In June 1925, Werner Heisenberg retreated to the German island of Helgoland seeking relief from hay fever and the conceptual disarray of the old quantum theory. On this remote, rocky outpost in the North Sea, he laid the foundations of matrix mechanics. Later, his “island epiphany” would pass through the hands of Max Born, Wolfgang Pauli, Pascual Jordan and several others, and become the first mature formulation of quantum theory. From 9 to 14 June 2025, almost a century later, hundreds of researchers gathered on Helgoland to mark the anniversary – and to deal with pressing and unfinished business.
Alfred D Stone (Yale University) called upon participants to challenge the folklore surrounding quantum theory’s birth. Philosopher Elise Crull (City College of New York) drew overdue attention to Grete Hermann, who hinted at entanglement before it had a name and anticipated Bell in identifying a flaw in von Neumann’s no-go theorem, which had been taken as proof that hidden-variable theories are impossible. Science writer Philip Ball questioned Heisenberg’s epiphany itself: he didn’t invent matrix mechanics in a flash, claims Ball, nor immediately grasp its relevance, and it took months, and others, to see his contribution for what it was (see “Lend me your ears” image).
Building on a strong base
A clear takeaway from Helgoland 2025 was that the foundations of quantum mechanics, though strongly built on Helgoland 100 years ago, nevertheless remain open to interpretation, and any future progress will depend on excavating them directly (see “Four ways to interpret quantum mechanics“).
Does the quantum wavefunction represent an objective element of reality or merely an observer’s state of knowledge? On this question, Helgoland 2025 could scarcely have been more diverse. Christopher Fuchs (UMass Boston) passionately defended quantum Bayesianism, which recasts the Born probability rule as a consistency condition for rational agents updating their beliefs. Wojciech Zurek (Los Alamos National Laboratory) presented the Darwinist perspective, for which classical objectivity emerges from redundant quantum information encoded across the environment. Although Zurek himself maintains a more agnostic stance, his decoherence-based framework is now widely embraced by proponents of many-worlds quantum mechanics (see “The minimalism of many worlds“).
The foundations of quantum mechanics remain open to interpretation, and any future progress will depend on excavating them directly
Markus Aspelmeyer (University of Vienna) made the case that a signature of gravity’s long-speculated quantum nature may soon be within experimental reach. Building on the “gravitational Schrödinger’s cat” thought experiment proposed by Feynman in the 1950s, he described how placing a massive object in a spatial superposition could entangle a nearby test mass through their gravitational interaction. Such a scenario would produce correlations that are inexplicable by classical general relativity alone, offering direct empirical evidence that gravity must be described quantum-mechanically. Realising this type of experiment requires ultra-low pressures and cryogenic temperatures to suppress decoherence, alongside extremely low-noise measurements of gravitational effects at short distances. Recent advances in optical and optomechanical techniques for levitating and controlling nanoparticles suggest a path forward – one that could bring evidence for quantum gravity not from black holes or the early universe, but from laboratories on Earth.
Information insights
Quantum information was never far from the conversation. Isaac Chuang (MIT) offered a reconstruction of how Heisenberg might have arrived at the principles of quantum information, had his inspiration come from Shannon’s Mathematical Theory of Communication. He recast his original insights into three broad principles: observations act on systems; local and global perspectives are in tension; and the order of measurements matters. Starting from these ingredients, one could in principle recover the structure of the qubit and the foundations of quantum computation. Taking the analogy one step further, he suggested that similar tensions between memorisation and generalisation – or robustness and adaptability – may one day give rise to a quantum theory of learning.
Helgoland 2025 illustrated just how much quantum mechanics has diversified since its early days. No longer just a framework for explaining atomic spectra, the photoelectric effect and black-body radiation, it is at once a formalism describing high-energy particle scattering, a handbook for controlling the most exotic states of matter, the foundation for information technologies now driving national investment plans, and a source of philosophical conundrums that, after decades at the margins, has once again taken centre stage in theoretical physics.
Active galactic nuclei (AGNs) are extremely energetic regions at the centres of galaxies, powered by accretion onto a supermassive black hole. Some AGNs launch plasma outflows moving near light speed. Blazars are a subclass of AGNs whose jets are pointed almost directly at Earth, making them appear exceptionally bright across the electromagnetic spectrum. A new analysis of an exceptional flare of BL Lacertae by NASA’s Imaging X-ray Polarimetry Explorer (IXPE) has now shed light on their emission mechanisms.
The spectral energy distribution of blazars generally has two broad peaks. The low-energy peak from radio to X-rays is well explained by synchrotron radiation from relativistic electrons spiraling in magnetic fields, but the origin of the higher-energy peak from X-rays to γ-rays is a longstanding point of contention, with two classes of models, dubbed hadronic and leptonic, vying to explain it. Polarisation measurements offer a key diagnostic tool, as the two models predict distinct polarisation signatures.
Model signatures
In hadronic models, high-energy emission is produced by protons, either through synchrotron radiation or via photo-hadronic interactions that generate secondary particles. Hadronic models predict that X-ray polarisation should be as high as that in the optical and millimetre bands, even in complex jet structures.
