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My question concerns the theory proposed in this classic paper by Misner and Wheeler. In the paper, the authors propose the idea of "charge without charge"--namely, that positive and negative particles might really be the ends of a wormhole, with field lines going into a mouth interpreted as a "negative" particle and the outgoing field lines at the other end as the "positive" particle.

However, I noticed that the paper didn't mention whether or not the wormholes were traversable. If the wormhole was not traversable by an external material source (i.e., they have unstable inner horizons, have curvature singularities, etc.), then could the field lines technically travel through the wormhole's neck, or would they, too, be blocked? I know that the "charge without charge" idea isn't probable due to the tiny wormhole tunnels collapsing to form black holes, but my question also concerns larger wormholes as well. Thus, could field lines travel through a macroscopic non-traversable wormhole?

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  • $\begingroup$ Sorry, @CuriousOne , but it is clearly untrue that the electric charge requires quantum mechanics. People have measured, played with, and classically described the electric charge centuries before QM was born. $\endgroup$ – Luboš Motl May 31 '16 at 4:42
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    $\begingroup$ What does stable matter have to do with anything here? Are you just trying to disrupt this server? The wormhole solutions of GR exist etc. which is why they're absolutely legitimate topics for papers such as Misner-Wheeler and questions and answers that build upon them. Electric charges were known many centuries ago - friction of the ebonite rod is enough - and people discovered Coulomb's force among charges, built capacitors, and most of the traditional electric industry that is all about charges a very long time before QM. To say that charges aren't interesting physics without QM is idiotic. $\endgroup$ – Luboš Motl May 31 '16 at 5:25
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First, regardless of what physicists thought many decades ago, it seems basically clear today that traversable black holes are forbidden in Nature. They either require some negative energy density which induces instabilities, or equivalently, they allow superluminal signaling which violates the relativistic causality, and so on.

Non-traversable black holes similar to the Einstein-Rosen bridge actually seem to be allowed and play a role in some research in quantum gravity in recent years (ER=EPR).

But regardless of the traversability, the field lines surely go through the wormhole neck. The flux through the neck is exactly equal to the flux around one of these charged particles. That's really the point of the Misner-Wheeler construction. Normally, the charges are the sources or sinks of the field lines and they basically say that the field lines continue and there's never any real source – they continue to the other side of the Universe through the neck of the wormhole.

If there were no flux through the wormhole, the whole wormhole would be useless for the description of the electromagnetic phenomena.

Also, there's nothing wrong about causality implied by the existence of the flux in the neck. The traversable wormholes themselves are a problem for causality but whether or not there is electric or other (especially static) field inside the wormhole doesn't make the situation any worse.

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