When light, sound or any kind of wave travels through a complex medium like fog, murky water, or biological tissue, it scatters in many directions. Each particle or irregularity in the medium changes the path of the waves, scrambling them and blurring the resulting image. This is why doctors struggle to image deep inside tissue using ultrasound, why optical microscopes can’t see through thick samples, and why radar and sonar sometimes miss objects hidden behind clutter.
Scientists have long looked for ways to focus waves through such disordered environments — and while many have tried to compensate for scattering, their success has been limited when the medium becomes very opaque.
A team led by Alexandre Aubry at ESPCI Paris and collaborators from Vienna and Aix-en-Provence wanted to turn this problem around. Instead of correcting or undoing the scattering, they wondered if something in the wave patterns remains stable even in the middle of all that complexity. That is, could they identify and locate a target based on the part of the signal that still carries its unique ‘fingerprint’?
Their new study, published in Nature Physics, introduces a mathematical tool called the fingerprint operator that allows exactly this. This operator can detect, locate, and even characterise an object hidden inside a strongly scattering medium by comparing the reflected light to a reference pattern recorded in simpler conditions. The method can work for sound, light, radar, and other kinds of waves.
At the heart of the technique is the reflection matrix, a large dataset recording how each source in an array of sources sends a wave into the medium and how every receiver picks up the returning echoes. Each element of this matrix contains information about how waves bounce off of different points, so together they capture the complete response of the system.
To find a target within this sea of signals, the researchers introduced the fingerprint operator, written as Γ = R × R₀†, where R is the measured reflection matrix from the complex medium and R₀ is a reference matrix measured for the same target in clear, homogenous conditions. The dagger (†) indicates a mathematical conjugate that makes the comparison sensitive to how well the two patterns match. By calculating how strongly the two matrices correlate, the team obtained a likelihood index, which indicates how likely it is that a target with certain properties — e.g. position, size or shape — is present at a given spot.
Effectively the team has developed a way to image hidden objects using scattered light.
The researchers tested this concept with ultrasound. They used arrays containing up to 1,024 transducers (devices that convert energy from one form to another) to send and receive sound waves. First, they embedded small metal spheres inside a suspension of glass beads mixed with water, making for a strongly scattering environment.
In the granular suspension, conventional ultrasound couldn’t see the buried metal spheres at all. The multiple scattering caused an exponential loss of contrast with depth, making the target signals roughly a 100x weaker than the background noise. Yet when the fingerprint operator was applied, the two spheres appeared sharply on the reconstructed likelihood map, each represented by a bright peak at its correct location. The contrast improvement reached factors of several hundred, strong enough to rule out false positive signals with a probability of error smaller than 1 in a hundred million.
This success came from the fingerprint operator’s ability to filter out diffuse, randomly scattered waves and isolate those faint waves that behave as if the medium were transparent. In simple terms, the operator is a mathematical tool that can use the complexity of the target’s own echo to cancel the complexity of the medium.
The same approach worked inside a foam that mimicked human tissue. A normal ultrasound image was dominated by speckle (random bright and dark spots caused by small scattering events), rendering a small pre-inserted marker nearly invisible. But when the fingerprint operator was applied to the data, the marker was revealed clearly and precisely.
To its credit, the fingerprint operator doesn’t require scientists to fully known the medium, only the ability to record a reflection matrix and a reference response. It can then use these resources to find patterns that survive scattering and extract meaningful information.
For medicine, this could improve ultrasound detection of small implants, needles, and markers that currently get lost in tissue noise. It could also help map the internal fibre structure of muscles or hearts, providing new diagnostic insights into diseases like cardiomyopathy and fibrosis. In materials science, it could reveal the orientation of grains in metals or composites. In military settings, it could locate targets hidden behind foliage or turbulent water.
The approach is also computationally efficient: according to the researchers’ paper, generating the likelihood map takes about the same time as developing a standard ultrasound image and can be adapted for moving targets by incorporating motion parameters into the fingerprint.
Finally, the idea animating the study also challenges a long-standing view that multiple scattering is purely a nuisance, incapable of being useful. The study overturns this view by extracting information from the multiple scattering data, using the fingerprint operator to account for how a target’s own echoes evolve through scattering, and leveraging those distortions to detect it more confidently.
Bayes’s rule is one of the most fundamental principles in probability and statistics. It allows us to update our beliefs in the face of new evidence. In its simplest form, the rule tells us how to revise the probability of a hypothesis once new data becomes available.
A standard way to teach it involves drawing coloured balls from a pouch: you start with some expectation (e.g. “there’s a 20% chance I’ll draw a blue ball”), then you update your belief depending on what you observe (“I’ve drawn a red ball, so the actual chance of drawing a blue ball is 10%”). While this example seems simple, the rule carries considerable weight: physicists and mathematicians have described it as the most consistent way to handle uncertainty in science, and it’s a central part of logic, decision theory, and indeed nearly every field of applied science.
There are two well-known ways of arriving at Bayes’s rule. One is the axiomatic route, which treats probability as a set of logical rules and shows that Bayesian updating is the only way to preserve consistency. The other is variational, which demands that updates should stay as close as possible to prior beliefs while remaining consistent with new data. This latter view is known as the principle of minimum change. It captures the intuition that learning should be conservative: we shouldn’t alter our beliefs more than is necessary. This principle explains why Bayesian methods have become so effective in practical statistical inference: because they balance a respect for new data with loyalty to old information.
A natural question arises here: can Bayes’s rule be extended into the quantum world?
Quantum theory can be thought of as a noncommutative extension of probability theory. While there are good reasons to expect there should be a quantum analogue of Bayes’s rule, the field has for a long time struggled to identify a unique and universally accepted version. Instead, there are several competing proposals. One of them stands out: the Petz transpose map. This is a mathematical transformation that appears in many areas of quantum information theory, particularly in quantum error correction and statistical sufficiency. Some scholars have even argued that it’s the “correct” quantum Bayes’s rule. Still, the situation remains unsettled.
In probability, the joint distribution is like a big table that lists the chances of every possible pair of events happening together. If you roll a die and flip a coin, the joint distribution specifies the probability of getting “heads and a 3”, “tails and a 5”, and so on. In this big table, you can also zoom out and just look at one part. For example, if you only care about the die, you can add up over all coin results to get the probability of each die face. Or if you only care about the coin, you can add up over all die results to get the probability of heads or tails. These zoomed-out views are called marginals.
The classical Bayes’s rule doesn’t just update the zoomed-out views but the whole table — i.e. the entire joint distribution — so the connection between the two events also remains consistent with the new evidence.
In the quantum version, the joint distribution isn’t a table of numbers but a mathematical object that records how the input and output of a quantum process are related. The point of the new study is that if you want a true quantum Bayes’s rule, you need to update that whole object, not just one part of it.
A new study by Ge Bai, Francesco Buscemi, and Valerio Scarani in Physical Review Letters has taken just this step. In particular, they’ve presented a quantum version of the principle of minimum change by showing that when the measure of change is chosen to be quantum fidelity — a widely used measure of similarity between states — this optimisation leads to a unique solution. Equally remarkably, this solution coincided with the Petz transpose map in many important cases. As a result, the researchers have built a strong bridge between classical Bayesian updating, the minimum change principle, and a central tool of quantum information.
The motivation for this new work isn’t only philosophical. If we’re to generalise Bayes’s rule to include quantum mechanics as well, we need to do so in a way that respects the structural constraints of quantum theory without breaking away from its classical roots.
The researchers began by recalling how the minimum change principle works in classical probability. Instead of updating only a single marginal distribution, the principle works at the level of the joint input-output distribution. Updating then becomes an optimisation problem, i.e. finding the subsequent distribution that’s consistent with the new evidence but minimally different from the evidence from before.
In ordinary probability, we talk about stochastic processes. These are rules that tell us how an input is turned into an output, with certain probabilities. For example if you put a coin into a vending machine, there might be a 90% chance you get a chips packet and a 10% chance you get nothing. This rule describes a stochastic process. This process can also be described with a joint distribution.
In quantum physics, however, it’s tricky. The inputs and outputs aren’t just numbers or events but quantum states, which are described by wavefunctions or density matrices. This makes the maths much more complex. The resulting stochastic processes also become sequences of events called completely positive trace-preserving (CPTP) maps.
