Thirty Years that Shook Physics by George Gamow

Author:George Gamow
Language: eng
Format: epub
ISBN: 9780486135168
Publisher: Dover Publications
Published: 2012-07-24T16:00:00+00:00

Since in the Theory of Relativity time (in the form ctt) serves as the fourth coordinate, and energy (in the form E/c) as the fourth component of mechanical momentum, one might expect that there would exist a fourth uncertainty relation

ΔEΔt ≅ h

and it was this topic that led to the incident at the Congress.

Einstein stepped forward to announce that he could propose an ideal experiment to contradict this fourth relation. He was thinking, he said, of a box inlaid with ideal mirrors (like Jeans’ box discussed in Chapter I) and filled with a certain amount of radiant energy. In one of the walls was some kind of idealized photographic shutter connected with an idealized alarm clock, which could be set so that the shutter would operate at any given time after the box was filled with radiation (Fig. 25). Since the clock was inside the box, and the shutter closed, the interior of the box was completely isolated from the outside world. Einstein proposed to weigh the box prior to the alarm clock action; the weighing could be done with any desired precision, given enough time. The shutter would open at the exact moment for which the alarm clock was set, and a certain amount of radiant energy E would be let out. After the shutter closed one could again weigh the box with any desired precision. The change of the mass of the box M2 - M1 could be obtained with any precision from the two weight measurements, and being multiplied by c2 would give the exact amount of emitted energy, so that ΔE = 0. On the other hand, the ideal clock would work perfectly, so that there would be no uncertainty in the time when this energy was emitted, and Δt = 0, too. Having ΔE = 0 along with Δt = 0 would kill the fourth uncertainty relation.

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