Papers

Stefan Bergman worked in the field of pure and applied mathematics and became known primarily for his work on complex analysis of several variables. He studied the theory of solutions to linear partial differential equations via integral operators and introduced the concept of the Bergmann kernel function. He also worked on problems in electrical engineering, the theory of elasticity, potential theory, and hydrodynamics, particularly supersonic flows. His academic career in Germany was cut short by the Nazi purge, leading to a peripatetic exile through the USSR and France before finally establishing a distinguished career in the United States, notably at Harvard and Stanford. The paper sketches his biography based on archival sources and complements a bibliography of his writings compiled by M.Skwarczy'nski in 1981 with a number of references primarily from his early career.

This work provides an introduction to the most influential hidden-variable interpretation of the quantum formalism, i.e., the de Broglie-Bohm pilot-wave theory. As the reader will see, the chapter offers a detailed discussion of the main formulations of the theory. Moreover, cogent topics such as the origin of the Born rule, the interpretation of probability, the nature of the wave function, the status of spin, as well as extensions of the pilot-wave approach beyond non-relativistic quantum mechanics will be examined. This essay, however, not only reviews existing relevant literature but also contributes new insights about (i) the existence of spin in the context of pilot-wave theory, and (ii) whether the latter framework is formally and conceptually simpler than standard quantum mechanics.

John Ellard Gore (1845-1910) was an Irish amateur astronomer, prolific science writer and civil engineer. He was an inaugural member of the British Astronomical Association when it was founded in 1890 and was invited to become the first Director of its Variable Star Section. Through careful reasoning, Gore reached remarkably modern conclusions about the nature of stars, including their sizes, distances and luminosities. This paper explores whether he might have been able to produce an early form of what is now known as the Hertzsprung-Russell (H-R) diagram.

The discovery of radar echoes from meteor trains at Jodrell Bank in December 1945 heralded the beginning of a new era in meteor astronomy. This paper examines the early collaboration between Bernard Lovell, whose expertise in radar and physics transformed wartime technology into a new astronomical technique, and J. P. Manning Prentice, Director of the British Astronomical Association Meteor Section, whose knowledge of visual meteor observation proved essential to interpreting the discoveries. Drawing on previously unpublished correspondence from the Lovell Archive at the University of Manchester, the paper traces the development of their partnership, including the pioneering 1946 Perseid and Giacobinid observations, the contribution of BAA observers, and the establishment of radar meteor research at Jodrell Bank. It reveals how complementary professional and amateur expertise combined to create a new field of astronomy and a lasting scientific friendship.

It is sometimes said that a reason to prefer Everettian quantum mechanics is that it allows one to avoid the kind of spooky action at a distance that is a consequence of quantum entanglement according to other approaches. There is a straightforward argument to show EQM has this virtue, however some advocates argue that this requires we see branching as a local causal process. I explain this reasoning and then show why, given the way Everettians standardly conceive of worlds and branching as emergent phenomena, branching need not be viewed as a causal process for EQM to be relativistically local. Forthcoming in Local Quantum Mechanics, OUP 2026.

We present a simple geometric proof of Kepler's first law. The core of the argument rests on a kinematic invariant that we call the velocity projection ratio - the ratio between the radial projection of the velocity and its projection onto a fixed direction parallel to the periapsis line. We show that the constancy of this ratio is an immediate consequence of Newton's laws, and that it leads directly to the focus-directrix property of the orbit. By establishing a direct link between planetary dynamics and the classical geometric definition of conics, our proof reveals the conic nature of the orbit as an inevitable consequence of the inverse-square law.

