A central question for the foundations of thermodynamics is which conceptual structures underpin the existence of entropy and temperature. Jauch claimed that entropy and temperature could be derived from a novel conservation law. This paper reconstructs the physics and mathematics of Jauch’s claim and finds that his original proof is not valid. Remarkably, his theorem is still true. We provide an alternative proof using geometric ideas from modern gauge theory, revealing a deep geometric structure in thermodynamics. This result also helps to settle an old debate by showing that entropy and temperature can be defined in a new, conceptually clear way without appeal to an irreversible assumption like the second law.
Decoherence explains why selected quantum histories behave as mutually exclusive alternatives with Born weights, but it does not by itself show that such alternatives are worlds. We formulate this as a geometric representability problem within decoherent histories. A world-bearing branch must support a local physical representation: a compatible spectral and local structure sufficient for spacetime-like observables, stable records, and observer-level description. For a history effect F_α =K_α ^† K_α and a positive spectral probe A , we introduce the branch-resolved heat trace Θ _α (t)=Tr(e^-tA/2F_α e^-tA/2) . Its small-time behavior tests the spectral supply carried by that branch. We prove that identical decoherence data can be realized by branches with inequivalent heat profiles, and that exact decoherent refinement can decompose a spectrally thick branch into probability-bearing but spectrally thin branches. A positive lower-bound theorem then shows that genuine branch-local spectral regularity forces corresponding heat-trace growth. Decoherence remains essential for probabilities, but branch ontology requires structural admissibility beyond decoherence.
Recently, Dunajski and Gundry (Commun. Math. Phys., 342(3), 2016) have developed a version of twistor theory for the non-relativistic domain. Unlike relativistic twistor theory, their approach is able to reproduce the entire space of models of Newton–Cartan theory. We critically assess the significance of non-relativistic twistors, in particular with respect to proposals by Dunajski and Penrose (Ann. Phys., 451, 2023) that using non-relativistic twistors to describe gravitationally induced collapse could play a part in solving the quantum measurement problem.
This special issue brings perspectivism, as a recent development in the philosophy of science, into contact with non-objectivist interpretations of quantum mechanics. By “objectivist interpretations,” broadly understood, we mean interpretations that seek to eliminate operational notions such as “measurement” from the fundamental postulates of the theory and insist that quantum mechanics, like classical mechanics, yields a purely objective, third-person description of how reality evolves in time. The guiding hypothesis, exemplified in several contributions to this issue, is that quantum mechanics supports perspectivist approaches to science, and that perspectivism can serve as a suitable philosophical-conceptual framework for certain interpretations of quantum mechanics.
With the classical distinction between context of discovery and context of justification considered by many to have been overcome, heuristics (understood in a broad sense) has increasingly rekindled the interest of philosophers of science. Building on this trend, a heuristic approach to the Voigt transformation (based on Rescher’s Aporetics) is first presented – a topic on which there seem to be no precedents in the literature. Second, the value of this approach is defended from a philosophical (and, indirectly, pedagogical) viewpoint. By using this approach, several conceptual links in the theory of space-time can be highlighted (links which go unnoticed in classical hypothetical-deductive methods leading to the Voigt transformation). Third, Rescher’s aporetics also suggests a heuristic path from the previously obtained Voigt transformation to the Lorentz transformation. Taken together, the proposed heuristic route enables the structure of the conceptual process underpinning the following chain of links (obviously not logical, but heuristic) Galileo ⇒ Voigt ⇒ Lorentz to be presented in an original and unified form. According to this route, an interesting sense is thus established in that the Voigt transformation occupies a natural place between the Galilean and Lorentz transformations.
While well-tested at solar system scales, Newtonian gravity exhibits anomalies at larger scales and accelerations below 10^-9 m/s^2 . Although Yukawa-like modifications can reconcile these anomalies with general relativity up to solar system scales, they face challenges at galactic scales. Notably, gravitational anomalies at accelerations ≤ 10^-9 m/s^2 for separations down to 50 μ m remain undetected experimentally. This paper presents a mathematical framework for Yukawa modification of Newtonian gravity in weak acceleration regimes (≤ 10^-9 m/s^2) and small separations ( ≤ 30 μ m) using an extended space model with an extra dimension. This model suggests a vacuum-sourced inertia effect from peculiar photons, with implications for the Mach principle. These photons’ entanglement scale ( ≤ 30 μ m) hints at the possibility of longer-range photon entanglement via analytic continuation, opening new avenues for research in quantum gravity and cosmology.
