David Peat

Quantum Uncertainty 19to measure the energy of a quantum system over smaller and smallertime intervals this same energy becomes more and more uncertain.For Bohr this ambiguity was basic to the quantum theory, whereas forEinstein, time and energy or position and momentum were objectiverealities “possessed” by the quantum theory. The only uncertainty, accordingto Einstein, lay in our inability or lack of ingenuity in measuringthe objective properties of such systems.When Bohr and Einstein met at the Solvay conference in 1930,Einstein presented Bohr with another thought experiment. Suppose,he said, we have a box filled with radiation and a shutter timed to openand close for a split second. The time interval is known with greatprecision, and in that interval a small amount of energy—a single photon—willescape from the box. Einstein now anticipated Bohr’s positionthat the shorter the time interval, the more uncertain will be ourknowledge of the amount of energy that has escaped. Einstein’s specialtheory of relativity showed that energy and mass are equivalent, asshown by the formula E=mc 2 . Therefore, if the box is weighed beforeand after the shutter opens, it will be lighter in the second weighing.This difference in mass gives a precise measure of how much energyhas escaped. In this way, an accurate measure of energy is determinedwithin a precise time interval. At this point, Einstein argued that hehad demolished Bohr’s claim about fundamental uncertainty.Bohr had to be equally ingenious, and so he looked in detail at theway the box would be weighed. He posited that, if the box weremounted on a spring balance with the pointer of the balance pointingto zero, energy would escape the box at the moment the shutter opens,and in consequence, the mass of the box would decrease very slightly,and the box would move. As the box moves, so too the clock inside thebox moves through the earth’s gravitational field. Einstein’s generaltheory of relativity tells us that the rate of a clock changes as it movesthrough a gravitational field. In this way Bohr was able to show that,because of changes in the rate of the clock, the more accurately weattempt to measure energy (via a change in the mass of the box) thegreater will be the uncertainty in the time interval when the shutter isopen. In this way Heisenberg’s uncertainty was restored and Einstein’sthought experiment was refuted.