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If you press a thermometer against the flywheel, it will pretty quickly heat up... It just behaves like a "white body" in terms of radiation.
But isn't it still possible that a simulation that lost its consciousness would still retain memories about consciousness that were sufficient, even without access to real consciousness, to generate potentially even 'novel' content about consciousness?
I would play lotto: if I win more than 10M$, I take the black box and leave. Otherwise I'd look in the black box: if it is full, I also take the small one. If not, I leave with just the empty black box. As this should be inconsistent, assuming a time traveling Omega, it would either make him not choose me for his experiment or let me win for sure (assuming time works in similar ways as in HPMOR). If I get nothing, it would prove the Omega wrong (and tell me quite a bit about how the Omega (and time) works). If his prediction was correct though, I win 11.000.000$, which is way better than either 'standard' variant.