Physics

A Scale-Invariant Theory of the Universe

Julian Barbour, Maria I. R. Lourenço

Featured August 11, 2026

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AI-generated analysis — This is SciGrove's AI interpretation of the paper, not peer-reviewed content. Always refer to the original paper.

Simply

By focusing only on shapes and how particles are arranged relative to each other, this theory removes the need for absolute size or time, showing how the universe's structure naturally grows and defines its own 'age'.

In depth

This paper proposes a radical reformulation of physics, particularly Newtonian gravity, by eliminating absolute structures like position, orientation, time, and crucially, scale. It argues that only dimensionless ratios and shapes are physically meaningful. The central innovation is the 'variety' (

V

), a scale-invariant quantity that quantifies the structure of N-body configurations and provides an emergent gravitational arrow of time, unifying previously distinct Newtonian solutions.

Key Takeaways

1
The paper advocates for a relational ontology in physics, removing absolute position, orientation, time, and scale, guided by Leibniz's principle of sufficient reason.
2
It introduces the variety ( $V$ ) as a central, scale-invariant measure of structure in N-body systems, derived from the ratio of root-mean-square and mean-harmonic lengths.
3
The framework suggests an emergent gravitational arrow of time defined by increasing variety and structure, offering an alternative to conventional entropic time and unifying total-collision and parabolic-escape solutions.

Conceptual Flow

HIGH LEVEL

Methodology: From Absolutes to Shapes

Instead of using fixed ideas of space, time, and size, the paper suggests we only look at how things are arranged relative to each other, like the shape of a group of stars.

Absolute Space

Absolute Time

Absolute Scale

Remove Fixed Ideas

Relative Positions

Relative Sizes

Shapes Only

Results: Structure Defines Time

By measuring how 'structured' a group of particles is, the paper shows that more complex arrangements naturally appear later, giving us a way to tell time without a clock.

Simple Particle Shape

Less Structure

Increase Complexity

Complex Particle Shape

More Structure

Emergent Time