The story of chemical bonding begins in 1916, when the American chemist Gilbert N. Lewis proposed that atoms are held together by pairs of shared electrons. Lewis developed this idea entirely without the benefit of quantum mechanics, which had not yet been formulated. His diagrams — now known as Lewis structures — are still taught in every introductory chemistry course and remain one of the most powerful tools for predicting molecular shape and reactivity. In 1927, the physicists Walter Heitler and Fritz London provided the first rigorous quantum mechanical account of a chemical bond, applying the newly developed Schrödinger equation to the hydrogen molecule. Their calculation showed that the stability of H₂ arises from the quantum mechanical exchange of electrons between the two atoms, a phenomenon with no counterpart in classical physics. These two theoretical traditions, valence bond theory and molecular orbital theory, have shaped how chemists think about bonds ever since.

Despite this long history, a precise and universal definition of a chemical bond remains elusive. Modern quantum chemistry can compute molecular properties with remarkable accuracy, but the more sophisticated the calculation, the harder it becomes to extract a simple, intuitive picture of bonding. Various tools have been developed to address this gap, but they often rely on different assumptions and sometimes give conflicting answers. Bond order, hybridization, aromaticity, these concepts are taught as concrete realities, yet they are better understood as interpretive frameworks rather than directly measurable quantities.

Entanglement as the right language

The new study approaches this problem from an unexpected direction: quantum entanglement. In quantum mechanics, two particles are said to be entangled when their properties are correlated in such a way that neither can be fully described without reference to the other, regardless of how far apart they are. Entanglement was first discussed theoretically in 1935 by Einstein, Podolsky, and Rosen, who regarded it as a paradox. It is now central to quantum computing and quantum communication. The study argues that entanglement is also the right language for describing chemical bonds, precisely because a covalent bond is itself a nonlocal phenomenon: the electrons involved are shared between atoms and do not belong exclusively to either one.

Maximally entangled atomic orbitals

To translate this idea into a practical tool, the study introduces a new type of mathematical object called maximally entangled atomic orbitals, or MEAOs. Atomic orbitals are the quantum mechanical wave functions that describe where electrons are likely to be found around individual atoms. The key innovation is to choose the orbitals not to resemble free atoms as closely as possible, as most existing methods do, but instead to maximise the quantum entanglement between different atomic centres. The result is a set of orbitals specifically designed to make bonding interactions as visible and as quantifiable as possible.

What happens when this approach is applied to real molecules is striking. In ethene (C₂H₄), for example, the MEAO analysis automatically identifies four carbon–hydrogen single bonds and two carbon–carbon bonds (one sigma bond and one pi bond) matching exactly the Lewis structure that any chemistry student would draw. Moreover, the carbon orbitals in the MEAO picture naturally adopt the shape of sp₂ hybrid orbitals, a consequence of quantum mechanics rather than an assumption imposed from outside. Hybridization, the idea that atomic orbitals mix to form new orbitals better suited to bonding, is a rigorous result of quantum mechanics, but the particular hybrid form adopted by an atom depends on its molecular environment. The MEAO framework finds that form automatically, without being told what to look for.

The strength of each bond can then be measured by the amount of entanglement between the two orbitals that form it. Strong covalent bonds, such as those in nitrogen gas (N₂) with its triple bond, show entanglement values close to the theoretical maximum. Moving from lithium dimer (Li₂) through lithium hydride (LiH) to lithium fluoride (LiF), the entanglement decreases progressively, tracking the well-known shift from covalent to increasingly ionic bonding. When tested on helium dimer (a weakly bound van der Waals complex rather than a true chemical bond) the method correctly returns zero entanglement.

The test of the harpoon mechanism

One of the most demanding tests of any bonding analysis method is the dissociation of lithium hydride. At its equilibrium geometry, LiH is predominantly an ionic molecule: the lithium atom effectively donates an electron to the hydrogen atom, producing Li⁺ and H^– ions. Yet some covalent character remains. As the bond is stretched, the molecule passes through what is known as an avoided crossing (a region where two electronic energy levels come very close together but do not intersect) and its character shifts from predominantly ionic to predominantly covalent. Beyond this point, as the atoms continue to separate, the bond ultimately breaks and the covalency decreases again. This transition, in which an electron appears to be “harpoon” back from the hydrogen, is called the harpoon mechanism and it produces a characteristic peak in bond covalency as a function of bond length. Detecting this peak is a recognised benchmark for bonding descriptors, and some orbital-based methods based on Hilbert space partitioning fail to reproduce it. The MEAO entanglement analysis detects it clearly, showing a peak in orbital entanglement that coincides with the avoided crossing.

Aromaticity and multicentre bonding

Many important molecules contain electrons shared among three or more atomic centres simultaneously. Such multicentre bonds cannot be captured by the two-orbital entanglement used for ordinary covalent bonds. For these cases, the study introduces a related quantity called genuine multipartite entanglement, which measures the degree to which a group of three or more orbitals is collectively and irreducibly entangled; that is, correlated in a way that cannot be reduced to a combination of pairwise correlations. Three-centre bonds in species such as the ethyl cation (C₂H₅⁺, an electron-deficient carbocation) and the allyl anion (C₃H₅^–) are correctly identified and assigned high values of this multipartite entanglement measure.

The most eye-catching application of multipartite entanglement in this work may very well be to aromaticity. Aromatic molecules are a special class of cyclic compounds, of which benzene (C₆H₆) is the archetype. In benzene, six electrons occupy six orbitals arranged in a ring above and below the plane of the molecule, and these electrons are not confined between any single pair of atoms but are delocalised around the entire ring. This delocalization gives aromatic compounds unusual stability and distinctive reactivity. The MEAO analysis identifies benzene’s six π orbitals as a single highly entangled cluster, assigning a multipartite entanglement value close to the theoretical maximum. In contrast, non-aromatic six-membered rings such as cyclohexane show values nearly a hundred times smaller. The method also correctly tracks the modest reduction in aromaticity when one or more of benzene’s carbon atoms is replaced by nitrogen, and the progressive decrease when the ring geometry is distorted from its equilibrium shape.

A particularly demanding test is provided by the Diels–Alder reaction, one of the most important bond-forming reactions in organic chemistry. First described by Otto Diels and Kurt Alder in 1928 (a work that earned them the Nobel Prize in 1950) the reaction involves a conjugated diene and a dienophile combining to form a six-membered ring. Neither the starting materials nor the final product is aromatic, but during the reaction the six π electrons involved pass through a transition state in which they are transiently delocalised around a forming ring, giving that fleeting arrangement a transient aromatic character. Several widely used aromaticity indices, including HOMA and FLU, fail to detect this transient aromaticity in the transition state. The multipartite entanglement measure shows a clear peak precisely where the transition state occurs, providing clean confirmation of this long-discussed but difficult-to-measure feature of the reaction.

The framework is also tested on chromium hexacarbonyl, Cr(CO)₆, a prototypical transition-metal complex. Carbon monoxide on its own has a very strong triple bond between the carbon and oxygen atoms. When CO coordinates to a metal centre, the well-known Dewar–Chatt–Duncanson model predicts that this bond should weaken as electron density is redistributed between the ligand and the metal. The MEAO analysis of Cr(CO)₆ correctly reproduces this weakening: the entanglement values for the C–O bond decrease relative to free CO, while new entanglement between the chromium centre and the carbon atoms appears, quantitatively consistent with the expected donation and back-donation of electron density.

Not a metaphor

The message is clear: chemical bonding can be understood as a manifestation of quantum entanglement. This is not merely a metaphor. The entanglement between atomic orbitals, when those orbitals are chosen to maximise it, turns out to encode quantitatively the bond orders, hybridization patterns, multicentre connections, and aromatic properties that chemists have been describing qualitatively for over a century. Concepts that have long been regarded as somewhat fuzzy or model-dependent emerge as precise, computable quantities from a single quantum mechanical principle.

This does not mean that Lewis structures or molecular orbital diagrams will disappear from chemistry textbooks. They remain powerful and intuitive. What the new framework offers is a rigorous foundation that unifies them: a way of asking, in the language of quantum information, exactly how deeply the parts of a molecule are connected to one another. In doing so, it draws together two fields, quantum chemistry and quantum information theory, that have until recently had surprisingly little overlap, and suggests that each has much to offer the other.

