A Continuous Measurement (Partial Observation) Model in Young's Double Slit Experiment

This paper presents a continuous measurement (partial observation) model for Young’s Double Slit Experiment, addressing the limitations of the traditional binary interpretation of the observer effect. 

In standard quantum mechanics, observation is often treated as a discrete event that collapses the wave function, leading to particle-like behavior. However, this work proposes that observation is inherently continuous and can be quantified using a dimensionless parameter α (0 ≤ α ≤ 1), representing the strength of measurement interaction.

Two functional models are introduced to describe the relationship between measurement strength and interference visibility: a linear model V = 1 − α and a more physically motivated exponential model V = e^{-α}. These models demonstrate a gradual transition from wave-like interference to particle-like behavior, consistent with decoherence theory and weak measurement concepts.

Theoretical analysis is supported by graphical and tabular representations, illustrating how interference visibility decreases continuously as measurement strength increases. The model also aligns with the fundamental wave-particle duality relation between visibility and distinguishability.

This work provides a simplified yet insightful framework for understanding the observer effect as a continuous process rather than an instantaneous collapse, with potential implications for quantum measurement theory, decoherence studies, and quantum information systems.