^-15 m. According to the team’s paper,

  The Orch OR based on the DP [Diósi-Penrose] theory is definitively ruled out for the case of [10^-15 m] separation, without needing to consider the impact of environmental decoherence; we also showed that the case of partial separation requires the brain to maintain coherent superpositions of tubulin of such mass, duration, and size that vastly exceed any of the coherent superposition states that have been achieved with state-of-the-art optomechanics and macromolecular interference experiments. We conclude that none of the scenarios we discuss … are plausible.

  However, the team hasn’t nearly eliminated Orch OR; instead, they wrote that they intend to refine the Diósi-Penrose scheme to a more “sophisticated” version that, for example, may not entail the release of electromagnetic radiation or provide a more feasible pathway for superposition collapse. So far, in their telling, they have used experimental results to learn where their theory should improve if it is to remain a plausible description of reality.

  If and when the ‘Science for Monks’ conferences, or those like it, resume after the pandemic, it seems we may still be able to put Orch OR on the discussion table.

  * I remember it was called ‘Science for Monks’ in 2018. Its name appears to have been changed since to ‘Science for Monks and Nuns’.

  2022.07.14

• The problem with rooting for science

  The idea that trusting in science involves a lot of faith, instead of reason, is lost on most people. More often than not, as a science journalist, I encounter faith through extreme examples – such as the Bloch sphere (used to represent the state of a qubit) or wave functions (‘mathematical objects’ used to understand the evolution of certain simple quantum systems). These and other similar concepts require years of training in physics and mathematics to understand. At the same time, science writers are often confronted with the challenge of making these concepts sensible to an audience that seldom has this training.

  More importantly, how are science writers to understand them? They don’t. Instead, they implicitly trust scientists they’re talking to to make sense. If I know that a black hole curves spacetime to such an extent that pairs of virtual particles created near its surface are torn apart – one particle entering the black hole never to exit and the other sent off into space – it’s not because I’m familiar with the work of Stephen Hawking. It’s because I read his books, read some blogs and scientific papers, spoke to physicists, and decided to trust them all. Every science journalist, in fact, has a set of sources they’re likely to trust over others. I even place my faith in some people over others, based on factors like personal character, past record, transparency, reflexivity, etc., so that what they produce I take only with the smallest pinch of salt, and build on their findings to develop my own. And this way, I’m already creating an interface between science and society – by matching scientific knowledge with the socially developed markers of reliability.

  I choose to trust those people, processes and institutions that display these markers. I call this an act of faith for two reasons: 1) it’s an empirical method, so to speak; there is no proof in theory that such ‘matching’ will always work; and 2) I believe it’s instructive to think of this relationship as being mediated by faith if only to amplify its anti-polarity with reason. Most of us understand science through faith, not reason. Even scientists who are experts on one thing take the word of scientists on completely different things, instead of trying to study those things themselves (see ad verecundiam fallacy).

  Sometimes, such faith is (mostly) harmless, such as in the ‘extreme’ cases of the Bloch sphere and the wave function. It is both inexact and incomplete to think that quantum superposition means an object is in two states at once. The human brain hasn’t evolved to cognate superposition exactly; this is why physicists use the language of mathematics to make sense of this strange existential phenomenon. The problem – i.e. the inexactitude and the incompleteness – arises when a communicator translates the mathematics to a metaphor. Equally importantly, physicists are describing whereas the rest of us are thinking. There is a crucial difference between these activities that illustrates, among other things, the fundamental incompatibility between scientific research and science communication that communicators must first surmount.

  As physicists over the past three or four centuries have relied increasingly on mathematics rather than the word to describe the world, physics, like mathematics itself, has made a “retreat from the word,” as literary scholar George Steiner put it. In a 1961 Kenyon Review article, Steiner wrote, “It is, on the whole, true to say that until the seventeenth century the predominant bias and content of the natural sciences were descriptive.” Mathematics used to be “anchored to the material conditions of experience,” and so was largely susceptible to being expressed in ordinary language. But this changed with the advances of modern mathematicians such as Descartes, Newton, and Leibniz, whose work in geometry, algebra, and calculus helped to distance mathematical notation from ordinary language, such that the history of how mathematics is expressed has become “one of progressive untranslatability.” It is easier to translate between Chinese and English — both express human experience, the vast majority of which is shared — than it is to translate advanced mathematics into a spoken language, because the world that mathematics expresses is theoretical and for the most part not available to our lived experience.

