The Physical Cost of Resolution: Spacetime Constraints on Polynomial-Time Computation

The P vs NP problem is traditionally formulated as a mathematical question concerningthe scaling of abstract computational time. In this work we explicitly distinguish betweenabstract computational time, defined as the number of steps in a formal model, and physicaloperational time, defined as causal duration in spacetime.Rather than challenging the formal definitions of complexity classes, we explore a physicalperspective on the feasibility of polynomial-time resolution under minimal and widely acceptedspacetime constraints. We argue that, for global problems with increasing complexity,resolution entails an irreducible physical cost associated with causal integration of distributedinformation.A relativistic thought experiment, the time-dilated environment chamber, is introducedto illustrate how expectations of operational polynomial-time resolution implicitly rely onextreme spacetime engineering. Within this perspective, we suggest that while the P vs NPproblem remains open as a mathematical question, its operational interpretation is stronglyconstrained by physical law.