Tag: Quantum mechanics

• 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

• Using 10,000 atoms and 1 to probe the Bohr-Einstein debate

  The double-slit experiment has often been described as the most beautiful demonstration in physics. In one striking image, it shows the strange dual character of matter and light. When particles such as electrons or photons are sent through two narrow slits, the resulting pattern on a screen behind them is not the simple outline of the slits, but a series of alternating bright and dark bands. This pattern looks exactly like the ripples produced by waves on the surface of water when two stones are thrown in together. But when detectors are placed to see which slit each particle passes through, the pattern changes: the wave-like interference disappears and the particles line up as if they had travelled like microscopic bullets.

  This puzzling switch between wave and particle behaviour became the stage for one of the deepest disputes of the 20th century. The two central figures were Albert Einstein and Niels Bohr, each with a different vision of what the double-slit experiment really meant. Their disagreement was not about the results themselves but about how these results should be interpreted, and what they revealed about the nature of reality.

  https://farfromeq.wordpress.com/2025/09/03/what-does-it-mean-to-interpret-quantum-physics/

  Einstein believed strongly that the purpose of physics was to describe an external reality that exists independently of us. For him, the universe must have clear properties whether or not anyone is looking. In a double-slit experiment, this meant an electron or photon must in fact have taken a definite path, through one slit or the other, before striking the screen. The interference pattern might suggest some deeper process that we don’t yet understand but, to Einstein, it couldn’t mean that the particle lacked a path altogether.

  Based on this idea, Einstein argued that quantum mechanics (as formulated in the 1920s) couldn’t be the full story. The strange idea that a particle had no definite position until measured, or that its path depended on the presence of a detector, was unacceptable to him. He felt that there must be hidden details that explained the apparently random outcomes. These details would restore determinism and make physics once again a science that described what happens, not just what is observed.

  Bohr, however, argued that Einstein’s demand for definite paths misunderstood what quantum mechanics was telling us. Bohr’s central idea was called complementarity. According to this principle, particles like electrons or photons can show both wave-like and particle-like behaviour, but never both at the same time. Which behaviour appears depends entirely on how an experiment is arranged.

  In the double-slit experiment, if the apparatus is set up to measure which slit the particle passes through, the outcome will display particle-like behaviour and the interference pattern will vanish. If the apparatus is set up without path detectors, the outcome will display wave-like interference. For Bohr, the two descriptions are not contradictions but complementary views of the same reality, each valid only within its experimental context.

  Specifically, Bohr insisted that physics doesn’t reveal a world of objects with definite properties existing independently of measurement. Instead, physics provides a framework for predicting the outcomes of experiments. The act of measurement is inseparable from the phenomenon itself. Asking what “really happened” to the particle when no one was watching was, for Bohr, a meaningless question.

  Thus, while Einstein demanded hidden details to restore certainty, Bohr argued that uncertainty was built into nature itself. The double-slit experiment, for Bohr, showed that the universe at its smallest scales does not conform to classical ideas of definite paths and objective reality.

  https://farfromeq.wordpress.com/2019/10/07/disentangling-entanglement/

  The disagreement between Einstein and Bohr was not simply about technical details but a clash of philosophies. Einstein’s view was rooted in the classical tradition: the world exists in a definite state and science should describe that state. Quantum mechanics, he thought, was useful but incomplete, like a map missing a part of the territory.

  Bohr’s view was more radical. He believed that the limits revealed by the double-slit experiment were not shortcomings of the theory but truths about the universe. For him, the experiment demonstrated that the old categories of waves and particles, causes and paths, couldn’t be applied without qualification. Science had to adapt its concepts to match what experiments revealed, even if that meant abandoning the idea of an observer-independent reality.

  Though the two men never reached agreement, their debate has continued to inspire generations of physicists and philosophers. The double-slit experiment remains the clearest demonstration of the puzzle they argued over. Do particles truly have no definite properties until measured, as Bohr claimed? Or are we simply missing hidden elements that would complete the picture, as Einstein insisted?

  A new study in Physical Review Letters has taken the double-slit spirit into the realm of single atoms and scattered photons. And rather than ask whether an electron goes through one slit or another, it has asked whether scattered light carries “which-way” information about an atom. By focusing on the coherence or incoherence of scattered light, the researchers — from the Massachusetts Institute of Technology — have effectively reopened the old debate in a modern setting.

  The researchers trapped rubidium atoms held in an optical lattice, a regular grid of light that traps atoms in well-defined positions, like pieces on a chessboard. By carefully preparing these atoms in a particular state, each lattice site contained exactly one atom in its lowest energy state. The lattice could then be suddenly switched off, letting the atoms expand as localised wavepackets (i.e. wave-like packets of energy). A short pulse of laser light was directed at these atoms. The photons it emitted were scattered off the atoms and collected by a detector.

  By checking whether the scattered light was coherent (with a steady, predictable phase) or incoherent (with a random phase), the scientists could tell if the photons carried hints of the motion of the atom that scattered them.

