Bitcoin Makes Time Travel Possible

Abstract

Reinganum (1986) argued informally that inexpensive time travel would drive nominal interest rates to zero. We formalise that claim in a dated-commodity model built on a Lewisian distinction between calendar time and personal time. Costless two-way transport of dollars across dates makes dated dollars technologically interchangeable, so the law of one price implies a zero nominal risk-free rate. The same logic does not carry over unchanged to native on-chain Bitcoin. A Bitcoin position is a holder-relative control claim over a specific unspent transaction output (UTXO) in the realised blockchain history. A valid dates immediate control claim requires the output already to exist in the dates chain prefix, to be unspent there, and to satisfy all applicable script, witness, timelock, and maturity conditions. Future-created outputs cannot generally be transported backwards. Same-date substitution into older outputs is history-dependent and capacity-constrained; exercise changes the single realised history rather than creating duplicate purchasing power. We define a Bitcoin-denominated zero-coupon claim as a promise of generic native settlement at a later date and give a two-date no-arbitrage counterexample with a non-zero Bitcoin-denominated interest rate. The substantive Bitcoin result is an incompatibility result: no single native on-chain Bitcoin object is simultaneously generic across outputs, immediately exercisable as native settlement, and universally transportable across calendar dates. A restricted same-output law of one price survives for dormant control bundles over already-existing outputs, but that result is too narrow to force Bitcoin-denominated rates to zero in general.