Author: César Tomé López is a science writer and the editor of Mapping Ignorance

Disclaimer: Parts of this article may have been copied verbatim or almost verbatim from the referenced research paper/s.

The post Chemical bonding as quantum entanglement appeared first on Mapping Ignorance.

 

From the air, you see it only through the constant jolt, tilt and shudder of the low-flying Cessna aircraft. The landscape of the Llanos de Moxos, northern Bolivia, appears as a disconnected patchwork of open grassland savannahs, forest islands and lakes.

It feels random, almost unreadable. Only gradually does the pattern resolve itself: raised causeways or paths fanning out to link the forest islands, and a dense, scattered web of canals threading the terrain. Slowly you realise it’s a structured network of intersecting lines, enclosures and roads – the imprint of past human design.

If you stand on the open savannah, there is almost nothing to see of this ancient network. The horizon feels open, with fires in the distance from local people burning pastures and clearing forest as dry season begins. The old geometry is still faintly perceptible, but you have to know how to look.

Step into the patches of forest and the canopy closes in. The earth softens underfoot and mosquitoes descend in relentless swarms. The sweat on your neck thickens into a humid film, carrying the familiar scent of suncream and the sharper, chemical note of DEET.

In the uneven light between the trees, the landscape dissolves into subtle rises and depressions. Against the rhythmic swish of machetes as our guides cut through the vegetation, your mind tries to piece together the fragments of structures into something coherent. Flying overhead doesn’t reveal anything about this forest area in the way that it does with the savannah. But fortunately recent advances in technology have transformed what we are able to see.

Archaeological explorations in this part of the world have been completely changed by lidar in the past couple of decades. Lidar maps an area from a plane or drone by bouncing rapid laser pulses off the Earth’s surface. Some of these pulses penetrate the forest canopy, reach the ground and reflect back to the sensor.

By measuring the return time, the system can generate highly precise three-dimensional models of the terrain. This allows you to strip away the camouflage of vegetation, making it possible to see what lies below the Amazonian forest for the first time.

It reveals the ancient Llanos de Moxos as not simply a collection of settlements, but an entire urbanised landscape. A large part in the south-east of this region belonged to the Casarabe culture, which dominated between around AD500 and 1400. It extends across 20,000km², which is roughly the size of New Jersey in the US.

The Casarabe organised into a hierarchy of four different sizes of settlements (those forest islands mentioned above). The biggest ones – the primary settlements – were as large as 3km² or 300 hectares. That’s enough space for over 400 football pitches, suggesting that they could have accommodated substantial numbers of people.

These settlements connect along the raised causeways to smaller secondary and tertiary sites a number of kilometres away, all of which were permanently inhabited as opposed to empty ceremonial hubs. A fourth tier consists of groups of isolated mounds located out in the pampas, which likely correspond to dwelling areas occupied by farmers who would have worked the fields.

It’s not possible to show a lidar image of these four different types of sites interconnecting because they are too far apart for the resolution available, but the image below of a primary settlement known as Loma Cotoca shows the kinds of things we are now documenting.

It features some very impressive civic-ceremonial architecture: conical pyramids over 20 metres tall and U-shaped structures that may have acted as areas for public gatherings for speeches or ceremonies. These were built on top of man-made platforms rising as much as five metres off the ground and extending over 20 hectares. To be clear, this is all still hiding under the forest, but the lidar data reveals the shape, height and layout of what lies below.

The volume of earth moved to create this architecture would have rivalled – and in some cases exceeded – that of well known Andean monuments such as Akapana a few hundred miles to the south-west on the other side of the Andes. Akapana was the epicentre of the Tiwanaku empire that dominated the southern Andes between about AD600 and 1000.

Yet where monuments like Akapana were surrounded by classic, compact bounded cities with thousands of inhabitants, the Casarabe equivalent was completely different. This was dispersed, low-density living amid extensive green space – a form of tropical urbanism that challenges longstanding assumptions about this area as sparsely populated and only lightly modified. It invites comparison with other low-density tropical urban landscapes such as the Maya in central America and the Angkor in latter day Cambodia.

Equally important is the coherence of the Casarabe system. The settlements are rarely isolated, part of a tightly connected network with shared water-management systems. It was clearly all planned and coordinated, designed not only as living spaces but for integrating the population across the region.

We can see that the Casarabe were sustained by drained-field agriculture: the canals were dug to make the land viable for planting during the wet season. The most prominent crop was maize, but there was a remarkable diversity of other produce. This was all embedded within a landscape that was engineered through reservoirs and farm ponds, which helped the Casarabe sustain cultivation and maintain access to water through the dry season in this extremely seasonal environment.

Also very noticeable is the fact that all the major architectural features and burial sites are oriented north-north-west. This suggests these people may have been led by cosmology, with important celestial bodies or regions of the night sky serving as symbolic reference points – hinting at a world where infrastructure, settlement and belief were inseparable.

Rethinking the Amazon

The Casarabe culture covered much less than 1% of Amazonia, which is the whole tropical interior of South America, spanning close to half of the entire continent. For much of the 20th century, this vast area was viewed by archaeologists as an environment that was limiting for human existence.

Poor soils, scarce game, extreme El Niño floods and droughts, and the challenges of tropical disease were all thought to constrain human populations to small, wandering groups living off the land as best they could. Large, settled societies – let alone towns or cities – were considered unlikely, if not impossible.

This view began to shift in the late 20th century for several reasons. Archaeologists realised that Amazonian people had been domesticating a diversity of plants since the end of the Ice Age. They manufactured some of the earliest ceramics in the Americas, and also devised soils known as Amazonian Dark Earths, which combined charcoal, bone and waste materials with the existing poor-quality soil to make it fertile enough for widespread farming.

It also became apparent that just like the Casarabe people, many other cultures across Amazonia had reclaimed vast expanses of seasonally flooded savannahs over several thousand years to create raised and drained field systems.

These discoveries were evidence of long-term settlement and landscape management far beyond what was previously thought possible. It meant Amazonia was not simply a backdrop to human activity; much of the landscape was shaped over the last 13 millennia by the people who lived there.

Enter lidar

Like lasers in the sky, lidar technology has accelerated this transformation in our understanding. The digital process feels near-magical, a “vegetation removal algorithm” that reveals the secrets below.

In practice, however, working with lidar in Amazonia is anything but straightforward. Running such a project here, as I have done, can feel like one of the greatest emotional rollercoasters in field archaeology. It’s all anticipation, frustration and sudden revelation – only comparable, perhaps, with shipwreck exploration.

Depending on what technology is available and most suitable for exploring a particular area, I’ve worked with lidar attached to drones, aeroplanes and helicopters. I’ve learned through trial and error that the technology is only as effective as the logistics and personalities behind it – above all on one occasion when we were trying to integrate a Hungarian lidar sensor with a Brazilian drone.

Lidar can perform beautifully one day and fail the next, depending on the equipment, weather, terrain, batteries, communications and the sheer difficulty of operating in remote Amazonian conditions.

Flights must be carefully planned in remote areas with limited infrastructure, where convective clouds, smoke from fires, wind and even vultures riding thermals can disrupt data acquisition. You have to arrange fuel in advance and improvise landings wherever a safe clearing can be found. Here’s our team refuelling a lidar helicopter in the football field of a small village in Acre state, western Brazil:

You also have to do constant troubleshooting with the technology, such as making sure it’s calibrated correctly and that the data from different flight paths all aligns. What appears in the final images as a seamless “removal” of the forest is, in reality, the product of improvisation, negotiation and persistence.

But given all these challenges, it makes the first successful images all the more powerful when they finally appear. The reward is that we’re finally finding the “lost civilisation” that explorers like Percy Fawcett were searching for a century ago, but by cajoling a drone rather than battering through jungle.

Incidentally, this technology also has important uses beyond archaeology. It can help people to locate and harvest crops like rubber or açaí palm fruits without having to clear so much rainforest. It is also used by pioneering projects such as Amazonia Revelada, which helps Indigenous and traditional people of the Amazon to prove their historic presence within an area to ward off modern commercial interests like loggers or farmers, while also protecting the living history and nature embedded in these landscapes.

Other lidar discoveries

Lidar surveys by French and Ecuadorian archaeologists have revealed that the Llanos de Moxos was certainly not the only example of large-scale, highly integrated society in Amazonia. The Upano Valley, which covers some 300-600km² on the mountainous forest of the Ecuadorian eastern flanks of the Andes, offers another striking example – this time from between about 500BC and AD600–700.