  The main finding was that even a single atom scattered light that was only partly coherent. In other words, the scattered light wasn’t completely wave-like: one part of it showed a clear phase pattern, another part looked random. The randomness came from the fact that the scattering process linked, or entangled, the photon with the atom’s movement. This was because each time a photon was scattered off, the atom recoiled just a little, and that recoil left behind a faint clue about which atom had scattered the photon. This in turn meant that if the scientists looked close enough, they could work out where the photon came from in theory.

  https://farfromeq.wordpress.com/2025/09/09/a-tribute-to-rubidium/

  To study this effect, the team compared three cases. First, they observed atoms still held tightly in the optical lattice. In this case, scattering could create sidebands — frequency shifts in the scattered light — that reflected changes in the atom’s motion. These sidebands represented incoherent scattering. Second, they looked at atoms immediately after switching off the lattice, before the expanding wavepackets had spread out. Third, they examined atoms after a longer expansion in free space, when the wavepackets had grown even wider.

  In all three cases, the ratio of coherent to incoherent light could be described by a simple mathematical term called the Debye-Waller factor. This factor depends only on the spatial spread of the wavepacket. As the atoms expanded in space, the Debye-Waller factor decreased, meaning more and more of the scattered light became incoherent. Eventually, after long enough expansion, essentially all the scattered light was incoherent.

  Experiments with two different atomic species supported this picture. With lithium-7 atoms, which are very light, the wavepackets expanded quickly, so the transition from partial coherence to full incoherence was rapid. With the much heavier dysprosium-162 atoms, the expansion was slower, allowing the researchers to track the change in more detail. In both cases, the results agreed with theoretical predictions.

  An especially striking observation was that the presence or absence of the trap made no difference to the basic coherence properties. The same mix of coherent and incoherent scattering appeared whether the atoms were confined in the lattice or expanding in free space. This showed that sidebands and trapping states were not the fundamental source of incoherence. Instead, what mattered was the partial entanglement between the light and the atoms.

  The team also compared long and short laser pulses. Long pulses could in principle resolve the sidebands while short pulses could not. Yet the fraction of coherent versus incoherent scattering was the same in both cases. This further reinforced the conclusion that coherence was lost not because of frequency shifts but because of entanglement itself.

  https://farfromeq.wordpress.com/2023/04/27/the-gap-between-language-and-quantum-mechanics/

  In 2024, another group in China also realised the recoiling-slit thought experiment in practice. Researchers from the University of Science and Technology of China trapped a single rubidium atom in an optical tweezer and cooled it to its quantum ground state, thus making the atom act like a movable slit whose recoil could be directly entangled with scattered photons.

  By tightening or loosening the trap, the scientists could pin the atom more firmly in place. When it was held tightly, the atom’s recoil left almost no mark on the photons, which went on to form a clear interference pattern (like the ripples in water). When the atom was loosely held, however, its recoil was easier to notice and the interference pattern faded. This gave the researchers a controllable way to show how a recoiling slit could erase the wave pattern — which is also the issue at the heart of Bohr-Einstein debate.

  Importantly, the researchers also distinguished true quantum effects from classical noise, such as heating of the atom during repeated scattering. Their data showed that the sharpness of the interference pattern wasn’t an artifact of an imperfect apparatus but a direct result of the atom-photon entanglement itself. In this way, they were able to demonstrate the transition from quantum uncertainty to classical disturbance within a single, controllable system. And even at this scale, the Bohr-Einstein debate couldn’t be settled.

  The results pointed to a physical mechanism for how information becomes embedded in light scattered from atoms. In the conventional double-slit experiment, the question was whether a photon’s path could ever be known without destroying the interference pattern. In the new, modern version, the question was whether a scattered photon carried any ‘imprint’ of the atom’s motion. The MIT team’s measurements showed that it did.

  The Debye-Waller factor — the measure of how much of the scattered light is still coherent — played an important role in this analysis. When atoms are confined tightly in a lattice, their spatial spread is small and the factor is relatively large, meaning a smaller fraction of the light is incoherent and thus reveals which-way information. But as the atoms are released and their wavepackets spread, the factor drops and with it the coherent fraction of scattered light. Eventually, after free expansion for long enough, essentially all of the scattered light becomes incoherent.

  Further, while the lighter lithium atoms expanded so quickly that the coherence decayed almost at once, the heavier dysprosium atoms expanded more slowly, allowing the researchers to track them in detail. Yet both atomic species followed a common rule: the Debye-Waller factor depended solely on how much the atom became delocalised as a wave, and not by the technical details of the traps or the sidebands. The conclusion here was that the light lost its coherence because the atom’s recoil became entangled with the scattered photon.

  https://farfromeq.wordpress.com/2013/05/20/bohr-and-the-breakaway-from-classical-mechanics/

  This finding adds substance to the Bohr-Einstein debate. In one sense, Einstein’s intuition has been vindicated: every scattering event leaves behind faint traces of which atom interacted with the light. This recoil information is physically real and, at least in principle, accessible. But Bohr’s point also emerges clearly: that no amount of experimental cleverness can undo the trade-off set by quantum mechanics. The ratio of coherent to incoherent light is dictated not by human knowledge or ignorance but by implicit uncertainties in the spread of the atomic wavepacket itself.

