= Solution
With signature $(+,-,-,-)$, the four-momenta are
$$
P_{\rm massive}=m\gamma(c,v),
\qquad
P_\gamma=\frac{\hbar\omega}{c}(1,e).
$$
In the rest frame of a future timelike $P_1$, one has $P_1=(Mc,0)$ and $P_2^0>0$, so $P_1\cdot P_2=McP_2^0>0$; Lorentz invariance proves the assertion in every frame.
The <impossibility of photon decay into two massive particles> follows because a photon has squared <four-momentum> zero. If it decayed into an electron and positron, conservation would give
$$
0=(P_-+P_+)^2=2m^2c^2+2P_-\cdot P_+>0,
$$
a contradiction.
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