Here we discuss direct links of the number of fundamental dimensions to the fundamental natural constants using simple arguments of dimensional analysis based on Maxwell’s dimensions length (L), time (T) and mass (M) as well as the constants G, c, ħ and e. We find that the form of the fine-structure constant is a direct consequence of this connection. Additionally, our approach emphasises that gravity is a quite distinct area of physics which is not yet successfully quantised, i.e. not yet combined with quantum mechanics. We also discuss different unit systems based on dimensional analysis and natural constants.
De Broglie gravitational waves form an axially symmetric class of vacuum solutions of the linearized Einstein equations. Unlike the well-known massless transverse perturbations in the weak-field regime, they possess an effective mass and exhibit longitudinal degrees of freedom, allowing them to act as guiding fields for elementary particles. In this paper, we show that the dynamics of the de Broglie gravitational wave, described in terms of the real part of a classical field ψ , is compatible with single particle Quantum Mechanics, and that the complex field ψ can be interpreted as the single particle wave function. In particular, we find that ψ satisfies the Schrödinger equation for a free particle and, using the principles of gravitational lensing, the same holds in the presence of a weak central potential. We show that when our gravitational wave passes through two closely separated slits, it diffracts and interferes, creating the characteristic pattern of bright and dark bands observed in quantum experiments. We propose two different interpretations: a wave-particle picture, in which wave and particle are two distinct entities, and an effective background field perspective, in the spirit of soliton theory. A variant of the double-slit experiment that could serve, in principle, as an experimental test of the proposed framework is also discussed.
Quantum theory brings into question the compatibility of the twin desiderata of exact knowability of the present state of the physical world and perfect predictability of its future states. Bohr's coordination-causality complementarity principle transforms this tension into one between properties (as ordinarily understood in classical physics) and deterministic causality. Here, we develop an explicit model of quantum properties which accommodates this essential tension. Our approach integrates operational, reconstructive, and metaphysical standpoints. In particular, we make use of an operational framework employed in a recent operational reconstruction of Feynman's formulation of quantum theory; base our property model on an analysis of property types; and use the notions of actuality and potentiality to frame the model. We show that this quantum property model provides a natural resolution of Zeno's paradox of motion, and provides reliable intuitions about phenomena such as electron diffraction and the non-local behaviour of entangled states of non-identical particles.
The Lorentz transformations may be derived based on the Principle of Relativity and a few other plausible physical assumptions, without introducing the Principle of the Constancy of the Velocity of Light. All existing derivations of this kind introduce a (pre-) causality (or equivalent) condition in order to constrain the transformations of coordinates to assume the form of the Lorentz transformations (or their Galilean limit). We show how such a condition may be dropped: as a consequence, the Principle of Relativity in itself implies any causal relationship to be conserved under a change of reference frame.
We propose an extension of Bell-type Bohmian quantum field theories, called Contextual Bohmian Quantum Field Theory (CBQFT), which integrates micro-level dynamics and macro-level contextual structure within a unified, ontologically explicit formalism. CBQFT introduces classical variables Λ that encode macroscopic contexts—such as detector configurations, thermal phases, or symmetry-breaking sectors—and allows these to modulate the underlying quantum dynamics in a lawlike way. We develop two versions of the model. CBQFT-1 treats context as a fixed but dynamically influential background, entering via a context-sensitive Hamiltonian and modified Bell-type jump rates on a single Fock space. CBQFT-2 upgrades context to a dynamical variable co-evolving with the particle (or field) configuration: Λ (x,t) selects a (typically inequivalent) representation of the field algebra on a Hilbert space, wavefunctions are realised as global sections of the resulting Hilbert bundle, and Bohmian trajectories are guided by globally well-defined velocity fields constructed from local currents. Context transitions in CBQFT-2 are governed by a stochastic kernel informed by particle (or field) configurations and histories. This yields a Bohmian QFT with an explicit feedback loop between quantum events and macroscopic structure, offering a hylomorphic account of measurement, decoherence, and top–down causation.