  Together with the MIT results, the second experiment showed that both Einstein’s and Bohr’s insights remain relevant: every scattering leaves behind a real, measurable recoil — yet the amount of interference lost is dictated by the unavoidable quantum uncertainties of the system. When a photon scatters off an atom, the atom must recoil a little bit to conserve momentum. That recoil in principle carries which-way information because it marks the atom as the source of the scattered photon. But whether that information is accessible depends on how sharply the atom’s momentum (and position) can be defined.

  According to the Heisenberg uncertainty principle, the atom can’t simultaneously have both a precisely known position and momentum. In these experiments, the key measure was how delocalised the atom’s wavepacket was in space. If the atom was tightly trapped, its position uncertainty would be small, so its momentum uncertainty would be large. The recoil from a photon is then ‘blurred’ by that momentum spread, meaning the photon doesn’t clearly encode which-way information. Ultimately, interference is preserved.

  By recasting the debate in the language of scattered photons and expanding wavepackets, the MIT experiment has thus moved the double-slit spirit into new terrain. It shows that quantum mechanics doesn’t simply suggest fuzziness in the abstract but enforces it in how matter and light are allowed to share information. The loss of coherence isn’t a flaw in the experimental technique or a sign of missing details, as Einstein might’ve claimed, but the very mechanism by which the microscopic world keeps both Einstein’s and Bohr’s insights in tension. The double-slit experiment, even in a highly sophisticated avatar, continues to reinforce the notion that the universe resists any single-sided description.

  (The researchers leading the two studies are Wolfgang Ketterle and Pan Jianwei, respectively a Nobel laureate and a rockstar in the field of quantum information likely to win a Nobel Prize soon.)

  Featured image created with ChatGPT.

  2025.10.01

• Dispelling Maxwell’s demon

  Maxwell’s demon is one of the most famous thought experiments in the history of physics, a puzzle first posed in the 1860s that continues to shape scientific debates to this day. I’ve struggled to make sense of it for years. Last week I had some time and decided to hunker down and figure it out, and I think I succeeded. The following post describes the fruits of my efforts.

  At first sight, the Maxwell’s demon paradox seems odd because it presents a supernatural creature tampering with molecules of gas. But if you pare down the imagery and focus on the technological backdrop of the time of James Clerk Maxwell, who proposed it, a profoundly insightful probe of the second law of thermodynamics comes into view.

  The thought experiment asks a simple question: if you had a way to measure and control molecules with perfect precision and at no cost, will you able to make heat flow backwards, as if in an engine?

  Picture a box of air divided into two halves by a partition. In the partition is a very small trapdoor. It has a hinge so it can swing open and shut. Now imagine a microscopic valve operator that can detect the speed of each gas molecule as it approaches the trapdoor, decide whether to open or close the door, and actuate the door accordingly.

  The operator follows two simple rules: let fast molecules through from left to right and let slow molecules through from right to left. The temperature of a system is nothing but the average kinetic energy of its constituent particles. As the operator operates, over time the right side will heat up and the left side will cool down — thus producing a temperature gradient for free. Where there’s a temperature gradient, it’s possible to run a heat engine. (The internal combustion engine in fossil-fuel vehicles is a common example.)

  

  But the possibility that this operator can detect and sort the molecules, thus creating the temperature gradient without consuming some energy of its own, seems to break the second law of thermodynamics. The second law states that the entropy of a closed system increases over time — whereas the operator ensures that the temperature will decrease, violating the law. This was the Maxwell’s demon thought experiment, with the demon as a whimsical stand-in for the operator.

  The paradox was made compelling by the silent assumption that the act of sorting the molecules could have no cost — i.e. that the imagined operator didn’t add energy to the system (the air in the box) but simply allowed molecules that are already in motion to pass one way and not the other. In this sense the operator acted like a valve or a one-way gate. Devices of this kind — including check valves, ratchets, and centrifugal governors — were already familiar in the 19th century. And scientists assumed that if they were scaled down to the molecular level, they’d be able to work without friction and thus separate hot and cold particles without drawing more energy to overcome that friction.

  This detail is in fact the fulcrum of the paradox, and the thing that’d kept me all these years from actually understanding what the issue was. Maxwell et al. assumed that it was possible that an entity like this gate could exist: one that, without spending energy to do work (and thus increase entropy), could passively, effortlessly sort the molecules. Overall, the paradox stated that if such a sorting exercise really had no cost, the second law of thermodynamics would be violated.

  The second law had been established only a few decades before Maxwell thought up this paradox. If entropy is taken to be a measure of disorder, the second law states that if a system is left to itself, heat will not spontaneously flow from cold to hot and whatever useful energy it holds will inevitably degrade into the random motion of its constituent particles. The second law is the reason why perpetual motion machines are impossible, why the engines in our cars and bikes can’t be 100% efficient, and why time flows in one specific direction (from past to future).

  Yet Maxwell’s imagined operator seemed to be able to make heat flow backwards, sifting molecules so that order increases spontaneously. For many decades, this possibility challenged what physicists thought they knew about physics. While some brushed it off as a curiosity, others contended that the demon itself must expend some energy to operate the door and that this expense would restore the balance. However, Maxwell had been careful when he conceived the thought experiment: he specified that the trapdoor was small and moved without friction, so it could in principle operate in a negligible way. The real puzzle lay elsewhere.

