arXiv subjects

Maria I. R. Lourenço

Publications and source records attributed to Maria I. R. Lourenço.

4 recordsLinked to original sources

arXiv2026

A Scale-Invariant Theory of the Universe

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.

gr-qc↗

arXiv2026

Structural morphology and the gravitational arrow of time

The Newtonian $N$-body problem in the zero-energy, zero-linear-momentum, and zero-angular-momentum sector provides a time-reversal-invariant setting in which generic complete solutions possess a Janus point and exhibit a gravitational arrow on both branches away from it. The dimensionless variety $V$, a global scale-invariant measure of clustering contrast, is not pointwise monotonic but fluctuates while growing between rising bounds away from the Janus region. Central configurations are critical shapes of the same scale-invariant landscape and therefore provide controlled probes of the structural information encoded by $V$. We investigate this question for two planar $N=5000$ central configurations using the numerical particle-coordinate data. Local morphology is quantified by the six-neighbour anisotropy $A_6$, which ranges from $0$ for an isotropic local environment to $1$ for an effectively one-dimensional one. Although the varieties of the two configurations differ by only $1.686\%$, their mean anisotropies differ by $156.8\%$, from $0.1331$ to $0.3419$. Moreover, $18.1\%$ of the particles in the higher-variety configuration satisfy $A_6>0.5$, whereas none do so in the lower-variety configuration. The anisotropy ordering persists for all tested neighbourhood sizes $4\le k\le12$, and the principal contrast survives a dimensionless close-pair robustness test. For this pair of critical shapes, nearby values of the global variety therefore coexist with markedly different local geometrical organization. Thus the scalar quantity whose long-term behavior characterizes the BKM gravitational arrow does not, by itself, uniquely specify morphology. This identifies local relational observables as a complementary level of description and provides a quantitative bridge between the static shape-space landscape and morphology along genuine Janus-point histories.

gr-qc↗

arXiv2026

The Emergence of Measured Geometry in Self-Gravitating Systems

This work investigates the geometrical properties of self-gravitating $N$-body systems from the perspective established by Henri Poincaré and Albert Einstein concerning the operational nature of measured geometry. Utilizing recent numerical analyses of central configurations--special equilibrium solutions to the Newtonian $N$-body problem--we uncover systematic spatial variations in nearest-neighbor particle separations correlated with the radial distance from the system's center of mass. We argue that these variations reflect a context-dependent, emergent effective geometry shaped by gravitational interactions, in accordance with Poincaré's assertion that measured geometry depends on the forces influencing measuring devices, and Einstein's view that rods and clocks define physical geometry through their local dynamics. By revisiting these foundational insights within a modern computational framework, we provide evidence that geometry in self-gravitating Newtonian systems is not a fixed background, but an emergent construct arising from internal physical interactions.

gr-qc↗

arXiv2026

Scale Invariance, Variety and Central Configurations

Scale invariance has received very little attention in physics. Nevertheless, it provides a natural conceptual foundation for a relational understanding of the universe, where absolute size loses meaning and only dimensionless ratios retain physical significance. We formalize this idea through the $N$-body problem, introducing a scale-invariant function--the variety, $V$--built from the square root of the center-of-mass moment of inertia and the Newtonian potential. Critical points of $V$, known as central configurations, correspond to special particle arrangements that preserve their shape under homothetic collapse or expansion. Numerical exploration of these critical points reveals that even slight deviations from the absolute minimum of $V$, which corresponds to a remarkably uniform configuration, lead to the spontaneous formation of filaments, loops, voids and other patterns reminiscent of the cosmic web. This behavior is a consequence of the intrinsic structure of shape space--the space of configurations modulo translations, rotations and dilatations--in which regions of higher variety act as attractors. Our results suggest that scale-invariant dynamics not only captures the relational nature of physical laws but also naturally generates organized patterns, offering a novel perspective on the formation of cosmic structures and on the emergence of a gravitational arrow of time from scale-invariant, relational dynamics.

physics.hist-ph↗