A CPTP map is the most general kind of physical evolution allowed: it takes a quantum state and transforms it into another quantum state. And in the course of doing so, it needs to follow two rules: it shouldn’t yield any negative probabilities and it should ensure the total probability adds up to 1. That is, your chance of getting a chips packet shouldn’t be –90% nor should it be 90% plus a 20% chance of getting nothing.
These complications mean that, while the joint distribution in classical Bayesian updating is a simple table, the one in quantum theory is more sophisticated. It uses two mathematical tools in particular. One is purification, a way to embed a mixed quantum state into a larger ‘pure’ state so that mathematicians can keep track of correlations. The other is Choi operators, a standard way of representing a CPTP map as a big matrix that encodes all possible input-output behaviour at once.
Together, these tools play the role of the joint distribution in the quantum setting: they record the whole picture of how inputs and outputs are related.
Now, how do you compare two processes, i.e. the actual forward process (input → output) and the guessed reverse process (output → input)?
In quantum mechanics, one of the best measures of similarity is fidelity. It’s a number between 0 and 1. 0 means two processes are completely different and 1 means they’re exactly the same.
In this context, the researchers’ problem statement was this: given a forward process, what reverse process is closest to it?
To solve this, they looked over all possible reverse processes that obeyed the two rules, then they picked the one that maximised the fidelity, i.e. the CPTP map most similar to the forward process. This is the quantum version of applying the principle of minimum change.
In the course of this process, the researchers found that in natural conditions, the Petz transpose map emerges as the quantum Bayes’s rule.
In quantum mechanics, two objects (like matrices) commute if the order in which you apply them doesn’t matter. That is, A then B produces the same outcome as B then A. In physical terms, if two quantum states commute, they behave more like classical probabilities.
The researchers found that when the CPTP map that takes an input and produces an output, called the forward channel, commutes with the new state, the updating process is nothing but the Petz transpose map.
This is an important result for many reasons. Perhaps foremost is that it explains why the Petz map has shown up consistently across different parts of quantum information theory. It appears it isn’t just a useful tool but the natural consequence of the principle of minimum change applied in the quantum setting.
The study also highlighted instances where the Petz transpose map isn’t optimal, specifically when the commutativity condition fails. In these situations, the optimal updating process depends more intricately on the new evidence. This subtlety departs clearly from classical Bayesian logic because in the quantum case, the structure of non-commutativity forces updates to depend non-linearly on the evidence (i.e. the scope of updating can be disproportionate to changes in evidence).
Finally, the researchers have shown how their framework can recover special cases of practical importance. If some new evidence perfectly agrees with prior expectations, the forward and reverse processes become identical, mirroring the classical situation where Bayes’s rule simply reaffirms existing beliefs. Similarly, in contexts like quantum error correction, the Petz transpose map’s appearance is explained by its status as the optimal minimal-change reverse process.
But the broader significance of this work lies in the way it unifies different strands of quantum information theory under a single conceptual roof. By proving that the Petz transpose map can be derived from the principle of minimum change, the study has provided a principled justification for its widespread use rather than being restricted to particular contexts. This fact has immediate consequences for quantum computing, where physicists are looking for ways to reverse the effects of noise on fragile quantum states. The Petz transpose map has long been known to do a good job of recovering information from these states after they’ve been affected by noise. Now that physicists know the map embodies the smallest update required to stay consistent with the observed outcomes, they may be able to design new recovery schemes that exploit the structure of minimal change more directly.
The study may also open doors to extending Bayesian networks into the quantum regime. In classical probability, a Bayesian network provides a structured way to represent cause-effect relationships. By adapting the minimum change framework, scientists may be able to develop ‘quantum Bayesian networks’ where the way one updates their expectations of a particular outcome respects the peculiar constraints of CPTP maps. This could have applications in quantum machine learning and in the study of quantum causal models.
There are also some open questions as well. For instance, the researchers have noted that if different measures of divergence other than fidelity are used, e.g. the Hilbert-Schmidt distance or quantum relative entropy, the resulting quantum Bayes’s rules may be different. This in turn indicates that there could be multiple valid updating rules, each suited to different contexts. Future research will need to map out these possibilities and determine which ones are most useful for particular applications.
In all, the study provides both a conceptual advance and a technical tool. Conceptually, it shows how the spirit of Bayesian updating can carry over into the quantum world; technically, it provides a rigorous derivation of when and why the Petz transpose map is the optimal quantum Bayes’s rule. Taken together, the study’s finding strengthens the bridge between classical and quantum reasoning and offers a deeper understanding of how information is updated in a world where uncertainty is baked into reality rather than being due to an observer’s ignorance.
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.
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.
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.
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.
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.
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.)
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.)
A schematic diagram of the Maxwell’s demon thought experiment. Htkym (CC BY-SA)
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.)
A (low-res) visualisation of a Szilard engine. Its simplest form has only one atom (i.e. N = 1) pushing against a piston. Credit: P. Fraundorf (CC BY-SA)
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.
Credit: Cdd20
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?
Credit: Amy Young/Unsplash
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.
Carbon is famous for its many solid forms. It’s the soot in air pollution, the graphite in pencil leads, and the glittering diamond in expensive jewellery. It’s also the carbon nanotubes in biosensors and fullerenes in organic solar cells.
However, despite its ability to exist in various shapes as a solid, carbon’s liquid form has been a long-standing mystery. The main reason is that carbon is very difficult to liquefy: at around 4,500º C of temperature and a hundred atmospheres’ worth of pressure — not something found even inside a blast furnace. Scientists have thus struggled to see what molten carbon actually looks like.
The question of its structure isn’t only scientific curiosity. Liquid carbon shows up in laser-fusion experiments and in the manufacture of nanodiamonds. The substance probably also exists deep inside planets like Uranus and Neptune.
In a 2020 review of the topic in Chemical Physics Letters, three researchers from the University of California Berkeley wrote:
[M]any intriguing unanswered questions remain regarding the properties of liquid carbon. While theory has produced a wide array of predictions regarding the structure, phase diagram, and electronic nature of the liquid, as of yet, few of these predictions have been experimentally tested, and several of the predicted properties of the liquid remain controversial.
In a major step forward, an international collaboration of researchers from China, Europe, the UK, and the UK recently reported that they had managed to briefly liquefy carbon — but long enough to observe the internal arrangement of its atoms in detail. They achieved the feat by blasting a carbon wafer with a powerful laser, then X-raying it in real time.
The researchers used glassy carbon, a hard form of carbon that absorbs laser energy evenly.
To create the extreme conditions required to liquefy, the team used the European XFEL (EuXFEL) research facility in Germany. Here, a power laser fired 515-nm light to the front of a glassy carbon wafer. The pulse lasted 5-10 nanoseconds, was roughly one-fourth of a millimetre wide, and carried up to 35 joules of energy.
That’s just one-tenth of the energy required to melt 1 g of ice. But because it was delivered in concentrated fashion, the pulse launched a shockwave through the wafer. Shock compression simultaneously squeezed and heated the material, quickly driving pressures to 7 lakh to 16 lakh times the earth’s atmosphere. The temperature in the wafer also soared above 6,000 K — well into the liquid-carbon regime.
Then,a device recorded the speed of the shockwaves and confirmed the wave stayed flat and steady across the region to be blasted by X-rays. With the wave speed and the sample’s thickness, the team calculated the pressure inside the sample to about 98,000 atm.
While the shockwaves were still rippling through the sample, the EuXFEL facility launched a 25-femtosecond-long flash of X-rays at the same spot.
The liquid carbon state lasted for only a few nanoseconds but a femtosecond is a million-times even shorter.
The X-rays scattered off the carbon atoms and were caught by two large detectors, where the radiation produced patterns called diffraction rings. Each ring encoded the distances between atoms, like a fingerprint of the sample’s internal structure.
Because the X-ray flash was intense, each flash revealed enough data to analyse the liquid’s structure.
For added measure, the team also varied laser power and the wafer’s thickness to collect data across a range of physical parameters. For example, the pressure varied from 1 atm (for reference) to 15 lakh atm. Each pressure level corresponded to a separate, single-shot X-ray measurement, so the whole dataset was assembled shot by shot.
At pressures of 7.5-8.2 lakh atm, the glassy carbon began turning into crystalline diamond. At 10-12 lakh atm, the signs in the data that were symptomatic of diamond weakened while broad humps characteristic of the liquid phase emerged and grew. The scientists interpreted this as evidence of a mixed state where solid diamond and liquid carbon coexist.
Then, at about 15 lakh atm, the data pertaining to the diamond form vanished completely, leaving only the broad liquid-form’s humps. The sample was now fully molten. According to the team, this means carbon under shock melts roughly between roughly 9.8 lakh and 16 lakh atm in the experiment.