  In 1929, the Hungarian physicist Leó Szilard sharpened the problem by boiling it down to a single-particle machine. This so-called Szilard engine imagined one gas molecule in a box with a partition that could be inserted or removed. By observing on which side the molecule lay and then allowing it to push a piston, the operator could apparently extract work from a single particle at uniform temperature. Szilard showed that the key step was not the movement of the piston but the acquisition of information: knowing where the particle was. That is, Szilard reframed the paradox to be not about the molecules being sorted but about an observer making a measurement.

  (Aside: Szilard was played by Máté Haumann in the 2023 film Oppenheimer.)

  

  The next clue to cracking the puzzle came in the mid-20th century from the growing field of information theory. In 1961, the German-American physicist Rolf Landauer proposed a principle that connected information and entropy directly. Landauer’s principle states that while it’s possible in principle to acquire information in a reversible way — i.e. to be able to acquire it as well as lose it — erasing information from a device with memory has a non-zero thermodynamic cost that can’t be avoided. That is, the act of resetting a memory register of one bit to a standard state generates a small amount of entropy (proportional to Boltzmann’s constant multiplied by the logarithm of two).

  The American information theorist Charles H. Bennett later built on Landauer’s principle and argued that Maxwell’s demon could gather information and act on it — but in order to continue indefinitely, it’d have to erase or overwrite its memory. And that this act of resetting would generate exactly the entropy needed to compensate for the apparent decrease, ultimately preserving the second law of thermodynamics.

  Taken together, Maxwell’s demon was defeated not by the mechanics of the trapdoor but by the thermodynamic cost of processing information. Specifically, the decrease in entropy as a result of the molecules being sorted by their speed is compensated for by the increase in entropy due to the operator’s rewriting or erasure of information about the molecules’ speed. Thus a paradox that’d begun as a challenge to thermodynamics ended up enriching it — by showing information could be physical. It also revealed to scientists that entropy is disorder in matter and energy as well as is linked to uncertainty and information.

  Over time, Maxwell’s demon also became a fount of insight across multiple branches of physics. In classical thermodynamics, for example, entropy came to represent a measure of the probabilities that the system could exist in different combinations of microscopic states. That is, the probabilities referred to the likelihood that a given set of molecules could be arranged in one way instead of another. In statistical mechanics, Maxwell’s demon gave scientists a concrete way to think about fluctuations. In any small system, random fluctuations can reduce entropy for some time in a small portion. While the demon seemed to exploit these fluctuations, the laws of probability were found to ensure that on average, entropy would increase. So the demon became a metaphor for how selection based on microscopic knowledge could alter outcomes but also why such selection can’t be performed without paying a cost.

  

  For information theorists and computer scientists, the demon was an early symbol of the deep ties between computation and thermodynamics. Landauer’s principle showed that erasing information imposes a minimum entropy cost — an insight that matters for how computer hardware should be designed. The principle also influenced debates about reversible computing, where the goal is to design logic gates that don’t ever erase information and thus approach zero energy dissipation. In other words, Maxwell’s demon foreshadowed modern questions about how energy-efficient computing could really be.

  Even beyond physics, the demon has seeped into philosophy, biology, and social thought as a symbol of control and knowledge. In biology, the resemblance between the demon and enzymes that sorts molecules has inspired metaphors about how life maintains order. In economics and social theory, the demon has been used to discuss the limits of surveillance and control. The lesson has been the same in every instance: that information is never free and that the act of using it imposes inescapable energy costs.

  I’m particularly taken by the philosophy that animates the paradox. Maxwell’s demon was introduced as a way to dramatise the tension between the microscopic reversibility of physical laws and the macroscopic irreversibility encoded in the second law of thermodynamics. I found that a few questions in particular — whether the entropy increase due to the use of information is a matter of an observer’s ignorance (i.e. because the observer doesn’t know which particular microstate the system occupies at any given moment), whether information has physical significance, and whether the laws of nature really guarantee the irreversibility we observe — have become touchstones in the philosophy of physics.

  In the mid-20th century, the Szilard engine became the focus of these debates because it refocused the second law from molecular dynamics to the cost of acquiring information. Later figures such as the French physicist Léon Brillouin and the Hungarian-Canadian physicist Dennis Gabor claimed that it’s impossible to measure something without spending energy. Critics however countered that these requirements stipulated the need for specific technologies that would in turn smuggle in some limitations — rather than stipulate the presence of a fundamental principle. That is to say, the debate among philosophers became whether Maxwell’s demon was prevented from breaking the second law by deep and hitherto hidden principles or by engineering challenges.

  This gridlock was broken when physicists observed that even a demon-free machine must leave some physical trace of its interactions with the molecule. That is, any device that sorts particles will end up in different physical states depending on the outcome, and to complete a thermodynamic cycle those states must be reset. Here, the entropy is not due to the informational content but due to the logical structure of memory. Landauer solidified this with his principle that logically irreversible operations such as erasure carry a minimum thermodynamic cost. Bennett extended this by saying that measurements can be made reversibly but not erasure. The philosophical meaning of both these arguments is that entropy increase isn’t just about ignorance but also about parts of information processing being irreversible.