Lidar discovery areas

In Upano, archaeologists have been able to map a vast network of settlements connected by extensive road systems, with large platforms and clusters of buildings arranged in organised layouts across a broad area.

What stands out is not just the scale – thousands of structures – but the rigour of the planning. The settlements didn’t just grow randomly, but as part of a deliberate design: we see straight lines of flat-topped platforms laid out in repeating rows and connected by straight paths that cut cleanly across the landscape, as you can see below.

Again, this is not urbanism in the conventional sense of dense, continuous occupation. There would have been none of the vertical stacking of buildings that you’d get in European settlements, and there were also green spaces between platform complexes – much more like a forest city.

Like the Casarabe region, this is a distributed settlement pattern that is both open and highly structured, but the arrangement is much more compact. This reflects the limited flat space available on the upper terraces of the Upano River, which rise up to 100 metres above the surrounding landscape.

Elsewhere in Amazonia, we see more variations. In the Upper Xingu of central Brazil, interconnected settlements were arranged around a shared ceremonial and road network, again suggesting a regionally coordinated social world.

Further north, the Tairona people of the Sierra Nevada de Santa Marta in present-day Colombia built terraced stone towns in the mountains, linked by paved paths. This was a form of urbanism shaped entirely by the demands of steep, high-altitude terrain. Below is a lidar image of one area in this region, with the platforms that would have housed the settlements marked in yellow. Below that, you can see what the platforms look like.

In western Amazonia, Acre adds another important variation. From around AD1–1000, people built large ditched enclosures, or geoglyphs, mainly in the south-eastern part of this region along the upper Purus River. These were square, circular, hexagonal or octagonal mounds, often 1-3 hectares in size, with ditches up to four metres deep. These were probably used as ceremonial gathering places rather than permanent settlements.

After about AD1000, these were followed by what we call circular mound villages, occupied until around AD 1650–1700. They featured rings of mounds around central plazas and straight roads radiating out like the rays of the Sun, often built to align with the four main compass points. These “Sun villages” were true settlements, and formed interconnected networks across the southern rim of Amazonia. You can see an example in the lidar image below.

Taken together, these discoveries fundamentally reshape our understanding of Amazonia. We now see a mosaic of managed landscapes, engineered environments and, in some cases, city-scale societies. What unites them is not a shared blueprint but a shared impulse: the organisation of people, space and movement across large landscapes in ways that were deliberate, durable and distinctly their own.

To stress, Amazonia was not uniformly dense or urban. It supported a diversity of types of settlements, from dispersed networks like Moxos to tighter grids like Upano, each of them adapted to local ecological conditions. They shared a low-density urbanism, in the sense of large, interconnected populations without the density of classic cities.

What we still don’t know

How were these societies organised politically and socially? How did they interact with variations in the climate and environment, ranging from the heavy rainfalls and droughts caused by El Niño to rivers forging new routes that could move them away from a settlement within a few generations?

What, if any, connections existed with mountain societies in the Andes? And perhaps most importantly, since both the Casarabe and Upano ceased to build monuments after 1492, what led to their transformation or decline before the arrival of Europeans?

There is active debate between archaeologists over whether these societies transformed because of environmental stress, internal political change, or shifts in things like trade routes or migration.

In the Llanos de Moxos, one possibility is that a prolonged period of climate change affected the Casarabe water-management systems that were so critical to feeding this thriving society. In the Upano Valley, volcanic eruptions and earthquakes may have disrupted settlements and agriculture, although it’s unclear whether that could have led to the area being abandoned.

It seems likely that as we uncover new things, it will reveal more and more integration between different societies. What we are seeing now in Amazonia is much like looking at a satellite image of a country at night: bright, isolated clusters of light – cities that appear disconnected. But as we continue to expand our coverage and fill in the gaps, I think this will change.

What now appear as isolated clusters may also resolve into extensive networks. For example a study across the southern rim of Amazonia has predicted that the kinds of settlement mounds that have been identified so far are likely to occur across about 400,000km², supporting an estimated regional population of roughly 500,000 to 1 million people in the era before the Europeans arrived.

Entire regions may emerge as previously unrecognised centres of population and landscape management. This could be particularly so for the Llanos de Moxos. The whole area covers as much as 200,000km², depending on where you draw the boundaries, stretching into Brazil and even Peru. It is often divided into several apparently distinct cultural regions — the Casarabe (aka the monumental mound region), and then two others called the platform ridge and zanjas (ditches) regions.

As lidar coverage expands and more archaeological work is conducted, we may begin to understand how these societies were economically specialised. We know, for example, that the fortified villages of the zanjas region had fish weirs spanning hundreds of miles that were capable of capturing vast quantities of migratory fish. The platform ridge region consisted of large drained fields, which could potentially produce surpluses of maize. It is conceivable that these belonged to a broader network that supported the more complex Casarabe centres.

Or perhaps – who knows – the relationships were more fluid and reciprocal. For now, the question remains open. But it is precisely this possibility of deep regional integration that lidar is beginning to bring into view. In time, we may even begin to identify Casarabe outposts scattered across the Llanos de Moxos.

What happens next

There’s still a huge amount to be done with lidar. Vast areas, particularly in the Ecuadorian and Peruvian Amazon – remain unexplored. One recent study suggested that there could be more than 10,000 more urban structures of the kind I’ve been describing still hidden throughout Amazonia, all of them dating from pre-European times.

Looking ahead 20 years, it is likely that our map of Amazonia will look very different. One promising technology is satellite-based lidar systems, which could provide broader, though less detailed, datasets across large areas. Advances in machine learning are also beginning to help us identify archaeological features within massive datasets, speeding up a labour-intensive process.

Against this, there are time pressures in some places. Llanos de Moxos, for instance, is unfortunately in rapid transition. The very ground that holds the traces of ancient networks is being transformed by mechanised agriculture and large-scale terraforming for rice cultivation and pastures.

We also need to keep reminding ourselves that lidar is only the first step. What really matters is how it’s brought together with other lines of evidence. Most sites discovered by lidar have yet to be excavated, so we’ll have to do much of that, looking for everything from bones and plants to ceramics and weapons.

So far, most excavation has been in the Casarabe area of the Llanos de Moxos. The reason, for instance, that we know the culture lived primarily on maize was through the discovery of over 60 human skeletons, which underwent carbon isotope analysis. The same research paper also analysed excavated duck bones to show that the Casarabe were feeding them maize too, suggesting animal domestication in a continent that was not generally known for it.

Another fascinating Casarabe find is a single buried skeleton who may have been a leader, because he had a collar of jaguar teeth around his neck. He was also wearing ear pieces made of armadillo shell, studded with mottled blue stones called sodalite – it’s not clear what these were for.

We’ll also need to obtain more precise dates for key events using techniques like radiocarbon dating, and more pinpoint accurate environmental data to help support theories about ancient changes to the climate – as opposed to the wider regional information we’ve tended to rely on until now. Lake sediments are great environmental archives, preserving evidence of things like vegetation change and landscape disturbance.

Also important is comparing genetic data from excavated bones with people who live in these areas today – in dialogue and collaboration with local communities whose histories, memories and knowledge are essential to understanding these landscapes.

It’s all a question of how lidar is brought together with all this other evidence. The most convincing reconstructions will come from the convergence of all of these. One further major challenge ahead, however, will be to bridge the gap between scientific reconstructions and how past peoples understood and inhabited their world. Archaeology is increasingly rich in data, but we have to relate it to lived experience.

That is no easy feat, but it is essential if we are to move from mapping past worlds to understanding them. Crucially, Amazonia – with its rich, still-vibrant Indigenous societies and ethnographic record – offers an exceptional opportunity to do this, providing rare continuities through which to anchor and critically engage our interpretations of the past.

Lessons for today

My own sense is that we will move towards a view of Amazonia not as an exception, in line with the old view that the people lived within an untouched paradise, but as part of a broader pattern of human-environment interaction. The rainforest will be understood not only as a biological system, but as a historical one – shaped, in part, by the people who lived within it.

This does not mean the Amazonian people who simply lived “in harmony” with nature; the evidence points to something more interesting. Although Amazonian societies developed complex, and at times intensive, forms of land use, the evidence consistently shows that they often did so while maintaining continuous forest cover. Far from the large-scale deforestation that we might assume was necessary for such elaborate forms of human life, their practices created mosaics of managed forest, gardens, orchards, wetlands and settlement areas.

