Why Local Physics Appears Markovian: Effective Dynamics in a Finite-Bandwidth Vacuum

Description The standard Markovian assumption implicitly endows the physical vacuum with infinite channel capacity. If information bounds restrict causal domains, the constitutive vacuum response cannot be strictly instantaneous. A retarded, non-Markovian sector necessarily arises. A structural correspondence problem follows: why do time-local formulations, such as the Schrödinger equation and General Relativity, successfully govern the accessible physical regimes? This letter demonstrates that effective Markovianity is the necessary low-energy manifestation of a bandwidth-limited universe, emerging through three distinct mechanisms. First, for a maximum-entropy exponential memory kernel, the non-Markovian convolution reduces exactly to a time-local differential equation on an augmented state space. On local laboratory timescales, the memory variable remains adiabatically frozen, acting as a rigid background. Second, at intermediate scales where neither infrared dissipation nor ultraviolet truncation dominates, the vacuum acts as an approximately lossless transmission channel. Within this protected regime, the dynamics admits a unitary leading-order representation. Third, at macroscopic scales, continuous environmental monitoring saturates the local information capacity. This suppression of phase-history dependence drives the reduced dynamics towards an effective Markovian GKSL semigroup, ensuring a robust classical limit. The apparent instantaneity of local physics is therefore not an axiomatic proof of a memoryless void. Within the present framework, the standard Markovian paradigm is identified as the adiabatic limit of a finite-capacity universe. Keywords: Non-Markovian dynamics, correspondence principle, timescale separation, decoherence, finite vacuum bandwidth, foundations of physics.