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I've just had a crazy idea, and I need some input on it. It is entirely theoretical, and maybe I don't understand much about how electromagnetism works, but what if particles could have complex charges?

By this, I mean having a charge with "real" and "imaginary" properties. Eg. $3-i$ or $\sqrt 2i$.

First, let's define a particle $q$ with a charge of $i\cdot e$, and a particle $p$ with charge $i^3\cdot e$, or $-i\cdot e$.

Initially, it becomes apparent that when two $q$ particles or two $p$ particles interact, they attract each other, while a $q$ and a $p$ particle will repell each other. This is because in Coulomb's Law, $F=k_e\frac{q_1q_2}{r^2}$, when using purely imaginary values ($i$,$-i$) for $q_1$ and $q_2$, $F$ is positive when the charges are like-signed, and negative when they are different.

So what would happen if a particle with a real charge interacted with a particle with an imaginary charge? $F$ would have an imaginary value. If we use a particle with a complex charge, $F$ would be complex.

What kind of effects would we see if $F$ was imaginary or complex? Am I completely wrong in how electromagnetism works? Is "imaginary" or complex charge already a thing, and I've got it all wrong?

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Basically, complex charges will introduce complex forces, and hence make the particles get locations and velocities that are complex. So the world presumably needs double the number of spatial dimensions.

Imaginary velocities imply negative kinetic energy. That means that a particle can reduce its energy indefinitely by moving faster and faster along the imaginary axis.

I think the formal structure of electromagnetism is totally fine with complex values of everything, but it does produce a universe that has very little to do with ours.

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  • $\begingroup$ Is it safe to say that this could be "possible" in science fiction? $\endgroup$
    – The Eye
    Oct 19, 2018 at 19:25
  • $\begingroup$ @TheEye - Sure. In much the same hard sf sense as in which Greg Egan has written novels about universes with a different metric signature. $\endgroup$ Oct 20, 2018 at 0:55

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