Foundations of Physics

Banerjee, Robi

doi: 10.1007/s10701-026-00929-7pmid: N/A

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, \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\hbar $$\end{document} 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.

Wells, James D.

doi: 10.1007/s10701-026-00930-0pmid: N/A

The Hierarchy Problem of elementary particle physics can be divided into two separate problems: the Intrinsic and Extrinsic Hierarchy Problems. The Intrinsic Hierarchy Problem (IHP) arises when the Wilsonian renormalization group induces a large \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Lambda _\textrm{UV}^2$$\end{document} cutoff dependence on a much lighter scalar mass, creating a large finetuning. The Extrinsic Hierarchy Problem (EHP) arises when the IR theory is augmented with generically assumed extra states and interactions in the UV, making the resulting IR effective theory appear highly finetuned. The IHP is straightforward to analyze within a theory, but has suspicious regulator dependence, which has been suggested by some to be indication of a faux problem. The EHP is less straightforward to analyze, but has strength of physical intuition. We analyze EHP as a formal paradox, spelling out its premises and reasoning. From this we classify solutions to the EHP in terms of premise violations, and we articulate why some purported solutions to the Hierarchy Problem only partially solve the IHP and leave the EHP unaddressed.

Kumar, Himanshu; Pourhassan, Behnam; Farahani, Hoda; Upadhyay, Sudhaker

doi: 10.1007/s10701-026-00932-ypmid: N/A

While well-tested at solar system scales, Newtonian gravity exhibits anomalies at larger scales and accelerations below \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$10^{-9} m/s^2$$\end{document}. 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 \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\le 10^{-9} m/s^2$$\end{document} for separations down to \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$50\, \mu$$\end{document}m remain undetected experimentally. This paper presents a mathematical framework for Yukawa modification of Newtonian gravity in weak acceleration regimes \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(\le 10^{-9} m/s^2)$$\end{document} and small separations (\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\le 30 \, \mu$$\end{document}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 (\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\le 30\, \mu$$\end{document}m) hints at the possibility of longer-range photon entanglement via analytic continuation, opening new avenues for research in quantum gravity and cosmology.

Pérez-Barragán, J. F.

doi: 10.1007/s10701-026-00935-9pmid: N/A

The multisymplectic Hamiltonian formalism is a generalization of the Hamiltonian formalism that manifestly preserves covariance in the description of fields and that has been proposed as a possible framework for developing a Lorentz-covariant, canonical quantization scheme. However, the possibility of defining multiple Poisson brackets within this formalism has significantly limited its practical use in field theory. In this paper, we establish a connection between the Lagrangian and multisymplectic descriptions of classical fields interacting with point particles in the field’s momentum representation by deriving the image of the de Donder–Weyl function for a general tensor representation of the Lorentz group. The calculation is carried out explicitly for the complex scalar field, the electromagnetic field, and the classical Dirac field. On this basis, we propose a Lorentz-covariant Poisson bracket with respect to the canonical variables of the fields, thereby opening the possibility of studying the complete system within a consistent relativistic and canonical framework.

Anselmi, Damiano

doi: 10.1007/s10701-026-00928-8pmid: N/A

Certain approaches to quantum gravity, such as the one based on the concept of purely virtual particles (fakeons), sacrifice the cause-effect relation at very small scales to reconcile renormalizability with unitarity. Other developments have also urged caution regarding the idea of causality as a fundamental principle. In this paper, we examine the problem from multiple perspectives, including locality and predictivity, and extend the existing skepticism in several directions. Emphasizing the impact of unruly “disruptors”, we point out that the illusory arrow of time associated with causality and predictivity is inherently statistical. This renders the cause-effect relation strained at the microscopic level. We also show that causation is a borderline concept that demands belief in entities which can act on nature without being part of it. Ultimately, not only is renouncing microcausality a reasonable price to pay for a consistent and predictive theory of quantum gravity (as is the one based on the fakeon idea), but the very notion of causality is misleading. Resting as it does on metaphysical assumptions, it should therefore be abandoned in fundamental physics.

Krátký, Matěj; Narra, Bhanu; Read, James

doi: 10.1007/s10701-026-00925-xpmid: N/A

String field theory is supposed to stand to perturbative string theory as quantum field theory stands to single-particle quantum theory; as such, it purports to offer a substantially more general and powerful perspective on string theory than the perturbative approach. In addition, string field theory has been claimed for several decades to liberate string theory from any fixed, background spatiotemporal commitments—thereby (if true) rendering it ‘background independent’. But is this really so? In this article, we undertake a detailed interrogation of this claim, finding that the verdict is sensitive both to one’s understanding of the notion of background independence, and also to how one understands string field theory itself. Although in the end our verdicts on the question of the background independence are therefore somewhat mixed, we hope that our study will elevate the levels of systematicity and rigour in these discussions, as well as equip philosophers of physics with a helpful introduction to string field theory and the variety of interesting conceptual questions which it raises.

Laraudogoitia, Jon Pérez

doi: 10.1007/s10701-026-00931-zpmid: N/A

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.