  

  In the quantum domain, the philosophical puzzles became more intense. When an object is measured in quantum mechanics, it isn’t just about an observer updating the information they have about the object — the act of measuring also seems to alter the object’s quantum states. For example, in the Schrödinger’s cat thought experiment, checking whether there’s a cat in the box also causes the cat to default to one of two states: dead or alive. Quantum physicists have recreated Maxwell’s demon in new ways in order to check whether the second law continues to hold. And over the course of many experiments, they’ve concluded that indeed it does.

  The second law didn’t break even when Maxwell’s demon could exploit phenomena that aren’t available in the classical domain, including quantum entanglement, superposition, and tunnelling. This was because, among others, quantum mechanics also has some restrictive rules of its own. For one, some physicists have tried to design “quantum demons” that use quantum entanglement between particles to sort them without expending energy. But these experiments have found that as soon as the demon tries to reset its memory and start again, it must erase the record of what happened before. This step destroys the advantage and the entropy cost returns. The overall result is that even a “quantum demon” gains nothing in the long run.

  For another, the no-cloning theorem states that you can’t make a perfect copy of an unknown quantum state. If the demon could freely copy every quantum particle it measured, it could retain flawless records while still resetting its memory, this avoiding the usual entropy cost. The theorem blocks this strategy by forbidding perfect duplication, ensuring that information can’t be ‘multiplied’ without limit. Similarly, the principle of unitarity implies that a system will always evolve in a way that preserves overall probabilities. As a result, quantum phenomena can’t selectively amplify certain outcomes while discarding others. For the demon, this means it can’t secretly limit the range of possible states the system can occupy into a smaller set where the system has lower entropy, because unitarity guarantees that the full spread of possibilities is preserved across time.

  All these rules together prevent the demon from multiplying or rearranging quantum states in a way that would allow it to beat the second law.

  Then again, these ‘blocks’ that prevent Maxwell’s demon from breaking the second law of thermodynamics in the quantum realm raise a puzzle of their own: is the second law of thermodynamics guaranteed no matter how we interpret quantum mechanics? ‘Interpreting quantum mechanics’ means to interpret what the rules of quantum mechanics say about reality, a topic I covered at length in a recent post. Some interpretations say that when we measure a quantum system, its wavefunction “collapses” to a definite outcome. Others say collapse never happens and that measurement is just entangled with the environment, a process called decoherence. The Maxwell’s demon thought experiment thus forces the question: is the second law of thermodynamics safe in a particular interpretation of quantum mechanics or in all interpretations?

  

  Landauer’s idea, that erasing information always carries a cost, also applies to quantum information. Even if Maxwell’s demon used qubits instead of bits, it won’t be able to escape the fact that to reuse its memory, it must erase the record, which will generate heat. But then the question becomes more subtle in quantum systems because qubits can be entangled with each other, and their delicate coherence — the special quantum link between quantum states — can be lost when information is processed. This means scientists need to carefully separate two different ideas of entropy: one based on what we as observers don’t know (our ignorance) and another based on what the quantum system itself has physically lost (by losing coherence).

  The lesson is that the second law of thermodynamics doesn’t just guard the flow of energy. In the quantum realm it also governs the flow of information. Entropy increases not only because we lose track of details but also because the very act of erasing and resetting information, whether classical or quantum, forces a cost that no demon can avoid.

  Then again, some philosophers and physicists have resisted the move to information altogether, arguing that ordinary statistical mechanics suffices to resolve the paradox. They’ve argued that any device designed to exploit fluctuations will be subject to its own fluctuations, and thus in aggregate no violation will have occurred. In this view, the second law is self-sufficient and doesn’t need the language of information, memory or knowledge to justify itself. This line of thought is attractive to those wary of anthropomorphising physics even if it also risks trivialising the demon. After all, the demon was designed to expose the gap between microscopic reversibility and macroscopic irreversibility, and simply declaring that “the averages work out” seems to bypass the conceptual tension.

  Thus, the philosophical significance of Maxwell’s demon is that it forces us to clarify the nature of entropy and the second law. Is entropy tied to our knowledge/ignorance of microstates, or is it ontic, tied to the irreversibility of information processing and computation? If Landauer is right, handling information and conserving energy are ‘equally’ fundamental physical concepts. If the statistical purists are right, on the other hand, then information adds nothing to the physics and the demon was never a serious challenge. Quantum theory can further stir both pots by suggesting that entropy is closely linked to the act of measurement, of quantum entanglement, and how quantum systems ‘collapse’ to classical ones by the process of decoherence. The demon debate therefore tests whether information is a physically primitive entity or a knowledge-based tool. Either way, however, Maxwell’s demon endures as a parable.

  Ultimately, what makes Maxwell’s demon a gift that keeps giving is that it works on several levels. On the surface it’s a riddle about sorting molecules between two chambers. Dig a little deeper and it becomes a probe into the meaning of entropy. If you dig even further, it seems to be a bridge between matter and information. As the Schrödinger’s cat thought experiment dramatised the oddness of quantum superposition, Maxwell’s demon dramatised the subtleties of thermodynamics by invoking a fantastical entity. And while Schrödinger’s cat forces us to ask what it means for a macroscopic system to be in two states at once, Maxwell’s demon forces us to ask what it means to know something about a system and whether that knowledge can be used without consequence.

