Assembly Theory and the Physics of Causation: How Life Emerges from Physical Possibility

This forum post explores The Physics of Causation, a paper by Leroy Cronin and Sara I. Walker (arXiv:2601.00515, v3), which uses Assembly Theory (AT) to pull causation out of abstract philosophical debate and into the measurable physical world, turning "why does this object exist?" into a quantifiable property of matter.

Key points

• Assembly space: Defined as the set of all causal possibilities, populated by structures built through recursive causal joins. Each object carries a finite causal path P; the shortest path's length is its assembly index a_i = |P| — the minimum number of recursive steps needed to construct it. This is a material property, as measurable as mass or charge, and it embeds causation within the object itself rather than requiring external laws or counterfactuals (as in Pearl's interventionism).
• Assembly index as a measurable invariant: Unlike Kolmogorov complexity (NP-hard to compute), the assembly index can be read experimentally, e.g., from mass spectrometry fragmentation paths. The paper's flagship example is Taxol (paclitaxel, C₄₇H₅₁NO₁₄, MW 853.91): with 11 chiral centers it has 2¹¹ = 2048 stereoisomers, a spontaneous probability below 10⁻²³, yet it exists at ~10¹⁶ molecules per gram in yew bark. Its minimal assembly path is 23 steps — evidence of evolutionary selection, not chance.
• Cross-scale thresholds: The paper derives a threshold formula:
\[a^* = \left\lfloor \frac{\ln N - \ln M}{\ln(1 + b)} - 1 \right\rfloor\]

where N is the total number of countable objects, M the measurement limit (minimum reliable copy number), and b the branching factor. It follows from a copy-number decay model n(d) = N / (1+b)^(d+1), plus a total assembly quantity A = W ∑ (n_i e^{a_i} / N). Thresholds are log-consistent across scales:

| Scale | Assembly index threshold | Meaning | |---|---|---| | Taxol molecule | a = 23 (10¹⁶ copies/g) | Biosynthetic selection, not randomness | | Lab millimole sample | a ~13–16 | Below M = 10,000 copies, unmeasurable without selection | | Planetary (Earth, ~10⁵² atoms) | ~44 | Causal history requires selection to persist | | Cosmic (~10⁸⁰ atoms) | ~71 | Physical boundary for open-ended evolution |

• An operational definition of life: Life is defined physically as structures producing persistent copies in a deep causal possibility space — i.e., a_i > a* and copy number n > M. This builds on 2023 Nature Communications work showing mass spectrometry can separate biological from non-biological molecules above a molecular threshold of ~15. The framework extends to agents, AI-generated artifacts, de novo synthetic life, drug "historical" complexity, and astrobiological biosignatures.
• Emergence of determinism: AT inverts tradition — determinism is not foundational but emerges later from selection acting on novelty and contingency. The future remains open while the past is causally closed; novelty arises as continuous possibility is discretized into persistent objects. "Virtual copy number" v(a) ≈ e^a quantifies the selection "debt" that high-a objects must repay.
• Open questions: The paper acknowledges simplifying assumptions (uniform branching factor, whether the discrete join rules J presuppose causation, quantum/continuous-system adjustments), framing them as scientific fuel rather than defects.

References cited in the post

1. Cronin, L. & Walker, S. I. *The Physics of Causation*. arXiv:2601.00515 (2026). 2. Cronin, L. et al. *Assembly theory and the emergence of selection*. Nat. Commun. (2023). 3. Walker, S. I. & Cronin, L. *Beyond prebiotic chemistry*. Science 352, 1174–1175 (2016). 4. Patarroyo, K. Y. et al. *AssemblyCA: A benchmark of open-endedness*. Nat. Commun. 9, 5177 (2018). 5. Cooper, G. J. T., Walker, S. I. & Cronin, L. *A universal chemical constructor*. In *Conflicting Models for the Origin of Life* (Wiley, 2023).