If the potencial of the sources do not have a common reference no current will flow from one circuit to another. It is easy to understand, take a voltimeter and take two bateries of different voltaje and not connected in any way, for instance, one of 1,5V and one of 9 V. Try to measure a voltaje between the positive of battery of 1.5V and the positive of battery of 9V. What your voltimeter shows? 0Volts, no + or - 7,5V. Why this happens? easy to understand, they are circuits with no references between them, so no current can go from one to another, and with no current, no voltage, Ohm's law. So you circuit will not work if you don't make a common reference. I mean, now join the negative part of each battery and take the measurement again. Now you will have + o - 7,5V. Why because there is a circuit closed by the voltimeter so a current can pass since one battery to another because they are tied together in one point and the voltimer closes the circuit so a current can circulate through the circuit. Is quite easy, open circuit no, current, closed circuit current an voltage. If you don't connect both gound of your batteries together in the arduino circuit, you will not have current between them because you have an open circuit. So it will not work.