Does Proper Acceleration Change the Muon Decay Rate? A Phenomenological Test of the Clock Hypothesis

Does Proper Acceleration Change the Muon Decay Rate? A Phenomenological Test of the Clock Hypothesis This paper investigates a fundamental question in relativistic physics: Does proper acceleration produce an additional measurable effect on the decay rate of an unstable particle? Special relativity predicts that moving muons have longer laboratory lifetimes than muons at rest. This prediction agrees with experimental measurements, including the CERN muon storage-ring experiment. The conventional interpretation assumes that a clock's rate depends on its instantaneous velocity rather than its acceleration. This assumption is known as the clock hypothesis. The paper examines whether proper acceleration introduces an additional contribution to the muon decay rate. It proposes a phenomenological mathematical model in which the decay rate depends on the square of proper acceleration. The model includes a characteristic acceleration scale and a dimensionless coupling parameter. The analysis derives the survival probability for both constant and variable acceleration. It then estimates the possible correction under conditions comparable to those of the CERN storage-ring experiment. For the proposed characteristic acceleration scale, a_* = m_\mu c^3/\hbar, the predicted correction is approximately 5.3 \times 10^{-26}\kappa. This result shows that the proposed correction is extremely small when the coupling parameter is of order unity. The model therefore does not explain the experimentally observed increase in muon lifetime. The paper also examines the constraints that existing measurements may place on the coupling parameter. It proposes experiments that compare muon populations with equal Lorentz factors but different proper accelerations. Such experiments can test whether acceleration contributes independently to particle decay. This work does not challenge the established experimental support for special relativity. It presents a testable phenomenological hypothesis and identifies the theoretical and experimental requirements for its further investigation. The paper is relevant to researchers in special relativity, particle physics, quantum field theory, theoretical physics, experimental physics, and the foundations of physical measurement. Scientific status: The acceleration-dependent decay law is a proposed phenomenological model. It is not an established physical law. Its theoretical derivation and experimental validation remain open research questions.