Julian Barbour and Maria I. R. Lourenço propose an alternative to quantum theory founded on the idea that the universe may be fundamentally defined by its shapes rather than its evolution through time. The work outlines a framework describing shapes through a single, scale-invariant function based on ratios of masses, charges and particle separations, eliminating the need to track change.

This approach assumes only point particles in Euclidean space and offers a potential path to understanding atomic and molecular structures without standard quantum mechanics. The researchers aim to account for observed phenomena with fewer assumptions, suggesting physics may have accumulated unnecessary conceptual layers.

Scale-Invariant Shapes as Fundamental Ontology

The framework proposes that the fundamental characteristics defining shapes are ratios of masses and charges, alongside ratios of mutual separations between particles, moving away from absolute values to emphasize relational properties. This approach diverges from conventional physics by asserting that the observed structures of atoms, molecules, and macroscopic bodies can be derived from spatial configurations alone, without requiring a focus on how those structures change over time.

Julian Barbour and Maria I. R. Lourenço posit that a single, scale-invariant function can describe these shapes, suggesting a potentially simpler underlying reality than current models imply. This theory challenges the long-held assumption that dynamical evolution is necessary to explain the universe, instead focusing on static configurations of point particles in Euclidean space. This contrasts sharply with Newtonian physics, which focuses on how particle distributions change, while this framework considers only the distribution itself, viewing different configurations as fundamentally distinct.

The work’s core concept is scale invariance, taking it as the most fundamental symmetry underlying physical theory and investigating whether the universe’s observed structures can be explained within this constraint. Unlike Newton’s theory of gravity, which concerns changes in particle distributions, this approach focuses solely on the distribution itself, defining shapes through a scale-invariant measure of particle uniformity or clustering.

The researchers suggest that observed effects might be explained solely by the structure of these shapes, potentially eliminating the need to introduce additional entities like photons. “Although it was Newton’s theory of gravity that motivated us to define and study the properties of the variety, its definition as a scale-invariant measure of the degree to which particles are uniformly distributed or clustered owes nothing to the theory of gravity, nor indeed to anything associated with dynamical evolution between states,” they explain.

The ambition of this framework extends to potentially deriving the patterns currently predicted by quantum theory from this non-dynamical, scale-invariant foundation. If a suitable scale-invariant function, defined on distributions of point particles, can accurately reproduce these patterns, it could offer an alternative to the mathematical formalism of quantum mechanics. This would retain the empirical success of quantum theory while grounding it in a simpler ontological basis. “most unlikely since square roots do not occur in basic equations,” they add, suggesting a departure from mathematical complexities inherent in standard quantum mechanics.

Mass and Charge Ratios Define Configurations

The fundamental geometry of a system, within this new framework, isn’t dictated by absolute particle masses or charges, but by their ratios alongside the ratios of their distances from one another. This relational emphasis diverges from traditional physics, where absolute values often take precedence in calculations and theoretical models.

Researchers have defined a function, termed the ‘variety’, as a dimensionless ratio comparing the root-mean-square length and the mean-harmonic length of particle distributions, offering a way to quantify the uniformity or clustering of particles. The variety’s value is determined solely by these ratios, independent of any overall scale, and provides a measure of configuration rather than change.

The work demonstrates that the variety can be calculated for a distribution of N particles, each with masses normalised to unity and defined Cartesian coordinates, using a specific formula involving the separations between particles. This calculation yields a value that describes how far a given configuration deviates from the most uniform arrangement possible for that set of particles. A configuration close to the absolute minimum of the variety exhibits a remarkably uniform distribution with a nearly perfect spherical boundary, as illustrated by simulations of 5,000 equal-mass particles.

The framework requires no concept of dynamical evolution. It focuses exclusively on the static spatial arrangement of particles. “Newton’s theory concerns how a distribution of particles changes, whereas we consider only the distribution itself,” the researchers state, highlighting a fundamental departure from conventional physics. The age of a shape, defined as the difference between its variety and the minimum attainable variety, provides a quantitative measure of how far a configuration is from this ideal uniform state.

The Scale-Invariant Function V and Uniformity

The variety, a dimensionless ratio defining a configuration’s deviation from perfect uniformity, is a central element in a novel approach to understanding physical structures. Defined as the root-mean-square length divided by the mean-harmonic length of a particle distribution, this function provides a measure of shape independent of scale, calculated from ratios of particle masses and their separations. For a finite set of N particles, each with a mass expressed as a fraction of the total mass M, the variety offers a quantifiable metric for spatial arrangement.

The researchers define the variety, V, as a ratio, allowing for comparisons between configurations regardless of overall size. This framework posits that remarkably uniform distributions arise when the variety approaches its absolute minimum, V₀, exhibiting nearly perfect spherical boundaries. The function’s construction, inspired by Leibniz’s Monadology, emphasizes relational properties over absolute values, focusing on how particles are positioned relative to one another.

The calculation of the variety involves summing over all particle pairs, considering both their masses and the distances between them, providing an assessment of the configuration’s structure. Newtonian gravity, reformulated in scale-invariant terms using this variety function, hints at a broader applicability beyond gravitational interactions. The team proposes that incorporating charge ratios into a revised variety function could potentially model electromagnetic phenomena.

Further extensions, though mathematically undefined at present, might even reach towards quantum mechanics, offering a non-dynamical alternative to the standard quantum formalism. The programme identifies a possible route by which such a derivation might be sought, emphasizing the exploratory nature of their work.

Long-Range Correlations Mirror Quantum Entanglement

The framework describes shapes through a single scale-invariant function, assuming only point particles in Euclidean space, characterised by ratios of masses (and charges) and by the ratios of their mutual separations. In principle, this framework provides a unified description of finite subsystems embedded in a configuration of infinitely many particles and offers a possible route to deriving the observed structures of atoms, molecules and macroscopic bodies without invoking standard quantum mechanics.

