Bohr's discussion of the fourth uncertainty relation revisited

Berthold‐Georg Englert

T. Tietz

Hrvoje Nikolić

In 1930, Einstein argued against the consistency of the time–energy uncertainty relation by discussing a thought experiment involving a measurement of the mass of the box which emitted a photon. Bohr seemingly prevailed over Einstein by arguing that Einstein's own general theory of relativity saves the consistency of quantum mechanics. We revisit this thought experiment from a modern point of view at a level suitable for an undergraduate readership and find that neither Einstein nor Bohr was correct. Instead, this thought experiment should be thought of as an early example of a system demonstrating nonlocal 'EPR' quantum correlations, five years before the famous Einstein–Podolsky–Rosen paper.

Pintu Bhunia, Mohammad Sal Moslehian

Yu Shi

Abstract The famous gedanken experiments of quantum mechanics have played crucial roles in developing the Copenhagen interpretation. They are studied here from the perspective of standard quantum mechanics, with no ontological interpretation involved. Bohr's investigation of these gedanken experiments, based on the uncertainty relation with his interpretation, was the origin of the Copenhagen interpretation and is still widely adopted, but is shown to be not consistent with the quantum mechanical view. We point out that in most of these gedanken experiments, entanglement plays a crucial role, while its buildup does not change the uncertainty of the concerned quantity in the way thought by Bohr. Especially, in the gamma ray microscope and recoiling double‐slit gedanken experiments, we expose the entanglement based on momentum exchange. It is shown that even in such cases, the loss of interference is only due to the entanglement with other degrees of freedom, while the uncertainty relation argument, which has not been questioned up to now, is not right.

Shoju Kudaka, Shuichi Matsumoto

We review Bohr’s reasoning in the Bohr–Einstein debate on the photon box experiment. The essential point of his reasoning leads us to an uncertainty relation between the proper time and the rest mass of the clock. It is shown that this uncertainty relation can be derived if only we take the fundamental point of view that the proper time should be included as a dynamic variable in the Lagrangian describing the system of the clock. Some problems and some positive aspects of our approach are then discussed.