Gedankenexperiment quantum mechanics: einstein’s box experiment (1930) 2:34 am Sunday, 19 October 2014 (GMT+4) Time in Moscow, Russia [the original text was translated into english by daria t.: miss daria is a native russian and ukrainian speaker, currently residing in ukraine. shes been learning english since she was 5. she holds ma degree in translation and interpreting (diploma with honors). her higher educational program included speaking and writing skills training, social and political translation, economic and legal translation, as well as translation of technical texts and sailing documents.] Einstein attempted to disprove quantum theory at the sixth Solvay Conference in 1930 with the “clock in the box experiment”. This involved a box with a hole in one wall covered by a shutter which could be opened and closed by a clock mechanism inside the box. The box also contained radiation which would add to the weight of the box. The box would be weighed and then at a given moment the clock would open the shutter allowing a single photon of radiation to escape. The box could then be re-weighed, the difference between the two weights telling us the amount of energy that escaped using the formula e = mc². Under the uncertainty principle it is not possible to obtain an exact measurement of the energy of the released photon and the time at which it was released. Einstein’s experiment was designed to show such exact measurements were possible, the clock measuring the time of release of the energy and the weighing of the box disclosing the amount of energy involved. A diagram showing Einstein’s idea is below. Bohr’s reply involved looking at the practicalities involved in making the required measurements. The box had to be weighed so it had to be suspended by a spring in a gravitational field. To weigh the box it is necessary to compare a pointer attached to the box against a scale. After the photon had left the box weights can be added to the box to restore the pointer to the same position against the scale as it had been before the photon escaped. The weight added to the box gives the weight of the escaped photon. However this involves a measurement of the box to ensure the pointer is back at its original position. This measurement is subject to the uncertainty principle concerning the position and momentum of the box which brings uncertainty into the measurement of the weight of the box. If there is uncertainty in the weight of the box, then there will be an uncertainty in the energy of the released photon. There will also be uncertainty in the time of the released energy as the speed of time depends upon the position of a clock in a gravitational field. This position is uncertain then the time of the release of the photon will also be uncertain. This means both the time and the amount of energy released will be uncertain so Einstein’s thought experiment did not contradict the uncertainty principle: ∆E∆t ≥ ħ/2 Einstein said that the box could be weighed at first and then a single photon be allowed to escape through a shutter controlled by a clock inside the box. The box would then be weighed again and the mass difference m determined. It appeared that both the photons energy and its time of emission could be determined! Bohr finally realized that there was a flaw in Einsteins reasoning. When the photon is released, the box will recoil (to conserve momentum) and the position of the box in the earths gravitational field will be uncertain. Einsteins very own general theory of relativity said that this would cause a corresponding uncertainty in the time recorded. Bohr had been saved by Einstein forgetting his own theory! This was the last serious assault – approximately 28 years after its inception at the hands of Planck, the foundations of quantum mechanics were complete.
Posted on: Sat, 18 Oct 2014 22:33:13 +0000
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