These correlations, unlike those in quantum mechanics, are not limited by range and instead increase without bound as the number of particles considered grows, suggesting a timeless connection between them. The theory posits that these connections are ‘instantaneously created’, independent of time and share characteristics with statistical correlations violating Bell inequalities, though the researchers emphasize this is not yet a complete alternative to quantum theory.

The observed patterns in quantum experiments, such as those from two-slit experiments, may be partially created by the experimental setup itself, a concept already acknowledged by pioneers like Bohr and Heisenberg. This scale-invariant approach suggests that observed correlations depend on the complete experimental arrangement, not just isolated subsystems, offering a potentially unifying perspective on quantum phenomena.

These geometrical correlations are dictated by the constraints of Euclidean space, where ratios of particle separations define shapes, and are not probabilistic like quantum entanglement. The authors note that these Euclidean correlations, like quantum entanglement, may ultimately be understood as timeless, aligning with the theory’s non-dynamical nature.

The work focuses on physical records and the correlations within them, suggesting that the experimental arrangement itself conditions the observed phenomena. If successful, this could retain the empirical accuracy of quantum mechanics while replacing its complex mathematical formalism with a simpler, non-dynamical system based on the correlations of points within shapes. The programme, they acknowledge, is ambitious, but offers a potential path to understanding the underlying structure of the universe. The researchers emphasize that what is experimentally accessible are ultimately physical records and the correlations between structures within those records, motivating a complete interpretation.

Limitations: Reproducing Quantum Predictions Remains Open

The empirical success of quantum theory does not automatically validate its underlying mathematical description of reality, prompting exploration of alternative ontological foundations capable of reproducing observed results with greater conceptual simplicity. While current frameworks rely on complex wave functions, recent mathematical discoveries suggest that some quantum phenomena may be explicable without them, raising the possibility of a more streamlined theoretical basis. This work demonstrates that a simple, scale-invariant geometrical structure can generate unexpectedly rich and highly organised configurations, though establishing a direct equivalence to quantum predictions remains a key challenge.

The ability to reproduce experimentally confirmed quantum correlations is not yet fully established; the current results demonstrate only the potential for such a derivation, not its completion. The framework’s capacity to select configurations mirroring quantum experimental outcomes, and to reproduce their statistical frequencies, is a test yet to be conclusively met.

A successful demonstration would not merely identify structures resembling quantum results, but would precisely replicate the statistical regularities observed in experiments, a distinction the authors emphasize. This focus on replicating statistical outcomes, rather than simply achieving structural similarity, highlights the rigorous standard for validation. Physics traditionally explains phenomena through a sequence of events ordered in time, but this approach may be fundamentally limited in its ability to describe the infinite.

The authors argue that explanations relying on temporal evolution are inadequate, particularly when attempting to extend understanding beyond finite systems. This perspective suggests that a complete description of the universe might not require invoking change in time, but could instead be fully captured by a static configuration of relationships. If the observed effects can be reproduced by a theory based solely on weighted points and scale-invariant principles, the need for entities like photons as additional explanatory components may be circumvented.

This consistency with established pre-quantum views offers a potential bridge between classical and quantum descriptions, suggesting a path toward a unified framework. The exploration of scale invariance extends beyond gravitational dynamics, hinting at its potential as a general foundation for all of physics, though further investigation is necessary to confirm this broader applicability.

The work begins with a minimal ontology of weighted points and the ratios of their separations, investigating whether a scale-invariant description of shape can be an alternative to quantum mechanics. The motivation for this approach stems from the enduring questions surrounding the ontological status of elements within quantum theory, such as wave functions, Hilbert spaces, and photons. The question of whether appropriate generalisations can account for the specific statistical structure of quantum phenomena remains open, and represents a central focus for future research.

Holistic Approach to Experimental Observation & Correlations

Experimental observations are inextricably linked to the conditions creating them, a perspective echoing early insights from Bohr and Heisenberg regarding the nature of quantum phenomena. The framework detailed in this work suggests observed correlations may stem from the complete experimental setup, not merely isolated components, potentially reframing the interpretation of entanglement as a consequence of well-defined geometrical constraints. This view challenges the traditional reductionist approach dominating physics since Newton’s introduction of absolute space and time, proposing a fundamentally different way to interpret physical reality.

The proposed ontology centers on weighted points defined by ratios of masses and separations within Euclidean space, a system where correlations aren’t merely coincidental but inherent to the geometry itself. These ratios, while correlated by spatial constraints, draw a parallel to the seemingly mysterious entanglement correlations in quantum mechanics, suggesting they may ultimately be as understandable as the relationships between points in a defined space.

The authors posit these correlations are “timeless,” aligning with the framework’s rejection of a need to track change in time as a fundamental aspect of the universe. This highlights the importance of considering the complete system when interpreting experimental results, a principle central to this approach. The framework also proposes a departure from the need to postulate arbitrary initial conditions in the distant past, a common requirement in many cosmological models.

Instead, it envisions a “first instant” of minimal variety, with shapes of increasing complexity existing within a timeless structure, requiring no further explanation. This concept removes the need for a defined beginning or evolution, suggesting the universe may be describable as a static configuration of relationships rather than a dynamic process unfolding over time. The work does not yet present a complete derivation of quantum mechanics from this framework, but it offers a potential path for future investigation.

👉 More information
🗞 An Alternative to Quantum Theory
✍️ Julian Barbour and Maria I. R. Lourenço
🧠 ArXiv: https://arxiv.org/abs/2611.12494

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