Leptonic models are powered by inverse Compton scattering, wherein relativistic electrons “upscatter” low-energy photons, boosting them to higher energies with low polarisation. Leptonic models can be further subdivided by the source of the inverse-Compton-scattered photons. If initially generated by synchrotron radiation in the AGN (synchrotron self-Compton, SSC), modest polarisation (~50%) is expected due to the inherent polarisation of synchrotron photons, with further reductions if the emission comes from inhomogeneous or multiple emitting regions. If initially generated by external sources (external Compton, EC), isotropic photon fields from the surrounding structures are expected to average out their polarisation.
IXPE launched on 9 December 2021, seeking to resolve such questions. It is designed to have 100-fold better sensitivity to the polarisation of X-rays in astrophysical sources than the last major X-ray polarimeter, which was launched half a century ago (CERN Courier July/August 2022 p10). In November 2023, it participated in a coordinated multiwavelength campaign spanning radio, millimetre and optical, and X-ray bands targeted the blazar BL Lacertae, whose X-ray emission arises mostly from the high-energy component, with its low-energy synchrotron component mainly at infrared energies. The campaign captured an exceptional flare, providing a rare opportunity to test competing emission models.
Optical telescopes recorded a peak optical polarisation of 47.5 ± 0.4%, the highest ever measured in a blazar. The short-mm (1.3 mm) polarisation also rose to about 10%, with both bands showing similar trends in polarisation angle. IXPE measured no significant polarisation in the 2 to 8 keV X-ray band, placing a 3σ upper limit of 7.4%.
The striking contrast between the high polarisation in optical and mm bands, and a strict upper limit in X-rays, effectively rules out all single-zone and multi-region hadronic models. Had these processes dominated, the X-ray polarisation would have been comparable to the optical. Instead, the observations strongly support a leptonic origin, specifically the SSC model with a stratified or multi-zone jet structure that naturally explains the low X-ray polarisation.
A key feature of the flare was the rapid rise and fall of optical polarisation
A key feature of the flare was the rapid rise and fall of optical polarisation. Initially, it was low, of order 5%, and aligned with the jet direction, suggesting the dominance of poloidal or turbulent fields. A sharp increase to nearly 50%, while retaining alignment, indicates the sudden injection of a compact, toroidally dominated magnetic structure.
The authors of the analysis propose a “magnetic spring” model wherein a tightly wound toroidal field structure is injected into the jet, temporarily ordering the magnetic field and raising the optical polarisation. As the structure travels outward, it relaxes, likely through kink instabilities, causing the polarisation to decline over about two weeks. This resembles an elastic system, briefly stretched and then returning to equilibrium.
A magnetic spring would also explain the multiwavelength flaring. The injection boosted the total magnetic field strength, triggering an unprecedented mm-band flare powered by low-energy electrons with long cooling times. The modest rise in mm-wavelength polarisation (green points) suggests emission from a large, turbulent region. Meanwhile, optical flaring (black points) was suppressed due to the rapid synchrotron cooling of high-energy electrons, consistent with the observed softening of the optical spectrum. No significant γ-ray enhancement was observed, as these photons originate from the same rapidly cooling electron population.
Turning point
These findings mark a turning point in high-energy astrophysics. The data definitively favour leptonic emission mechanisms in BL Lacertae during this flare, ruling out efficient proton acceleration and thus any associated high-energy neutrino or cosmic-ray production. The ability of the jet to sustain nearly 50% polarisation across parsec scales implies a highly ordered, possibly helical magnetic field extending far from the supermassive black hole.
The results cement polarimetry as a definitive tool in identifying the origin of blazar emission. The dedicated Compton Spectrometer and Imager (COSI) γ-ray polarimeter is soon set to complement IXPE at even higher energies when launched by NASA in 2027. Coordinated campaigns will be crucial for probing jet composition and plasma processes in AGNs, helping us understand the most extreme environments in the universe.
Fermilab’s Muon g-2 collaboration has given its final word on the magnetic moment of the muon. The new measurement agrees closely with a significantly revised Standard Model (SM) prediction. Though the experimental measurement will likely now remain stable for several years, theorists expect to make rapid progress to reduce uncertainties and resolve tensions underlying the SM value. One of the most intriguing anomalies in particle physics is therefore severely undermined, but not yet definitively resolved.
The muon g-2 anomaly dates back to the late 1990s and early 2000s, when measurements at Brookhaven National Laboratory (BNL) uncovered a possible discrepancy by comparison to theoretical predictions of the so-called muon anomaly, aμ = (g-2)/2. aμ expresses the magnitude of quantum loop corrections to the leading-order prediction of the Dirac equation, which multiplies the classical gyromagnetic ratio of fundamental fermions by a “g-factor” of precisely two. Loop corrections of aμ ~ 0.1% quantify the extent to which virtual particles emitted by the muon further increase the strength of its interaction with magnetic fields. Were measurements to be shown to deviate from SM predictions, this would indicate the influence of virtual fields beyond the SM.
Move on up
In 2013, the BNL experiment’s magnetic storage ring was transported from Long Island, New York, to Fermilab in Batavia, Illinois. After years of upgrades and improvements, the new experiment began in 2017. It now reports a final precision of 127 parts per billion (ppb), bettering the experiment’s design precision of 140 ppb, and a factor of four more sensitive than the BNL result.
