= Solution
In the <rest frame>, <conservation of energy> would require $E_\gamma=mc^2$, whereas <conservation of momentum> would require the <photon> <momentum> to vanish. These contradict $|\mathbf p_\gamma|=E_\gamma/c$. More generally, <four-momentum> conservation would equate the initial massive <four-momentum> to a null <four-momentum>, although their <Minkowski norms> differ:
$$
P_\mu P^\mu=m^2c^2>0,\qquad p_{\gamma\mu}p_\gamma^\mu=0.
$$
\b[An isolated massive particle cannot decay into one <photon> in any <inertial frame>.] Directly, a laboratory <speed> $u<c$ gives $E=\gamma mc^2$ and $|\mathbf p|=\gamma mu$; matching a <photon> would require $E=c|\mathbf p|$, hence $u=c$. Recoil against another object could change the kinematics, but would introduce an additional participant.
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