Some Implications of the Independence Postulate for Physics
Samuel Epstein
TL;DR
This work examines whether the Independence Postulate (IP) – a finitary information bound limiting how much of a sequence can be found in nature – can coexist with two information-centric physical theories: the Many Worlds Theory (MWT) and Constructor Theory (CT). It argues that memory leaks and encoded information such as prefixes of the halting sequence $\Omega_m$ can arise in MWT branches with non-negligible probability, challenging IP; similarly, CT faces tension because its counterfactual constraints can clash with IP’s prohibition on finding certain sequences. Through idealized spin-measurement scenarios, the paper highlights concrete mechanisms by which IP could be violated and outlines three core issues that obstruct straightforward reconciliation between IP, MWT, and CT, including the fate of large information prefixes and the role of preparers and measurers. The analysis suggests that, without modifying IP or the foundational premises of CT or MWT, a universal reconciliation remains unresolved, underscoring a deep tension between information-theoretic limits and foundational physical theories. The work motivates further exploration of how finitary information bounds interact with quantum interpretational frameworks and counterfactual physics.
Abstract
The Many Worlds Theory and Constructor Theory are in conflict with the Independence Postulate. The conflict with the Many Worlds Theory is shown through the existence of a finite experiment that measures the spin of a large number of electrons. After the experiment there are branches of positive probability which contain forbidden sequences that break the Independence Postulate. Constructor Theory consists of counterfactuals, decreeing certain processes can or cannot occur. However this binary classification meets challenges when describing whether a forbidden sequence can be found or created.