“First and foremost, an increase in the number of stored muons allowed us to reduce our statistical uncertainty to 98 ppb compared to 460 ppb for BNL,” explains co-spokesperson Peter Winter of Argonne National Laboratory, “but a lot of technical improvements to our calorimetry, tracking, detector calibration and magnetic-field mapping were also needed to improve on the systematic uncertainties from 280 ppb at BNL to 78 ppb at Fermilab.”
This formidable experimental precision throws down the gauntlet to the theory community
The final Fermilab measurement is (116592070.5 ± 11.4 (stat.) ± 9.1(syst.) ± 2.1 (ext.)) × 10–11, fully consistent with the previous BNL measurement. This formidable precision throws down the gauntlet to the Muon g-2 Theory Initiative (TI), which was founded to achieve an international consensus on the theoretical prediction.
The calculation is difficult, featuring contributions from all sectors of the SM (CERN Courier March/April 2025 p21). The TI published its first whitepaper in 2020, reporting aμ = (116591810 ± 43) × 10–11, based exclusively on a data-driven analysis of cross-section measurements at electron–positron colliders (WP20). In May, the TI updated its prediction, publishing a value aμ = (116592033 ± 62) × 10–11, statistically incompatible with the previous prediction at the level of three standard deviations, and with an increased uncertainty of 530 ppb (WP25). The new prediction is based exclusively on numerical SM calculations. This was made possible by rapid progress in the use of lattice QCD to control the dominant source of uncertainty, which arises due to the contribution of so-called hadronic vacuum polarisation (HVP). In HVP, the photon representing the magnetic field interacts with the muon during a brief moment when a virtual photon erupts into a difficult-to-model cloud of quarks and gluons.
Significant shift
“The switch from using the data-driven method for HVP in WP20 to lattice QCD in WP25 results in a significant shift in the SM prediction,” confirms Aida El-Khadra of the University of Illinois, chair of the TI, who believes that it is not unreasonable to expect significant error reductions in the next couple of years. “There still are puzzles to resolve, particularly around the experimental measurements that are used in the data-driven method for HVP, which prevent us, at this point in time, from obtaining a new prediction for HVP in the data-driven method. This means that we also don’t yet know if the data-driven HVP evaluation will agree or disagree with lattice–QCD calculations. However, given the ongoing dedicated efforts to resolve the puzzles, we are confident we will soon know what the data-driven method has to say about HVP. Regardless of the outcome of the comparison with lattice QCD, this will yield profound insights.”
We are making plans to improve experimental precision beyond the Fermilab experiment
On the experimental side, attention now turns to the Muon g-2/EDM experiment at J-PARC in Tokai, Japan. While the Fermilab experiment used the “magic gamma” method first employed at CERN in the 1970s to cancel the effect of electric fields on spin precession in a magnetic field (CERN Courier September/October 2024 p53), the J-PARC experiment seeks to control systematic uncertainties by exercising particularly tight control of its muon beam. In the Japanese experiment, antimatter muons will be captured by atomic electrons to form muonium, ionised using a laser, and reaccelerated for a traditional precession measurement with sensitivity to both the muon’s magnetic moment and its electric dipole moment (CERN Courier July/August 2024 p8).
“We are making plans to improve experimental precision beyond the Fermilab experiment, though their precision is quite tough to beat,” says spokesperson Tsutomu Mibe of KEK. “We also plan to search for the electric dipole moment of the muon with an unprecedented precision of roughly 10–21 e cm, improving the sensitivity of the last results from BNL by a factor of 70.”
With theoretical predictions from high-order loop processes expected to be of the order 10–38 e cm, any observation of an electric dipole moment would be a clear indication of new physics.
“Construction of the experimental facility is currently ongoing,” says Mibe. “We plan to start data taking in 2030.”
Just as water takes the form of ice, liquid or vapour, QCD matter exhibits distinct phases. But while the phase diagram of water is well established, the QCD phase diagram remains largely conjectural. The STAR collaboration at Brookhaven National Laboratory’s Relativistic Heavy Ion Collider (RHIC) recently completed a new beam-energy scan (BES-II) of gold–gold collisions. The results narrow the search for a long-sought-after “critical point” in the QCD phase diagram.
“BES-II precision measurements rule out the existence of a critical point in the regions of the QCD phase diagram accessed at LHC and top RHIC energies, while still allowing the possibility at lower collision energies,” says Bedangadas Mohanty of the National Institute of Science Education and Research in India, who co-led the analysis. “The results refine earlier BES-I indications, now with much reduced uncertainties.”
At low temperatures and densities, quarks and gluons are confined within hadrons. Heating QCD matter leads to the formation of a deconfined quark–gluon plasma (QGP), while increasing the density at low temperatures is expected to give rise to more exotic states such as colour superconductors. Above a certain threshold in baryon density, the transition from hadron gas to QGP is expected to be first-order – a sharp, discontinuous change akin to water boiling. As density decreases, this boundary gives way to a smooth crossover where the two phases blend. A hypothetical critical point marks the shift between these regimes, much like the endpoint of the liquid–gas coexistence line in the phase diagram of water (see “Phases of QCD” figure).
Heavy-ion collisions offer a way to observe this phase transition directly. At the Large Hadron Collider, the QGP created in heavy-ion collisions transitions smoothly to a hadronic gas as it cools, but the lower energies explored by RHIC probe the region of phase space where the critical point may lie.
