The Continuous-Discrete Duality: A Geometric Foundation for Quantum and Classical Behaviors
Payman Sattari
Philosopher, Researcher
Abstract
Quantum mechanics and classical physics appear to describe two distinct realms of reality, with wave-particle duality epitomizing this apparent divide. We demonstrate that both domains emerge naturally from a more fundamental principle: the continuous-discrete duality. This geometric relationship explains why quantum systems exhibit wave-like behavior in some contexts and particle-like behavior in others, while classical behavior emerges at larger scales. The framework makes specific, testable predictions about the transition between quantum and classical regimes, including observable patterns in interference experiments and decoherence processes. These predictions can be tested using existing experimental techniques, offering a direct path to verification. The continuous-discrete duality provides a natural explanation for wave-particle duality without requiring separate frameworks for quantum and classical phenomena, suggesting a more fundamental understanding of physical reality.
Research Overview
Theoretical Context
This work addresses a longstanding question in physics: why quantum systems exhibit both wave-like and particle-like behavior, and how classical behavior emerges from quantum foundations. Rather than proposing additional mechanisms or interpretations, the framework approaches the problem from geometry. It suggests that quantum and classical behaviors reflect different modes of expression of a single structural principle that is always present but revealed differently depending on scale and measurement context.
Key Predictions
The framework makes several specific, testable predictions that distinguish it from conventional frameworks. Most significantly, it predicts that the transition between wave-like and particle-like behavior follows geometric patterns that are both regular and scale-dependent. These patterns should be observable in modified versions of classic quantum experiments, particularly in:
- The spatial distribution of individual detection events in interference experiments
- Scale-dependent correlations between successive quantum measurements
- Geometric regularities in decoherence processes
Theoretical Implications
The continuous-discrete relationship offers a natural way of understanding several aspects of quantum behavior without requiring new postulates or additional interpretive layers. It reframes measurement as a geometric process rather than a conceptual mystery, clarifies why classical definiteness emerges at larger scales, and provides a unified structural foundation for wave-particle duality.
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