- Mar 31, 2012
- Reaction score
Precisely.The argument made by the model is that the Poynting vector decreases over distance in such a way that when it hits the other wall, there's less energy flow and less momentum flow. <--- Herein lies the problem. If the energy flow and momentum flow weakens, where does it go? If we don't want to throw the conservation of momentum out of the window, it has to be reabsorbed by the device or dumped overboard. Dumping overboard would just create a typical photon rocket.
This demonstrates that there is a net energy flow from the small end towards the big end. Now, if the energy is flowing into the big end, it must be dissipated there somehow, either by localized heating or production of thrust by whatever mechanism.
Next, observe that radiation pressure of photons hitting a surface (think solar sail) is <S>/c, where <S> is average of Poynting vector over time, and c is the speed of light -- thus the force exerted on the sail with surface A is <S>*A/c. The simulation shows that <S> is zero on the wide end, while it is non-zero on the narrow end. This means that an (inward!) force is exerted on the narrow end, but not on the wide end. Thrust!
But there is still an (apparent?) violation of conservation of momentum. The force comes from the momentum of photons hitting the wall being transferred to the frustum: a photon flying towards the wall carrying the momentum of +p hits the frustum and transfers its momentum to it. So far so good; at this point conservation of momentum holds. But, conservation of momentum should also hold at the antenna, so the act of emission of a photon with momentum +p should have exerted momentum -p on the antenna. So the frustum should have received momentum -p at photon's emission and +p at absorption, resulting in the net momentum of zero.