We know partly from lake sediment data that people enriched the forests with species that provided food, building materials, medicines and other resources, from açaí and cacao to palms, cinchona and copaiba. The fact that some of these species endure today suggests that past land use left lasting ecological legacies.

In the context of today’s climate crisis, the long-term balance that these people achieved offers a powerful lesson: it is possible to sustain complex societies without destroying the forest, if land use is guided by principles that integrate ecological knowledge, cultural values and a commitment to the continuity of the living landscape.

What lies beneath the Amazon is not just a hidden past. It is a reminder that even the most seemingly untouched landscapes can carry deep histories, waiting – sometimes just beneath our feet – to be revealed.

 

 

This article is republished from The Conversation under a Creative Commons license.  Original article.

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Early asteroid strikes were responsible for significant changes in Earth’s crust, which was primarily basaltlike at the time. Shock waves from collisions fractured the crust and increased porosity, allowing fluids and gases to move through the rocks. Prior research suggests that the resulting hydrothermal systems—such as the network of geysers around Yellowstone National Park—provided the environment for the origin and evolution of early life on Earth.

New research ¹ explored how surface impacts during the Hadean and Archean allowed fluids and gases to move through crustal environments. The authors built a large suite of impact simulations with the iSALE shock physics code, varying parameters such as basalt crust thickness, geothermal gradients and the presence or absence of a 5-kilometer-deep (3-mile-deep) ocean.

The simulations detailed how collisions on the surface shaped permeability in the crust. The researchers then integrated a model for ancient bombardment data to understand the cumulative effects of repeated strikes over time.

The results indicate that before 4.3 billion years ago, impacts may have made the crust far more permeable, particularly in its top 8 kilometers (5 miles). From the simulations, the authors inferred that the size of permeable regions depended on impact energy and that geothermal gradients and rock composition in the crust affected the degree of fragmentation after impact. These porous domains formed potential settings for prebiotic chemistry within the early crust.

The research is the first comprehensive study of impact-generated permeability in early Earth’s outermost layer. The results provide a novel framework for evaluating how bombardment influenced hydrothermal circulation and geochemical alteration during the Hadean and Archean eons, with implications for understanding the origin and evolution of life in Earth’s earliest days.

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In our previous entry, I explicated two different concepts that in many languages are subsumed under a single term ‘life’, or equivalent, but that in ancient Greek were separated as two truly distinct things: zoé, or life in the biological sense, and bíos, or life in the biographical sense. I argued that these two things, or properties of a living being, lead to very different ways of ethically evaluating that being and its circumstances, and in particular, that the distinction between bíos and zoé explains our strong intuitions about why there are certain ways of dying, and of being treated after death, that can be considered dignified or undignified.

Before considering the other temporal extremes of human life (i.e., birth or conception), this reference to our intuitions allows me now to point to the fact that we usually make these kinds of moral considerations in a largely pre-reflective way —that is, they are emotional judgments rather than logical conclusions drawn from purely abstract and ‘cold’ philosophical arguments— and that is not a bad thing. After all, even the many ethical evaluations we make in a clearly reflective and dialogically developed manner must ultimately be based on premises or principles that we accept because we feel it would be undignified and aberrant to deny them. In the cases under consideration, our system of moral emotions leads us to intuitively value life in the sense of bíos as ethically more relevant than life in the sense of zoé, even though philosophical and metaethical speculations often push us to accept moral norms that may appear prima facie contrary to those intuitions (for example, when some people claim that intensive livestock farming is a crime exactly as aberrant as the Holocaust, or even more so; cf. ¹).

My argument does not seek to assert that we must in every case give priority to our pre-reflective moral emotions over norms developed through abstract philosophical construction; I merely note that there can be a tension between the two, and that it is not set in stone that in every case and without exception the apparently logical conclusions of philosophical argumentation must prevail over our more intuitive and pre-reflective moral emotions.

Returning to our topic, I believe that similar reflections can be made with respect to the other end of what we call the “limits of life,” that is, its beginning rather than its end. As I noted above, the fact is that we attribute a much higher value to human life than to animal life because the former is not only “organic life” (and not even only “sentient life”), but “life with meaning,” a “life story,” and this means that, in the system of moral emotions of many people, the magnitude of the “moral harm” involved in ending the life of a human embryo of only a few days or weeks, just as in the case of a patient in the final stages of Alzheimer’s disease, for example, is considerably smaller than that involved in the death of other human beings. It is not that these people (among whom I confess I include myself) consider that this “moral harm” (that is, the death of the embryo or of the incurably ill and suffering patient) is totally irrelevant from a moral point of view, but simply that our negative emotional reaction towards someone who decides to have an abortion, or who decides to end the suffering of a beloved dying person with total dementia, is not severe enough to drive us to categorically prohibit such acts.

After all, the embryo does not yet have a bíos (or, for example, if the abortion is justified by some genetic malformation, it is reasonable to think that the bíos it would have if born would not be minimally dignified), just as we can say that the severely ill Alzheimer’s patient no longer has one, except insofar as it may persist in the memory of their loved ones. What abortion or euthanasia takes away from these beings is only a zoé, something that we feel society has a certain right to allow to be eliminated if doing so produces or promotes some other “good” that we consider sufficiently relevant from a moral point of view (for example, in the case of abortion, avoiding serious inconvenience and psychological suffering for the mother or the child, and in the case of euthanasia, sparing the dying person pain).

I suspect that this emotional reaction is shared even by the vast majority of people who would like these practices to be absolutely prohibited. This is shown, for example, by the fact that —with the exception of a tiny minority among the most fanatical anti-abortion activists— almost no one calls for abortion to be considered, from a criminal-law perspective, a type of murder, but rather, at most, a lesser offense, which would certainly be illogical if we think that in the case of abortion, if the embryo or fetus truly had the status of a full person, the conditions for classifying the act as one of the most serious forms of murder (premeditation, defenselessness of the victim, etc.) would clearly be present. Nor does almost anyone “fight against abortion” in the way they surely would if the government suddenly decided that one out of every ten children under the age of three had to be killed; the usual slogans according to which abortion is a kind of “genocide” or “holocaust” clash head-on with the fact that those who make such claims do not consider it worthwhile to respond in the same way and with the same resolve as, for example, armed civil resistance to the Nazi army did on numerous occasions, which strips those accusations of “genocide” bare and reveals them as a crude rhetorical strategy.

Similarly, at the other end of human life, almost no one objects to people in very advanced stages of Alzheimer’s disease receiving less invasive medical treatment than other patients with better prognoses, whereas if their lives truly had as much value as those of these other patients, it would be completely discriminatory not to devote exactly the same effort and the same resources to them. That is to say, these “defenders of the value of life” find within themselves, at least at the emotional level, that the value they assign to some lives is nowhere near as high as the value they assign to others, even though they allow themselves to be guided by whatever philosophical or religious theory they have adopted to explain to themselves what makes things right or wrong (e.g., the “theory” that “human life is sacred under any circumstances,” or something similar). The fact that this theory fits poorly with many of their own moral emotions does not strike them as a sufficiently serious problem, and of course everyone is free to live with their contradictions.

Naturally, all these reflections leave completely open the question of what the limits should be exactly (that is, the length of pregnancy, or the severity and irreversibility of an illness) before or after which abortion and euthanasia should be considered crimes, and it is reasonable that the social agreements reached on these matters should take into account the very wide diversity of opinions. But I think it is honest to acknowledge that almost all of us emotionally experience an almost total moral indifference when abortion and euthanasia take place as close as possible to the extremes: I do not think that anyone in their right mind would believe that a woman who takes a medication that merely prevents the implantation of a fertilized egg in the uterus, or the doctor and family members who decide to administer to a dying person a dose of painkillers so high that, in addition to relieving pain, it will certainly accelerate their death by a few hours or a few days, should be punished with the same penalties established for the worst cases of murder. The debate over when abortion and euthanasia are justifiable or socially acceptable should always begin with the recognition that this is what almost all of us experience emotionally, and only later allow arguments based on more abstract premises to enter the discussion.

