arXiv subjects

Julian Barbour

Publications and source records attributed to Julian Barbour.

At least 19 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 Poincar\'e 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 Poincar\'e'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↗

arXiv2024

Complexity and Its Creation

Except for crystalline or random structures, an agreed definition of complexity for intermediate and hence interesting cases does not exist. We fill this gap with a notion of complexity that characterises shapes formed by any finite number of particles greater than or equal to the three needed to define triangle shapes. The resulting shape complexity is a simple scale-invariant quantity that measures the extent to which a collection of particles has a uniform or clustered distribution. As a positive-definite number with an absolute minimum realised on the most uniform distribution the particles can have, it not only characterises all physical structures from crystals to the most complex that can exist but also determines for them a measure that makes richly structured shapes more probable than bland ones. Strikingly, the criterion employed to define the shape complexity forces it to be the product of the two functions that define Newtonian universal gravitation. This suggests both the form and solutions the law of a universe of such particles should have and leads to a theory that not only determines the complexity and probability of any individual shape but also its creation from the maximally uniform shape. It does this moreover in a manner which makes it probable that the cosmological principle, according to which on a sufficiently large scale the universe should have the same appearance everywhere, holds. Our theory relies on universal group-theoretical principles that may allow generalisation to include all forces and general relativity.

gr-qc↗

arXiv2023

Quantum without Quantum

In my contribution to the collection at https://dd70th.weebly.com marking the 70th birthday of David Deutsch I suggest that hitherto unrecognised properties of the Newton gravitational potential made scale-invariant through multiplication by the N-body root-mean-square length hint at redundancy of quantum wave functions for the explanation of physical effects.

quant-ph↗

arXiv2023

Gravity's Creative Core

I argue that the essence of gravity can be understood only in the context of the universe and that unrecognised implicit retention of Newtonian absolute scale and the impact of thermodynamics have obscured it. Typical attempts to resolve the conflict between maximal matter entropy in the early universe and the second law of thermodynamics illustrate my case. Rovelli, for example, argues that the scale factor, and with it the overall state, was out of equilibrium. He illustrates subsequent entropy-increasing interaction with other degrees of freedom in two models: particles in a box interacting with a piston initially out of equilibrium and Newtonian gravitating particles. However, the piston's position and momentum, like the particles", are defined relative to the box, while unobservable absolute space defines those of the gravitating particles. Their representation using observable scale-invariant variables shows that the box and gravitational statistics differ greatly: in the latter a single degree of freedom, gravity's creative core, drives the system in every solution from entropic-like disorder to ever increasing ordered structure. Since in many ways such particles are a good approximation to general relativity, this may also be true for our universe.

gr-qc↗

arXiv2022

Time's Arrow and Simultaneity: A Critique of Rovelli's Views

In the joint paper "Bridging the neuroscience and physics of time" Rovelli, as the physicist coauthor of neuroscientist Dean Buonomano, makes statements that rely on theoretical frameworks employed when the laws of thermodynamics and general relativity were discovered. Their reconsideration in the light of subsequent insights suggests growth of entropy is not the origin of time's arrow and that a notion of universal simultaneity may exist within general relativity. This paper is a slightly extended form of my invited contribution to the forthcoming Frontiers in Psychology special issue "Physical time within human time".

gr-qc↗

arXiv2021

Entropy and Cosmological Arrows of Time

Deutsch and Aguirre have recently shown that the solutions of certain dynamical systems typically contain a point of minimum size that they identify as an entropy minimum and from which the size and entropy increase to infinity in both directions of time. They argue that in such systems entropic arrows of time exist without the need for a special condition imposed in the past. In this paper I sharpen and extend the conditions under which such solutions exist but argue that the resulting arrows of time should not be interpreted as entropic since they point towards greater order and not disorder.

gr-qc↗

arXiv2021

Variability as a better characterization of Shannon entropy

The Shannon entropy, one of the cornerstones of information theory, is widely used in physics, particularly in statistical mechanics. Yet its characterization and connection to physics remain vague, leaving ample room for misconceptions and misunderstanding. We will show that the Shannon entropy can be fully understood as measuring the variability of the elements within a given distribution: it characterizes how much variation can be found within a collection of objects. We will see that it is the only indicator that is continuous and linear, that it quantifies the number of yes/no questions (i.e. bits) that are needed to identify an element within the distribution, and we will see how applying this concept to statistical mechanics in different ways leads to the Boltzmann, Gibbs and von Neumann entropies.

cond-mat.stat-mech↗

arXiv2016

Janus Points and Arrows of Time

We clarify and strengthen our demonstration that arrows of time necessarily arise in unconfined systems. Contrary to a recent claim, this does not require an improbable selection principle.

gr-qc↗

arXiv2016

Arrows of time in unconfined systems

Entropy and the second law of thermodynamcs were discovered through study of the behaviour of gases in confined spaces. The related techniques developed in the kinetic theory of gases have failed to resolve the apparent conflict between the time-reversal symmetry of all known laws of nature and the existence of arrows of time that at all times and everywhere in the universe all point in the same direction. I will argue that the failure may due to unconscious application to the universe of the conceptual framework developed for confined systems. If, as seems plausible, the universe is an unconfined system, new concepts are needed.