Gisin has provided an argument for the conclusion that no covariant nonlocal model can reproduce the operational statistics observed in Bell experiments. Gisin's argument applies only to deterministic models and we argue that proposed generalizations of the argument beyond determinism based solely on statistical notions are unconvincing, as they lack the resources to formulate a satisfactory notion of no-retrocausality. We introduce the framework of frame-indexed causal models in order to extend Gisin's argument to the genuinely probabilistic case. Frame-indexed causal models associate potentially different causal models with different reference frames while requiring corresponding operational variables to agree runwise. Within this framework, we establish two no-go results based on Gisin's argument. First, we show that no empirically adequate frame-indexed causal model can jointly satisfy Independent Settings, No-Retrocausality, and Causal Lorentz Invariance. Second, it is established that this result continues to hold when Causal Lorentz Invariance is weakened to Lorentz Invariance of Causal Connections, which requires only the skeleton of the causal structure to remain invariant, thereby allowing the direction of causal influence to depend on the choice of reference frame. These results are discussed in the context of relativistic interpretations of quantum theory and nonclassical causal inference.

Astrobiology occupies an unusual position within the philosophy of science. Confronted with the n = 1 problem - having only a single example of life to study - it attempts to investigate life beyond Earth while relying entirely on Earth's biosphere as its reference point, a constraint that creates unique epistemic challenges. Unlike traditional sciences with clear predictive frameworks, astrobiology operates as what we might call a transient science: a discipline functioning without foundational certainties, relying predominantly on abductive reasoning, and confronting hypotheses that may remain untestable for decades. It is, in essence, a science of absence - of evidence, certainty, and analogy - where progress lies in refining conceptual and experimental tools to recognize unfamiliar forms of life. This positions astrobiology alongside emerging fields like artificial intelligence and cognitive science within a broader transformation of how scientific knowledge is constructed when dealing with phenomena that transcend direct empirical access.

Nonequilibrium statistical mechanics is the science of time as it manifests itself in the transient or steady entropy producing dynamical condition of many-body systems. Beyond the vivid multiformity of the phenomena themselves, three foundational issues lie at its heart. The first question concerns the very origin of entropy production, which gives macroscopic processes their direction and thereby defines the arrow of time: how does an atomistic mechanical world give rise to dissipated heat, thermalization, and time-reversal symmetry breaking? The second asks why, far beyond the familiar behavior of equilibrium systems, driving or agitation may produce and select stable and functionally rich structures: what is it about far-from-equilibrium, low-entropy driving that unleashes the wealth and intricacy of the natural world? The third issue is partly methodological: to determine how, and for which subclass of such wildly diverse nonequilibrium systems, a systematic, unified description and modeling from first principles remains possible. This essay addresses these issues in an informal, semi-popular-science style, offering a personally engaging yet wide-ranging introduction to the complementary roles of entropy production and the less familiar, more recently coined notion of frenesy in the dynamical fluctuations of steadily driven systems. Together, we argue, they provide a more complete starting point for understanding physical time on mesoscopic to macroscopic scales.

Recent discussions of QBism have turned increasingly toward the question of its ontology. I argue that key insights into QBism's ontology of agency can be identified by reconstructing its response to Wigner's friend paradox. I clarify the relation between two formulations of that response: one grounded in the claim that quantum states are agents' personal probability assignments, and another grounded in the injunction to treat all users of quantum theory as agents on equal footing. Once disambiguated, these formulations reveal an implicit commitment to a mutually recognitive conception of agency, according to which the agential status of a user of quantum theory depends constitutively on the acknowledgement of other agents. This analysis clarifies what is at stake in recent QBist engagements with phenomenology - namely, the search for a more philosophically robust account of this conception of agency. I show how Merleau-Ponty's account of intersubjectivity underpins the recognitive structure implicated in QBism before tracing these themes to Hegel's account of mutual recognition. By locating QBism within a longstanding tradition of mutual recognition, I claim that we not only illuminate its theoretical structure but also open up novel conceptual resources for the rigorous articulation and justification of its ontology.

