physics.soc-phFeb 23, 2026

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

Authors: Alec Litowitz, Nick Polson, Vadim Sokolov

Organizations: QStar Capital · University of Chicago · George Mason University

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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 6.5×10176.5 \times 10^{17} tokens per year, or 225,000 tokens per person per day -- more than three orders of magnitude above estimated mid-2024 utilization.

Figures & tables

 20242028 (proj.)Units
Demand (observed) and capacity (projected)
AI electricity consumption65326TWh/yr
Token capacity (at 5×10−45\times 10^{-4} Wh/token)1.3×10171.3\times 10^{17}6.5×10176.5\times 10^{17}tokens/yr
Observed tokens per person per day∼\sim 125 ∗—tokens/person/day
Capacity per person per day44,500225,000tokens/person/day
Supply (grid)
Table 1: Token economy balance sheet, United States. The 2024 observed figure ( ∼\sim 125 tokens/person/day) is estimated global demand divided by world population (see text for sources and uncertainty); capacity figures assume all AI electricity is used for inference at 5×10−45\times 10^{-4} Wh/token. In practice, training consumes 30–40% of AI electricity (declining as inference grows), so realized inference capacity is correspondingly lower. AI electricity midpoint: 65 TWh is the center of the 53–76 TWh range.
 Questions/person/day
Tokens/question65 TWh165 TWh326 TWh650 TWh
1004501,1302,2004,500
2501804509001,800
50090225450900
1,00045113225450
Table 2: Sensitivity of the daily question budget per person to energy budget and conversation length. Assumes 5×10−45\times 10^{-4} Wh/token and 8 billion people. The 326 TWh column uses the 2028 US upper-bound projection; the 650 TWh column approximates global AI energy if non-US capacity is included.
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