Quantum Principles from Time-Phase Geometry: A Relativistic Foundation for Uncertainty, Superposition, and Interference
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In this paper, we extend the framework introduced in [1], which proposed a two-dimensional model of time as a means to reconcile relativistic invariance with quantum discreteness. Building on this foundation, we derive key principles of quantum theory such as the uncertainty and exclusion principles and also introduce a fourth postulate: “The probability of an event is the same in all inertial frames of reference (IFR), independent of the observer's position in space.” This postulate enables us also to derive the probability amplitude interference from a purely relativistic time-phase geometry. We show that trajectories in the two-dimensional time plane, governed by relativistic constraints and discrete frequency-phase dynamics, naturally give rise to quantized measurements and path-based superposition. Using the Mach-Zehnder interferometer as an illustrative case, we demonstrate that the square of the proper time trajectory corresponds to quantum probability and interference phenomena emerge from the structure of phase evolution in time. Our formulation also aligns with Feynman’s path integral framework, showing that quantum mechanics can be interpreted as a direct geometric consequence of extended relativistic principles.
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