I was wondering if anyone considered a photon entering the Einstein-box, say because outside is 'hotter'. Would an increase in mass-energy be observable? Some may consider this a trivial question but I'm asking anyway.
The 'Einstein box' is a thought-experiment Einstein proposed to observe both the size of an energy change & the time at which it came to be.
A box has a 'perfect' shutter so you can let just 1 photon exit. The mass of the is box is decreased because the photon carries away energy ($E=mc^2$). The box is weighed before and after so you know the energy of the photon and the 'perfect' shutter allows you to know when the photon exited. Knowing both energy & time of course violates Heisenberg. Bohr showed that Einstein proposal was flawed.
I hope this is clear enough?