If I hold a laser pointer and press the trigger does the emission of the beam generate kick-back in the opposite direction through conservation of momentum. I understand it would be tiny, so my question is "in principle". And since the beam itself has no mass but does have energy, what would the correct equation be for calculating the reaction force?


Yes indeed there will be a "kick back". When you emit light of energy $E$ in a direction defined by the unit vector $\hat{X}$, that light bears momentum $\frac{E}{c}\hat{X}$, so the magnitude of the momentum is $E/c$. If your energy output per unit time is $P$, then the impulse imparted on you in that time is $-\frac{P}{c}\hat{X}$, so this is the force imparted on you. It's tiny of course, unless you're outputting an appreciable fraction of a kilogram as light energy per second!

Each photon bears momentum $\hbar\,k$, where $k$ is its wavenumber, so this measures the kickback per photon.

Incidentally, these equations follow from the massless case of the equation for the 4-momentum norm for a particle of total energy $E$, momentum $p$ and rest mass $m$:

$$E^2 - p^2 c^2 = m^2\,c^4$$

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  • $\begingroup$ Kick is a big word for a small impulse... instructive to compute the net force for a 5 mW laser pointer: $1.7\cdot 10^{-11} N$ $\endgroup$ – Floris Jun 21 '15 at 14:26

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