Invisible wrote:
> Apparently, all I have to do is generate a sufficiently low-frequency 
> wave, with V and I sufficiently far out of phase, and we arrive at an 
> impossible situation. I could have a system with an arbitrarily large 
> current passing through it, for an arbitrarily long time, despite the 
> entire system having zero potential difference.

Yes. But the system would have to be arbitrarily large. :-)  That's what 
people call "ground potential".

It has to be at least large enough to hold one wave.

> Obviously, electrons don't just move around for the hell of it. 

Actually, at the quantum level, yeah, they do. That's why you can't make 
abitrarily *small* transistors.

> The equations might make perfect sense in the presence of complex 
> numbers, but that doesn't mean they match the real world.

But they do. All current is measured in complex numbers. All the 
weirdness of quantum mechanics is caused by probabilities that are 
complex numbers.  What's the probability of this electron emitting a 
photon?  0.3 + sqrt(-1.4).

-- 
   Darren New / San Diego, CA, USA (PST)
     "That's pretty. Where's that?"
          "It's the Age of Channelwood."
     "We should go there on vacation some time."

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