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The original Hong–Ou–Mandel experiment

The original Hong–Ou–Mandel experiment, carried out by physicists Chung-Ki Hong, Zhe-Yu Ou, and Leonard Mandel at the University of Rochester, involves two identical photons arriving simultaneously at a beam splitter, an optical device that normally sends each incoming particle randomly to one of two outputs. Classical reasoning suggests each photon should independently choose a path, sometimes landing in different outputs. Quantum mechanics predicts something strikingly different. If the photons are truly indistinguishable, the two paths by which they could exit separately cancel each other out through destructive interference. The result: both photons always emerge together from the same output port. This counterintuitive bunching behavior, impossible to explain without quantum mechanics, has since become a cornerstone of quantum optics and a key tool in quantum information science.

The atomic equivalent of a paired photon input

The new work explores what happens when this idea is extended far beyond two particles. Instead of photons, the experiment uses ultracold rubidium atoms gathered into a Bose–Einstein condensate, a state of matter first predicted in 1924 by Satyendra Nath Bose and Albert Einstein, and first created in the laboratory in 1995. In a Bose–Einstein condensate, a gas of atoms is cooled to temperatures just a tiny fraction of a degree above absolute zero, so cold that the atoms lose their individual identities and collectively occupy the same lowest-energy quantum state, behaving as a single coherent quantum entity. Through a process called spin-changing collisions, in which pairs of atoms are created simultaneously in two distinct quantum spin states, the experiment reliably produces states where exactly equal numbers of atoms occupy each of those two modes. These balanced, paired states are the atomic equivalent of the paired photon inputs used in the original Hong–Ou–Mandel setup.

A matter of counting

A major obstacle has long prevented such experiments from reaching larger numbers of atoms: counting them accurately enough. Quantum interference involving many particles produces very specific statistical patterns, and even small detection errors can obscure or mimic the effect. The key technical achievement of this research is a fluorescence-detection method capable of resolving individual atoms with a counting uncertainty far below one ato (specifically, just 0.2 atoms on average). Atoms released from the trap scatter light from carefully tuned laser beams; a high-quality camera captures that glow and translates it into an integer count of atoms in each output channel. This single-atom resolution is the critical enabling step for everything that follows.

After preparing equal numbers of atoms in two input modes, the experiment mixes them using a precisely timed sequence of microwave pulses, the atomic analogue of the beam splitter. Quantum theory predicts a striking outcome. Certain combinations of atom numbers in the two outputs should almost never appear, while others become unusually probable. In particular, only even numbers of atoms should appear in each output channel, creating a distinctive checkerboard-like pattern in the measurement statistics. The experiment revealed exactly this behavior for systems containing up to twelve atoms, providing a direct observation of many-particle Hong–Ou–Mandel interference in an atomic platform.

Bosonic bunching

The results also demonstrate a phenomenon known as bosonic bunching. Because the atoms are bosons (the same category of particles as photons, characterized by an integer quantum spin) they have a natural tendency to crowd into the same quantum state. After interference, outcomes in which many atoms gather at the same output become far more probable than classical reasoning would suggest. This collective behavior is a hallmark of quantum statistics and becomes increasingly pronounced as the number of particles grows.

Multipartite entanglement

Beyond demonstrating an elegant quantum effect, the experiment probes one of the most important resources in modern quantum science: entanglement. Entangled particles cannot be described independently; their properties are linked through a shared quantum state in ways that have no classical counterpart. By analyzing the measured atom-number distributions, the experiment shows that the generated states possess genuine multipartite entanglement, meaning the entanglement involves more than just pairs of particles. For systems containing up to eight atoms, the evidence indicates that all atoms participate in a single, fully entangled state. Even for twelve atoms, at least ten are certified to be mutually entangled.

The significance of this entanglement becomes clear when considering precision measurements. In ordinary, classical measurements, unavoidable statistical noise means that doubling the number of particles only improves the measurement precision by a factor of roughly 1.4 (the square root of two). Quantum entanglement can do much better. The ultimate limit allowed by quantum mechanics is known as the Heisenberg limit, where measurement error decreases in inverse proportion to the total number of particles, a quadratic improvement over the classical case. Reaching this regime is a central goal of a field called quantum metrology.

Metrological potential

To test the metrological potential of their states, the experiment measured the quantum Fisher information, a quantity from probability theory and quantum mechanics that captures how sensitively a quantum state responds to small changes in a physical parameter. The higher the Fisher information, the more precisely that parameter can be estimated. The observed Fisher information grew with the number of atoms following a scaling exponent of approximately 1.95, remarkably close to the theoretical value of 2 expected at the Heisenberg limit, and well above the classical scaling of 1. For twelve atoms, this represents a sensitivity enhancement of 6.4 decibels beyond what is achievable without entanglement.

Scalable capabilities

These results mean that it is certainly possible to combine three capabilities that are rarely achieved simultaneously: negligible particle loss, single-atom detection, and controllable many-particle interference. Photonic experiments have demonstrated related effects before, but photon loss and imperfect indistinguishability become increasingly problematic as particle numbers grow, ultimately limiting how large such experiments can be scaled. Neutral atoms offer a promising alternative: they can be trapped, manipulated, and detected while retaining exceptionally high fidelity, and the platform is in principle scalable to hundreds or thousands of atoms.

This experiment therefore represents more than a new demonstration of a textbook quantum effect. It shows that large groups of identical atoms can be prepared, interfered, counted one by one, and used to generate highly entangled states with near-optimal measurement sensitivity. Such capabilities point toward future quantum sensors, high-precision atom interferometers, and fundamental tests of quantum mechanics (including multiparticle Bell tests) operating in regimes that were previously inaccessible.

Author: César Tomé López is a science writer and the editor of Mapping Ignorance

Disclaimer: Parts of this article may have been copied verbatim or almost verbatim from the referenced research paper/s.

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Kovi Rose, University of Sydney

A pair of stars spiralling around each other. That’s the origin of a new source of repeating radio bursts we’ve detected, called ASKAP J1745.

In recent years, astronomers have been puzzling over mysterious bursts of radio signals, known as long-period transients because of how slowly they repeat. They were first discovered by chance with telescopes scanning large chunks of the sky.

To date, astronomers have only found a dozen of these weird sources, and we’re still trying to understand exactly what they are.

In a new study published in Nature Astronomy, we describe a first-of-its-kind detection – both radio and X-ray bursts repeating with each orbit.

ASKAP J1745 is exciting because we’ve figured out what it is, unlike 10 of the 12 known long-period transients. Even better, we were able to detect it with a bunch of different telescopes that observe all different kinds of light.

Bearing the same message in three forms of writing, the famous Rosetta stone once helped scholars decipher ancient Egyptian hieroglyphs. Similarly, this extra information we found about ASKAP J1745 will help astronomers better understand the mystery of all long-period transients.

What do long-period radio transients look like?

Long-period transients are things in space that produce bright, repeating bursts of light at radio wavelengths. Little is known about the origins of most long-period transients. In addition, many have been discovered close to the dusty region in the middle of our galaxy, so it can be hard to see them with visible-light telescopes.

Even with just a dozen of these strange sources discovered so far, they seem to come in a few different shapes and sizes. Their radio bursts repeat on timescales of minutes to hours.

Some have been making regular pulses for more than 30 years, while others turn off for days at a time or go permanently radio-silent.

Where do they come from?

Astronomers initially thought long-period transients were just very slowly spinning neutron stars, called pulsars. These are the fast-rotating dense cores left after the supernova explosions of massive stars.

The first few of these radio transients discovered were repeating roughly every 20 minutes. That’s much slower than the average pulsar, which repeats every few seconds.

Furthermore, when pulsars slow down their spin, they should stop producing radio light. This means we shouldn’t see radio bursts from neutron stars rotating so slowly.

So astronomers investigated other theories involving white dwarfs – the slowly cooling dead centres of less massive stars. And recently we discovered some long-period transients in binary systems (two stars in a close orbit) with evidence of both a white dwarf and a lower-mass red dwarf star.

The discovery of ASKAP J1745

ASKAP J1745 is a new long-period radio transient we found with the ASKAP radio telescope, owned and operated by CSIRO, Australia’s national science agency. It’s the first one of these strange sources that we’ve identified as a “cataclysmic variable”.

Cataclysmic variables are systems with two stars – one of them a white dwarf – that orbit each other closely enough to interact. If the stars are close enough, the white dwarf’s gravity can pull (or “accrete”) material from the other star. That’s why these systems are also known as accreting white dwarf binaries.

Another long-period radio transient was recently discovered with X-ray bursts, repeating with the same regularity as the radio. However, the origin of the bursts and their shared timing remained unclear.