Recent no-go theorems on interpretations of quantum theory featuring an assumption of ‘Absoluteness of Observed Events’ (AOE) are shown to have an unexpectedly strong corollary: one cannot reject AOE and at the same time assume that the ‘observed events’ in question can all be (i) single-valued and (ii) embedded within a single background space-time common to all observers. Consequently, interpretations that reject AOE appear incompatible with a ‘block universe’ view of space-time.
Relational Quantum Mechanics (RQM) treats quantum states as observer-dependent facts rather than absolute properties. While this relational stance is conceptually attractive, it raises concerns about empirical confirmation, particularly in multi-observer scenarios. Existing responses within RQM focus on securing agreement between observers by strengthening the status, stability, or accessibility of recorded outcomes. However, they leave open a more basic question: what grounds the persistence of an observer across time? Scientific observation presupposes stable records and the capacity to relate outcomes across successive measurements. We argue that the minimal definition of the observer in RQM as a merely interacting physical system is insufficient to support this requirement. We propose a complementary account of the observer that distinguishes physical interaction from informational coherence, and show how this distinction supports empirical confirmation in Wigner’s friend–type scenarios.
A first-principles derivation of deformed quantum mechanics is presented for the α ' -corrected heterotic string. Upon compactification, the leading corrections induces a quartic momentum correction term to a scalar dispersion relation. This modification is precisely equivalent to a deformed canonical commutator whose single deformation parameter is set by the Calabi-Yau volume, internal curvature, and background fluxes, thereby establishing a finite minimal length. Positivity of the four-derivative coupling confines the Lee-Wick ghost to scales far above the higher-derivative cutoff, whose value and thus the threshold for stringy corrections is fixed by the same geometric data. Moreover, these inputs can amplify the deformation, pushing the minimal length well beyond the string scale. Earlier proposals based on generalized-uncertainty-principle deformations suggested, on purely phenomenological grounds, that quantum-gravity effects might emerge at such elevated scales; the present analysis provides the first rigorous string-theoretic foundation for that scenario. Finally, unlike standard phenomenological models, the deformation derived here depends on the probe mass, yielding significant implications for important physical problems such as species-sensitive black-hole bounds.
This paper argues that von Neumann entropy plays two conceptually distinct roles in quantum theory. When applied to global mixed states, it expresses the quantum analogue of the informational entropy. But when applied to reduced states of entangled systems, it measures objective physical correlations. We propose that this second usage realizes a new informational kind, which we call relational information. Unlike information in communication theory, it reflects structural interdependence between systems, not probability about a certain outcome. We further suggest that this informational kind has ontological significance: relational information is a physically instantiated feature of entangled systems, and not merely an agent-relative concept.
We introduce a minimal, mathematically controlled modification of the classical action principle that embeds a small, divergence-free field f_μ (x) into the Euler–Lagrange equations primarily through modifications in electrodynamics. This modification preserves locality, causality, and charge conservation while generating controlled, small deviations from standard classical trajectories, providing a unified, quantitative framework for mild classical indeterminism. The field f_μ is Lorentz-covariant and characterized by a physically motivated spectral density, ensuring consistency across particle, scalar, and gauge systems. To leading order, we derive corrected forces, compute ensemble-averaged trajectory shifts, and identify spectral signatures accessible to high-precision experiments such as Penning traps and cathode beams. With ultraviolet-regularized spectra, the predicted deviations lie within current experimental sensitivity, establishing a direct bridge between foundational theory and empirical testability.
Collapse theories provide one of the main approaches to the quantum measurement problem. Roderich Tumulka’s collapse theory (GRWf) has attracted interest because it offers a relativistic collapse theory. GRWf utilises an ontology of flashes to accommodate EPR-Bell type non-local influences within a relativistic theory, an idea suggested by John Bell. Tim Maudlin raises a concern with Tumulka’s flash ontology, arguing that it is too sparse to convincingly account for certain microscopic phenomena. This paper proposes a modification to GRWf that addresses the problem of sparseness, whilst retaining a relativistic treatment of quantum non-locality. The proposal, referred to as the space-time normalisation interpretation (STN), combines the GRWf flash ontology with a statistical interpretation of the wavefunction. The statistical structure of the interpretation is presented as a Hawkes process, consisting of flashes and an intensity function governing their occurrence. For a single-particle system, the square modulus of a renormalised wavefunction serves as the intensity function of the Hawkes process.