To search for possible signatures of a critical point, the STAR collaboration measured gold–gold collisions at centre-of-mass energies between 7.7 and 27 GeV per nucleon pair. The collaboration reports that their data deviate from frameworks that do not include a critical point, including the hadronic transport model, thermal models with canonical ensemble treatment, and hydrodynamic approaches with excluded-volume effects. Depending on the choice of observable and non-critical baseline model, the significance of the deviations ranges from two to five standard deviations, with the largest effects seen in head-on collisions when using peripheral collisions as a reference.
“None of the existing theoretical models fully reproduce the features observed in the data,” explains Mohanty. “To interpret these precision measurements, it is essential that dynamical model calculations that include critical-point physics be developed.” The STAR collaboration is now mapping lower energies and higher baryon densities using a fixed target (FXT) mode, wherein a 1 mm gold foil sits 2 cm below the beam axis.
“The FXT data are a valuable opportunity to explore QCD matter at high baryon density,” says Mohanty. “Data taking will conclude later this year when RHIC transitions to the Electron–Ion Collider. The Compressed Baryonic Matter experiment at FAIR in Germany will then pick up the study of the QCD critical point towards the end of the 2020s.”
Precise measurements of the Higgs self-coupling and its effects on the Higgs potential will play a key role in testing the validity of the Standard Model (SM). 150 physicists discussed the required experimental and theoretical manoeuvres on the serene island of Elba from 11 to 17 May at the Higgs Pairs 2025 workshop.
The conference mixed updates on theoretical developments in Higgs-boson pair production, searches for new physics in the scalar sector, and the most recent results from Run 2 and Run 3 of the LHC. Among the highlights was the first Run 3 analysis released by ATLAS on the search for di-Higgs production in the bbγγ final state – a particularly sensitive channel for probing the Higgs self-coupling. This result builds on earlier Run 2 analyses and demonstrates significantly improved sensitivity, now comparable to the full Run 2 combination of all channels. These gains were driven by the use of new b-tagging algorithms, improved mass resolution through updated analysis techniques, and the availability of nearly twice the dataset.
Complementing this, CMS presented the first search for ttHH production – a rare process that would provide additional sensitivity to the Higgs self-coupling and Higgs–top interactions. Alongside this, ATLAS presented first experimental searches for triple Higgs boson production (HHH), one of the rarest processes predicted by the SM. Work on more traditional final states such as bbττ and bbbb is ongoing at both experiments, and continues to benefit from improved reconstruction techniques and larger datasets.
Beyond current data, the workshop featured discussions of the latest combined projection study by ATLAS and CMS, prepared as part of the input to the upcoming European Strategy Update. It extrapolates results of the Run 2 analyses to expected conditions of the High-Luminosity LHC (HL-LHC), estimating future sensitivities to the Higgs self-coupling and di-Higgs cross-section in scenarios with vastly higher luminosity and upgraded detectors. Under these assumptions, the combined sensitivity of ATLAS and CMS to di-Higgs production is projected to reach a significance of 7.6σ, firmly establishing the process.
These projections provide crucial input for analysis strategy planning and detector design for the next phase of operations at the HL-LHC. Beyond the HL-LHC, efforts are already underway to design experiments at future colliders that will enhance sensitivity to the production of Higgs pairs, and offer new insights into electroweak symmetry breaking.
In 2018 and 2019, the LHCb collaboration published surprising measurements of the Ξc0 and Ωc0 baryon lifetimes, which were inconsistent with previous results and overturned the established hierarchy between the two. A new analysis of their hadronic decays now confirms this observation, promising insights into the dynamics of baryons.
The Λc+, Ξc+, Ξc0 and Ωc0 baryons – each composed of one charm and two lighter up, down or strange quarks – are the only ground-state singly charmed baryons that decay predominantly via the weak interaction. The main contribution to this process comes from the charm quark transitioning into a strange quark, with the other constituents acting as passive spectators. Consequently, at leading order, their lifetimes should be the same. Differences arise from higher-order effects, such as W-boson exchange between the charm and spectator quarks and quantum interference between identical particles, known as “Pauli interference”. Charm hadron lifetimes are more sensitive to these effects than beauty hadrons because of the smaller charm quark mass compared to the bottom quark, making them a promising testing ground to study these effects.
Measurements of the Ξc0 and Ωc0 lifetimes prior to the start of the LHCb experiment resulted in the PDG averages shown in figure 1. The first LHCb analysis, using charm baryons produced in semi-leptonic decays of beauty baryons, was in tension with the established values, giving a Ωc0 lifetime four times larger than the previous average. The inconsistencies were later confirmed by another LHCb measurement, using an independent data set with charm baryons produced directly (prompt) in the pp collision (CERN Courier July/August 2021 p17). These results changed the ordering of the four single-charm baryons when arranged according to their lifetimes, triggering a scientific discussion on how to treat higher-order effects in decay rate calculations.
Using the full Run 1 and 2 datasets, LHCb has now measured the Ξc0 and Ωc0 lifetimes with a third independent data sample, based on fully reconstructed Ξb–→Ξc0 (→ pK–K–π+)π– and Ω–b→ Ωc0 (→ pK–K–π+)π– decays. The selection of these hadronic decay chains exploits the long lifetime of the beauty baryons, such that the selection efficiency is almost independent of the charm baryon decay time. To cancel out the small remaining acceptance effects, the measurement is normalised to the kinematically and topologically similar B–→ D0(→ K+K–π+π–)π– channel, minimising the uncertainties with only a small additional correction from simulation.