  Samuel Matlack, ‘Quantum Poetics’, The New Atlantic, 2017

  However, the faith becomes more harmful the further we move away from the ‘extreme’ examples – of things we’re unlikely to stumble on in our daily lives – and towards more commonplace ideas, such as ‘how vaccines work’ or ‘why GM foods are not inherently bad’. The harm emerges from the assumption that we think we know something when in fact we’re in denial about how it is that we know that thing. Many of us think it’s reason; most of the time it’s faith. Remember when, in Friends, Monica Geller and Chandler Bing ask David the Scientist Guy how airplanes fly, and David says it has to do with Bernoulli’s principle and Newton’s third law? Monica then turns to Chandler with a knowing look and says, “See?!” To which Chandler says, “Yeah, that’s the same as ‘it has something to do with wind’!”

  The harm is to root for science, to endorse the scientific enterprise and vest our faith in its fruits, without really understanding how these fruits are produced. Such understanding is important for two reasons.

  First, if we trust scientists, instead of presuming to know or actually knowing that we can vouch for their work. It would be vacuous to claim science is superior in any way to another enterprise that demands our faith when science itself also receives our faith. Perhaps more fundamentally, we like to believe that science is trustworthy because it is evidence-based and it is tested – but the COVID-19 pandemic should have clarified, if it hasn’t already, the continuous (as opposed to discrete) nature of scientific evidence, especially if we also acknowledge that scientific progress is almost always incremental. Evidence can be singular and thus clear – like a new avian species, graphene layers superconducting electrons or tuned lasers cooling down atoms – or it can be necessary but insufficient, and therefore on a slippery slope – such as repeated genetic components in viral RNA, a cigar-shaped asteroid or water shortage in the time of climate change.

  Physicists working with giant machines to spot new particles and reactions – all of which are detected indirectly, through their imprints on other well-understood phenomena – have two important thresholds for the reliability of their findings: if the chance of X (say, “spotting a particle of energy 100 GeV”) being false is 0.27%, it’s good enough to be evidence; if the chance of X being false is 0.00006%, then it’s a discovery (i.e., “we have found the particle”). But at what point can we be sure that we’ve indeed found the particle we were looking for if the chance of being false will never reach 0%? One way, for physicists specifically, is to combine the experiment’s results with what they expect to happen according to theory; if the two match, it’s okay to think that even a less reliable result will likely be borne out. Another possibility (in the line of Karl Popper’s philosophy) is that a result expected to be true, and is subsequently found to be true, is true until we have evidence to the contrary. But as suitable as this answer may be, it still doesn’t neatly fit the binary ‘yes’/’no’ we’re used to, and which we often expect from scientific endeavours as well (see experience v. reality).

  (Minor detour: While rational solutions are ideally refutable, faith-based solutions are not. Instead, the simplest way to reject their validity is to use extra-scientific methods, and more broadly deny them power. For example, if two people were offering me drugs to suppress the pain of a headache, I would trust the one who has a state-sanctioned license to practice medicine and is likely to lose that license, even temporarily, if his prescription is found to have been mistaken – that is, by asserting the doctor as the subject of democratic power. Axiomatically, if I know that Crocin helps manage headaches, it’s because, first, I trusted the doctor who prescribed it and, second, Crocin has helped me multiple times before, so empirical experience is on my side.)

  Second, if we don’t know how science works, we become vulnerable to believing pseudoscience to be science as long as the two share some superficial characteristics, like, say, the presence and frequency of jargon or a claim’s originator being affiliated with a ‘top’ institute. The authors of a scientific paper to be published in a forthcoming edition of the Journal of Experimental Social Psychology write:

  We identify two critical determinants of vulnerability to pseudoscience. First, participants who trust science are more likely to believe and disseminate false claims that contain scientific references than false claims that do not. Second, reminding participants of the value of critical evaluation reduces belief in false claims, whereas reminders of the value of trusting science do not.

  (Caveats: 1. We could apply the point of this post to this study itself; 2. I haven’t checked the study’s methods and results with an independent expert, and I’m also mindful that this is psychology research and that its conclusions should be taken with salt until independent scientists have successfully replicated them.)

