As far as I know, for light and particles taking special relativity into account:
\begin{align} E^2 &= (T + m_0c^2)^2\\ &= p^2 c^2 + m_0^2 c^4 &\text{ (particles)}\\[1.5em] E &= p c & \text{ (photons)}\\[1.5em] F &= \frac{d\,p}{dt\phantom\,} \ne ma.^† \end{align}
If I have a bottle of hydrogen or xenon and 100% efficient and massless ion engine and light to electricity converters, I can accelerate away from a laser beam both by absorbing their momentum and by using their energy to accelerate ions back towards the source of the laser.
I think but am not sure that it is difficult to impossible to accelerate directly into the beam because 1) this comment and 2) a given amount of energy imparts more momentum to a photon than to a particle with nonzero rest mass $m_0$.
Questions:
Is that right? Even with 100% efficient and massless light to energy converters and ion engines, I can never accelerate directly into a beam of light?
If so, for a given particle energy $T$ and rest mass $m_0$ what is the highest angle at which I can accelerate in the half-space (hemisphere) towards the laser beam, if any? Or can I only accelerate into the half-space away from it?
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