Then, to convert the diffraction patterns into information about the arrangement of atoms, the team used maths and simulations.
The team members calculated the static structure factor, a framework that described how the atoms in liquid carbon scattered the X-ray radiation. Then they used the factor to estimate the chance of finding another carbon atom at some distance from a reference atom. These distances indicated the distances the atoms preferred to keep and the average number of nearest neighbours.
Next, they used quantum density-functional theory molecular dynamics (DFT-MD) to simulate how 64 carbon atoms move at a chosen density and temperature. The simulations produced static structure factor data that the researchers compared directly to their data. By adjusting the density and temperature in the simulation, they found the best-fit values that matched each experiment.
The team performed this comparison because it could rule out models of liquid carbon’s structure that were incompatible with the findings. For example, the Lennard-Jones model predicted the average number of neighbouring carbon atoms to be 11-12, contrary to the data.
The team estimated that carbon melted temperature to around 6,700 K and a pressure of 12 lakh atm. When fully molten, each carbon atom had about four immediate neighbours on average. This is reminiscent of the way carbon atoms are arranged in diamond, although the bonds in liquid carbon are also constantly breaking and reforming.
The near-perfect fit between experiment and DFT-MD for the structure factor indicated that existing quantum simulation techniques could capture liquid carbon’s behaviour accurately at high pressure. The success will give researchers confidence when using the same methods to predict even harsher conditions, such as those inside giant exoplanets.
Indeed, ice-giants like Neptune may contain layers where methane breaks down and carbon forms a liquid‐like ocean. Knowing the density and the atomic arrangement in such a liquid can help predict the planet’s magnetic field and internal heat flow.
Similarly, in inertial-confinement fusion — of the type that recently breached the break-even barrier at a US facility — a thin diamond shell surrounds the fuel. Designers must know exactly how that shell melts during the first shocks to generate power more efficiently.
Many advanced carbon materials such as nanotubes and nanodiamonds form when liquid carbon cools rapidly. Understanding how the liquid’s atoms establish short-range order could suggest pathways to tailor these materials.
Finally, the team wrote in its paper, the experiment showed that single-shot X-ray diffraction combined with a high-repetition laser can map the liquid structure of any light element at extreme pressure and temperature. Running both the laser and EuXFEL at their full capabilities could thus allow scientists to put together large datasets in minutes rather than weeks.
At the heart of particle physics lies the Standard Model, a theory that has stood for nearly half a century as the best description of the subatomic realm. It tells us what particles exist, how they interact, and why the universe is stable at the smallest scales. The Standard Model has correctly predicted the outcomes of several experiments testing the limits of particle physics. Even then, however, physicists know that it’s incomplete: it can’t explain dark matter, why matter dominates over antimatter, and why the force of gravity is so weak compared to the other forces. To settle these mysteries, physicists have been conducting very detailed tests of the Model, each of which has either tightened their confidence in a hypothetical explanation or has revealed a new piece of the puzzle.
A central character in this story is a subatomic particle called the W boson — the carrier of the weak nuclear force. Without it, the Sun wouldn’t shine because particle interactions involving the weak force are necessary for nuclear fusion to proceed. W bosons are also unusual among force carriers: unlike photons (the particles of light), they’re massive, about 80-times heavier than a proton. This mass difference — of a massless photon and a massive W boson — arises due to a process called the Higgs mechanism. Physicists first proposed this mechanism in 1964 and confirmed it was real when they found the Higgs boson particle at the Large Hadron Collider (LHC) in 2012.
The particles of the Standard Model of particle physics. The W bosons are shown among the force-carrier particles on the right. The photon is denoted γ. The electron (e) and muon (µ) are shown among the leptons on the right. The corresponding neutrino flavours are showing on the bottom row, denoted ν. Credit: Daniel Dominguez/CERN
But finding the Higgs particle was only the beginning. To prove that the Higgs mechanism really works the way the theory says, physicists need to check its predictions in detail. One of the sharpest tests involves how W bosons scatter off each other at high energies. The key to achieving this is the W boson’s polarisation states. Both photons and W bosons have a property called quantum spin, but whereas for photons its value is zero, for W bosons its non-zero. The spin also has a direction. If it points sideways, the W boson is said to be transverse polarised; if it’s pointing along the particle’s direction of travel, the W boson is said to be longitudinally polarised. The longitudinal ones are special because their behaviour is directly tied to the Higgs mechanism.
Specifically, if the Higgs mechanism and the Higgs boson don’t exist, calculations involving the longitudinal W bosons scattering off of each other quickly give rise to nonsensical mathematical results in the theory. The Higgs boson acts like a regulator in this engine, preventing the mathematics from ‘blowing up’. In fact, in the 1970s, the theoretical physicists Benjamin Lee, Chris Quigg, and Hugh Thacker showed that without the Higgs boson, the weak force would become uncontrollably powerful at high energies, leading to the breakdown of the theory. Their work was an important theoretical pillar that justified building the colossal LHC machine to search for the Higgs boson particle.
The terms Higgs boson, Higgs field, and Higgs mechanism describe related but distinct ideas. The Higgs field is a kind of invisible medium thought to fill all of space. Particles like W bosons and Z bosons interact with this field as they move and through that interaction they acquire mass. This is the Higgs mechanism: the process by which particles that would otherwise be massless become heavy.
The Higgs boson is different: it’s a particle that represents a vibration or a ripple in the Higgs field, just as a photon is a ripple in the electromagnetic field. Its discovery in 2012 confirmed that the field is real and not just something that appears in the mathematics of the theory. But discovery alone doesn’t prove the mechanism is doing everything the theory demands. To test that, physicists need to look at situations where the Higgs boson’s balancing role is crucial.
The scattering of longitudinally polarised W bosons is a good example. Without the Higgs boson, the probabilities of the scatterings occurring uncontrollably at higher energy, but with the Higgs boson in the picture, they stay within sensible bounds. Observing longitudinally polarised W bosons behaving as predicted is thus evidence for the particle as well as a check on the field and the mechanism behind it.
Imagine a roller-coaster without brakes. As it goes faster and faster, there’s nothing to stop it from flying off the tracks. The Higgs mechanism is like the braking system that keeps the ride safe. Observing longitudinally polarised W bosons in the right proportions is equivalent to checking that the brakes actually work when the roller-coaster speeds up.
Credit: Skyler Gerald
Another path that physicists once considered and that didn’t involve a Higgs boson at all was called technicolor theory. Instead of a single kind of Higgs boson giving the W bosons their mass, technicolor proposed a brand-new force. Just as the strong nuclear force binds quarks into protons and neutrons, the hypothetical technicolor force would bind new “technifermion” particles into composite states. These bound states would mimic the Higgs boson’s job of giving particles mass, while producing their own new signals in high-energy collisions.
The crucial test to check whether some given signals are due to the Higgs boson or due to technicolor lies in the behaviour of longitudinally polarised W bosons. In the Standard Model, their scattering is kept under control by the Higgs boson’s balancing act. In technicolor, by contrast, there is no Higgs boson to cancel the runaway growth. The probability of the scattering of longitudinally polarised W bosons would therefore rise sharply with more energy, often leaving clearly excessive signals in the data.
Thus, observing longitudinally polarised W bosons at consistent with the predictions of the Standard Model, and not finding any additional signals, would also strengthen the case for the Higgs mechanism and weaken that for technicolor and other “Higgs-less” theories.
At the Large Hadron Collider, the cleanest way to study look for such W bosons is in a phenomenon called vector boson scattering (VBS). In VBS, two protons collide and the quarks inside them emit W bosons. These W bosons then scatter off each other before decaying into lighter particles. The leftover quarks form narrow sprays of particles, or ‘jets’, that fly far forward.
If the two W bosons happen to have the same electric charge — i.e. both positive or both negative — the process is even more distinctive. This same-sign WW scattering is quite rare and that’s an advantage because then it’s easy to spot in the debris of particle collisions.
Both ATLAS and CMS, the two giant detectors at the LHC, had previously observed same-sign WW scattering without breaking down the polarisation. In 2021, the CMS detector reported the first hint of longitudinal polarisation but at a statistical significance only of 2.3 sigma, which isn’t good enough (particle physicists prefer at least 3 sigma). So after the LHC completed its second run in 2018, collecting data from around 10 quadrillion collisions between protons, the ATLAS collaboration set out to analyse it and deliver the evidence. This group’s study was published in Physical Review Letters on September 10.