The signal decays are separated from the remaining background by fits to the Ξc0 π– and Ωc0 π– invariant mass spectra, providing 8260 ± 100 Ξc0 and 355 ± 26 Ωc0 candidates. The decay time distributions are obtained with two independent methods: by determining the yield in each of a specific set of decay time intervals, and by employing a statistical technique that uses the covariance matrix from the fit to the mass spectra. The two methods give consistent results, confirming LHCb’s earlier measurements. Combining the three measurements from LHCb, while accounting for their correlated uncertainties, gives τ(Ξc0) = 150.7 ± 1.6 fs and τ(Ωc0) = 274.8 ± 10.5 fs. These new results will serve as experimental guidance on how to treat higher-order effects in weak baryon decays, particularly regarding the approach-dependent sign and magnitude of Pauli interference terms.
The discovery of the Higgs boson at the LHC in 2012 provided strong experimental support for the Brout–Englert–Higgs mechanism of spontaneous electroweak symmetry breaking (EWSB) as predicted by the Standard Model. The EWSB explains how the W and Z bosons, the mediators of the weak interaction, acquire mass: their longitudinal polarisation states emerge from the Goldstone modes of the Higgs field, linking the mass generation of vector bosons directly to the dynamics of the process.
Yet, its ultimate origins remain unknown and the Standard Model may only offer an effective low-energy description of a more fundamental theory. Exploring this possibility requires precise tests of how EWSB operates, and vector boson scattering (VBS) provides a particularly sensitive probe. In VBS, two electroweak gauge bosons scatter off one another. The cross section remains finite at high energies only because there is an exact cancellation between the pure gauge-boson interactions and the Higgs-boson mediated contributions, an effect analogous to the role of the Z boson propagator in WW production at electron–positron colliders. Deviations from the expected behaviour could signal new dynamics, such as anomalous couplings, strong interactions in the Higgs sector or new particles at higher energy scales.
This result lays the groundwork for future searches for new physics hidden within the electroweak sector
VBS interactions are among the rarest observed so far at the LHC, with cross sections as low as one femtobarn. To disentangle them from the background, researchers rely on the distinctive experimental signature of two high-energy jets in the forward detector regions produced by the initial quarks that radiate the bosons, with minimal hadronic activity between them. Using the full data set from Run 2 of the LHC at a centre-of-mass energy of 13 TeV, the CMS collaboration carried out a comprehensive set of VBS measurements across several production modes: WW (with both same and opposite charges), WZ and ZZ, studied in five final states where both bosons decay leptonically and in two semi-leptonic configurations where one boson decays into leptons and the other into quarks. To enhance sensitivity further, the data from all the measurements have now been combined in a single joint fit, with a complete treatment of uncertainty correlations and a careful handling of events selected by more than one analysis.
All modes, one analysis
To account for possible deviations from the expected predictions, each process is characterised by a signal strength parameter (μ), defined as the ratio of the measured production rate to the cross section predicted by the Standard Model. A value of μ near unity indicates consistency with the Standard Model, while significant deviations may suggest new physics. The results, summarised in figure 1, display good agreement with the Standard Model predictions: all measured signal strengths are consistent with unity within their respective uncertainties. A mild excess with respect to the leading-order theoretical predictions is observed across several channels, highlighting the need for more accurate modelling, in particular for the measurements that have reached a level of precision where systematic effects dominate. By presenting the first evidence for all charged VBS production modes from a single combined statistical analysis, this CMS result lays the groundwork for future searches for new physics hidden within the electroweak sector.
The 16th International Workshop on Hadron Physics (Hadrons 2025) welcomed 135 physicists to the Federal University of Rio Grande do Sul (UFRGS) in Porto Alegre, Brazil. Delayed by four months due to a tragic flood that devastated the city, the triennial conference took place from 10 to 14 March, despite adversity maintaining its long tradition as a forum for collaboration among Brazilian and international researchers at different stages of their careers.
The workshop’s scientific programme included field theoretical approaches to QCD, the behaviour of hadronic and quark matter in astrophysical contexts, hadronic structure and decays, lattice QCD calculations, recent experimental developments in relativistic heavy-ion collisions, and the interplay of strong and electroweak forces within the Standard Model.
Fernanda Steffens (University of Bonn) explained how deep-inelastic-scattering experiments and theoretical developments are revealing the internal structure of the proton. Kenji Fukushima (University of Tokyo) addressed the theoretical framework and phase structure of strongly interacting matter, with particular emphasis on the QCD phase diagram and its relevance to heavy-ion collisions and neutron stars. Chun Shen (Wayne State University) presented a comprehensive overview of the state-of-the-art techniques used to extract the transport properties of quark–gluon plasma from heavy-ion collision data, emphasising the role of Bayesian inference and machine learning in constraining theoretical models. Li-Sheng Geng (Beihang University) explored exotic hadrons through the lens of hadronic molecules, highlighting symmetry multiplets such as pentaquarks, the formation of multi-hadron states and the role of femtoscopy in studying unstable particle interactions.
