Obviously is the switch is open (no complete current path) there will not be any current flow in the white wire, but there will also not be any current flow in the black wire either.
Kirchoff's current law strikes again!
Ok, ok. Let me qualify that statement about the black wire and the white wire.
If the switch is open(off) then the potential difference as measured between the white wire and a suitable ground(metal conduit, or a screw on a junction box cover plate for instance) is zero, but not so for the black wire.
I guess I was thinking "volt meter" even though the post read "current meter" I don't see the value of using a "current meter" when checking houshold wiring and I can't really think of any time I've used one. When checking wires for "power", what you really want to know is "will this wire zap the sh*t out of me if I touch it?" and also "If I hook this wire up to an electrical device, will that device function?". And a current meter ain't gonna tell you that, is it?
And from now on, I guess I gotta put quotes around the word "power", whenever I use it in laymans terms insead of textbook electricity theory terms.
Here's some layman's term definitions for ya:
"juice" is what the "POWERplant" sends ta yer household "wyerin" by way of the main fuzebox. And that's why the technical term for "juice" is "power". And if'n there ain't no "power" in yer "wyerin", then yer TV ain't gonna work real good no matter how many times ya change the baddrees in yer reemote. An' sometimes if ya ain't gettin no juice ta yer wyerin, It's 'cause ya gotta take yer fuze outta yer fuze box an wrap it in tinfoil an THEN screw it back in again. Either that'er ya fergot to pay yer "power" bill and they shut yer "power" off an that's why ya ain't gettin no "juice" ta yer "wyerin". An if ya did ferget to pay, well then there's ways a fixin that too, but ya gotta go outside an find yer lectric meter in back a yer trailer, and then...well I'll tell ya the res later when there ain't no one else 'round.