  2025.09.19

• 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

• My heart of physics

  Every July 4, I have occasion to remember two things: the discovery of the Higgs boson, and my first published byline for an article about the discovery of the Higgs boson. I have no trouble believing it’s been eight years since we discovered this particle, using the Large Hadron Collider (LHC) and its ATLAS and CMS detectors, in Geneva. I’ve greatly enjoyed writing about particle physics in this time, principally because closely engaging with new research and the scientists who worked on them allowed me to learn more about a subject that high school and college had let me down on: physics.

  In 2020, I haven’t been able to focus much on the physical sciences in my writing, thanks to the pandemic, the lockdown, their combined effects and one other reason. This has been made doubly sad by the fact that the particle physics community at large is at an interesting crossroads.

  In 2012, the LHC fulfilled the principal task it had been built for: finding the Higgs boson. After that, physicists imagined the collider would discover other unknown particles, allowing theorists to expand their theories and answer hitherto unanswered questions. However, the LHC has since done the opposite: it has narrowed the possibilities of finding new particles that physicists had argued should exist according to their theories (specifically supersymmetric partners), forcing them to look harder for mistakes they might’ve made in their calculations. But thus far, physicists have neither found mistakes nor made new findings, leaving them stuck in an unsettling knowledge space from which it seems there might be no escape (okay, this is sensationalised, but it’s also kinda true).

  Right now, the world’s particle physicists are mulling building a collider larger and more powerful than the LHC, at a cost of billions of dollars, in the hopes that it will find the particles they’re looking for. Not all physicists are agreed, of course. If you’re interested in reading more, I’d recommend articles by Sabine Hossenfelder and Nirmalya Kajuri and spiralling out from there. But notwithstanding the opposition, CERN – which coordinates the LHC’s operations with tens of thousands of personnel from scores of countries – recently updated its strategy vision to recommend the construction of such a machine, with the ability to produce copious amounts of Higgs bosons in collisions between electrons and positrons (a.k.a. ‘Higgs factories’). China has also announced plans of its own build something similar.

  Meanwhile, scientists and engineers are busy upgrading the LHC itself to a ‘high luminosity version’, where luminosity represents the number of interesting events the machine can detect during collisions for further study. This version will operate until 2038. That isn’t a long way away because it took more than a decade to build the LHC; it will definitely take longer to plan for, convince lawmakers, secure the funds for and build something bigger and more complicated.

  There have been some other developments connected to the current occasion in terms of indicating other ways to discover ‘new physics’, which is the collective name for phenomena that will violate our existing theories’ predictions and show us where we’ve gone wrong in our calculations.

  The most recent one I think was the ‘XENON excess’, which refers to a moderately strong signal recorded by the XENON 1T detector in Italy that physicists think could be evidence of a class of particles called axions. I say ‘moderately strong’ because the statistical significance of the signal’s strength is just barely above the threshold used to denote evidence and not anywhere near the threshold that denotes a discovery proper.

  It’s evoked a fair bit of excitement because axions count as new physics – but when I asked two physicists (one after the other) to write an article explaining this development, they refused on similar grounds: that the significance makes it seem likely that the signal will be accounted for by some other well-known event. I was disappointed of course but I wasn’t surprised either: in the last eight years, I can count at least four instances in which a seemingly inexplicable particle physics related development turned out to be a dud.

  The most prominent one was the ‘750 GeV excess’ at the LHC in December 2015, which seemed to be a sign of a new particle about six-times heavier than a Higgs boson and 800-times heavier than a proton (at rest). But when physicists analysed more data, the signal vanished – a.k.a. it wasn’t there in the first place and what physicists had seen was likely a statistical fluke of some sort. Another popular anomaly that went the same way was the one at Atomki.

  But while all of this is so very interesting, today – July 4 – also seems like a good time to admit I don’t feel as invested in the future of particle physics anymore (the ‘other reason’). Some might say, and have said, that I’m abandoning ship just as the field’s central animus is moving away from the physics and more towards sociology and politics, and some might be right. I get enough of the latter subjects when I work on the non-physics topics that interest me, like research misconduct and science policy. My heart of physics itself is currently tending towards quantum mechanics and thermodynamics (although not quantum thermodynamics).

  One peer had also recommended in between that I familiarise myself with quantum computing while another had suggested climate-change-related mitigation technologies, which only makes me wonder now if I’m delving into those branches of physics that promise to take me farther away from what I’m supposed to do. And truth be told, I’m perfectly okay with that. 🙂 This does speak to my privileges – modest as they are on this particular count – but when it feels like there’s less stuff to be happy about in the world with every new day, it’s time to adopt a new hedonism and find joy where it lies.

  2020.07.04

• The molecule that was also a wave

  According to the principles of quantum mechanics, you’re a wave – just like light is both a particle and a wave. It’s just that your wavelength is so small that your wave nature doesn’t matter, and you’re treated like a particle. The larger an object is, the smaller its wavelength, and vice versa. We’re confused about whether light is a particle or a wave because photons, the particles of light, are so small and have a measurable wavelength as a result. Scientists know that electrons, protons, neutrons, even neutrinos have the properties of a wave.

