You don't really understand the difference between theoretical-math based quantum mechanics and observation based quantum mechanics. The former (math-based) says a whole bunch of crazy stuff, like we can violate the first law under certain conditions. The latter (science, observation based) says the first law is good to go.
Crap. There's no discrepancy. You can violate the first law only on time scales set out by the uncertainty principle, since energy and time are conjugate variables. You can demonstrate this experimentally.
To: Right Wing Professor
I'd be interested in how they can prove that experimentally.
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