  Later from the same paper:

  Our four experiments and meta-analysis demonstrated that people, and in particular people with higher trust in science (Experiments 1-3), are vulnerable to misinformation that contains pseudoscientific content. Among participants who reported high trust in science, the mere presence of scientific labels in the article facilitated belief in the misinformation and increased the probability of dissemination. Thus, this research highlights that trust in science ironically increases vulnerability to pseudoscience, a finding that conflicts with campaigns that promote broad trust in science as an antidote to misinformation but does not conflict with efforts to install trust in conclusions about the specific science about COVID-19 or climate change.

  In terms of the process, the findings of Experiments 1-3 may reflect a form of heuristic processing. Complex topics such as the origins of a virus or potential harms of GMOs to human health include information that is difficult for a lay audience to comprehend, and requires acquiring background knowledge when reading news. For most participants, seeing scientists as the source of the information may act as an expertise cue in some conditions, although source cues are well known to also be processed systematically. However, when participants have higher levels of methodological literacy, they may be more able to bring relevant knowledge to bear and scrutinise the misinformation. The consistent negative association between methodological literacy and both belief and dissemination across Experiments 1-3 suggests that one antidote to the influence of pseudoscience is methodological literacy. The meta-analysis supports this.

  So rooting for science per se is not just not enough, it could be harmful vis-à-vis the public support for science itself. For example (and without taking names), in response to right-wing propaganda related to India’s COVID-19 epidemic, quite a few videos produced by YouTube ‘stars’ have advanced dubious claims. They’re not dubious at first glance, if also because they purport to counter pseudoscientific claims with scientific knowledge, but they are – either for insisting a measure of certainty in the results that neither exist nor are achievable, or for making pseudoscientific claims of their own, just wrapped up in technical lingo so they’re more palatable to those supporting science over critical thinking. Some of these YouTubers, and in fact writers, podcasters, etc., are even blissfully unaware of how wrong they often are. (At least one of them was also reluctant to edit a ‘finished’ video to make it less sensational despite repeated requests.)

  Now, where do these ideas leave (other) science communicators? In attempting to bridge a nearly unbridgeable gap, are we doomed to swing only between most and least unsuccessful? I personally think that this problem, such as it is, is comparable to Zeno’s arrow paradox. To use Wikipedia’s words:

  He states that in any one (duration-less) instant of time, the arrow is neither moving to where it is, nor to where it is not. It cannot move to where it is not, because no time elapses for it to move there; it cannot move to where it is, because it is already there. In other words, at every instant of time there is no motion occurring. If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible.

  To ‘break’ the paradox, we need to identify and discard one or more primitive assumptions. In the arrow paradox, for example, one could argue that time is not composed of a stream of “duration-less” instants, that each instant – no matter how small – encompasses a vanishingly short but not nonexistent passage of time. With popular science communication (in the limited context of translating something that is untranslatable sans inexactitude and/or incompleteness), I’d contend the following:

  • Awareness: ‘Knowing’ and ‘knowing of’ are significantly different and, I hope, self-explanatory also. Example: I’m not fluent with the physics of cryogenic engines but I’m aware that they’re desirable because liquefied hydrogen has the highest specific impulse of all rocket fuels.
  • Context: As I’ve written before, a unit of scientific knowledge that exists in relation to other units of scientific knowledge is a different object from the same unit of scientific knowledge existing in relation to society.
  • Abstraction: 1. perfect can be the enemy of the good, and imperfect knowledge of an object – especially a complicated compound one – can still be useful; 2. when multiple components come together to form a larger entity, the entity can exhibit some emergent properties that one can’t derive entirely from the properties of the individual components. Example: one doesn’t have to understand semiconductor physics to understand what a computer does.

  An introduction to physics that contains no equations is like an introduction to French that contains no French words, but tries instead to capture the essence of the language by discussing it in English. Of course, popular writers on physics must abide by that constraint because they are writing for mathematical illiterates, like me, who wouldn’t be able to understand the equations. (Sometimes I browse math articles in Wikipedia simply to immerse myself in their majestic incomprehensibility, like visiting a foreign planet.)

  Such books don’t teach physical truths; what they teach is that physical truth is knowable in principle, because physicists know it. Ironically, this means that a layperson in science is in basically the same position as a layperson in religion.