  But while the math of quantum mechanics says you’re a wave, how can we know for sure if we can’t measure it? There are two ways. One, we don’t have any evidence to the contrary. Two, scientists have been checking if larger and larger particles, as far as they can go, exhibit the properties of a wave – and at every step of the way, they’ve come up with positive results. Both together, we have no reason to believe that we’re not also waves.

  Such tests reaffirm the need for quantum mechanics to understand the nature of reality because the rules of classical mechanics alone don’t explain wave-particle duality.

  On September 23, scientists from Austria, China, Germany and Switzerland reported that they had measured the wavelength of a group of molecules called oligoporphyrins. Specifically, they used “oligo-tetraphenylporphyrins enriched by a library of up to 60 fluoroalkylsulphanyl chains”. Altogether, they consisted “of up to 2,000 atoms”, becoming the heaviest object directly known to exhibit wave-like properties.

  

  According to the scientists’ peer-reviewed paper, the molecules had a wavelength of around 53 femtometers, about 100,000-times smaller than the molecules themselves.

  * * *

  We have known since at least the 11th century, through the work of the Arab scholar Ibn al-Haytham, that light is a wave. In 1670, Isaac Newton propounded that light is made up of small particles, and spent three decades supplying evidence for his argument. His push birthed a conflict: was light wave-like or made up of particles?

  The British polymath Thomas Young built on the 17th century Dutch physicist Christiaan Huygens to devise an experiment in 1801 that definitively proved light was a wave. It is known widely today as the Young’s double-slit experiment. It is so simple even as its outcomes are so immutable that it has become a mainstay of modern tests of quantum mechanics. Physicists use upgraded versions of the experiment to this day to study the nature and properties matter-waves.

  (If you would like to know more, I highly recommend Anil Ananthaswamy’s biography of this experiment, Through Two Doors At Once; here’s an excerpt.)

  In the experiment, light from a common source – such as a candle – is allowed to pass through two fine slits separated by a short distance. A sheet of paper sufficiently behind the slits then shows a strange pattern of alternating light and dark bands instead of just two patches of light. This is because light waves passing through the two slits interfere with each other, producing the famous interference pattern. Since only waves can interfere, the experiment shows that light has to be a wave.

  

  The particulate nature of light would get its proper due only in 1900, when Max Planck stumbled upon a mathematical inconsistency that forced him to conclude light had to be made up of smaller packets of energy. It was the birth of quantum mechanics.

  * * *

  The international group’s test went roughly as follows: the scientists pulsed a laser onto a glass plate coated with the oligoporphyrins to release a stream of the molecules; collected them into a beam using collimators; randomly chopped the beam into smaller bits; passed each bit through diffraction gratings to split it up; then had the two little beams interfere with each other. Finally, they counted the number of molecules striking the detector while the detector registered the interference pattern.

  They had insulated the whole device, about 2m long, from extremely small disturbances, like vibrations, to prevent the results from being corrupted. In their paper, the scientists even write that the final interference pattern was blurred thanks to Earth’s rotation, and which they were able to “compensate for” using effects due to Earth’s gravity.

  

  To ascertain that the pattern they were seeing on the detector was in fact due to interference, the scientists performed a variety of checks each of which established a relationship between the shapes on the detector with the properties of the components of the interferometer according to the rules of quantum mechanics. They were also able to rule out alternative, i.e. classical, explanations this way.

  For example, the scientists fired a laser through the cloud of molecules post-interference. Each molecule split the laser light into two separate beams, which recombined to produce an interference pattern of their own. This way, scientists could elicit the molecules’ interference pattern by studying the laser’s interference pattern. As they varied the laser power, they found that the visibility distribution of the molecules more closely matched with quantum mechanical models than with classical models, confirming interference.

  

  What these scientists have achieved isn’t only a feat of measurement. Their findings also help refine the border between the classical and the quantum. The force of gravity governs the laws of classical mechanics, which deals with macroscopic objects, while the electromagnetic, strong nuclear and weak nuclear forces rule the microscopic world. Although macroscopic and microscopic objects occupy the same universe, physicists haven’t yet understood how classical and quantum mechanics can be combined into a single theory.

  One of the problems standing in the way of this union is knowing where – and how – the macroscopic world ends and the microscopic world begins. So by observing quantum mechanical effects at the scale of thousands of atoms, scientists have quite literally pushed the boundaries of what we know about how the universe works.

  2019.12.12

• 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

• Jayant Narlikar’s pseudo-defence of Darwin

  Jayant Narlikar, the noted astrophysicist and emeritus professor at the Inter-University Centre for Astronomy and Astrophysics, Pune, recently wrote an op-ed in The Hindu titled ‘Science should have the last word’. There’s probably a tinge of sanctimoniousness there, echoing the belief many scientists I’ve met have that science will answer everything, often blithely oblivious to politics and culture. But I’m sure Narlikar is not one of them.

  Nonetheless, the piece IMO was good and not great because what Narlikar has written has been written in the recent past by many others, with different words. It was good because the piece’s author was Narlikar. His position on the subject is now in the public domain where it needs to be if only so others can now bank on his authority to stand up for science themselves.

