This project presents a conceptual and mathematical hypothesis concerning the apparent randomness of radioactive decay. While current nuclear physics models describe decay as a fundamentally stochastic and random process with a constant decay rate, this work explores the possibility that the randomness may come from rapidly fluctuating internal nuclear states that are not directly obsercable by measurement. The central idea is that the effective decay constant measured experimentally represents a time-averaged quantity over a distribution of internal configurations, associated with slightly different decay probabilities. In this framework, radioactive decay remains statistically exponential at observable timescales, while allowing for hidden internal dynamics consistent with established quantum mechanical principles. My work does not claim experimental verification. Instead, it aims to outline a phenomenological structure compatible with known decay laws and to identify conditions under which small, systematic deviations might arise under perturbations.
The decay law, $N={N}_{0}{e}^{\ensuremath{-}\ensuremath{\lambda}t}$, is based on the assumption that the probability
w of an atom disintegrating in unit time is constant. The question arises whether this assumption is necessary. It might happen that atoms of different ages have different decay probabilities; and
w might depend on age in such a way that exponential decay curves would result. A theorem of Wolfke, however, can be interpreted in such a manner as to show that
w cannot depend on the age of the atom. This result is generalized. Consider a series whose members
A,
B, etc., have decay probabilities
wA,
wB, etc. If all members decay exponentially, if all
w′s are smooth and continuous functions of their variables and if each
w is, at most, a function of the age of the atom, the ages of its ancestors and the ages of its descendants; then the
w′s are constant; and so in this more general case, the assumption of constant decay probability which underlies the wave mechanical theory of disintegration is necessary as well as sufficient.
A critical examination of the theory of resonance radiation has been carried through, employing the mathematical technique of Laplace and Stieltjes transforms. Particular attention has been devoted to the question of the temporal behavior of the excited state. With no restrictions on the interaction between atom and radiation field other than that it be real, and that processes of sufficiently high frequency contribute only negligible effects, one can prove that the probability amplitude of the excited state cannot decay according to the general law ${\ensuremath{\Sigma}}_{\ensuremath{\mu},\ensuremath{\nu}}{C}_{\ensuremath{\mu}\ensuremath{\nu}}{t}^{{\ensuremath{\lambda}}_{\ensuremath{\mu}}}{e}^{\ensuremath{-}{\ensuremath{\beta}}_{\ensuremath{\nu}}t},$ where the ${\ensuremath{\lambda}}_{\ensuremath{\mu}}$ and ${\ensuremath{\beta}}_{\ensuremath{\nu}}$ are complex constants lying in the right half-plane and the ${C}_{\ensuremath{\mu}\ensuremath{\nu}}$ are arbitrary complex coefficients. The deviation from the law just cited can be termed a straggling phenomenon since exact analysis shows that the probability amplitude, for sufficiently long times, is greater than that defined according to the radioactive decay law.Rigorous analysis of the source of this apparently anomalous behavior reveals the following explanation. Although the probability amplitude of the excited state is, strictly speaking, a functional of the interaction between the transition current in the atom and the photon states of the electromagnetic field, the essential features are determined principally by those states lying near the resonance frequency. Three elementary observations are immediately apparent. First, a particularly tractable analytical approximation for the interaction can be made such that the value of the actual interaction is reproduced at the resonance frequency and such that the behavior for high and low frequency photon states is at least qualitatively correct. Exact solutions in closed form can be obtained for this interaction. Second, in terms of the preceding representation it is possible to show that, associated with the transition between two atomic states, one is presented with a concomitant picture of a damped oscillation of charge describable in purely classical terms. Third, this classical motion can be interpreted as forming a source function for a continuous stochastic process in terms of which one finally derives the representation of the probability amplitude of the excited state. The straggling phenomenon previously cited is therefore that associated with all diffusion processes. The consideration of the exact interaction leads to more involved diffusion phenomena but does not in any case permit a radioactive decay law.
This paper states a narrow interpretive claim about stable and radioactive bound configurations under the matter-side reading of the Timeless Light Model. It introduces no new equations and alters no predictive content of atomic physics, nuclear physics, or quantum mechanics. The claim is that stable and radioactive bound configurations are two presentations of the same structural reading: each is timeless lawful structure in force, registered in spacetime when called on, with registrations governed by lawful content. Stable configurations have no admissible spontaneous decay channel under the operative description; nothing registers, and nothing accumulates. Radioactive configurations have at least one decay channel in their lawful content; channel realizations register along the worldline at rate λ fixed by content. The paper argues that neither stable nor radioactive matter undergoes substance-aging. Stable atoms do not grow older as degraded versions of themselves, and radioactive atoms do not age toward decay. A radioactive nucleus that has not yet realized its decay channel retains the same decay probability per unit proper time in the experimentally dominant exponential regime. Bulk decay curves describe cumulative counting of channel realizations across an ensemble, not individual atomic wear. The result is interpretive only. It preserves the standard exponential-decay law, the standard treatment of stationary states, and the standard predictive machinery of atomic and nuclear physics. Its contribution is ontological: stability and radioactivity are content-level distinctions, not different categories of being.