Why are the neutral wires not connected in this box?
This looks like it used to hold a light fixture that was controlled by a switch. One white conductor is a grounded (neutral) conductor, the other is a switched ungrounded (hot) conductor (presumably).

To verify, follow the cable in both directions (one direction at a time, unless you have a split personality) and see if it eventually runs to another light fixture or a switch.

Alternatively, you could carefully connect a multimeter to the two wires. Then run about wildly flipping switches until either a reading is displayed, or the reading goes to 0.