Can I connect these two grounds together? (famous last words)

[opusensemble]

I have floating a HV circuit (transformer 2200V AC secondary) and a floating LV circuit (transformer 24V AC secondary), for which I would like to connect their floating grounds GND1 and GND2 together (image attached). Can this be done without defying any basic rule in physics or electronics?

If you're asking why I need this:
The LV circuit will supply an opto-isolated IC (with 4kVpeak isolation) which allows voltage measurement through a resistor voltage divider in the floating HV circuit. A common ground is thus required.

[Fungus]

Yes.

(And thanks for such an amazingly clear, informative, well presented question)

[NEYi]

You can always measure the voltage difference between two grounds.
If there's like 310V difference – I'm pretty sure it's obvious that connecting them won't lead to anything productive.

[opusensemble]

Thank you for confirming Fungus. Thank you too Neyi, Blueskull.

[Marco]

If the positive output of your HV transformer for some reason gets grounded your 24 transformer will see high voltage across it's isolation, might as well get one which is hipot tested at =>2.5kv.

[Nerull]

You can always measure the voltage difference between two grounds.
If there's like 310V difference – I'm pretty sure it's obvious that connecting them won't lead to anything productive.

Capacitive coupling could produce large voltage differences, so that's only reliable if you do a low impedance measurement.