Great Blunders of the Great Bohr-Einstein Debate
The Bohr Einstein debate of the light box gedanken experiment was probably one of the best well known scientific debates. But rarely any one noticed that both of these two great men made fatal mistakes in the logoc of their argument.
Bohr's detailed recount of the debate can be read here:
In summary, Einstein proposed a light box in which a fast acting shuttle releases a photon at a very precise moment. Before and after the release of the photon, the total weight of the light box can be weighed arbitrarily accurately to deduce the exactly mass-energy of the photon release. Therefore, both the photon's emitting time and mass-energy can be known to arbitrary precision, hence break the Heisenberg uncertainty principle which says the time and energy can not both be known precisely.
Bohr could not dispute Einstein's arguments. He could not sleep and spent the whole night desperately trying to find an argument to disprove Einstein. Next morning he did figure out a way to rescue the uncertainty principle, using time dilation of Einstein's own General Relativity. Einstein never thought his own theory will be used against his arguments. So Einstein was defeated.
But what Einstein never realized was that Bohr's logic was frauded. Intentionally or un-intentionally, he confused two completely different logical concept. One is the uncertainty of time measurement, Delta T, which should be the time internal during which the shuttle is open. Another concept, also expressed using the same symbol Delta T, is the time difference caused by time dilation due to general relativity.
See equation (7). The Delta T there was general relativity time dilation. It is definite, know, precisely calculable quantity. It is the difference between two clocks and has absolutely nothing to do with uncertainty of time measurement.
Bohr successfully confused Einstein by using the same symbol to represent both the time dilation and time uncertainty, two different quantities, and treat them as if they are the same thing. A confused Einstein got lost and could not see that Logic Fraud.
But certainly, Einstein's argument was also frauded, but for a totally different reason that Bohr also failed to see. That is, a photon of certain energy has a certain frequency and wavelength. If you open the shuttle for too short a time, shorter than one period of oscillation of the photon's frequency, then you would not be able to release a full photon. You would have choped a whole wavelength of the photon in halfs. Therefore, you either have not release a photon of the expected frequency, or you have released a photon who has a shorted wavelength and higher frequency.
In any case, the emitted photon would have a wavelength shorted than the distance light can travel within the short time interval that the shuttle is opened. So the uncertainty principle is still exactly true.