Ostrogradsky's theorem shows that higher-derivative dynamical systems inevitably yields a Hamiltonian featuring a ghost mode that is unbounded from below. However, we argue that this theorem is inapplicable to gravitational systems, as the Hamiltonian constraint, which encodes background independence by dictating that the total Hamiltonian vanishes, holds strictly. The ghost mode obeying this constraint constitutes an indispensable component in the construction of space and time. Nevertheless, it should be underscored that the use of the weak-field (graviton) approximation, being a background-dependent scheme presupposing the existence of absolute time, invokes this theorem; consequently, it is allowed only in the domain below the Planck scale, where second derivative terms dominate.

Understanding is a generally acknowledged aim of science, but the way in which understanding is pursued and criteria for when it is achieved differ widely across scientific disciplines. This paper offers a comparative analysis of this disciplinary variation, aimed at revealing differences as well as commonalities in methods and criteria for achieving understanding. Starting point is the contextual theory of scientific understanding (De Regt 2017), which was developed to accommodate contextual variation in criteria for understanding. While this work focused on historical variation and used mainly case studies from the history of physics, the current paper applies the contextual theory to disciplinary variation. We present brief descriptive accounts of how understanding figures in nine scientific disciplines: mathematics, theoretical physics, astrophysics, chemistry, geoscience, biology, neuroscience, psychology, and the engineering sciences. Subsequently, we compare and evaluate these accounts in light of the contextual theory of scientific understanding.

We apply persistent homology to a six-layer temporal network model of the Inca Empire (Tawantinsuyu), built from the Qhapaq Ñan road system ($6{,}546$ segments; $12{,}031$~km): 4,492 nodes (4,452 active; 40 isolated removed), $4{,}358$ edges, $57$ temporal snapshots (1400–1572~CE). The complete flag complex yields $\beta_1 = 32$ cycles ($26$ macro-continental, $6$ meso-regional) and $\beta_0 = 264$ components at the finest filtration, evaluated across six layers: infrastructure, Inca political control, Spanish alliance growth, Andean tribute commerce, and Spanish legal/effective administration. Five results. (i) Infrastructure entropy $H_{\mathrm{infra}}=1.486\pm0.0001$ stays constant throughout, indicating no detectable topological disruption of the Qhapaq Ñan at this resolution. (ii) Inca political entropy $H_{\mathrm{inca}}$ is stable through the Cajamarca capture (1532~CE), then collapses to zero by 1537~CE; the dominant break is at Vilcabamba ($F=120.7$), not Cajamarca ($F=11.5$). (iii) Four of six layers reach the critical regime at 1532~CE, while infrastructure stays marginally below threshold ($\mathrm{ICT}=0.495$); trade and political reach the highest values ($\mathrm{ICT}=0.976$, $0.968$), marking Cajamarca as a synchronised multi-layer phase transition. (iv) Spanish legal administration converges to the infrastructure topology by 1572~CE ($W_1=5\times10^{-6}\approx0$): Substitution Topology, infrastructure-preserving collapse via topology transfer. (v) Legal–effective divergence decays from $W_1=0.591$ (1532) to $0.002$ (1572), quantifying resolution of colonial legal fiction. Together, these results support a distinct collapse mode—Substitution Topology—differing from erosion-dominated Roman/Byzantine collapse, Han fragmentation, and Aztec military destruction.

We apply persistent homology and a dual-model topological pipeline to a multilayer network of the Aztec Empire (Triple Alliance, 1427–1521 CE), constructed from tribute records and geographic adjacency among 38 nodes (Tenochtitlan-Centro, 36 tribute-paying provinces, and the Tlaxcala enclave) and 208 edges. We report four main results: (i) The tribute (control) layer is a pure extraction tree ($\bettione = 0$, $H = 0.000$ at all epochs): structurally more fragile than any documented configuration in the Roman, Byzantine, or Han administrative datasets analyzed with the same pipeline. (ii) Single-node removal of Tenochtitlan-Centro collapses the giant component from 1.000 to 0.630 and eliminates 30 redundancy cycles simultaneously, a structural asymmetry ratio of $>4$:1 relative to random perturbation. (iii) The Tlaxcala–Puebla region coincides with the dominant $\bettione$ class of the imperial geographic point cloud (persistence $= 22.09$~km, versus $< 3$~km for all others), a structural void that exists identically whether Tlaxcala is modeled as absent or present in the filtration. (iv) A logistic regression confirms that commercial centrality in the geographic layer ($r = +0.462$, $p = 0.004$) is the dominant predictor of early alliance formation, while tribute burden is uncorrelated ($r = -0.033$, $p = 0.845$). These four results define a new imperial collapse mode, the void-occupied tree, in which zero topological redundancy in the control layer coincides with a dominant geometric void occupied by an autonomous enclave—a configuration not previously documented in historical network TDA.