The layout of the Large Hadron Collider complex at CERN. Protons (p) are pre-accelerated to higher energies in steps — at the Proton Synchrotron (PS) and then the Super Proton Synchrotron (SPS) — before being injected into the the LHC ring. The machine then draws two opposing beams of protons from the SPS and accelerates them to nearly the speed of light before colliding them head-on at four locations, under the gaze of the four detectors. ATLAS and CMS are two of them. Credit: Arpad Horvath (CC BY-SA)
The challenge of finding longitudinally polarised W bosons is like finding a particular needle in a very large haystack where most of the needles look nearly identical. So ATLAS designed a special strategy.
When one W boson decays, the result is one electron or muon and one neutrino. If the W boson is positively charged, for example, the decay could be to one anti-electron and one electron-neutrino or to one anti-muon and a muon-neutrino. Anti-electrons and anti-muons are positively charged. If the W boson is negatively charged, the products could one electron and one electron-antineutrino or one muon and one muon-antineutrino. So first, ATLAS zeroed in on the fact that it was looking for two electrons, two muons, or one of each, both carrying the same electric charge. Neutrinos however are really hard to catch and study, so the ATLAS group look for their absence rather than their presence. In all these particle interactions, the law of conservation of momentum holds — which means in a given interaction, a neutrino’s presence can be elucidated when the momenta of the electrons or muons add up to be slightly lower than that of the W boson; the missing amount would have been carried away by the neutrino, like money unaccounted for in a ledger.
This analysis also required an event of interest to have at least two jets (reconstructed from streams of particles) with a combined energy above 500 GeV and separated widely in rapidity (which is a measure of their angle relative to the beam). This particular VBS pattern — two electrons/muons, two jets, and missing momentum — is the hallmark of same-sign WW scattering.
Second, even with these strict requirements, impostors creep in. The biggest source of confusion is WZ production, a process in which another subatomic particle called the Z boson decays invisibly or one of its decay products goes unnoticed, making the event resemble WW scattering. Other sources include electrons having their charges mismeasured, jets can masquerading as electrons/muons, and some quarks producing electrons/muons that slip into the sample. To control for all this noise, the ATLAS group focused on control regions: subsets of events that produced a distinct kind of noise that the group could cleanly ‘subtract’ from the data to reveal same-sign WW scattering, thus also reducing uncertainty in the final results.
Third, and this is where things get nuanced: the differences between transverse and longitudinally polarised W bosons show up in distributions — i.e. how far apart the electrons/muons are in angle, how the jets are oriented, and the energy of the system. But since no single variable could tell the whole story, the ATLAS group combined them using deep neural networks. These machine-learning models were fed up to 20 kinematic variables — including jet separations, particle angles, and missing momentum patterns — and trained to distinguish between three groups:
(i) Two transverse polarised W bosons;
(ii) One transverse polarised W boson and one longitudinally polarised W boson; and
(iii) Both longitudinally polarised W bosons
Fourth, the group combined the outputs of these neural networks and fit with a maximum likelihood method. When physicists make measurements, they often don’t directly see what they’re measuring. Instead, they see data points that could have come from different possible scenarios. A likelihood is a number that tells them how probable the data is in a given scenario. If a model says “events should look like this,” they can ask: “Given my actual data, how likely is that?” And the maximum likelihood method will help them decide the parameters that make the given data most likely to occur.
For example, say you toss a coin 100 times and get 62 heads. You wonder: is the coin fair or biased? If it’s fair, the chance of exactly 62 heads is small. If the coin is slightly biased (heads with probability 0.62), the chance of 62 heads is higher. The maximum likelihood estimate is to pick the bias, or probability of heads, that makes your actual result most probable. So here the method would say, “The coin’s bias is 0.62” — because this choice maximises the likelihood of seeing 62 heads out of 100.
In their analysis, the ATLAS group used the maximum likelihood method to check with the LHC data ‘preferred’ a contribution from longitudinal scattering, after subtracting what background noise and transverse-only scattering could explain.
The results are a milestone in experimental particle physics. In the September 10 paper, ATLAS reported evidence for longitudinally polarised W bosons in same-sign WW scattering with a significance of 3.3 sigma — sufficiently close to 4, which is the calculated significance based on the predictions of the Standard Model. This means the data behaved as theory predicted, with no unexpected excess or deficit.
It’s also bad news for technicolor theory. By observing longitudinal W bosons at exactly the rates predicted by the Standard Model, and not finding any additional signals, the ATLAS data strengthens the case for the Higgs mechanism providing the check on the W bosons’ scattering probability, rather than the technicolor force.
The measured cross-section for events with at least one longitudinally polarised W boson was 0.88femtobarns, with an uncertainty of 0.3 femtobarns. These figures essentially mean that there were only a few hundred same-sign WW scattering events in the full dataset of around 10 quadrillion proton-proton collisions. The fact that ATLAS could pull this signal out of such a background-heavy environment is a testament to the power of modern machine learning working with advanced statistical methods.
The group was also able to quantify the composition of signals. Among others:
About 58% of events were genuine WW scattering
Roughly 16% were from WZ production
Around 18% arose from irrelevant electrons/muons, charge misidentification or the decay of energetic photons
One way to appreciate the importance of these findings is by analogy: imagine trying to hear a faint melody being played by a single violin in the middle of a roaring orchestra. The violin is the longitudinal signal; the orchestra is the flood of background noise. The neural networks are like sophisticated microphones and filters, tuned to pick out the violin’s specific tone. The fact that ATLAS couldn’t only hear it but also measured its volume to match the score written by the Standard Model is remarkable.
Perhaps in the same vein, these results are more than just another tick mark for the Standard Model. It’s a direct test of the Higgs mechanism in action. The discovery of the Higgs boson particle in 2012 was groundbreaking but proving that the Higgs mechanism performs its theoretical role requires demonstrating that it regulates the scattering of W bosons. By finding evidence for longitudinally polarised W bosons at the expected rate, ATLAS has done just that.
The results also set the stage for the future. The LHC is currently being upgraded to a form called the High-Luminosity LHC and it will begin operating later this decade, collect datasets about 10x larger than what the LHC did in its second run. With that much more data, physicists will be able to study differential distributions, i.e. how the rate of longitudinal scattering varies with energy, angle or jet separation. These patterns are sensitive to hitherto unknown particles and forces, such as additional Higgs-like particles or modifications to the Higgs mechanism itself. That is, even small deviations from the Standard Model’s predictions could hint at new frontiers in particle physics.
Indeed, history has often reminded physicists that such precision studies often uncover surprises. Physicists didn’t discover neutrino oscillations by finding a new particle but by noticing that the number of neutrinos arriving from the Sun at detectors on Earth didn’t match expectations. Similarly, minuscule mismatches between theory and observations in the scattering of W bosons could someday reveal new physics — and if they do, the seeds will have been planted by studies like that of the ATLAS group.
On the methodological front, the analysis also showcases how particle physics is evolving. ‘Classical’ analyses once banked on tracking single variables; now, deep learning has played a starring role by combining many variables into a single discriminant, allowing ATLAS to pull the faint signal of longitudinally polarised W bosons from the noise. This approach could only become more important as both datasets and physicists’ ambitions expand.
Perhaps the broadest lesson in all this is that science often advances by the unglamorous task of verifying the details. The discovery of the Higgs boson answered one question but opened many others; among them, measuring how it affects the scattering of W bosons is one of the ore direct ways to probe whether the Standard Model is complete or just the first chapter of a longer story. Either way, the pursuit exemplifies the spirit of checking, rechecking, testing, and probing until scientists truly understand how nature works at extreme precision.
Featured image: The massive mural of the ATLAS detector at CERN painted by artist Josef Kristofoletti. The mural is located at the ATLAS Experiment site and shows on two perpendicular walls the detector with a collision event superimposed. The event on the large wall shows a simulation of an event that would be recorded in ATLAS if a Higgs boson was produced. The cavern of the ATLAS Experiment with the detector is 100 m directly below the mural. The height of the mural is about 12 m. The actual ATLAS detector is more than twice as big. Credit: Claudia Marcelloni, Michael Barnett/CERN.
Rubidium isn’t respectable. It isn’t iron, whose strength built railways and bridges and it isn’t silicon, whose valley became a dubious shrine to progress. Rubidium explodes in water. It tarnishes in air. It’s awkward, soft, and unfit for the neat categories by which schoolteachers tell their students how the world is made. And yet, precisely because of this unruly character, it insinuates itself into the deepest places of science, where precision, control, and prediction are supposed to reign.
