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The transformation of canonical decay laws of moving unstable quantum systemsis studied by approximating, over intermediate times, the decay laws at restwith superpositions of exponential modes via the Prony analysis. The survivalprobability $\mathcal{P}_p(t)$, which is detected in the laboratory referenceframe where the unstable system moves with constant linear momentum $p$, isrepresented by the transformed form $\mathcal{P}_0\left(\varphi_p(t)\right)$ ofthe survival probability at rest $\mathcal{P}_0(t)$. The transformation of theintermediate times, which is induced by the change of reference frame, isobtained by evaluating the function $\varphi_p(t)$. Under determinedconditions, this function grows linearly and the survival probabilitytransforms, approximately, according to a scaling law over an estimated timewindow. The relativistic dilation of times holds, approximately, over the timewindow if the mass of resonance of the mass distribution density is consideredto be the effective mass at rest of the moving unstable quantum system.

Transformation of intermediate times in the decays of moving unstable quantum systems via the exponential modes