Now, for the first time, we have combined observations from radio, X-ray and optical telescopes to find that ASKAP J1745 produces both X-ray and radio bursts with each orbit of its two stars.

In these rapidly orbiting systems, the X-ray light is thought to come from the material heating up as it streams onto the white dwarf.

The bright radio bursts were a bit more of a mystery. But knowing that this is an accreting binary system helped us figure things out.

The type of pulsed radio light we detected is typically caused by energetic particles interacting with strong magnetic fields. Here, we have the perfect combination: two stars with strong magnetic fields (typically thousands of times stronger than an MRI machine), with charged particles flowing towards the white dwarf from the other star.

What this means for the future of astronomy

This discovery is unique because we have more information and at more different wavelengths than any other previous long-period transient.

Just like the Rosetta stone was key to decoding ancient Egyptian symbols, ASKAP J1745 will be key to deciphering the origins of other long-period radio transients that lack information at other wavelengths.

ASKAP J1745 is the first long-period transient showing signs of accretion across the spectrum of light – from radio waves to visible to X-rays. And this stream of charged material is a crucial ingredient for making the radio light we detect from these systems.

Exploring the mechanism that produces long-period radio bursts gives us a new laboratory to learn about extreme physics such as plasma flows and magnetic fields in conditions we can’t recreate on Earth.

We acknowledge the Wajarri Yamaji as the Traditional Owners and Native Title Holders of Inyarrimanha Ilgari Bundara, the CSIRO Murchison Radio-astronomy Observatory where ASKAP is located.

 

This article is republished from The Conversation under a Creative Commons license.  Original article.

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The researchers analyzed two decades of water quality observations collected between 2001 and 2021 across Biscayne Bay.

“Biscayne Bay is changing in measurable ways as climate change accelerates,” said co-author Maria Josefina Olascoaga, a co-author of the study and a professor in the Department of Ocean Sciences at the Rosenstiel School. “We observed that parts of the bay are becoming saltier and warmer, while pH levels are declining, making the water more acidic. These changes can affect seagrasses, fisheries, wildlife, and the broader coastal ecosystem that South Florida communities depend on.”

The researchers evaluated long-term records of salinity, temperature, dissolved oxygen, and pH collected monthly from 34 monitoring stations throughout the bay. They compared changes across decades, seasons, and geographic regions of Biscayne Bay to identify climate-related trends.

The findings show a significant increase in salinity across several regions of Biscayne Bay, especially near canal mouths, where researchers also detected saltwater intrusion in bottom waters. Water temperatures rose throughout the bay, with North Bay warming the fastest. Overall, median temperatures increased by 0.5 degrees Celsius during the study’s second decade.

Researchers also documented declining pH levels in most areas, indicating a growing influence of ocean acidification. Together, these changes point to a shift away from historically fresher, estuarine conditions toward saltier, warmer, and more ocean-like waters, reflecting the combined effects of climate change and sea level rise.

Long-term environmental monitoring is critical to understanding how a changing climate is affecting Biscayne Bay at the local level, providing data that help communities and resource managers anticipate and prepare for future impacts on coastal ecosystems and water resources. The authors note that these findings can also inform decisions on water management, restoration projects, and coastal protection efforts aimed at strengthening the bay’s resilience.

Biscayne Bay encompasses approximately 429 square miles within the boundaries of Miami-Dade County and the City of Miami. It supports South Florida’s economy, tourism, fisheries, recreation, and wildlife habitats. In 2025, scientists from the Shark Research and Conservation Program identified Biscayne Bay as essential nursery habitat for juvenile great hammerhead sharks. The bay also plays a critical role in regional environmental health, including seagrass ecosystems, which are crucial sources of shelter and food for tiny invertebrates, fish, crabs, sea turtles, manatees, and other marine mammals.

Furthermore, the bay offers coastal resilience for Miami-Dade County. Rising salinity and temperature may place additional stress on aquatic organisms and habitats already experiencing environmental pressures.

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One of the principal values of philosophical thought has traditionally been the promotion of conceptual clarity: helping us to understand as well as possible what it is we are thinking when we think what we think. In the debate over the moral aspects of the limits of life, it is therefore important to reflect on the main concept at stake: the concept of life. It is neither necessary—nor probably possible—to arrive at a definitive definition of that concept, but it is indeed advisable to make the greatest possible effort to clarify the potential ambiguities to which our thinking and our discourse may be subject, often unconsciously, when we use an idea that is supposedly so clear. As I have argued in one recent book, the main reason why we tend to assign a qualitatively and quantitatively very different moral value to human lives than to the lives of other animals or living beings is the fact that, although both possess “life” in the sense of the ancient Greek concept of zoé (that is, biological life—what distinguishes a living entity, not only animals but also plants, fungi or bacteria, from an inanimate entity), only humans possess “life” in the sense of the ancient concept of bíos (that is, biographical life, a life that understands itself as a story).

The key element in this difference is, naturally, our capacity for language, since without language there are no stories worth speaking of; after all, one of the most universal ethical norms is the one that says that if an entity can talk to you, you should not eat it—not to mention the many major moral theories philosophers have developed on the basis of our rational capacity (the Greek lógos) to explain not only our capacity for moral judgment (that is, our status as moral agents), but also our nature as beings endowed with moral dignity. Of course, the boundaries are not completely sharp and well-defined, as nothing ever is in nature or in society: the question “which was your first ancestor who intrinsically possessed a right to life—that is, whom it would have been morally wrong to sacrifice and eat?” is difficult to answer both for those who think that only humans possess that right, and for those who think only animals do, or even for those who believe it is an intrinsic right of every living being. But for thousands of years we have managed quite well to function in society using more or less fuzzy concepts and negotiating diffuse boundaries on a case-by-case basis when we encounter them, so neither in this case does the problem of delimitation necessarily obscure the relative clarity with which we can generally apply in most cases, without much difficulty, the distinction between bíos and zoé.

This radically different moral status between humans and animals, based on the fact that the former have a biography and the latter do not, can be illustrated even with examples that do not refer to the question of whether a given being possesses a right to life. Consider the case of a simple corpse. If we find a human corpse whose identity we cannot ascertain, it seems that we have a moral duty to treat it with a minimum of dignity, including, at the very least, not leaving it exposed to the elements and at the mercy of scavengers. By contrast, if we are walking through the countryside and come across the corpse of a rabbit (say), it does not occur to us that we have an obligation to bury it with dignity or anything of the sort, nor does it seem wrong to us to leave it where it is so that within a few hours it will have been devoured by other animals (who also have a right to eat… as long as they are not feeding on humans). Having an ethically decorous post-mortem status seems to us to be an essential part of what constitutes a humanly dignified life. This is precisely the sense of the recent controversy sparked by the British Museum’s decision to stop calling the Egyptian mummies on display “mummies” and instead label them “mummified persons,” something that does not appear likely to be imitated by the neighboring Natural History Museum by renaming fossils as “fossilized animals” (I am referring, of course, to animal fossils; although, to be honest, I do not know whether the British Museum is also going to call the mummies of cats or crocodiles “mummified animals,” an expression which, if I am not mistaken, may already have been in use—not so much out of moral respect for the corpses of those creatures, but because calling them “mummies” might initially lead us to think they were human mummies… which, if that were the case, would mean that the semantics of the word “mummy” already by default includes the sense of “person” or “human being,” making the recent terminological decision redundant).

From these reflections, some might conclude that since we continue to regard human beings as “worthy of respect” even after death, it follows all the more that their lives must be respected while they are alive, and therefore that causing the death of a human being is never ethically justifiable—not even in cases of euthanasia or abortion that many people do accept. The error in this reasoning lies in continuing to assume the mistaken premise that what gives human life its dignity is biological life (zoé), rather than biographical life (bíos). Obviously, the dignity with which we believe a human corpse must be treated does not stem from the fact that the entity is biologically alive (for the very fact of no longer being alive is what makes it a corpse), but rather from our sense that bíos and zoé do not necessarily coincide in a precise manner: it is instead the fact that a person’s biography does not automatically end with their biological death (that is, the fact that even after death we can continue to regard her as “part of our community”) that leads us to accept the moral obligation to continue treating the person with respect even after she has died.

