Hmm, this is a very interesting line of argument: I am very much focused on electrostatic reasoning here, and I haven't given significant thought to frames of r

Hmm, this is a very interesting line of argument: I am very much focused on electrostatic reasoning here, and I haven't given significant thought to frames of reference at all. My instinct is still that it won't change my overall conclusions here, but I'd love to be proven wrong: that would be pretty cool. For what it's worth, gravitational slingshots (like everything else) have to conserve total momentum in any frame: (e.g.) when Voyager speeds up, Jupiter must correspondingly slow down (though Jupiter's change would be nearly zero, of course). The CM frame is certainly very handy for "elastic collision" calculations like this, but the laws of physics (like momentum conservation) can't care what frame you're in. But that by itself doesn't say anything about whether the changes in motion of these charged objects might change the potential reasoning. Hmm... honestly, it's late at night and I don't think I have time to really sort through this in detail. (I tried to sketch an argument for the simple case of circular parallel plates with all motion limited to be along their central axis. The electric field parallel to the relative motion of the primed frame should be unchanged, but I just don't have the time to sort out how to reconcile that with the inevitable Lorentz contraction of positions along that axis. Glancing at tables of field transformations, it looks like charge density and potential should both be increased by a factor of gamma while distances along the axis are reduced by the same factor: that should mean that the integrals to find potential come out the same, at least for the cases that I've used in my argument. But there are some nagging details bugging me about it: I think they'll sort themselves out, but if you or your wife or someone else can use this reasoning to change the result, that would be neat to see.) (Also, I'm completely ignoring any effects of radiation due to accelerated charges in this story. I haven't seen anyone say that's relevant and my impression is that the calculations used in the original paper are based on much more basic physics, and I'd be shocked if somehow radiating away energy wound up being the secret to making this work. But again, if someone does a more detailed calculation and discovers that radiation really does make it work, that would be fascinating.)