Assembly Theory: Can Causation Be a Measurable Physical Property That Defines Life?

> *arXiv:2601.00515* | Leroy Cronin & Sara I. Walker | University of Glasgow, Arizona State University, Santa Fe Institute

This post is a full translation of a Chinese forum discussion of the paper *The Physics of Causation*.

1. Physics's 'Causal Blind Spot'

Open any quantum field theory or general relativity textbook and you will find mass, charge, spin, energy, momentum, curvature—but you will not find the word causation. This is no accident: fundamental laws (Schrödinger, Maxwell, Einstein's field equations) are time-symmetric. Reverse the arrow of time and the equations still hold. At the most basic level, past and future are not fundamentally different, and 'cause' and 'effect' have no place in fundamental physics.

In early 2026, chemist Leroy Cronin and astrobiologist Sara I. Walker proposed a striking claim in *The Physics of Causation*:

> Causation is not a logical relation, a cognitive construct, or a statistical inference—it is a measurable material property, like charge, spin, or mass.

Their entry point into this problem is a familiar phenomenon that still lacks a precise definition: life.

2. From LEGO Bricks to the Assembly Index

Imagine building with blocks. A single block needs no assembly steps. Joining two blocks takes one operation; reusing already-built substructures makes construction efficient.

Assembly Theory's core concept, the Assembly Index (AI), is a counter: the minimum number of recursive steps needed to construct a specific object from basic building blocks. Examples:

• Molecule H₂O: AI ≈ 2
• Molecule benzene (C₆H₆): AI ≈ 5
• Molecule glucose (C₆H₁₂O₆): AI ≈ 9
• Molecule artemisinin (C₁₅H₂₂O₅): AI ≈ 15
• Protein insulin: AI > 30

Crucially, AI is not a measure of information but a measure of causal path. It does not ask 'how complex is this object' (like Shannon entropy or Kolmogorov complexity) but 'how many ordered construction steps did the universe minimally need to produce it'. Cronin and Walker argue AI is an invariant—independent of measurement technique (IR, mass spec, NMR) or mathematical representation—claiming for it the same status as the speed of light \(c\) or electric charge: a physical scale of causation.

3. Copy Number: The Second Key Quantity

AI alone cannot define life. You also need copy number.

Suppose you find one crystal on Mars with AI = 12—high by terrestrial standards. It might be the product of some rare geological process. But if you find ten thousand copies of the same crystal in a meteorite, the story changes: high AI means 'hard to form naturally', high copy number means 'a persistent mechanism is mass-producing it'. Together they point to selection.

Cronin and Walker define assembly space as 'the set of all causal possibilities'. Within it lies a selective threshold:

• Below the threshold: objects can arise from random processes or simple physicochemical laws
• Above the threshold: objects with such high AI could not have formed by random fluctuation over observable cosmic history—unless some selection mechanism 'remembers' and 'reuses' existing construction paths

That threshold is where life (and its descendants: intelligence, technology, culture) resides.

4. The Threshold of 15: A Clear Divide

Cronin's team measured assembly indices of thousands of molecules via mass spectrometry, revealing a striking pattern:

There is an almost impassable gap at AI ≈ 15.

Molecules below 15 are ubiquitous—in meteorites, deep-sea hydrothermal vents, and Miller–Urey-style experiments. Molecules above 15 are found only in living organisms or in human chemists' flasks (and chemists are themselves living).

This divide is not arbitrary; it follows mathematically from combinatorial explosion. A small protein of length 50 from 20 amino acids has \(20^{50}\) possible sequences—a number exceeding the particle count of the observable universe. Without a mechanism that remembers and reuses successful construction paths, random collisions producing a specific functional protein are effectively impossible.

In the Assembly Theory view, life is not a mystical 'vital force' or vague emergent property. It is a physical fact: life is a mechanism found in the universe that persistently and selectively explores high-AI regions of assembly space. The abundance of high-AI objects is physical evidence that causation is encoded in matter.