gr-qc↗

arXiv2015

Entropy and the Typicality of Universes

The universal validity of the second law of thermodynamics is widely attributed to a finely tuned initial condition of the universe. This creates a problem: why is the universe atypical? We suggest that the problem is an artefact created by inappropriate transfer of the traditional concept of entropy to the whole universe. Use of what we call the relational $N$-body problem as a model indicates the need to employ two distinct entropy-type concepts to describe the universe. One, which we call entaxy, is novel. It is scale-invariant and decreases as the observable universe evolves. The other is the algebraic sum of the dimensionful entropies of branch systems (isolated subsystems of the universe). This conventional additive entropy increases. In our model, the decrease of entaxy is fundamental and makes possible the emergence of branch systems and their increasing entropy. We have previously shown that all solutions of our model divide into two halves at a unique `Janus point' of maximum disorder. This constitutes a common past for two futures each with its own gravitational arrow of time. We now show that these arrows are expressed through the formation of branch systems within which conventional entropy increases. On either side of the Janus point, this increase is in the same direction in every branch system. We also show that it is only possible to specify unbiased solution-determining data at the Janus point. Special properties of these `mid-point data' make it possible to develop a rational theory of the typicality of universes whose governing law, as in our model, dictates the presence of a Janus point in every solution. If our self-gravitating universe is governed by such a law, then the second law of thermodynamics is a necessary direct consequence of it and does not need any special initial condition.

gr-qc↗

arXiv2014

Identification of a gravitational arrow of time

It is widely believed that special initial conditions must be imposed on any time-symmetric law if its solutions are to exhibit behavior of any kind that defines an `arrow of time'. We show that this is not so. The simplest non-trivial time-symmetric law that can be used to model a dynamically closed universe is the Newtonian $N$-body problem with vanishing total energy and angular momentum. Because of special properties of this system (likely to be shared by any law of the Universe), its typical solutions all divide at a uniquely defined point into two halves. In each a well-defined measure of shape complexity fluctuates but grows irreversibly between rising bounds from that point. Structures that store dynamical information are created as the complexity grows and act as `records'. Each solution can be viewed as having a single past and two distinct futures emerging from it. Any internal observer must be in one half of the solution and will only be aware of the records of one branch and deduce a unique past and future direction from inspection of the available records.

gr-qc↗

arXiv2013

A Gravitational Origin of the Arrows of Time

The only widely accepted explanation for the various arrows of time that everywhere and at all epochs point in the same direction is the `past hypothesis': the Universe had a very special low-entropy initial state. We present the first evidence for an alternative conjecture: the arrows exist in all solutions of the gravitational law that governs the Universe and arise because the space of its true degrees of freedom (shape space) is asymmetric. We prove our conjecture for arrows of complexity and information in the Newtonian N-body problem. Except for a set of measure zero, all of its solutions for non-negative energy divide at a uniquely defined point into two halves. In each a well-defined measure of complexity fluctuates but grows irreversibly between rising bounds from that point. Structures that store dynamical information are created as the complexity grows. Recognition of the division is a key novelty of our approach. Each solution can be viewed as having a single past and two distinct futures emerging from it. Any internal observer must be in one half of the solution and will only be aware of one past and one future. The `paradox' of a time-symmetric law that leads to observationally irreversible behaviour is fully resolved. General Relativity shares enough architectonic structure with the N-body problem for us to prove the existence of analogous complexity arrows in the vacuum Bianchi IX model. In the absence of non-trivial solutions with matter we cannot prove that arrows of dynamical information will arise in GR, though they have in our Universe. Finally, we indicate how the other arrows of time could arise.

gr-qc↗

arXiv2013

The Solution to the Problem of Time in Shape Dynamics

The absence of unique time evolution in Einstein's spacetime description of gravity leads to the hitherto unresolved `problem of time' in quantum gravity. Shape Dynamics is an objectively equivalent representation of gravity that trades spacetime refoliation invariance for three-dimensional conformal invariance. Its logical completion presented here gives a dimensionless description of gravitational dynamics. We show that in this framework the classical problem of time is completely solved. Since a comparable definitive solution is impossible within the spacetime description, we believe Shape Dynamics provides a key ingredient for the creation of quantum gravity.

gr-qc↗

arXiv2013

Scale Anomaly as the Origin of Time

We explore the problem of time in quantum gravity in a point-particle analogue model of scale-invariant gravity. If quantized after reduction to true degrees of freedom, it leads to a time-independent Schrödinger equation. As with the Wheeler--DeWitt equation, time disappears, and a frozen formalism that gives a static wavefunction on the space of possible shapes of the system is obtained. However, if one follows the Dirac procedure and quantizes by imposing constraints, the potential that ensures scale invariance gives rise to a conformal anomaly, and the scale invariance is broken. A behaviour closely analogous to renormalization-group (RG) flow results. The wavefunction acquires a dependence on the scale parameter of the RG flow. We interpret this as time evolution and obtain a novel solution of the problem of time in quantum gravity. We apply the general procedure to the three-body problem, showing how to fix a natural initial value condition, introducing the notion of complexity. We recover a time-dependent Schrödinger equation with a repulsive cosmological force in the `late-time' physics and we analyse the role of the scale invariant Planck constant. We suggest that several mechanisms presented in this model could be exploited in more general contexts.

gr-qc↗

arXiv2011

Mach's Principle: A Response to Mashhoon and Wesson's Paper arXiv: 1106.6036

In their recent "Mach's principle and higher-dimensional dynamics", Mashhoon and Wesson argue that Mach's principle is not properly incorporated into general relativity and that in Einstein's theory "the origin of inertia remains essentially the same as in Newtonian physics." While it is true that the motion of a single test particle in a Newtonian inertial frame of reference appears essentially the same as in an Einsteinian local inertial frame, this misses the point. The issue is not what motion looks like in an inertial frame of reference but what is the origin of the inertial frame. Unlike Newtonian dynamics, general relativity does implement Mach's principle when considered from this correctly formulated point of view.

gr-qc↗