Editing Uncertainty principle (section)

=== Einstein's box ===
Bohr was present when Einstein proposed the thought experiment which has become known as [[Einstein's box]]. Einstein argued that "Heisenberg's uncertainty equation implied that the uncertainty in time was related to the uncertainty in energy, the product of the two being related to the Planck constant."<ref name="Gamow">Gamow, G., ''The great physicists from Galileo to Einstein'', Courier Dover, 1988, p.260.</ref> Consider, he said, an ideal box, lined with mirrors so that it can contain light indefinitely. The box could be weighed before a clockwork mechanism opened an ideal shutter at a chosen instant to allow one single photon to escape. "We now know, explained Einstein, precisely the time at which the photon left the box."<ref>Kumar, M., ''Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality'', Icon, 2009, p. 282.</ref> "Now, weigh the box again. The change of mass tells the energy of the emitted light. In this manner, said Einstein, one could measure the energy emitted and the time it was released with any desired precision, in contradiction to the uncertainty principle."<ref name="Gamow" />

Bohr spent a sleepless night considering this argument, and eventually realized that it was flawed. He pointed out that if the box were to be weighed, say by a spring and a pointer on a scale, "since the box must move vertically with a change in its weight, there will be uncertainty in its vertical velocity and therefore an uncertainty in its height above the table. ... Furthermore, the uncertainty about the elevation above the Earth's surface will result in an uncertainty in the rate of the clock",<ref>Gamow, G., ''The great physicists from Galileo to Einstein'', Courier Dover, 1988, pp. 260–261. {{ISBN?}}</ref> because of Einstein's own theory of [[Gravitational time dilation|gravity's effect on time]]. "Through this chain of uncertainties, Bohr showed that Einstein's light box experiment could not simultaneously measure exactly both the energy of the photon and the time of its escape."<ref>{{cite book |last=Kumar |first=M. |title=Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality |publisher=Icon |year=2009 |page=287}}</ref>