Einstein's theoretical challange as retold by
Stuart Clark, author of
'The Day Without Yesterday'.
Background: Einstein was not a fan of quantum theory and the uncertainty principle. Apparently he came up with a thought experiment for Bohr and Heisenberg.
Quote p217: 'It concerns the trade-off between knowing the energy of a process and the duration of the process.'
P218: "Imagine a box filled with light and placed on a weighing machine. Next to the box is a clock. The box opens at a particular time and a single photon is emitted. The weight of the box instantly changes, and that will give us the precise amount of energy released. The clock will have told us exactly when the photon was emitted. Both can therefore be known with certainty. There is no uncertainty between energy and time.'
'If the uncertainty principle is true, you should be able to give me a theoretical reason why the clock will be affected by the release of the photon. How can those two things be physically related?'
According to Clark, Bohr came up with a solution for Einstein:
P219:
'You have given me a sleepless night,' Bohr said to Einstein, 'but I have an answer for you. When the photon leaves the box, the box will weigh less. It will therefore rise a little on the scales.' Einstein inclined his head in agreement. 'At its new height it will feel a weaker pull of Earth's gravity than before. According to general relativity, the rate at which time passes is dependent upon the strength of the gravitational field. So, time for the box slows down during the emission of the photon. In other words, the emission of the photon causes time to pass at a differnet rate after the release than before. The difference in this rate introduces an uncertainty into the measurement of the clock standing beside the apparatus. As you see, Albert, the uncertainty predicted by general relativity is exactly the same as predicted by Heisenberg's principle. You forgot your own theory.'
I don't know if how Clark retold this story is historically accurate but the details of the challenge got my cogs turning:- Even though this is a theoretical challenge, light is without mass. How could the box register a lower weight?
- As time slows down for the box, my understanding is that time for the released photon speeds up.
Edit: Apologies, this thread probably belongs in the Amateur Science section of the forum.