Similarly, the very process of dying can occur in ways that are more dignified or more undignified, and for many people what is most undignified of all is being reduced to what some authors (starting with the Italian philosopher Giorgio Agamben) have called bare life (or nuda vita) to a mere biological life in which only some vital functions remain, while almost everything that defined the person as a free and autonomous subject has disappeared. Of course, some people may feel that consciously or semi-consciously experiencing the intense suffering that can accompany such a state is part of their dignity, and they have every right to be allowed to continue suffering if that is their wish, or if that is how they interpret the teachings of their religion, or whatever. But other people have the same right not to go through that ordeal, or to do so in the shortest and least painful way possible. “They died quickly and without pain, when nothing but a long period of unbearable suffering awaited them, and were then mourned with respect” is something that many people would consider a fairly dignified ending to their biography, or at least far more dignified than the alternative of an endless agony.

In the next entry we shall apply the bíos – zoé distinction to the other extreme of human life, i.e., birth and conception.

References

Agamben, Giorgio, 1998, Homo sacer: sovereign power and bare life, Stanford University Press.

Zamora Bonilla, Jesus, 2021, Contra apocalípticos: ecologismo, animalismo, posthumanismo, Shackleton Books.

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This ultrafast process is known as intramolecular vibrational redistribution. When one vibrational mode is excited, its energy spreads into other vibrations through subtle couplings that arise from the anharmonic nature of molecular motion. Real molecules do not behave like perfectly independent springs. Their vibrations interact, allowing energy to travel through the molecule. Understanding these pathways is essential for any attempt to steer chemistry at the molecular scale.

New research ¹ explores whether intramolecular vibrational redistribution can be detected in a single molecule using highly sensitive optical techniques based on surface-enhanced Raman spectroscopy, or SERS. Raman spectroscopy works by shining laser light on a molecule and measuring the frequency shifts that appear when photons exchange energy with molecular vibrations. Normally these signals are extremely weak, but metallic nanostructures can concentrate electromagnetic fields — through a quantum optical phenomenon called plasmon resonance — into nanoscale regions and amplify the interaction enormously. In carefully engineered structures, the signal becomes strong enough to detect a single molecule.

The study places a molecule inside a plasmonic nanocavity: a tiny gap, roughly one nanometer wide, between metallic structures that trap light very efficiently. The concentrated electromagnetic field inside this gap strongly enhances Raman scattering. The theoretical model combines quantum optics with molecular vibration theory to describe how light, cavity modes, and molecular vibrations interact simultaneously.

A molecular coupling with a long history

Particular attention is given to a mechanism called a Fermi resonance. This occurs when the energy of one vibrational mode nearly matches the combined energy of two quanta of another vibration, causing the two states to become strongly coupled. Rather than behaving independently, they mix into hybrid states that can exchange energy efficiently. The phenomenon is named after physicist Enrico Fermi, who first explained it in 1931 to account for unexpected doublings in the spectrum of carbon dioxide.

One signature of this coupling can appear directly in Raman spectra. What would otherwise be a single spectral peak can split into two nearby peaks, forming what is known as a Fermi doublet. However, in realistic molecules the splitting is often small and difficult to distinguish from coincidental overlaps with other spectral features. The work therefore investigates whether the time evolution of vibrational populations offers clearer evidence of intramolecular vibrational redistribution.

Two strategies to catch energy in motion

Two pump-and-probe strategies are analyzed. In the first, visible laser pulses excite molecular vibrations through Raman scattering itself. Stokes Raman processes deposit energy into a vibrational mode, while anti-Stokes Raman scattering — which requires the molecule to already be vibrationally excited — reveals how the vibrational populations evolve over time. The calculations show that when one vibration is pumped strongly, energy flows into a second coupled vibration through the Fermi resonance, producing a measurable increase in the anti-Stokes signal associated with that second mode.

Under pulsed excitation, the dynamics become especially revealing. After the laser pulse excites one vibration, the energy oscillates back and forth between the two coupled vibrational states before eventually dissipating. These oscillations closely resemble Rabi oscillations, a well-known quantum mechanical phenomenon in which two coupled quantum systems coherently exchange energy. In the molecule studied, the predicted oscillation period is about 1.5 trillionths of a second — a timescale that falls within the detectable range of current experiments.

Another important signature is a delayed buildup of population in the secondary vibration. The first vibration is excited almost immediately by the laser pulse, but the second gains significant population only after energy has been transferred through the Fermi resonance pathway. This delay, lasting several hundred trillionths of a trillionth of a second (hundreds of femtoseconds), provides direct evidence that the second mode is populated through intramolecular vibrational redistribution rather than by direct optical excitation.

The study also investigates a second approach using infrared pumping. In this configuration, an infrared cavity mode resonantly drives a specific molecular vibration directly, while visible-light Raman scattering simultaneously probes the resulting populations. Infrared excitation drives the selected vibration into a coherent quantum state, producing a sharp and intense anti-Stokes signal. At higher pumping strengths, population transfer through the Fermi resonance again enhances the Raman signal of the coupled vibration, revealing the underlying intramolecular vibrational redistribution pathway with a clarity that pure spectral inspection cannot provide.

Within reach of experiments

The calculations use realistic parameters for gold and silver plasmonic nanocavities and for a molecule commonly studied in SERS experiments: 4-nitrobenzenethiol. The predicted coupling strengths, vibrational lifetimes, cavity losses, and field enhancements are all consistent with values reported in current experiments. The work therefore suggests that observing intramolecular vibrational redistribution at the single-molecule level may already be within reach of existing nanophotonic platforms, particularly when operated at cryogenic or near-cryogenic temperatures where thermal noise is reduced.

Beyond spectroscopy, the results point toward a broader ambition: controlling how energy moves through molecules. If individual vibrational pathways can be monitored and eventually manipulated, it may become possible to direct chemical reactions with unprecedented precision. Nanophotonic cavities could then act not only as ultrasensitive detectors, but also as tools for engineering molecular dynamics themselves — turning what was once an invisible and uncontrollable process into something that can be seen, studied, and ultimately steered.

Author: César Tomé López is a science writer and the editor of Mapping Ignorance

Disclaimer: Parts of this article may have been copied verbatim or almost verbatim from the referenced research paper/s.

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Last week, OpenAI shocked the mathematical community by revealing that one of its internal artificial intelligence (AI) models had found a counterexample to a famous conjecture made by legendary Hungarian mathematician Paul Erdős in 1946.

The planar unit distance problem, or Erdős problem 90, has intrigued mathematicians for decades. The new result is no mere curiosity. Canadian mathematician Daniel Litt described it as “the first result produced autonomously by an AI that I find interesting in itself”.

The breakthrough, produced with a general-purpose AI model rather than one specialised for mathematics, also highlights how AI is changing mathematical research itself. Days after OpenAI’s paper, US mathematician Will Sawin followed the same line of reasoning to an improved result. Also last week, a team from Google DeepMind used one of their own models to resolve nine lesser open problems left by Erdős.

At the same time, results like this show us what kind of mathematics current AI models are good at – and where their capabilities are still uncertain.

Dots and lines

Paul Erdős was one of the most prolific mathematicians of the twentieth century. He was famous for asking deceptively simple questions whose solutions often resisted decades of effort.

At first glance, the underlying problem seems relatively straightforward. Suppose you have some number of points – call the number n – drawn on an infinitely large piece of paper. Given you can arrange the points any way you like, how many pairs of points can be positioned exactly one unit of distance away from each other?

If you try this problem yourself (on a presumably finite piece of paper), you may quickly gravitate towards a square grid as a promising candidate for the best arrangement. The spacing of the grid naturally creates many pairs at a regular distance apart.

This intuition influenced much of the early thinking about the problem. As the number of points grows, grid-like arrangements continue to appear to be remarkably effective.

For decades it was widely believed these highly regular structures were about as good as it gets. Erdős himself conjectured that no construction could improve substantially on these intuitive arrangements, even for an extremely large number of points. (The new best result, by Sawin, reportedly only starts to yield improvements for around 10^2000000 points – that’s a one followed by two million zeroes.)

Over the past 80 years, mathematicians have tried to prove Erdős either right or wrong. Their efforts have linked the problem to other areas of mathematics called incidence geometry, graph theory and extremal combinatorics. While a full proof remained elusive, there was a general feeling that Erdős’ conjecture was probably true.

However, OpenAI’s recent breakthrough proved Erdős’ intuition wrong. The new result uses tools from an area of mathematics called algebraic number theory to show there are patterns of dots that involve many more unit-distance pairs than the square grid, for infinitely many values of n.

