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*From*: David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>*Date*: Fri, 2 Feb 2001 12:03:50 -0500

I guess I should qualify the response of my last post a bit. I wrote:

.... But *if* the spacelike sections of spacetime

are topologically compact (so that the universe is spatially closed) it

is a easily provable theorem that the universe must be charge-neutral

(for essentially the reason illustrated by Bill) because all electric

flux lines must stop & start on opposite charges and there is no

spatial infinity for any excess such lines to escape to.

I should point out that I phrased the sentence badly. I meant to say

that all flux lines that happen to have an endpoint must also possess

an oppositely charged endpoint, and this guarantees global charge

neutrality, because any flux line that had one endpoint must either have

another endpoint (of necessarily opposite charge) or it must escape to

asymptotic spatial infinity. If there is no such asymptotic spatial

infinity for the excess one-ended flux lines to go to, there can be no

such excess.

It is always possible to have E field flux lines that have no endpoints

at all by simply having them form a loop (such as when such loops are

induced by Faraday's law or when they might globally loop the entire

universe if it is compact).

David Bowman

David_Bowman@georgtowncollege.edu

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