Egyptian Folklore II

Since the measurement of time takes place in a gravitational field, the lapse in time during which the box is open must also depend on the box's position.
The uncertainty in position is an additional factor that Einstein had not taken into account, and this, according to Bohr, resolved the paradox. Einstein was sent packing.
Of course, this is not a very satisfactory answer to the modern eye. It implies, for one thing, that quantum mechanics requires general relativity to be consistent, an idea that modern physicists would roundly reject.

Nikoli says this problem has never been satisfactorily analyzed from a modern perspective. Until now.

He says the proper resolution is to think of the total energy of the system, which is the energy of the box and the energy of the photon. The total energy is constant and governed by a single mathematical entity, even after the photon is emitted.

So the box and the photon must be entangled.
This immediately raises the problem that Einstein later hit on in the EPR paradox. A measurement on the box immediately influences the photon and vice versa--spooky action at a distance.
For this reason, the photon paradox is equivalent to the EPR paradox, says Nikoli. Had Einstein noticed it, he could have stopped Bohr in his tracks.
That's an interesting historical footnote. Bohr's triumph over Einstein on this occasion is widely thought to have been his greatest.
But now it's easy to see that things could have been significantly different if Einstein had reformulated his argument in terms of entanglement.

A photon is an elementary particle, the quantum of light and all other forms of electromagnetic radiation, and the force carrier for the electromagnetic force, even when static via virtual photons. The effects of this force are easily observable at both the microscopic and macroscopic level, because the photon has zero rest mass; this allows long distance interactions. Like all elementary particles, photons are currently best explained by quantum mechanics and exhibit wave–particle duality, exhibiting properties of both waves and particles. For example, a single photon may be refracted by a lens or exhibit wave interference with itself, but also act as a particle giving a definite result when its position is measured.