  Speaking of authority: there is a gaffe in the piece that its fans – and The Hindu‘s op-ed desk – appear to have glazed over. If they didn’t, it’s possible that Narlikar asked for his piece to be published without edits, and which could have either been further proof of sanctimoniousness or, of course, distrust of journalists. He writes:

  Recently, there was a claim made in India that the Darwinian theory of evolution is incorrect and should not be taught in schools. In the field of science, the sole criterion for the survival of a theory is that it must explain all observed phenomena in its domain. For the present, Darwin’s theory is the best such theory but it is not perfect and leaves many questions unanswered. This is because the origin of life on earth is still unexplained by science. However, till there is a breakthrough on this, or some alternative idea gets scientific support, the Darwinian theory is the only one that should continue to be taught in schools.

  @avinashtn, @thattai and @rsidd120 got the problems with this excerpt, particularly the part in bold, just right in a short Twitter exchange, beginning with this tweet (please click-through to Twitter to see all the replies):

  https://twitter.com/avinashtn/status/964883532144304128

  Gist: the origin of life is different from the evolution of life.

  But even if they were the same, as Narlikar conveniently assumes in his piece, something else should have stopped him. That something else is also what is specifically interesting for me. Sample what Narlikar said next and then the final line from the excerpt above:

  For the present, Darwin’s theory is the best such theory but it is not perfect and leaves many questions unanswered. … However, till there is a breakthrough on this, or some alternative idea gets scientific support, the Darwinian theory is the only one that should continue to be taught in schools.

  Darwin’s theory of evolution got many things right, continues to, so there is a sizeable chunk in the domain of evolutionary biology where it remains both applicable and necessary. However, it is confusing that Narlikar believes that, should some explanations for some phenomena thus far not understood arise, Darwin’s theories as a whole could become obsolete. But why? It is futile to expect a scientific theory to be able to account for “all observed phenomena in its domain”. Such a thing is virtually impossible given the levels of specialisation scientists have been able to achieve in various fields. For example, an evolutionary biologist might know how migratory birds evolved but still not be able to explain how some birds are thought to use quantum entanglement with Earth’s magnetic field to navigate.

  The example Mukund Thattai provides is fitting. The Navier-Stokes equations are used to describe fluid dynamics. However, scientists have been studying fluids in a variety of contexts, from two-dimensional vortices in liquid helium to gas outflow around active galactic nuclei. It is only in some of these contexts that the Navier-Stokes equations are applicable; that they are not entirely useful in others doesn’t render the equations themselves useless.

  Additionally, this is where Narlikar’s choice of words in his op-ed becomes more curious. He must be aware that his own branch of study, quantum cosmology, has thin but unmistakable roots in a principle conceived in the 1910s by Niels Bohr, with many implications for what he says about Darwin’s theories.

  Within the boundaries of physics, the principle of correspondence states that at larger scales, the predictions of quantum mechanics must agree with those of classical mechanics. It is an elegant idea because it acknowledges the validity of classical, a.k.a. Newtonian, mechanics when applied at a scale where the effects of gravity begin to dominate the effects of subatomic forces. In its statement, the principle does not say that classical mechanics is useless because it can’t explain quantum phenomena. Instead, it says that (1) the two mechanics each have their respective domain of applicability and (2) the newer one must be resemble the older one when applied to the scale at which the older one is relevant.

  Of course, while scientists have been able to satisfy the principle of correspondence in some areas of physics, an overarching understanding of gravity as a quantum phenomenon has remained elusive. If such a theory of ‘quantum gravity’ were to exist, its complicated equations would have to be able to resemble Newton’s equations and the laws of motion at larger scales.

  But exploring the quantum nature of spacetime is extraordinarily difficult. It requires scientists to probe really small distances and really high energies. While lab equipment has been setup to meet this goal partway, it has been clear for some time that it might be easier to learn from powerful cosmic objects like blackholes.

  And Narlikar has done just that, among other things, in his career as a theoretical astrophysicist.

  I don’t imagine he would say that classical mechanics is useless because it can’t explain the quantum, or that quantum mechanics is useless because it can’t be used to make sense of the classical. More importantly, should a theory of quantum gravity come to be, should we discard the use of classical mechanics all-together? No.

  I too was wondering about that para — forgot about the panspermia thing. But even if earth was seeded by extraterrestrial microbes, Darwinian evolution still works after that… For that matter, little evidence today supporting steady state theory!

  — Rahul Siddharthan (@rsidd120) February 17, 2018

  In the same vein: should we continue to teach Darwin’s theories for lack of a better option or because it is scientific, useful and, through the fossil record, demonstrable? And if, in the future, an overarching theory of evolution comes along with the capacity to subsume Darwin’s, his ideas will still be valid in their respective jurisdictions.

  As Thattai says, “Expertise in one part of science does not automatically confer authority in other areas.” Doesn’t this sound familiar?

  Featured image credit: sipa/pixabay.

  2018.02.24

• All the science in ‘The Cloverfield Paradox’

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

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

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

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

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

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

  Spoilers ahead

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

  Spoilers end

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

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

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

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

  2018.02.07