Physicist Julian Barbour proposes that the universe is built purely from ratios — relationships between particles — with no absolute space, time, or scale. He argues that quantum mechanics may not be fundamental at all, but rather a manifestation of classical physics misunderstood, and that time itself is an illusion generated by consciousness playing through static snapshots of reality.
The Core Idea: Nothing But Ratios
Barbour’s minimal ontology assumes only point particles in Euclidean space, with zero size. What is real is not the particles themselves or their absolute separations, but the ratios of distances between them. This eliminates the need for an external ruler or clock outside the universe.
If the universe consisted of only three particles, it would be meaningless to speak of the triangle’s “size” — only its shape (the ratios of its sides) is physically meaningful.
This is motivated by Leibniz’s insight that variety (difference) is the most fundamental feature of existence: without differences between things, nothing could be perceived or said to exist.
Variety: A Scale-Invariant Measure of Structure
Barbour defines a quantity called variety that characterizes how points are distributed in space. For three particles with pairwise separations a, b, and c, the simplest scale-invariant form is the square root of the sum of squared separations, multiplied by the sum of their reciprocals (1/a + 1/b + 1/c).
This quantity is scale-invariant: multiplying all distances by any factor leaves it unchanged. It therefore cannot involve Planck’s constant (which has dimensions of action), meaning Planck’s constant would need to emerge from the theory rather than be assumed.
Variety is at the heart of Newton’s theory of gravity when reformulated relationally — it is, in a precise sense, the “beginning and end” of Newtonian gravity for three particles.
The Newtonian Big Bang and the Arrow of Time
In Newtonian gravity, if three particles start in an equilateral triangle with zero angular momentum, the equations break down — this is a singularity that corresponds to a Newtonian Big Bang, discovered by Finnish mathematician Sundman in 1907, two decades before Hubble’s discovery of cosmic expansion.
After this instant, the triangle becomes more “pointed”: two particles orbit each other while the third flies away. This defines a natural arrow of time based purely on the changing ratios of separations — no entropy increase is needed.
For any number of particles, the initial state is a nearly uniform spherical distribution (not perfectly uniform), and structure forms naturally as variety increases. This contrasts with the standard FLRW cosmological model, which struggles to explain structure formation and relies on ad hoc inflation.
Barbour, along with collaborators Tim Koslovsky and Flavio Mercati, published this alternative arrow of time in Physical Review Letters about 11 years ago, where it was recognized as a notable contribution.
Why Entropy Does Not Explain Time’s Arrow
The standard explanation for time’s arrow relies on the second law of thermodynamics (entropy increases) and the past hypothesis (the universe began in an extremely low-entropy state). Barbour argues this is a naive extrapolation from systems confined in a box.
The second law applies to confined systems. The universe is not in a box — it is open and can expand indefinitely. In an unbounded system, entropy arguments fail (as Gibbs himself noted as a caveat).
The past hypothesis requires an unexplained special initial condition. Barbour’s alternative — that the arrow of time comes from increasing variety in an open universe — needs no such assumption.
If Barbour is right, the universe will continue to develop ever-richer structure forever, contradicting the “heat death” scenario.
Quantum Mechanics Without Wave Functions
Barbour’s most radical claim: all evidence for quantum mechanics can be explained without wave functions or Planck’s constant. The evidence consists of photographs and printouts — patterns of dots on paper — which are always interpreted through the lens of processed data (wavelengths, frequencies).
His alternative explanation is holistic: a snapshot of the entire universe is one of many possible shapes that all share the same value of variety. The probability of finding a particular laboratory configuration within such a shape is determined by the statistics of shapes at that variety value.
This is fundamentally different from reductionist physics, which only considers what happens in a laboratory. Barbour argues the whole universe matters.
Shape Space, Best Matching, and the Shape Sphere
For three particles, all possible triangle shapes can be represented as points on a shape sphere (since two angles define a triangle’s shape). The equilateral triangle sits at the poles; degenerate (collinear) triangles lie on the equator.
Best matching is the procedure of superimposing two shapes to minimize their difference. This defines a unique distance between shapes and underlies all gauge theories, including general relativity. The simplest non-Abelian gauge theory is the three-body Newtonian problem with zero angular momentum.
On the shape sphere, the variety has a minimum at the equilateral triangle and increases toward infinity as two particles approach each other. Contour lines of constant variety play the role of time (or “age”), and the probability of finding a shape within a region is proportional to its area divided by 4π — this is a Born density without any wave function.
Age Instead of Time
Barbour replaces the concept of time with age, defined as the difference between the current value of variety and its absolute minimum. The universe’s age is zero at the most uniform distribution and increases as structure develops.
Substructures within the universe (stars, organisms) have their own relative ages. We intuitively judge age by structure — wrinkles in a face, the composition of a star, the size of a tree.
This is a concrete, observable quantity, unlike Newton’s “absolute time which flows equitably without relation to anything external.”
Consciousness as Movie Projector
Barbour argues that consciousness creates the illusion of motion and change. What we actually experience are static snapshots encoded in our neurons — like frames of a film — and consciousness “plays the movie” for us.
When we see a kingfisher in flight, what is really in the brain is six or seven snapshots with the bird’s wings in different positions relative to the background. The experience of motion is generated by consciousness.
Similarly, heat is not caused by particles moving rapidly (the standard kinetic theory), but is the experience correlated with greater separations between particles. Temperature is a measure of relative distances, not motion.
Consciousness is a “great gift” that makes us aware of structure and makes life exciting, but it also deceives us monumentally — leading physicists to build theories around motion, change, and locality that may be fundamentally misguided.
Implications for Fundamental Physics
Pauli exclusion principle: In Barbour’s framework, the reason two fermions cannot occupy the same state is that as two particles approach each other, the term 1/a in the variety expression diverges to infinity. At a fixed value of variety (a given “age” of the universe), this is forbidden. This could explain the stability of matter.
Entanglement: The mysterious instantaneous correlations in quantum entanglement may simply reflect the fact that all separations in Euclidean space are correlated — there are ~n²/2 ratios for n particles, all determined simultaneously in a single snapshot. The evidence for entanglement is always in a single photograph.
Photons and fields: Barbour is suspicious of whether photons exist as fundamental entities. Maxwell introduced the electromagnetic field to avoid action at a distance, but this may have been a mistake driven by conscious experience. Faraday’s lines of force and the entire framework of fields may be unnecessary complications.
Geometry: Barbour follows Poincaré in questioning whether curved space is physical or merely a convenient mathematical representation. Our ability to mold plasticine into different shapes may have misled theorists into believing space itself can take arbitrary shapes. Poincaré argued that Euclidean geometry plus the behavior of measuring instruments (held together by forces) could account for all observations — a view Einstein acknowledged as logically sound in his 1917 paper “Geometry and Experience.”
The Challenge Going Forward
Barbour’s program is to explain everything using the absolute minimum ontology: points in Euclidean space, with only ratios of separations as physically real. Mass ratios and charge ratios are allowed as additional structure.
A student in Lisbon (Maria Lorenzo) is running supercomputer simulations of 1,000+ particles in three dimensions, finding filamentary structures and hierarchies of separations that resemble features seen in the large-scale structure of the universe.
The hierarchy of separations discovered by Spanish student Manuel Esquerdo — where particle separations fall into distinct scales — is a major discovery in Newtonian gravity, only four years old, with no explanation yet.
Barbour acknowledges he may be wrong, but argues the possibility that the universe is “incredibly much simpler than anybody thinks” deserves serious exploration. At 88, he hopes others will take up the challenge.
