tl;dr Passing a charged particle through a wormhole does not leave the mouth charged
https://arxiv.org/pdf/1904.04103.pdf
This pretty conclusively resolves the discussion between Luke and I in my favor.
Note Figure 6 (the standard argument) vs. Figure 9, which is essentially what I argued: Stoke’s Theorem does not hold in non-trivial topologies.
An extra technical consideration is the “Gauge-free” condition, which essentially says that background Maxwell fields (e.g. H) are well-defined.
I did not consider the gauge-free condition. Both are required for charge conservation to occur, and both are violated in intra-universal wormholes (see the end of section V).
By the way, this is a good thing. If it were not true, you could generate infinite charge from a single charged particle by repeatedly passing it through wormhole mouths.
In this formulation, the charge is still the same no matter how many times it’s threaded through the wormhole.
https://arxiv.org/pdf/1904.04103.pdf
This pretty conclusively resolves the discussion between Luke and I in my favor.
Note Figure 6 (the standard argument) vs. Figure 9, which is essentially what I argued: Stoke’s Theorem does not hold in non-trivial topologies.
An extra technical consideration is the “Gauge-free” condition, which essentially says that background Maxwell fields (e.g. H) are well-defined.
I did not consider the gauge-free condition. Both are required for charge conservation to occur, and both are violated in intra-universal wormholes (see the end of section V).
By the way, this is a good thing. If it were not true, you could generate infinite charge from a single charged particle by repeatedly passing it through wormhole mouths.
In this formulation, the charge is still the same no matter how many times it’s threaded through the wormhole.