This edition of Hadrons was dedicated to the memory of two individuals who left a profound mark on the Brazilian hadronic-physics community: Yogiro Hama, a distinguished senior researcher and educator whose decades-long contributions were foundational to the development of the field in Brazil, and Kau Marquez, an early-career physicist whose passion for science remained steadfast despite her courageous battle with spinal muscular atrophy. Both were remembered with deep admiration and respect, not only for their scientific dedication but also for their personal strength and impact on the community.
Its mission is to cultivate a vibrant and inclusive scientific environment
Since its creation in 1988, the Hadrons workshop has played a central role in developing Brazil’s scientific capacity in particle and nuclear physics. Its structure facilitates close interaction between master’s and doctoral students, and senior researchers, thus enhancing both technical training and academic exchange. This model continues to strengthen the foundations of research and collaboration throughout the Brazilian scientific community.
This is the main event for the Brazilian particle- and nuclear-physics communities, reflecting a commitment to advancing research in this highly interactive field. By circulating the venue across multiple regions of Brazil, each edition further renews its mission to cultivate a vibrant and inclusive scientific environment. This edition was closed by a public lecture on QCD by Tereza Mendes (University of São Paolo), who engaged local students with the foundational questions of strong-interaction physics.
The next edition of the Hadrons series will take place in Bahia in 2028.
The 23rd edition of Flavor Physics and CP Violation (FPCP) attracted 100 physicists to Cincinnati, USA, from 2 to 6 June 2025. The conference reviews recent experimental and theoretical developments in CP violation, rare decays, Cabibbo–Kobayashi–Maskawa matrix elements, heavy-quark decays, flavour phenomena in charged leptons and neutrinos, and the interplay between flavour physics and high-pT physics at the LHC.
The highlight of the conference was new results on the muon magnetic anomaly. The Muon g-2 experiment at Fermilab released its final measurement of aμ = (g-2)/2 on 3 June, while the conference was in progress, reaching a precision of 127 ppb on the published value. This uncertainty is more than four times smaller than that reported by the previous experiment. One week earlier, on 27 May, the Muon g-2 Theory Initiative published their second calculation of the same quantity, following that published in summer 2020. A major difference between the two calculations is that the earlier one used experimental data and the dispersion integral to evaluate the hadronic contribution to aμ, whereas the update uses a purely theoretical approach based on lattice QCD. The strong tension with the experiment of the earlier calculation is no longer present, with the new calculation compatible with experimental results. Thus, no new physics discovery can be claimed, though the reason for the difference between the two approaches must be understood (see “Fermilab’s final word on muon g-2“).
The MEG II collaboration presented an important update to their limit on the branching fraction for the lepton-flavour-violating decay μ → eγ. Their new upper bound of 1.5 × 10–13 is determined from data collected in 2021 and 2022. The experiment recorded additional data from 2023 to 2024 and expects to continue data taking for two more years. These data will be sensitive to a branching fraction four to five times smaller than the current limit.
LHCb, Belle II, BESIII and NA62 all discussed recent results in quark flavour physics. Highlights include the first measurement of CP violation in a baryon decay by LHCb and improved limits on CP violation in D-meson decay to two pions by Belle II. With more data, the latter measurements could potentially show that the observed CP violation in charm is from a non-Standard-Model source.
The Belle II collaboration now plans to collect a sample between 5 to 10 ab–1 by the early 2030s before undergoing an upgrade to collect a 30 to 50 ab–1 sample by the early 2040s. LHCb plan to run to the end of the High-Luminosity LHC and collect 300 fb–1. LHCb recorded almost 10 fb–1 of data last year – more than in all their previous running, and now with a fully software-based trigger with much higher efficiency than the previous hardware-based first-level trigger. Future results from Belle II and the LHCb upgrade are eagerly anticipated.
The 24th FPCP conference will be held from 18 to 22 May 2026 in Bad Honnef, Germany.
Physicists have long been suspicious of the “quantum measurement problem”: the supposed puzzle of how to make sense of quantum mechanics. Everyone agrees (don’t they?) on the formalism of quantum mechanics (QM); any additional discussion of the interpretation of that formalism can seem like empty words. And Hugh Everett III’s infamous “many-worlds interpretation” looks more dubious than most: not just unneeded words but unneeded worlds. Don’t waste your time on words or worlds; shut up and calculate.
But the measurement problem has driven more than philosophy. Questions of how to understand QM have always been entangled, so to speak, with questions of how to apply and use it, and even how to formulate it; the continued controversies about the measurement problem are also continuing controversies in how to apply, teach and mathematically describe QM. The Everett interpretation emerges as the natural reading of one strategy for doing QM, which I call the “decoherent view” and which has largely supplanted the rival “lab view”, and so – I will argue – the Everett interpretation can and should be understood not as a useless adjunct to modern QM but as part of the development in our understanding of QM over the past century.
The view from the lab
The lab view has its origins in the work of Bohr and Heisenberg, and it takes the word “observable” that appears in every QM textbook seriously. In the lab view, QM is not a theory like Newton’s or Einstein’s that aims at an objective description of an external world subject to its own dynamics; rather, it is essentially, irreducibly, a theory of observation and measurement. Quantum states, in the lab view, do not represent objective features of a system in the way that (say) points in classical phase space do: they represent the experimentalist’s partial knowledge of that system. The process of measurement is not something to describe within QM: ultimately it is external to QM. And the so-called “collapse” of quantum states upon measurement represents not a mysterious stochastic process but simply the updating of our knowledge upon gaining more information.