5. The Trouble with Interventionist Causation

The paper's impact on philosophy stems from its direct challenge to the foundations of modern causal inference. Judea Pearl's interventionist account of causation dominates the field: 'X causes Y' means that an idealized intervention on X (holding all else fixed) changes Y. This framework underlies epidemiology, economics, and machine learning.

But Cronin and Walker point out a fundamental problem: interventionism does not apply in fundamental physics. Closed physical systems contain no 'external intervener'—you cannot 'hold one electron still and watch the other'. Fundamental laws are global, time-symmetric, and have no place for an 'outside observer'. As the paper puts it:

> *"A more parsimonious explanation is that complex objects must be caused to exist, but this is incompatible with current physics, which has no concept of 'cause'."*

Assembly Theory attempts to repair this gap by grounding causation directly in an object's material structure: AI is an intrinsic property, like mass. No intervention is needed to measure it—only observation of the object itself.

6. Determinism Is Emergent; Novelty Is Fundamental

A deeper philosophical consequence: determinism is no longer fundamental but emergent.

Traditional physics treats determinism (or probabilistic determinism) as basic. Cronin and Walker invert this:

> The past is determined, but the future is undetermined—because the universe has not yet constructed itself into the future.

The possibilities of assembly space are not pre-existing. Before each assembly step, high-AI objects do not yet exist in the possibility space; they become 'possible' only after being built. This echoes Stuart Kauffman's 'adjacent possible', formalized here as a physical quantity. In this framework, novelty is fundamental: the universe continuously produces unprecedented objects that were not even within the realm of possibility before appearing. Walker has said:

> *"Life is not merely a special case of computation but something more fundamental: a physical reality that can be measured, quantified, and understood through invariant physical laws."*

7. Controversy: An Ongoing Scientific Debate

Assembly Theory has attracted sharp criticism, notably from Hector Zenil and colleagues in 2024:

1. AT approximates algorithmic complexity: the assembly index is similar to LZ-compression-based measures and offers no real novelty. 2. Fixed thresholds are unjustified: a universal 'life detection threshold' is arbitrary; life cannot be reduced to a number. 3. It cannot distinguish types of selection: AT detects 'bias' but cannot tell whether it stems from natural selection, self-organization, or environmental forcing.

Cronin and Walker respond that these critiques miss AT's core claim: AT does not say 'any high-AI object must be biological'—rather, given a large enough combinatorial space, certain configurations simply cannot exist without systematic bias (selection). This is a physical proposition, not a computational one, and there is no experimental evidence that non-living processes can produce arbitrarily high-AI objects in natural settings.

Johannes Jaeger's balanced commentary notes that AT "has merits but is far less novel or revolutionary than claimed". It cannot replace Darwinian evolution or explain the mechanism of natural selection. But it does offer a useful lens for detecting the emergence of new levels of organization and their causal influence on lower-level phenomena—what philosophers call downward causation.

8. Conclusion: A New Physical Worldview

Assembly Theory ultimately proposes:

• Causation is material: a physical quantity measurable in the laboratory, not a cognitive framework imposed on the world.
• Time is an object property: an object's AI encodes the historical depth required to build it—its 'temporal size'.
• Life is operationally definable: life is a physical structure that crosses the selective threshold in assembly space and possesses persistent copies.
• Novelty is fundamental: the universe's future is not a pre-written script but continuously created with each new object.

Is Assembly Theory a 'theory of everything'? Almost certainly not—much detail, boundary clarification, and mathematical rigor remain. But it opens a new door: when physics is finally ready to take causation seriously, we may find, as with the discoveries of charge, energy, and information, not merely a new physical quantity but an opportunity to reinterpret reality itself.

And life—perhaps the universe's greatest puzzle—may eventually find its place in a clear physical law: not as an exception, not as an emergent illusion, but as the inevitable product of the material properties of causation.

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*This post is based on arXiv:2601.00515 and related Assembly Theory literature. Leroy Cronin is a chemist at the University of Glasgow; Sara I. Walker is an astrobiologist and theoretical physicist at Arizona State University; both are researchers at the Santa Fe Institute. The controversies discussed reference critical work by Hector Zenil, Narsis Kiani, Johannes Jaeger, and others.*