For centuries astronomers counted the stars, then engineers counted pendulums and springs — all good and respectable. But when humankind’s machines demanded nanosecond accuracy, it was rubidium, a soft metal that no practical mind would have chosen, that became the metronome of the world. In its hyperfine transitions, coaxed by lasers and microwave cavities, the second is carved more finely than human senses can comprehend. Without rubidium’s unstable grace, GPS collapses, financial markets fall into confusion, trains and planes drift out of sync. The fragile and the explosive have become the custodians of order.
What does this say about the hierarchies of knowledge? Textbooks present a suspiciously orderly picture: noble gases are inert, alkali metals are reactive, and their properties can be arranged neatly in columns of the periodic table, they say. Thus rubidium is placed there like a botanical specimen. But in practice, scientists turned to it not because of its box in a table but because of accidents, conveniences, and contingencies. Its resonance lines happen to fall where lasers can reach them easily. Its isotopes are abundant enough to trap, cool, and measure. The entire edifice of atomic clocks and exotic Bose-Einstein condensates rests not on an inevitable logic of discovery but on this convenient accident. Had rubidium’s levels been slightly different, perhaps caesium or potassium would have played the starring role. Rational reconstruction will never admit this. It prefers tidy sequences and noble inevitabilities. Rubidium, however, laughs at such tidiness.
Take condensed matter. In the 1990s and 2000s, solar researchers sought efficiency in perovskite crystals. These crystals were fragile, prone to decomposition, but again rubidium slipped in: a small ion among larger ones, it stabilised the lattice. A substitution here, a tweak there, and suddenly the efficiency curve rose. Was this progress inevitable? No; it was bricolage: chemists trying one ion after another until the thing worked. And the journals now describe rubidium as if it were always destined to “enhance stability”. But destiny is hindsight dressed as foresight. What actually happened was messy. Rubidium’s success was contingent, not planned.
Then there’s the theatre of optics. Rubidium’s spectral lines at 780 nm and 795 nm became the experimentalist’s playground. When lasers cooled atoms to microkelvin temperatures and clouds of rubidium atoms became motionless, they merged into collective wavefunctions and formed the first Bose-Einstein condensates. The textbooks now call this a triumph of theory, the “inevitable” confirmation of quantum statistics. Nonsense! The condensates weren’t predicted as practical realities — they were curiosities, dismissed by many as impossible in the laboratory. What made them possible was a melange of techniques: magnetic traps, optical molasses, sympathetic cooling. And rubidium, again, happened to be convenient, its transitions accessible, its abundance generous, its behaviour forgiving. Out of this messiness came a Nobel Prize and an entire field. Rubidium teaches us that progress comes not from the logical unfolding of ideas but from playing with elements that allegedly don’t belong.
Rubidium rebukes dogma. It’s neither grand nor noble, yet it controls time, stabilises matter, and demonstrates the strangest predictions of quantum theory. It shows science doesn’t march forward by method alone. It stumbles, it improvises, it tries what happens to be at hand. Philosophers of science prefer to speak of method and rigour yet their laboratories tell a story of messy rooms where equipment is tuned until something works, where grad students swap parts until the resonance reveals itself, where fragile metals are pressed into service because they happen to fit the laser’s reach.
Rubidium teaches us that knowledge is anarchic. It isn’t carved from the heavens by pure reason but coaxed from matter through accidents, failures, and improvised victories. Explosive in one setting, stabilising in another; useless in industry, indispensable in physics — the properties of rubidium are contradictory and it’s precisely this contradiction that makes it valuable. To force it into the straitjacket of predictable science is to rewrite history as propaganda. The truth is less comfortable: rubidium has triumphed where theory has faltered.
And yet, here we are. Our planes and phones rely on rubidium clocks. Our visions of renewable futures lean on rubidium’s quiet strengthening of perovskite cells. Our quantum dreams — of condensates, simulations, computers, and entanglement — are staged with rubidium atoms as actors. An element kings never counted and merchants never valued has become the silent arbiter of our age. Science itself couldn’t have planned it better; indeed, it didn’t plan at all.
Rubidium is the fragment in the mosaic that refuses to fit yet holds the pattern together. It’s the soft yet explosive, fragile yet enduring accident that becomes indispensable. Its lesson is simple: science also needs disorder, risk, and the unruliness of matter to thrive.
Featured image: A sample of rubidium metal. Credit: Dnn87 (CC BY).
In science, paradoxes often appear when familiar rules are pushed into unfamiliar territory. One of them is Parrondo’s paradox, a curious mathematical result showing that when two losing strategies are combined, they can produce a winning outcome. This might sound like trickery but the paradox has deep connections to how randomness and asymmetry interact in the physical world. In fact its roots can be traced back to a famous thought experiment explored by the US physicist Richard Feynman, who analysed whether one could extract useful work from random thermal motion. The link between Feynman’s thought experiment and Parrondo’s paradox demonstrates how chance can be turned into order when the conditions are right.
Imagine two games. Each game, when played on its own, is stacked against you. In one, the odds are slightly less than fair, e.g. you win 49% of the time and lose 51%. In another, the rules are even more complex, with the chances of winning and losing depending on your current position or capital. If you keep playing either game alone, the statistics say you will eventually go broke.
But then there’s a twist. If you alternate the games — sometimes playing one, sometimes the other — your fortune can actually grow. This is Parrondo’s paradox, proposed in 1996 by the Spanish physicist Juan Parrondo.
The answer to how combining losing games can result in a winning streak lies in how randomness interacts with structure. In Parrondo’s games, the rules are not simply fair or unfair in isolation; they have hidden patterns. When the games are alternated, these patterns line up in such a way that random losses become rectified into net gains.
Say there’s a perfectly flat surface in front of you. You place a small bead on it and then you constantly jiggle the surface. The bead jitters back and forth. Because the noise you’re applying to the bead’s position is unbiased, the bead simply wanders around in different directions on the surface. Now, say you introduce a switch that alternates the surface between two states. When the switch is ON, an ice-tray shape appears on the surface. When the switch is OFF, it becomes flat again. This ice-tray shape is special: the cups are slightly lopsided because there’s a gentle downward slope from left to right in each cup. At the right end, there’s a steep wall. If you’re jiggling the surface when the switch is OFF, the bead diffuses a little towards the left, a little towards the right, and so on. When you throw the switch to ON, the bead falls into the nearest cup. Because each cup is slightly tilted towards the right, the bead eventually settles near the steep wall there. Then you move the switch to OFF again.
As you repeat these steps with more and more beads over time, you’ll see they end up a little to the right of where they started. This is Parrando’s paradox. The jittering motion you applied to the surface caused each bead to move randomly. The switch you used to alter the shape of the surface allowed you to expend some energy in order to rectify the beads’ randomness.
The reason why Parrondo’s paradox isn’t just a mathematical trick lies in physics. At the microscopic scale, particles of matter are in constant, jittery motion because of heat. This restless behaviour is known as Brownian motion, named after the botanist Robert Brown, who observed pollen grains dancing erratically in water under a microscope in 1827. At this scale, randomness is unavoidable: molecules collide, rebound, and scatter endlessly.
Scientists have long wondered whether such random motion could be tapped to extract useful work, perhaps to drive a microscopic machine. This was Feynman’s thought experiment as well, involving a device called the Brownian ratchet, a.k.a. the Feynman-Smoluchowski ratchet. The Polish physicist Marian Smoluchowski dreamt up the idea in 1912 and which Feynman popularised in a lecture 50 years later, in 1962.
Picture a set of paddles immersed in a fluid, constantly jolted by Brownian motion. A ratchet and pawl mechanism is attached to the paddles (see video below). The ratchet allows the paddles to rotate in one direction but not the other. It seems plausible that the random kicks from molecules would turn the paddles, which the ratchet would then lock into forward motion. Over time, this could spin a wheel or lift a weight.
In one of his physics famous lectures in 1962, Feynman analysed the ratchet. He showed that the pawl itself would also be subject to Brownian motion. It would jiggle, slip, and release under the same thermal agitation as the paddles. When everything is at the same temperature, the forward and backward slips would cancel out and no net motion would occur.
This insight was crucial: it preserved the rule that free energy can’t be extracted from randomness at equilibrium. If motion is to be biased in only one direction, there needs to be a temperature difference between different parts of the ratchet. In other words, random noise alone isn’t enough: you also need an asymmetry, or what physicists call nonequilibrium conditions, to turn randomness into work.
