Photons = Tokens: The Physics of AI and the Economics of Knowledge
Treats the token as a physical quantity with a measurable thermodynamic cost (Landauer's principle + Shannon channel capacity) and builds a supply/demand balance sheet for global token production — deriving the energy->token bridge the KB's 'no energy pass-through leg' gap was missing: the projected 2028 US AI energy allocation of 326 TWh could support ~6.5x10^17 tokens/yr ~225,000 tokens/person/day, >3 orders of magnitude above mid-2024 utilization (i.e. energy is not the near-term binding constraint on token VOLUME; direction — which questions are worth asking — is). Order-of-magnitude policy-framing estimates, not a measured per-SKU cost series.
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.