Photons = Tokens: The Physics of AI and the Economics of Knowledge

Abstract

"Debates about artificial intelligence capabilities and risks are often conducted without quantitative grounding. This paper applies the methodology of MacKay (2009) — who reframed energy policy as arithmetic — to the economy of AI computation. We define the token, the elementary unit of large language model input and output, as a physical quantity with measurable thermodynamic cost. Using Landauer's principle, Shannon's channel capacity, and current infrastructure data, we construct a supply-and-demand balance sheet for global token production. We then derive a finite question budget: the number of meaningful queries humanity can direct at AI systems under physical, information-theoretic, and economic constraints. We apply Coase's theory of the firm and the durable-goods monopoly problem to the AI value chain — from photon to atom to chip to power to token to question — to identify where economic value concentrates and where regulatory intervention is warranted. We argue that the expansion of the token budget does not resolve a deeper constraint: under structural uncertainty, the decisive variable is not how many questions can be answered but which questions are worth asking — a problem of agency and direction that computation alone cannot solve. We connect limits of measurement in the token economy to a structural parallel between Goodhart's law and the Heisenberg uncertainty principle, and to Arrow's impossibility result for efficient information pricing. The framework yields order-of-magnitude estimates that discipline policy discussion: at current efficiency, the projected 2028 US AI energy allocation of 326 TWh could support roughly 6.5×10^17 tokens per year, or 225,000 tokens per person per day — more than three orders of magnitude above estimated mid-2024 utilization."

Key Contributions

• Token as a physical unit with a thermodynamic floor (Landauer's principle) and an information ceiling (Shannon channel capacity).
• A supply/demand balance sheet for global token production built from infrastructure data — the first-principles energy→token bridge.
• A derived "finite question budget" — the count of meaningful queries possible under physical + economic constraints.
• Value-chain mapping "photon → atom → chip → power → token → question" via Coase + durable-goods-monopoly theory, locating where economic rent concentrates.

Results — the energy→token numbers (why this closes the gap)

• 326 TWh (projected 2028 US AI energy allocation) → ≈ 6.5×10^17 tokens/year at current efficiency.
• ≈ 225,000 tokens / person / day — the per-capita token budget that energy allocation implies.
• > 3 orders of magnitude above estimated mid-2024 utilization — i.e. energy is not the near-term binding constraint on token volume; the binding constraint is which questions are worth asking.
• Supplies the KB's missing $/kWh → $/token conversion basis (via TWh → token-count) — a top-down complement to the bottom-up ~5×10⁻⁴ Wh/token literature.

Limitations

• Order-of-magnitude / policy-framing estimates, not a measured per-SKU cost series.
• "Photons = tokens" is a modelling abstraction; real serving efficiency varies by model, hardware, and workload (reasoning-mode draws 5–12× more).
• The economic conclusions (value concentration, regulation) are theory-driven, not empirical.

Why it matters (inference-economics lens)

Closes the frontier's "no energy / power-cost pass-through leg" gap with a first-principles frame: it makes the token a thermodynamically-priced good and shows that at projected 2028 US energy, token volume is abundant (225k/person/day) — relocating the true scarcity to direction (which questions), not capacity. Anchors the [depreciation-conveyor] and [price-decline-distribution] discussions on the physical floor beneath the price.

Source: Photons = Tokens (arXiv:2603.06630), submitted 2026-02-23, Litowitz, Polson & Sokolov. Ingested 2026-07-24 at abstract grade. Provenance [preprint]; the order-of-magnitude estimates are the paper's own, explicitly policy-disciplining not SKU-measured.