Valued measurements
The lab view has led to important physics. In particular, the “positive operator valued measure” idea, central to many aspects of quantum information, emerges most naturally from the lab view. So do the many extensions, total and partial, to QM of concepts initially from the classical theory of probability and information. Indeed, in quantum information more generally it is arguably the dominant approach. Yet outside that context, it faces severe difficulties. Most notably: if quantum mechanics describes not physical systems in themselves but some calculus of measurement results, if a quantum system can be described only relative to an experimental context, what theory describes those measurement results and experimental contexts themselves?
One popular answer – at least in quantum information – is that measurement is primitive: no dynamical theory is required to account for what measurement is, and the idea that we should describe measurement in dynamical terms is just another Newtonian prejudice. (The “QBist” approach to QM fairly unapologetically takes this line.)
One can criticise this answer on philosophical grounds, but more pressingly: that just isn’t how measurement is actually done in the lab. Experimental kit isn’t found scattered across the desert (each device perhaps stamped by the gods with the self-adjoint operator it measures); it is built using physical principles (see “Dynamical probes” figure). The fact that the LHC measures the momentum and particle spectra of various decay processes, for instance, is something established through vast amounts of scientific analysis, not something simply posited. We need an account of experimental practice that allows us to explain how measurement devices work and how to build them.
Perhaps this was viable in the 1930s, but today measurement devices rely on quantum principles
Bohr had such an account: quantum measurements are to be described through classical mechanics. The classical is ineliminable from QM precisely because it is to classical mechanics we turn when we want to describe the experimental context of a quantum system. To Bohr, the quantum–classical transition is a conceptual and philosophical matter as much as a technical one, and classical ideas are unavoidably required to make sense of any quantum description.
Perhaps this was viable in the 1930s. But today it is not only the measured systems but the measurement devices themselves that essentially rely on quantum principles, beyond anything that classical mechanics can describe. And so, whatever the philosophical strengths and weaknesses of this approach – or of the lab view in general – we need something more to make sense of modern QM, something that lets us apply QM itself to the measurement process.
Practice makes perfect
We can look to physics practice to see how. As von Neumann glimpsed, and Everett first showed clearly, nothing prevents us from modelling a measurement device itself inside unitary quantum mechanics. When we do so, we find that the measured system becomes entangled with the device, so that (for instance) if a measured atom is in a weighted superposition of spins with respect to some axis, after measurement then the device is in a similarly-weighted superposition of readout values.
In principle, this courts infinite regress: how is that new superposition to be interpreted, save by a still-larger measurement device? In practice, we simply treat the mod-squared amplitudes of the various readout values as probabilities, and compare them with observed frequencies. This sounds a bit like the lab view, but there is a subtle difference: these probabilities are understood not with respect to some hypothetical measurement, but as the actual probabilities of the system being in a given state.
Of course, if we could always understand mod-squared amplitudes that way, there would be no measurement problem! But interference precludes this. Set up, say, a Mach–Zehnder interferometer, with a particle beam split in two and then re-interfered, and two detectors after the re-interference (see “Superpositions are not probabilities” figure). We know that if either of the two paths is blocked, so that any particle detected must have gone along the other path, then each of the two outcomes is equally likely: for each particle sent through, detector A fires with 50% probability and detector B with 50% probability. So whicheverpath the particle went down, we get A with 50% probability and B with 50% probability. And yet we know that if the interferometer is properly tuned and both paths are open, we can get A with 100% probability or 0% probability or anything in between. Whatever microscopic superpositions are, they are not straightforwardly probabilities of classical goings-on.
Unfeasible interference
But macroscopic superpositions are another matter. There, interference is unfeasible (good luck reinterfering the two states of Schrödinger’s cat); nothing formally prevents us from treating mod-squared amplitudes like probabilities.
Anddecoherence theory has given us a clear understanding of just why interference is invisible in large systems, and more generally when we can and cannot get away with treating mod-squared amplitudes as probabilities. As the work of Zeh, Zurek, Gell-Mann, Hartle and many others (drawing inspiration from Everett and from work on the quantum/classical transition as far back as Mott) has shown, decoherence – that is, the suppression of interference – is simply an aspect of non-equilibrium statistical mechanics. The large-scale, collective degrees of freedom of a quantum system, be it the needle on a measurement device or the centre-of-mass of a dust mote, are constantly interacting with a much larger number of small-scale degrees of freedom: the short-wavelength phonons inside the object itself; the ambient light; the microwave background radiation. We can still find autonomous dynamics for the collective degrees of freedom, but because of the constant transfer of information to the small scale, the coherence of any macroscopic superposition rapidly bleeds into microscopic degrees of freedom, where it is dynamically inert and in practice unmeasurable.
Emergence and scale
Decoherence can be understood in the familiar language of emergence and scale separation. Quantum states are not fundamentally probabilistic, but they are emergently probabilistic. That emergence occurs because for macroscopic systems, the timescale by which energy is transferred from macroscopic to residual degrees of freedom is very long compared to the timescale of the macroscopic system’s own dynamics, which in turn is very long compared to the timescale by which information is transferred. (To take an extreme example, information about the location of the planet Jupiter is recorded very rapidly in the particles of the solar wind, or even the photons of the cosmic background radiation, but Jupiter loses only an infinitesimal fraction of its energy to either.) So the system decoheres very rapidly, but having done so it can still be treated as autonomous.
