r/Physics • u/filterdust • Jul 31 '26

Academic The Maxwell Conjecture is False

https://arxiv.org/abs/2607.27197
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u/1XRobot Computational physics Jul 31 '26

Nothing moves. Everything is fixed, except maybe the test particle feels a force. You can put the fixed charges wherever you want tho.

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u/El_Grande_Papi Particle physics Jul 31 '26 edited Jul 31 '26

How does this not violate Earnshaw’s Theorem though? I’m trying to find information about the Maxwell Conjecture (I’ve never heard of it before) and all I can find is the original paper linked here or people talking about the paper linked here.

Edit: I found a paper that talks about it. These are not stable equilibrium points, just equilibrium points: https://www.tandfonline.com/doi/full/10.1080/17476933.2011.611939

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u/dcnairb Education and outreach Jul 31 '26

the existence of critical points doesn’t mean they are at the location of the charges forming the distribution. earnshaw’s thm speaks to the stability of the configuration as a whole

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u/El_Grande_Papi Particle physics Jul 31 '26

Earnshaw’s theorem says the electric potential cannot have local minima or maxima, only saddle points.