With Maxwell's equations, it is known that radiation carries momentum. However, I don't see how light can provide such "longitudinal" momentum if its electric component is perpendicular to its direction of travel, and its magnetic component is supposed to be weak.

I am wondering is there is a more gritty, bottoms-up explanation just in terms of the $\vec{E}$ and $\vec{B}$ fields.

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    $\begingroup$ Yes. If the electric field is up/down and the magnetic field is right/left, the electric field induces up/down oscillations of charged particles. Since $\text{up} \times \text{right}$ is forward, the Lorentz force then pushes the particles forward. $\endgroup$ – knzhou Apr 17 '17 at 0:48
  • $\begingroup$ That's very interesting. Just for reference, the answers here physics.stackexchange.com/questions/198026/… imply that EM waves do not interact with neutral charges, so that makes sense. $\endgroup$ – SpiralRain Apr 17 '17 at 0:53
  • $\begingroup$ Also, I agree that it's sometimes unintuitive how transverse waves can carry longitudinal momentum. I asked the same question for waves on a string a while back, where it's even trickier. $\endgroup$ – knzhou Apr 17 '17 at 0:56
  • $\begingroup$ @knzhou That first comment is an answer. $\endgroup$ – dmckee Apr 17 '17 at 3:29
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    $\begingroup$ @SpiralRain Objects (like atoms) can be net-neutral but still possessed charged sub-structure, and electromagnetic fields can interact with that sub-structure. Indeed those interactions are responsible for all the ways in which net neutral matter interacts with light (index of refraction, reflectivity, polariod behavior and so on). $\endgroup$ – dmckee Apr 17 '17 at 3:31

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