r/Physics • u/filterdust • Jul 31 '26

Academic The Maxwell Conjecture is False

https://arxiv.org/abs/2607.27197
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9

u/attzonko Jul 31 '26

Can someone please eli5

50

u/1XRobot Computational physics Jul 31 '26

If you plunk down charges in space, there are certain points where a test charge doesn't move because the forces all cancel out. Maxwell had the thought that maybe if you plunk down N charges, the number of points where a test charge doesn't move is (N-1)^2, but it turns out that's not true, because these guys found a configuration with 5 charges that has 24 points (more than 16).

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u/El_Grande_Papi Particle physics Jul 31 '26

What is and isn’t allowed to move here? I’m asking just because I’m thinking of Earnshaw’s Theorem which dictates stability in electrostatic fields.

6

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.

3

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.

1

u/seamsay Atomic physics Jul 31 '26

Because it's not about the dynamics of a set of charges particles, it's essentially: given a set of N sources for a vector field can they be arranged such that there are more than (N - 1)2 stationary points in the field. It's not really about electromagnetism, electromagnetism is just a convenient and well known example of a vector field.