This doctoral dissertation on the foundations of quantum theory isolates and then formalizes a physically relevant concept that I have called "Epistemic Constraint." Here, epistemic constraints are the definite, intersubjectively agreeable, ordinary-language conditions under which experiments are described. The usual formulation of the quantum measurement problem, which I call the Schrodingerian measurement problem, has the structure of an anomaly: if we take quantum theory at face value, we expect no definite values, and yet we see definite values in experiments. The responses to this problem have been either to solve it or to dissolve it. These responses, which have taken the form of interpretation, modification, or reconstruction of quantum mechanics, seek either to derive (conceptually or mathematically) epistemic constraints from within quantum mechanics or suitable modifications of it, as is the case with certain interpretations and modifications, or to posit the epistemic constraint, or parts of it, as a primitive assumption with the goal of deriving quantum mechanics, as is the case in some reconstruction programs. In contrast to the Schrodingerian measurement problem, which had the structure of an anomaly, this dissertation develops the Bohrian Program, which (for lack of a better comparison) has a structure similar to the problem historically associated with Euclid's fifth postulate. It seeks to keep epistemic constraints as primitive in an onto-epistemic sense. It then seeks new physical conclusions from the joint consideration of quantum mechanics and epistemic constraints, without seeking to derive one from the other. Among other results, this leads to a notion of the probability of instantiability of the Born Rule that specifies when to apply the Born Rule and when to apply a unitary transformation to a quantum state.

This year marks 360 years since the founding of the French Academy of Sciences. This is the story of the academy's daring 17th century expedition to measure the Earth-sun distance. A truncated version first appeared in National Geographic Magazine; the following is closer to the original draft, with updated information and references.

Erwin Schrödinger is often portrayed as a reactionary who resisted the indeterminism introduced by quantum mechanics, but on closer inspection his views on determinism prove to be more complex and more radical.

Recent results from the Dark Energy Spectroscopic Instrument (DESI) have suggested that dark energy, long considered to be a cosmological constant, may actually be \lq{}dynamical\rq{}. To clarify what follows from these results, we distinguish three claims: (D1) the data disfavour the \LCDM expansion history; (D2) within the phenomenological Chevallier–Polarski–Linder (CPL) parametrisation, the data prefer $(w_0,w_a)\neq(-1,0)$; and (D3) there exist one or more genuine dynamical dark-energy degrees of freedom in the matter-sector, within GR and coupled to the standard sectors only gravitationally, whose dynamics account for the departure from the \LCDM expansion history. We demonstrate that DESI establishes D2, which supports D1, but does not establish D3. The \lq{}designer\rq{} construction in $f(R)$ gravity provides a gravitational realisation of the same background history, so that no observable determined solely by that history can discriminate, even in principle, between its \lq{}matter\rq{} and \lq{}gravitational\rq{} readings. Furthermore, non-minimally coupled models admit regular effective phantom-crossing realisations of the relevant phenomenology, while the selected crossing places additional pressure on a single-component, minimally coupled realisation of the matter-sector reading. We characterise the resulting underdetermination between matter and gravitational interpretations—exact at the level of background history, but breakable beyond it—and draw the corresponding norm for survey reporting.