No hesitation

In an article OpenAI published alongside the new paper, several leading mathematicians remarked on the result.

Fields Medallist Timothy Gowers wrote that if a human researcher had submitted the paper with this result to the prestigious journal Annals of Mathematics, he would have recommended publication “without any hesitation”. He also added that no previous AI-generated proof had come close to this level of sophistication.

This breakthrough also represents the first major mathematical open problem solved with AI with minimal human intervention beyond the initial prompt. The accompanying paper shows the prompt given to the model, as well as a recount of the “chain of thought” conducted by the model.

This has renewed broader questions about the capabilities of AI to aid in, and perform, mathematical research.

Three keys to mathematical research

Research mathematicians have been using computers for a long time, but their work is rarely driven by computation alone. Most major breakthroughs emerge from a delicate combination of three things: expertise developed over years, sustained effort to apply that expertise creatively to explore ideas (many of which turn out to be dead ends), and occasional conceptual leaps that suddenly reorganise how a problem is understood.

The first two are domains where AI models excel: as noted by Gowers, large language models such as ChatGPT have an “encyclopaedic knowledge of mathematics”. Moreover, they can follow huge numbers of speculative lines of enquiry, even those unlikely to lead anywhere, without human time constraints.

The latter seems to be what provided the key to success here. In hindsight, it seems an expert given a small number of hints would be likely to be able to reach the same proof. As Gowers notes:

Many of the ideas needed for the proof were present in the literature already, and for such ideas either no hint is needed, since the expert is aware of that piece of literature, or a highly generic “look it up” hint would be enough.

Lightbulb moments

The harder question is how much AI can contribute to genuine conceptual leaps. These acute moments of insight, where a lightbulb moment reframes a problem in an entirely new way, are often seen as the most human part of mathematics.

These leaps are hard to formalise and even harder to predict. It remains unclear whether AI models can replicate them, even with recent advances.

What is clear is that AI models are causing a seismic shift in the way mathematics is discovered.

For centuries, progress in mathematics depended almost entirely on human creativity and persistence. Now, for the first time, researchers are working alongside systems capable of autonomously exploring enormous spaces of ideas and contributing to problems once thought accessible only to human insight.

 

This article is republished from The Conversation under a Creative Commons license.  Original article.

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The entanglement-is-just-a-wormhole idea

The initials point back to two landmark ideas from 1935. “ER” refers to Einstein and Rosen’s proposal of bridges or wormholes, as they are known today, hypothetical tunnels linking distant regions of spacetime. “EPR” refers to the famous paper by Einstein, Podolsky, and Rosen on quantum entanglement, the puzzling phenomenon in which two particles can share a single quantum state, instantly correlated even when far apart.

For decades these concepts lived in separate worlds. Wormholes belonged to Einstein’s theory of gravity. Entanglement belonged to quantum mechanics. But in recent years, physicists exploring quantum gravity have found hints that spacetime geometry may itself emerge from quantum entanglement. In this view, the fabric of space and time is not fundamental but arises from deep quantum connections.

The ER = EPR conjecture takes this further. It proposes that whenever particles are entangled, they are connected not just by shared quantum information but by an actual, though quantum-scale, wormhole. These would not be tunnels you could travel through, but subtle geometric links in spacetime.

How to test the ER = EPR conjecture

Testing such an idea seems extraordinarily difficult. Yet two physicists, Irfan Javed and Edward Wilson-Ewing, have proposed a clever way ¹ to look for its possible effects using the simplest atom in nature: hydrogen

Hydrogen consists of one proton and one electron. Because of its simplicity, physicists have measured its properties with breathtaking precision over many decades. Its energy levels and transitions have served as crucial testing grounds for quantum theory since the early 20th century.

According to ER = EPR, if the electron in a hydrogen atom is entangled, a quantum wormhole should exist. The researchers make a reasonable but unproven assumption: some of the electric field surrounding the electron might leak into this wormhole. To an outside observer who cannot access the wormhole, the electron would appear to have a slightly reduced electric influence, as if its effective charge were a tiny bit smaller.

This small change would affect the attraction between the proton and electron. The atom would become ever so slightly larger. More importantly, it would alter the atom’s energy structure in measurable ways.

Hyperfine structure and net charge

The most sensitive test comes from the hyperfine structure of hydrogen—the tiny energy differences caused by the interaction between the spins of the proton and electron. One famous transition produces the 21-centimeter radio wave that astronomers use to map hydrogen clouds across the galaxy. This frequency has been measured to extraordinary accuracy, with no unexplained deviations.

If electric field leakage occurred, the hyperfine splitting would shift slightly. The fact that we see no such shift places strong limits on how large any such effect can be. The researchers also consider the electrical neutrality of the hydrogen atom. Experiments show that the positive charge of the proton and the negative charge of the electron cancel each other with remarkable precision. If some of the electron’s electric field disappeared into a non-traversable wormhole, the atom would carry a tiny net charge, something that has never been observed. This neutrality provides an even tighter constraint.

Assumptions are key

The paper concludes that, under their assumptions, any leakage effect must be extraordinarily suppressed. The wormhole connection, if it exists, has almost no noticeable impact on the everyday behavior of the hydrogen atom.

Importantly, the authors emphasize that their work relies on specific assumptions about how wormholes and entanglement might interact with electric fields. They assume the effect matters for point-like particles such as the electron but not for larger composite objects like the proton. They also focus on non-traversable wormholes, as originally suggested in the ER = EPR proposal, though they briefly discuss traversable cases in an appendix.

Unresolved

This research does not prove or disprove ER = EPR. No direct evidence for microscopic wormholes has been found. What it does show is how precision measurements in ordinary laboratory systems can begin to test ideas once thought to belong only to the most extreme environments, namely black holes or the early universe.

Hydrogen played a starring role a century ago in the birth of quantum mechanics, when its spectral lines helped physicists move beyond classical physics. Today, the same humble atom is helping scientists probe an even deeper question: whether the structure of spacetime itself is woven from quantum entanglement.

The work illustrates a hopeful trend in modern physics. Even the most exotic ideas about quantum gravity may eventually face the quiet judgment of high-precision experiments in a lab. Whether ER = EPR survives these tests or not, the conversation between theory and experiment continues.

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How can scientists see the intricate details inside cells far too small for regular light microscopes? A powerful technique called expansion microscopy ¹ is revolutionizing how researchers study tiny organisms from plankton to developing embryos.

Making the invisible visible

Expansion microscopy works by doing the opposite to what we had been doing until now: instead of using more powerful lenses to see smaller structures, scientists physically expand the samples themselves. To do so, they embed cells or tissues in a clear gel that swells when it absorbs water like a sponge, magnifying the sample up to 16 times its original size!

Remarkably, the internal structures remain intact during this process and expand proportionally, allowing researchers to see details that would normally require expensive, specialized equipment. The technique has proven especially valuable for studying microbial eukaryotes—tiny organisms notoriously difficult to examine as many cannot be genetically modified to make their structures glow under microscopes and/or their tough cell walls prevent traditional staining methods from working.

Exploring ocean life at unprecedented scale

One major application involves studying plankton, the microscopic organisms floating in the ocean that produce most of our planet’s oxygen and are the basis of marine food chains. Using this new technique, scientists observed hundreds of planktonic species, revealing diverse patterns of organisation of the cytoskeleton—the internal scaffolding that helps cells maintain their shape, divide, and move.

By analyzing these structures across many species, researchers could make predictions about how cellular organization evolved over millions of years. ² This will allow us to develop an encyclopedia of planktonic cellular architecture that links physical structure to evolution.

The technique also allows studying diatoms, microscopic algae with glass-like silica cell walls and extremely difficult to study conventionally. However, with expansion microscopy researchers could overcome ³ previous limitations and examine their internal structures.

Beyond microscopic organisms, researchers are applying expansion microscopy to understand tissue development. Scientists studying limb formation in mouse embryos used it to observe how cells orient themselves during development, preserving three-dimensional spatial information that would be lost with traditional methods.

Unlike electron microscopy requiring expensive specialized equipment, expansion microscopy can be performed with standard laboratory microscopes, making it accessible to more research teams worldwide. This makes the technique a go-to resource for looking into the intricate structures of living organisms as they are, without the distortion associated with most other methods of fixating and labelling samples for imaging.

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