On this decoherent view of QM, there is ultimately only the unitary dynamics of closed systems; everything else is a limiting or special case. Probability and classicality emerge through dynamical processes that can be understood through known techniques of physics: understanding that emergence may be technically challenging but poses no problem of principle. And this means that the decoherent view can address the lab view’s deficiencies: it can analyse the measurement process quantum mechanically; it can apply quantum mechanics even in cosmological contexts where the “measurement” paradigm breaks down; it can even recover the lab view within itself as a limited special case. And so it is the decoherent view, not the lab view, that – I claim – underlies the way quantum theory is for the most part used in the 21st century, including in its applications in particle physics and cosmology (see “Two views of quantum mechanics” table).
Two views of quantum mechanics
Quantum phenomenon
Lab view
Decoherent view
Dynamics
Unitary (i.e. governed by the Schrödinger equation) only between measurements
Always unitary
Quantum/classical transition
Conceptual jump between fundamentally different systems
Purely dynamical: classical physics is a limiting case of quantum physics
Measurements
Cannot be treated internal to the formalism
Just one more dynamical interaction
Role of the observer
Conceptually central
Just one more physical system
But if the decoherent view is correct, then at the fundamental level there is neither probability nor wavefunction collapse; nor is there a fundamental difference between a microscopic superposition like those in interference experiments and a macroscopic superposition like Schrödinger’s cat. The differences are differences of degree and scale: at the microscopic level, interference is manifest; as we move to larger and more complex systems it hides away more and more effectively; in practice it is invisible for macroscopic systems. But even if we cannot detect the coherence of the superposition of a live and dead cat, it does not thereby vanish. And so according to the decoherent view, the cat is simultaneously alive and dead in the same way that the superposed atom is simultaneously in two places. We don’t need a change in the dynamics of the theory, or even a reinterpretation of the theory, to explain why we don’t see the cat as alive and dead at once: decoherence has already explained it. There is a “live cat” branch of the quantum state, entangled with its surroundings to an ever-increasing degree; there is likewise a “dead cat” branch; the interference between them is rendered negligible by all that entanglement.
Many worlds
At last we come to the “many worlds” interpretation: for when we observe the cat ourselves, we too enter a superposition of seeing a live and a dead cat. But these “worlds” are not added to QM as exotic new ontology: they are discovered, as emergent features of collective degrees of freedom, simply by working out how to use QM in contexts beyond the lab view and then thinking clearly about its content. The Everett interpretation – the many-worlds theory – is just the decoherent view taken fully seriously. Interference explains why superpositions cannot be understood simply as parameterising our ignorance; unitarity explains how we end up in superpositions ourselves; decoherence explains why we have no awareness of it.
(Forty-five years ago, David Deutsch suggested testing the Everett interpretation by simulating an observer inside a quantum computer, so that we could recohere them after they made a measurement. Then, it was science fiction; in this era of rapid progress on AI and quantum computation, perhaps less so!)
Could we retain the decoherent view and yet avoid any commitment to “worlds”? Yes, but only in the same sense that we could retain general relativity and yet refuse to commit to what lies behind the cosmological event horizon: the theory gives a perfectly good account of the other Everett worlds, and the matter beyond the horizon, but perhaps epistemic caution might lead us not to overcommit. But even so, the content of QM includes the other worlds, just as the content of general relativity includes beyond-horizon physics, and we will only confuse ourselves if we avoid even talking about that content. (Thus Hawking, who famously observed that when he heard about Schrödinger’s cat he reached for his gun, was nonetheless happy to talk about Everettian branches when doing quantum cosmology.)
Alternative views
Could there be a different way to make sense of the decoherent view? Never say never; but the many-worlds perspective results almost automatically from simply taking that view as a literal description of quantum systems and how they evolve, so any alternative would have to be philosophically subtle, taking a different and less literal reading of QM. (Perhaps relationalism, discussed in this issue by Carlo Rovelli, see “Four ways to interpret quantum mechanics“, offers a way to do it, though in many ways it seems more a version of the lab view. The physical collapse and hidden variables interpretations modify the formalism, and so fall outside either category.)
The Everett interpretation is just the decoherent view taken fully seriously
Does the apparent absurdity, or the ontological extravagance, of the Everett interpretation force us, as good scientists, to abandon many-worlds, or if necessary the decoherent view itself? Only if we accept some scientific principle that throws out theories that are too strange or that postulate too large a universe. But physics accepts no such principle, as modern cosmology makes clear.
Are there philosophical problems for the Everett interpretation? Certainly: how are we to think of the emergent ontology of worlds and branches; how are we to understand probability when all outcomes occur? But problems of this kind arise across all physical theories. Probability is philosophically contested even apart from Everett, for instance: is it frequency, rational credence, symmetry or something else? In any case, these problems pose no barrier to the use of Everettian ideas in physics.
The case for the Everett interpretation is that it is the conservative, literal reading of the version of quantum mechanics we actually use in modern physics, and there is no scientific pressure for us to abandon that reading. We could, of course, look for alternatives. Who knows what we might find? Or we could shut up and calculate – within the Everett interpretation.
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