For more than three centuries, Newton's Second Law (F=ma) has governed mechanics with undisputed success, yet its epistemic authority has rested on empirical adequacy alone. That empirical contingency vanishes under two physical principles - the Principle of Excluded Perpetual Motion (PEPM) and the Weak Equivalence Principle (WEP) - from which the law emerges as a structural necessity of admissible mechanics. Under the PEPM constraint, Suppes' operational measurement protocol grounds gravitational mass and force as independent primitives. The fusion of Stevin's static and Galileo's kinematic inclined-plane analyses establishes F/a as a well-defined, object-intrinsic quantity - the operational definition of inertial mass. The WEP compels the equivalence of inertial and gravitational mass without presupposing Newton's Second Law. Substituting this equivalence into the definition of inertial mass yields the law as a theoretical identity between independently defined quantities. The derivation is anchored in gravity because weight uniquely bridges statics and kinematics, yet the result is independent of the underlying force mechanism. The derivation carries structural consequences: modified-inertia formulations of MOND are inadmissible under the PEPM-WEP constraint; the location-invariance of the Kibble-balance realization of the SI kilogram is secured on first principles; and under the PEPM alone, torsion-balance and free-fall experiments constitute equally direct tests of the WEP. More fundamentally, Newton's Second Law is not an irreducible axiom of mechanics, but a structural consequence of deeper physical principles: energy conservation and the Einstein Equivalence Principle.

Modern physics has achieved extraordinary empirical success while retaining much of the absolute, unobservable structure introduced by Newton, largely without questioning its necessity. We investigate how far this structure can be eliminated by adopting a relational ontology guided by Leibniz's principle of sufficient reason. Removing absolute position, orientation, time and, finally, scale leads naturally to a formulation of the gravitational $N$-body problem where only dimensionless ratios are physically meaningful. Within this framework, the scale-invariant variety $V$ becomes a central quantity, providing a measure of structure, a natural ordering of shapes, and an emergent gravitational arrow of time. We argue that the resulting formulation unifies classes of Newtonian solutions previously regarded as distinct, uncovering a possible new symmetry, suggests a notion of explanation based on timeless spatial correlations rather than temporal evolution, and points towards a more economical ontology. Although developed in the context of Newtonian gravity, the principles proposed here may also offer a new perspective on general relativity and quantum mechanics.

We present preliminary results of the analysis of the precise spatial orientation of colonial Christian churches located in the city of Las Palmas, capital of the island of Gran Canaria (Spain), and its surroundings. Our sample consists of 27 churches, 15 of which belong to the city proper while the rest are situated within roughly 12 km away inland. Most of these churches were constructed between the first decades after the Castilian conquest of the island, and the end of the 19th century. In our analysis we examine whether these orientations respond to calendrical coincidences, to the main features of the landscape, or whether the standard tradition was followed regarding the orientation of the churches' apses eastwards. We find that no church in the sample is oriented towards points of the horizon on which the Sun rises on the day of the patronal feasts. Furthermore, we find no correlation between the global orientation pattern and the orography of the island which, near the local prominent Guiniguada ravine, could have been an important factor at the time of the construction of the churches. What we do find is that most of the orientations fit within the solar range, mainly to the east but also with a few historic churches oriented towards the west, while less than 20% have astronomical declinations outside of this range. In the statistical analysis, the declination histogram for the sample shows a pattern where the apses of the churches point consistently to the north of due east. This might signal constructions that were oriented to the rising Sun on dates close to Easter. We briefly discuss the implications these findings may have for a future study of the rest of Gran Canaria, which includes several dozens of historic churches scattered throughout the valleys, slopes, and volcanic calderas of the island.

Some authors have argued that spacetime in general relativity should be given a radically different interpretation from the ones given to spacetime in other theories in virtue of it being a gauge theory. In this article I review this sort of argument and argue against this view. That is, I argue that spacetime in general relativity can be understood analogously to spacetime in other models and that the argument from the diffeomorphism invariance of the theory misapplies the concepts of gauge theory to a context in which they are of limited application.