The Continuous-Discrete Duality: A Geometric Foundation for Quantum and Classical Behaviors
Payman Sattari
Independent 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 Significance
This work addresses one of the most persistent challenges in modern physics: the apparent disconnect between quantum and classical descriptions of reality. Rather than treating these as separate domains requiring different frameworks, we demonstrate how both emerge from a more fundamental geometric principle. This approach provides a natural explanation for wave-particle duality while maintaining scientific rigor and experimental testability.
Key Predictions
The framework makes several specific, testable predictions that distinguish it from conventional quantum mechanics. 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 framework has profound implications for our understanding of quantum mechanics and physical reality. It suggests that quantum measurement, long considered mysterious, represents a natural manifestation of the geometric relationship between continuous and discrete aspects of reality. This resolves the measurement problem without requiring conscious observers or wave function collapse, while providing new insights into quantum entanglement and non-locality.
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