Let’s return to Parrondo’s paradox now. The paradoxical games are essentially a discrete-time abstraction of Feynman’s ratchet. The losing games are like unbiased random motion: fluctuations that on their own can’t produce net gain because the gains become cancelled out. But when they’re alternated cleverly, they mimic the effect of adding asymmetry. The combination rectifies the randomness, just as a physical ratchet can rectify the molecular jostling when a gradient is present.
This is why Parrondo explicitly acknowledged his inspiration from Feynman’s analysis of the Brownian ratchet. Where Feynman used a wheel and pawl to show how equilibrium noise can’t be exploited without a bias, Parrondo created games whose hidden rules provided the bias when they were combined. Both cases highlight a universal theme: randomness can be guided to produce order.
The implications of these ideas extend well beyond thought experiments. Inside living cells, molecular motors like kinesin and myosin actually function like Brownian ratchets. These proteins move along cellular tracks by drawing energy from random thermal kicks with the aid of a chemical energy gradient. They demonstrate that life itself has evolved ways to turn thermal noise into directed motion by operating out of equilibrium.
Parrondo’s paradox also has applications in economics, evolutionary biology, and computer algorithms. For example, alternating between two investment strategies, each of which is poor on its own, may yield better long-term outcomes if the fluctuations in markets interact in the right way. Similarly, in genetics, when harmful mutations alternate in certain conditions, they can produce beneficial effects for populations. The paradox provides a framework to describe how losing at one level can add up to winning at another.
Feynman’s role in this story is historical as well as philosophical. By dissecting the Brownian ratchet, he demonstrated how deeply the laws of thermodynamics constrain what’s possible. His analysis reminded physicists that intuition about randomness can be misleading and that only careful reasoning could reveal the real rules.
In 2021, a group of scientists from Australia, Canada, France, and Germany wrote in Cancers that the mathematics of Parrondo’s paradox could also illuminate the biology of cancerous tumours. Their starting point was the observation that cancer cells behave in ways that often seem self-defeating: they accumulate genetic and epigenetic instability, devolve into abnormal states, sometimes stop dividing altogether, and often migrate away from their original location and perish. Each of these traits looks like a “losing strategy” — yet cancers that use these ‘strategies’ together are often persistent.
The group suggested that the paradox arises because cancers grow in unstable, hostile environments. Tumour cells deal with low oxygen, intermittent blood supply, attacks by the immune system, and toxic drugs. In these circumstances, no single survival strategy is reliable. A population of only stable tumour cells would be wiped out when the conditions change. Likewise a population of only unstable cells would collapse under its own chaos. But by maintaining a mix, the group contended, cancers achieve resilience. Stable, specialised cells can exploit resources efficiently while unstable cells with high plasticity constantly generate new variations, some of which could respond better to future challenges. Together, the team continued, the cancer can alternate between the two sets of cells so that it can win.
The scientists also interpreted dormancy and metastasis of cancers through this lens. Dormant cells are inactive and can lie hidden for years, escaping chemotherapy drugs that are aimed at cells that divide. Once the drugs have faded, they restart growth. While a migrating cancer cell has a high chance of dying off, even one success can seed a tumor in a new tissue.
On the flip side, the scientists argued that cancer therapy can also be improved by embracing Parrondo’s paradox. In conventional chemotherapy, doctors repeatedly administer strong drugs, creating a strategy that often backfires: the therapy kills off the weak, leaving the strong behind — but in this case the strong are the very cells you least want to survive. By contrast, adaptive approaches that alternate periods of treatment with rest or that mix real drugs with harmless lookalikes could harness evolutionary trade-offs inside the tumor and keep it in check. Just as cancer may use Parrondo’s paradox to outwit the body, doctors may one day use the same paradox to outwit cancer.
On August 6, physicists from Lanzhou University in China published a paper in Physical Review E discussing just such a possibility. They focused on chemotherapy, which is usually delivered in one of two main ways. The first, called the maximum tolerated dose (MTD), uses strong doses given at intervals. The second, called low-dose metronomic (LDM), uses weaker doses applied continuously over time. Each method has been widely tested in clinics and each one has drawbacks.
MTD often succeeds at first by rapidly killing off drug-sensitive cancer cells. In the process, however, it also paves the way for the most resistant cancer cells to expand, leading to relapse. LDM on the other hand keeps steady pressure on a tumor but can end up either failing to control sensitive cells if the dose is too low or clearing them so thoroughly that resistant cells again dominate if the dose is too strong. In other words, both strategies can be losing games in the long run.
The question the study’s authors asked was whether combining these two flawed strategies in a specific sequence could achieve better results than deploying either strategy on its own. This is the sort of situation Parrondo’s paradox describes, even if not exactly. While the paradox is concerned with combining outright losing strategies, the study has discussed combining two ineffective strategies.
To investigate, the researchers used mathematical models that treated tumors as ecosystems containing three interacting populations: healthy cells, drug-sensitive cancer cells, and drug-resistant cancer cells. They applied equations from evolutionary game theory that tracked how the fractions of these groups shifted in different conditions.
The models showed that in a purely MTD strategy, the resistant cells soon took over, and in a purely LDM strategy, the outcomes depended strongly on drug strength but still ended badly. But when the two schedules were alternated, the tumor behaved differently. The more sensitive cells were suppressed but not eliminated while their persistence prevented the resistant cells from proliferating quickly. The team also found that the healthy cells survived longer.
Of course, tumours are not well-mixed soups of cells; in reality they have spatial structure. To account for this, the team put together computer simulations where individual cells occupied positions on a grid; grew, divided or died according to fixed rules; and interacted with their neighbours. This agent-based approach allowed the team to examine how pockets of sensitive and resistant cells might compete in more realistic tissue settings.
Their simulations only confirmed the previous set of results. A therapeutic strategy that alternated between MTD and LDM schedules extended the amount of time before the resistant cells took over and while the healthy cells dominated. When the model started with the LDM phase in particular, the sensitive cancer cells were found to compete with the resistant cancer cells and the arrival of the MTD phase next applied even more pressure on the latter.
This is an interesting finding because it suggests that the goal of therapy may not always be to eliminate every sensitive cancer cell as quickly as possible but, paradoxically, that sometimes it may be wiser to preserve some sensitive cells so that they can compete directly with resistant cells and prevent them from monopolising the tumor. In clinical terms, alternating between high- and low-dose regimens may delay resistance and keep tumours tractable for longer periods.
Then again this is cancer — the “emperor of all maladies” — and in silico evidence from a physics-based model is only the start. Researchers will have to test it in real, live tissue in animal models (or organoids) and subsequently in human trials. They will also have to assess whether certain cancers, followed by a specific combination of drugs for those cancers, will benefit more (or less) from taking the Parrando’s paradox way.
[University of London mathematical oncologist Robert] Noble … says that the method outlined in the new study may not be ripe for a real-world clinical setting. “The alternating strategy fails much faster, and the tumor bounces back, if you slightly change the initial conditions,” adds Noble. Liu and colleagues, however, plan to conduct in vitro experiments to test their mathematical model and to select regimen parameters that would make their strategy more robust in a realistic setting.
Neutrinos are among the most mysterious particles in physics. They are extremely light, electrically neutral, and interact so weakly with matter that trillions of them pass through your body each second without leaving a trace. They are produced in the Sun, nuclear reactors, the atmosphere, and by cosmic explosions. In fact neutrinos are everywhere — yet they’re almost invisible.
Despite their elusiveness, they have already upended physics. In the late 20th century, scientists discovered that neutrinos can oscillate, changing from one type to another as they travel, which is something that the simplest version of the Standard Model of particle physics — the prevailing theory of elementary particles — doesn’t predict. Because oscillations require neutrinos to have mass, this discovery revealed new physics. Today, scientists study neutrinos for what they might tell us about the universe’s structure and for possible hints of particles or forces yet unknown.
When neutrinos travel through space, they are known to oscillate between three types. This visualisation plots the composition of neutrinos (of 4 MeV energy) by type at various distances from a nuclear reactor. Credit: Public domain
However, detecting neutrinos is very hard. Because they rarely interact with matter, experiments must build massive detectors filled with dense material in the hopes that a small fraction of neutrinos will collide inside with atoms. One way to detect such collisions uses Cherenkov radiation, a bluish glow emitted when a charged particle moves through a medium like water or mineral oil faster than light does in that medium.
