Proper Time as an Emergent Ratio of Quantum Uncertainties: New Predictions for Quantum Time Dilation and Gravitational Effects

A.B.M Masum Billah Mim

Published Apr 16, 2026• 0 citations

Abstract

We propose that time is not a fundamental background but emerges from the quantum uncertainties of position, momentum, and energy. This is captured by the postulate \(\Delta \tau = \frac{\Delta x \,\Delta p}{\gamma \,\Delta E}\),where \(\Delta \tau\) is the proper time interval, \(\Delta x,\Delta p,\Delta E\) are the standard quantum uncertainties, and \(\gamma = 1/\sqrt{1-v^2/c^2}\) is the Lorentz factor associated with the average velocity \(v\). Using the standard wave‑packet relation \(\Delta E = v \Delta p\), our equation reduces exactly to the special relativistic proper time \(\Delta \tau = \Delta x/(\gamma v)\), demonstrating consistency with all existing tests. However, for non‑classical quantum states where \(\Delta E \neq v \Delta p\) (e.g., a superposition of widely separated momenta), our equation predicts new measurable effects: (i) a significant modification of the decay length of unstable particles (muons), (ii) a dependence of clock rates on the spatial spread \(\Delta x\) even in flat spacetime, and (iii) a quantum correction to gravitational time dilation when the Lorentz factor is replaced by the general relativistic factor \(\Gamma\). These predictions are falsifiable and provide a concrete experimental window into the emergent nature of time.

DOI: 10.5281/zenodo.19602789

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