  Adam Kirsch, ‘The Ontology of Pop Physics’, Tablet Magazine, 2020

  But by offering these reasons, I don’t intend to over-qualify science communication – i.e. claim that, given enough time and/or other resources, a suitably skilled science communicator will be able to produce a non-mathematical description of, say, quantum superposition that is comprehensible, exact and complete. Instead, it may be useful for communicators to acknowledge that there is an immutable gap between common English (the language of modern science) and mathematics, beyond which scientific expertise is unavoidable – in much the same way communicators must insist that the farther the expert strays into the realm of communication, the closer they’re bound to get to a boundary beyond which they must defer to the communicator.

  2021.07.28

• Scientists make video of molecule rotating

  A research group in Germany has captured images of what a rotating molecule looks like. This is a significant feat because it is very difficult to observe individual atoms and molecules, which are very small as well as very fragile. Scientists often have to employ ingenious techniques that can probe their small scale but without destroying them in the act of doing so.

  The researchers studied carbonyl sulphide (OCS) molecules, which has a cylindrical shape. To perform their feat, they went through three steps. First, the researchers precisely calibrated two laser pulses and fired them repeatedly – ~26.3 billion times per second – at the molecules to set them spinning.

  Next, they shot a third laser at the molecules. The purpose of this laser was to excite the valence electrons forming the chemical bonds between the O, C and S atoms. These electrons absorb energy from the laser’s photons, become excited and quit the bonds. This leaves the positively charged atoms close to each other. Since like charges repel, the atoms vigorously push themselves apart and break the molecule up. This process is called a Coulomb explosion.

  At the moment of disintegration, an instrument called a velocity map imaging (VMI) spectrometer records the orientation and direction of motion of the oxygen atom’s positive charge in space. Scientists can work backwards from this reading to determine how the molecule might have been oriented just before it broke up.

  In the third step, the researchers restart the experiment with another set of OCS molecules.

  By going through these steps repeatedly, they were able to capture 651 photos of the OCS molecule in different stages of its rotation.

  These images cannot be interpreted in a straightforward way – the way we interpret images of, say, a rotating ball.

  

  This is because a ball, even though it is composed of millions of molecules, has enough mass for the force of gravity to dominate proceedings. So scientists can understand why a ball rotates the way it does using just the laws of classical mechanics.

  But at the level of individual atoms and molecules, gravity becomes negligibly weak whereas the other three fundamental forces – including the electromagnetic force – become more prominent. To understand the interactions between these forces and the particles, scientists use the rules of quantum mechanics.

  This is why the images of the rotating molecules look like this:

  

  These are images of the OCS molecule as deduced by the VMI spectrometer. Based on them, the researchers were also able to determine how long the molecule took to make one full rotation.

  As a spinning ball drifts around on the floor, we can tell exactly where it is and how fast it is spinning. However, when studying particles, quantum mechanics prohibits observers from knowing these two things with the same precision at the same time. You probably know this better as Heisenberg’s uncertainty principle.

  So if you have a fix on where the molecule is, that measurement prohibits you from knowing exactly how fast it is spinning. Confronted with this dilemma, scientists used the data obtained by the VMI spectrometer together with the rules of quantum mechanics to calculate the probability that the molecule’s O, C and S atoms were arranged a certain way at a given point of time.

  The images above visualise these probabilities as a colour-coded map. With the position of the central atom (presumably C) fixed, the probability of finding the other two atoms at a certain position is represented on a blue-red scale. The redder a pixel is, the higher the probability of finding an atom there.

  

  For example, consider the images at 12 o’clock and 6 o’clock: the OCS molecule is clearly oriented horizontally and vertically, resp. Compare this to the measurement corresponding to the image at 9 o’clock: the molecule appears to exist in two configurations at the same time. This is because, approximately speaking, there is a 50% probability that it is oriented from bottom-left to top-right and a 50% probability that it is oriented from bottom-right to top-left. The 10 o’clock figure represents the probabilities split four different ways. The ones at 4 o’clock and 8 o’clock are even more messy.

  But despite the messiness, the researchers found that the image corresponding to 12 o’clock repeated itself once every 82 picoseconds. Ergo, the molecule completed one rotation every 82 picoseconds.

  This is equal to 731.7 billion rpm. If your car’s engine operated this fast, the resulting centrifugal force, together with the force of gravity, would tear its mechanical joints apart and destroy the machine. The OCS molecule doesn’t come apart this way because gravity is 100 million trillion trillion times weaker than the weakest of the three subatomic forces.

  The researchers’ study was published in the journal Nature Communications on July 29, 2019.

  2019.08.08