(This is allowed. The only speed limit is that of light in vacuum: 299,792,458 m/s.)
The MiniBooNE experiment at Fermilab used a large mineral-oil Cherenkov detector. When neutrinos from the Booster Neutrino Beamline struck the atomic nuclei in the mineral oil, the interaction released charged particles, which sometimes produced rings of Cherenkov radiation (like ripples) that the detector recorded. In MiniBooNE’s data, the detection events were classified by the type of light ring produced. An “electron-like” event was one that looked like it had been caused by an electron. But because photons can also produce nearly identical rings when they strike the nuclei, the detector couldn’t always tell the difference. A “muon-like” event, on the other hand, had the distinctive ring pattern of a muon, which is a subatomic particle like the electron but 200-times heavier, and which travels in a straighter, longer track. To be clear, these labels described the detector’s view; they didn’t guarantee which particle was actually present.
MiniBooNE began operating in 2002 to test an anomaly that had been reported at the LSND experiment at Los Alamos. LSND had recorded more electron-like” events than predicted, especially at low energies below about 600 MeV. This came to be called the “low-energy excess” and has become one of the most puzzling results in particle physics. It raised the possibility that neutrinos might be oscillating into a hitherto unknown neutrino type, sometimes called the sterile neutrino — or it might have been a hint of unexpected processes that produced extra photons. Since MiniBooNE couldn’t reliably distinguish electrons from photons, the mystery remained unresolved.
To address this, scientists built the MicroBooNE experiment at Fermilab. It uses a very different technology: the liquid argon time-projection chamber (LArTPC). In a LArTPC, charged particles streak through an ultra-pure mass of liquid argon, leaving a trail of ionised atoms in their wake. An applied electric field causes these trails to drift towards fine wires, where they are recorded. At the same time, the argon emits light that provides the timing of the interaction. This allows the detector to reconstruct interactions in three dimensions with millimetre precision. Crucially, it lets physicists see where the particle shower begins, so they can tell whether it started at the interaction point or some distance away. This capability prepared MicroBooNE to revisit the “low-energy excess” anomaly.
MicroBooNE also had broader motivations. With an active mass of about 90 tonnes of liquid argon inside a 170-tonne cryostat, and 8,256 wires in its readout planes, it was the largest LArTPC in the US when it began operating. It served as a testbed for the much larger detectors that scientists are developing for the Deep Underground Neutrino Experiment (DUNE). And it was also designed to measure the rate at which neutrinos interacted with argon atoms, to study nuclear effects in neutrino scattering, and to contribute to searches for rare processes such as proton decay and supernova neutrino bursts.
(When a star goes supernova, it releases waves upon waves of neutrinos before it releases photons. Scientists were able to confirm this when the star Sanduleak -69 202 exploded in 1987.)
This image, released on February 24, 2017, shows Supernova 1987a (centre) surrounded by dramatic red clouds of gas and dust within the Large Magellanic Cloud. This supernova, first discovered on February 23, 1987, blazed with the power of 100 million Suns. Since that first sighting, SN 1987A has continued to fascinate astronomers with its spectacular light show. Caption and credit: NASA, ESA, R. Kirshner (Harvard-Smithsonian Centre for Astrophysics and Gordon and Betty Moore Foundation), and M. Mutchler and R. Avila (STScI)
Initial MicroBooNE analyses using partial data already challenged the idea that MiniBooNE’s excess was due to the anomaly. However, the collaboration didn’t cover the full range of parameters until recently. On August 21, MicroBooNE published results from five years of operations, corresponding to 1.11 x 1021 protons on target, which was about a 70% increase over previous analyses. This complete dataset together with higher sensitivity and better modelling has provided the most decisive test so far of the anomaly.
The MicroBooNE detector recorded neutrino interactions from the Booster Neutrino Beamline, a setup that produces neutrinos, using its LArTPC detector, which operated at about 87 K inside a cryostat. Charged particles from neutrino interactions produced ionisation electrons that drifted across the detector and were recorded by the wire. Simultaneous flashes of argon scintillation light, seen by photomultiplier tubes, gave the precise time of each interaction.
In neutrino physics, a category of events grouped by what the detector sees in the final state is called a channel. Researchers call it a signal channel when it matches the kind of event they are specifically looking for, as opposed to background signals from other processes. With MicroBooNE, the team stayed on the lookout for two signal channels: (i) one electron and no visible protons or pions (abbreviated as 1e0p0π) and (ii) one electron and at least one proton above 40 MeV (1eNp0π). These categories reflect what MiniBooNE would’ve seen as electron-like events while exploiting MicroBooNE’s ability to identify protons.
One important source of background noise the team had to cut from the data was cosmic rays — high-energy particles from outer space that strike Earth’s atmosphere, creating particle showers that can mimic neutrino signals. In 2017, MicroBooNE added a suite of panels around the detector. For the full dataset, the panels cut an additional 25.4% of background noise in the 1e0p0π channel while preserving 98.9% of signal events.
When a cosmic-ray proton collides with a molecule in the upper atmosphere, it produces a shower of particles that includes pions, muons, photons, neutrons, electrons, and positrons. Credit: SyntaxError55 (CC BY-SA)
In the final analysis, the MicroBooNE data showed no evidence of an anomalous excess of electron-like events. When both channels were combined, the observed events matched the expectations of the Standard Model of particle physics well. The agreement was especially strong in the 1e0p0π channel.
In the 1eNp0π channel, MicroBooNE actually detected slightly fewer events than the Model predicted: 102 events v. 134. This shortfall, of about 24%, is however not enough to claim a new effect but enough to draw attention. But rather than confirming MiniBooNE’s excess, this result suggests there’s some tension in the models the scientists use to simulate how the neutrinos and argon atoms will interact. Argon has a large and complex nucleus, which makes accurate predictions challenging. The scientists have in fact stated in their paper that the deficit may reflect these uncertainties rather than new physics.
The new MicroBooNE results have far-reaching consequences. Foremost, the results reshape the sterile-neutrino debate. For two decades, the LSND and MiniBooNE anomalies had been cited together as signs that the neutrino was oscillating into a previously undetected state. By showing that MiniBooNE’s excess was not due to extra electron-like interactions, MicroBooNE shows that the ‘extra’ events were not caused by excess electron neutrinos. This in turn casts doubt on the simplest explanation, of sterile neutrinos.
As a result, theoretical models that once seemed straightforward now face strong tension. While more complex scenarios remain possible, the easy explanation is no longer viable.
The MicroBooNE cryostat inside which the LArTPC is placed. Credit: Fermilab
Second, they demonstrate the maturity of the LArTPC technology. The MicroBooNE team successfully operated a large detector for years, maintaining the argon’s purity and low-noise electronics required for high-resolution imaging. Its performance validates the design choices for larger detectors like DUNE, which use similar technology but at kilotonne scales. The experiment also showcases innovations such as cryogenic electronics, sophisticated purification systems, protection against cosmic rays, and calibration with ultraviolet lasers, proving that such systems can deliver reliable data over long periods of operation.
Third, the modest deficit in the 1eNp0π channel points to the importance of better understanding neutrino-argon interactions. Argon’s heavy nucleus produces complicated final states where protons and neutrons may scatter or be absorbed, altering the visible event. These nuclear effects can lead to mismatches between simulation and data (possibly including the 24% deficit in the 1eNp0π signal channel). For DUNE, which will also use argon as its target, improving these models is critical. MicroBooNE’s detailed datasets and sideband constraints will continue to inform these refinements.
Fourth, the story highlights the value of complementary detector technologies. MiniBooNE’s Cherenkov detector recorded more events but couldn’t tell electrons from photons; MicroBooNE’s LArTPC recorded fewer events but with much greater clarity. Together, they show how one experiment can identify a puzzle and another can test it with a different method. This multi-technology approach is likely to continue as experiments worldwide cross-check anomalies and precision measurements.
Finally, the MicroBooNE results show how science advances. A puzzling anomaly inspired new theories, new technology, and a new experiment. After five years of data-taking and with the most complete analysis yet, MicroBooNE has said that the MiniBooNE anomaly was not due to electron-neutrino interactions. The anomaly itself remains unexplained, but the field now has a sharper focus. Whether the cause lies in photon production, detector effects or actually new physics, the next generation of experiments can start on firmer footing.
