I was reading a book on the history of Quantum Mechanics and I got intrigued by the gendankenexperiment proposed by Einstein to Bohr at the 6th Solvay conference in 1930.
For context, the thought experiment is a failed attempt by Einstein to disprove Heisenberg's Uncertainty Principle.
Einstein considers a box (called Einstein's box; see figure) containing electromagnetic radiation and a clock which controls the opening of a shutter which covers a hole made in one of the walls of the box. The shutter uncovers the hole for a time Δt which can be chosen arbitrarily. During the opening, we are to suppose that a photon, from among those inside the box, escapes through the hole. In this way a wave of limited spatial extension has been created, following the explanation given above. In order to challenge the indeterminacy relation between time and energy, it is necessary to find a way to determine with adequate precision the energy that the photon has brought with it. At this point, Einstein turns to his celebrated relation between mass and energy of special relativity: $E = mc^2$. From this it follows that knowledge of the mass of an object provides a precise indication about its energy.
Bohr's response was quite surprising: there was uncertainty in the time because the clock changed position in a gravitational field and thus it's rate could not be measured precisely.
Bohr showed that [...] the box would have to be suspended on a spring in the middle of a gravitational field. [...] After the release of a photon, weights could be added to the box to restore it to its original position and this would allow us to determine the weight. [...] The inevitable uncertainty of the position of the box translates into an uncertainty in the position of the pointer and of the determination of weight and therefore of energy. On the other hand, since the system is immersed in a gravitational field which varies with the position, according to the principle of equivalence the uncertainty in the position of the clock implies an uncertainty with respect to its measurement of time and therefore of the value of the interval Δt.
Question: How can Bohr invoke a General Relativity concept when Quantum Mechanics is notoriously incompatible with it? Shouldn't HUP hold up with only the support of (relativistic) quantum mechanics?
Clarifying a bit what my doubt is/was: I thought that HUP was intrinsic to QM, a derived principle from operator non-commutability. QM shouldn't need GR concepts to be self consistent. In other words - if GR did not exist, relativistic QM would be a perfectly happy theory. I was surprised it's not the case.