i think you should buy a new voltmeter that's not possible with the given circuit
Good point there. I thought it shouldn't be possible either.
Here's some more information:
The power came from a wall wart 12V 2A adapter (switching power supply?)
I set this up on a breadboard
The multimeter is Fluke 87V and I have no reason to believe that it's malfunctioning.
What's more bizarre...
if I disconnected the positive from the breadboard, so that only the negative from the wallwart is connected to the breadboard, things get more interesting. In theory, I should not read any voltage on the circuit. Indeed when I measured either side of the resistor, it reads as 0V.
However, the base reads 5.7V and Emitter 3.4V
This is with the + from the wall wart supply disconnected from the breadboard. Only one wire - the negative, goes to the breadboard.