I was dumping some packing peanuts into a trash can and they stopped pouring in — enough charge had built up that the additional peanuts were repelled by the ones in the can. Here’s a couple of attempts to throw peanuts in.

You might be tempted to think you could confine a peanut (or any charged particle) this way — all of the charges repel, so you form a potential well which traps the extra charge. Unfortunately it doesn’t work out. The electric field you get will counteract gravity, but there’s no field directed radially inward, at all points, and no way to get one. Electric fields only converge on charges. The best you could get would be a field that was “leaky” — inward at one point, but outward somewhere else. All of this is shown mathematically in Earnshaw’s theorem. It works for magnetic fields, too, with the loophole that it doesn’t apply to diamagnets. (but Earnshaw didn’t know about those)

A Tale of Two Twins

I’d like to say it is a far, far better video than I have ever seen — the animation and explanation of the light clock, which is the standard explanation of time dilation, are nice. But there is one glaring mistake in it, where it is claimed that time dilation doesn’t happen in an accelerating frame. The GPS satellite constellation would be surprised to hear that, were they not distracted by me anthropomorphizing them.

The key is that time dilation is symmetric in inertial frames, and an acceleration removes that asymmetry. In inertial frames neither twin can say that his measurement is “right” and the other one “wrong,” since there is no absolute reference frame. They both have to be valid measurements. Acceleration removes that symmetry — you can tell if you are accelerating, so you can no longer claim to be at rest — and the clock that accelerates will be slow as compared to one that does not.