Quantum_ Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar [147]
From the arguments he deployed at Solvay 1927, Bohr held that any measurement of the position of the light box would lead to an inherent uncertainty in its momentum, because to read the scale would require it to be illuminated. The very act of measuring its weight would cause an uncontrollable transfer of momentum to the light box because of the exchange of photons between the pointer and the observer causing it to move. The only way to improve the accuracy of the position measurement was to carry out the balancing of the light box, the positioning of the pointer at zero, over a comparatively long time. However, Bohr argued that this would lead to a corresponding uncertainty in the momentum of the box. The more accurately the position of the box was measured, the greater the uncertainty attached to any measurement of its momentum.
Unlike at Solvay 1927, Einstein was attacking the energy–time uncertainty relation, not the position–momentum incarnation. It was now, in the early hours of the morning, that a tired Bohr suddenly saw the flaw in Einstein's gedankenexperiment. He reconstructed the analysis bit by bit until he was satisfied that Einstein had indeed made an almost unbelievable mistake. Relieved, Bohr went to sleep for a few hours, knowing that when he awoke it would be to savour his triumph over breakfast.
In his desperation to destroy the Copenhagen view of quantum reality, Einstein had forgotten to take into account his own theory of general relativity. He had ignored the effects of gravity on the measurement of time by the clock inside the light box. General relativity was Einstein's greatest achievement. 'The theory appeared to me then, and it still does, the greatest feat of human thinking about Nature, the most amazing combination of philosophic penetration, physical intuition, and mathematical skill', said Max Born.6 He called it 'a great work of art, to be enjoyed and admired from a distance'. When the bending of light predicted by general relativity was confirmed in 1919, it made headlines around the world. J.J. Thomson told one British newspaper that Einstein's theory was 'a whole new continent of new scientific ideas'.7
One of these new ideas was gravitational time dilation. Two identical and synchronised clocks in a room with one fixed to the ceiling and the other on the floor would be out of step by 300 parts in a billion billion, because time flows more slowly at the floor than at the ceiling.8 The reason was gravity. According to general relativity, Einstein's theory of gravity, the rate at which a clock ticks depends upon its position in a gravitational field. Also, a clock moving in a gravitational field ticks slower than one that is stationary. Bohr realised that this implied that weighing the light box affected the time-keeping of the clock inside.
The position of the light box in the earth's gravitational field is altered by the act of measuring the pointer against the scale. This change in position would alter the rate of the clock and it would no longer be synchronised with the clock in the laboratory, making it impossible to measure as accurately as Einstein presumed the precise time the shutter opened and the photon escaped from the box. The greater the accuracy in measuring the energy of the photon, via E=mc2, the greater the uncertainty in the position of the light box within the gravitational field. This uncertainty of position prevents, due to gravity's ability to affect the flow of time, the determination of the exact time the shutter opens and the photon escapes. 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