The United Nations has designated 2025 the International Year of Quantum Science and Technology. Many physics magazines and journals have taken the opportunity to publish more articles on quantum physics than they usually do, and that has meant quantum physics research has often been on my mind. Nirmalya Kajuri, an occasional collaborator, an assistant professor at IIT Mandi, and an excellent science communicator, recently asked other physics teachers on X.com how much time they spend teaching the interpretations of quantum physics. His question and the articles I’ve been reading inspired me to write the following post. I hope it’s useful in particular to people like me, who are interested in physics but didn’t formally train to study it.
Quantum physics is often described as the most successful theory in science. It explains how atoms bond, how light interacts with matter, how semiconductors and lasers work, and even how the sun produces energy. With its equations, scientists can predict experimental results with astonishing precision — up to 10 decimal places in the case of the electron’s magnetic moment.
In spite of this extraordinary success, quantum physics is unusual compared to other scientific theories because it doesn’t tell us a single, clear story about what reality is like. The mathematics yields predictions that have never been contradicted within their tested domain, yet it leaves open the question of what the world is actually doing behind those numbers. This is what physicists mean when they speak of the ‘interpretations’ of quantum mechanics.
In classical physics, the situation is more straightforward. Newton’s laws describe how forces act on bodies, leading them to move along definite paths. Maxwell’s theory of electromagnetism describes electric and magnetic fields filling space and interacting with charges. Einstein’s relativity shows space and time are flexible and curve under the influence of matter and energy. These theories predict outcomes and provide a coherent picture of the world: objects have locations, fields have values, and spacetime has shape. In quantum mechanics, the mathematics works perfectly — but the corresponding picture of reality is still unclear.
The central concept in quantum theory is the wavefunction. This is a mathematical object that contains all the information about a system, such as an electron moving through space. The wavefunction evolves smoothly in time according to the Schrödinger equation. If you know the wavefunction at one moment, you can calculate it at any later moment using the equation. But when a measurement is made, the rules of the theory change. Instead of continuing smoothly, the wavefunction is used to calculate probabilities for different possible outcomes, and then one of those outcomes occurs.
For instance, if an electron has a 50% chance of being detected on the left and a 50% chance of being detected on the right, the experiment will yield either left or right, never both at once. The mathematics says that before the measurement, the electron exists in a superposition of left and right, but after the measurement only one is found. This peculiar structure, where the wavefunction evolves deterministically between measurements but then seems to collapse into a definite outcome when observed, has no counterpart in classical physics.
The puzzles arise because it’s not clear what the wavefunction really represents. Is it a real physical wave that somehow ‘collapses’? Is it merely a tool for calculating probabilities, with no independent existence? Is it information in the mind of an observer rather than a feature of the external world? The mathematics doesn’t say.
The measurement problem asks why the wavefunction collapses at all and what exactly counts as a measurement. Superposition raises the question of whether a system can truly be in several states at once or whether the mathematics is only a convenient shorthand. Entanglement, where two particles remain linked in ways that seem to defy distance, forces us to wonder whether reality itself is nonlocal in some deep sense. Each of these problems points to the fact that while the predictive rules of quantum theory are clear, their meaning is not.
Over the past century, physicists and philosophers have proposed many interpretations of quantum mechanics. The most traditional is often called the Copenhagen interpretation, illustrated by the Schrödinger’s cat thought experiment. In this view, the wavefunction is not real but only a computational tool. In many Copenhagen-style readings, the wavefunction is a device for organising expectations while measurement is taken as a primitive, irreducible step. The many-worlds interpretation offers a different view that denies the wavefunction ever collapses. Instead, all possible outcomes occur, each in its own branch of reality. When you measure the electron, there is one version of you that sees it on the left and another version that sees it on the right.
In Bohmian mechanics, particles always have definite positions guided by a pilot wave that’s represented by the wavefunction. In this view, the randomness of measurement outcomes arises because we can’t know the precise initial positions of the particles. There are also objective collapse theories that take the wavefunction as real but argue that it undergoes genuine, physical collapse triggered randomly or by specific conditions. Finally, an informational approach called QBism says the wavefunction isn’t about the world at all but about an observer’s expectations for experiences upon acting on the world.
Most interpretations reproduce the same experimental predictions (objective-collapse models predict small, testable deviations) but tell different stories about what the world is really like.
It’s natural to ask why interpretations are needed at all if they don’t change the predictions. Indeed, many physicists work happily without worrying about them. To build a transistor, calculate the energy of a molecule or design a quantum computer, the rules of standard quantum mechanics suffice. Yet interpretations matter for several reasons, but especially because they shape our philosophical understanding of what kind of universe we live in.
They also influence scientific creativity because some interpretations suggest directions for new experiments. For example, objective collapse theories predict small deviations from the usual quantum rules that can, at least in principle, be tested. Interpretations also matter in education. Students taught only the Copenhagen interpretation may come away thinking quantum physics is inherently mysterious and that reality only crystallises when it’s observed. Students introduced to many-worlds alone may instead think of the universe as an endlessly branching tree. The choice of interpretation moulds the intuition of future physicists. At the frontiers of physics, in efforts to unify quantum theory with gravity or to describe the universe as a whole, questions about what the wavefunction really is become unavoidable.
In research fields that apply quantum mechanics to practical problems, many physicists don’t think about interpretation at all. A condensed-matter physicist studying superconductors uses the standard formalism without worrying about whether electrons are splitting into multiple worlds. But at the edges of theory, interpretation plays a major role. In quantum cosmology, where there are no external observers to perform measurements, one needs to decide what the wavefunction of the universe means. How we interpret entanglement, i.e. as a real physical relation versus as a representational device, colours how technologists imagine the future of quantum computing. In quantum gravity, the question of whether spacetime itself can exist in superposition renders interpretation crucial.
Interpretations also matter in teaching. Instructors make choices, sometimes unconsciously, about how to present the theory. One professor may stick to the Copenhagen view and tell students that measurement collapses the wavefunction and that that’s the end of the story. Another may prefer many-worlds and suggest that collapse never occurs, only branching universes. A third may highlight information-based views, stressing that quantum mechanics is really about knowledge and prediction rather than about what exists independently. These different approaches shape the way students can understand quantum mechanics as a tool as well as as a worldview. For some, quantum physics will always appear mysterious and paradoxical. For others, it will seem strange but logical once its hidden assumptions are made clear.
Interpretations also play a role in experiment design. Objective collapse theories, for example, predict that superpositions of large objects should spontaneously collapse. Experimental physicists are now testing whether quantum superpositions survive for increasingly massive molecules or for diminutive mechanical devices, precisely to check whether collapse really happens. Interpretations have also motivated tests of Bell’s inequalities, an idea that shows no local theory with “hidden variables” can reproduce the correlations predicted by quantum mechanics. The scientists who conducted these experiments confirmed entanglement is a genuine feature of the world, not a residue of the mathematical tools we use to study it — and won the Nobel Prize for physics in 2022. Today, entanglement is exploited in technologies such as quantum cryptography. Without the interpretative debates that forced physicists to take these puzzles seriously, such developments may never have been pursued.
The fact that some physicists care deeply about interpretation while others don’t reflects different goals. Those who work on applied problems or who need to build devices don’t have to care much. The maths provides the answers they need. Those who are concerned with the foundations of physics, with the philosophy of science or with the unification of physical theories care very much, because interpretation guides their thinking about what’s possible and what’s not. Many physicists switch back and forth, ignoring interpretation when calculating in the lab but discussing many-worlds or informational views over chai.
Quantum mechanics is unique among physical theories in this way. Few chemists or engineers spend time worrying about the ‘interpretation’ of Newtonian mechanics or thermodynamics because these theories present straightforward pictures of the world. Quantum mechanics instead gives flawless predictions but an under-determined picture. The search for interpretation is the search for a coherent story that links the extraordinary success of the mathematics to a clear vision of what the world is like.
To interpret quantum physics is therefore to move beyond the bare equations and ask what they mean. Unlike classical theories, quantum mechanics doesn’t supply a single picture of reality along with its predictions. It leaves us with probabilities, superpositions, and entanglement, and it remains ambiguous about what these things really are. Some physicists insist interpretation is unnecessary; to others it’s essential. Some interpretations depict reality as a branching multiverse, others as a set of hidden particles, yet others as information alone. None has won final acceptance, but all try to close the gap between predictive success and conceptual clarity.
In daily practice, many physicists calculate without worrying, but in teaching, in probing the limits of the theory, and in searching for new physics, interpretations matter. They shape not only what we understand about the quantum world but also how we imagine the universe we live in.
