Electrical – Connecting Two Grounds Together

You should be able to connect your arduino ground to the 24V ground, unless the power supplies are somehow referenced to one another. If one or the other or both of your supplies happens to be a battery, then you don't have a concern. If both supplies are transformer isolated AC supplies, you shouldn't have a problem. Even if both supplies tie their DC return side to the earth-ground lug of the AC mains, you should be ok.

If you bridge the two grounds through a 10K resistor, and a DVM across that resistor shows anything more than a volt or so, your supplies probably aren't isolated enough to just connect the grounds.

No, I would not tie the grounds together for such a distance. That does make the data connection more tricky though. In your case, the two grounds shouldn't be all that different since presumably they are tied together back at the breaker box in your house. In that case you could use differential signalling, knowing that the common mode offset should stay bounded to a few volts at most.

However, I think real isolation of the data signal is a better idea. If you can use ethernet, then you don't have to do anything further since that is already isolated. Otherwise, it's probably easier to use a opto-coupler at the receiver. The transmitter would send pulses of a few mA, which is enough to light the LED in the opto at the other end.

One simple scheme is to use UARTS, with the line idle level being no current. Cheap optos can be surprisingly slow, so either get fast optos or run the UARTs at a slow baud rate. Even a really slow opto can support 9600 baud well enough, and you can go much faster with the right choice of opto. If you need high data rate, then ethernet starts to sound good.