Einstein and thought experiments [+ Maxwell's demon]

Sabine Hossenfelder, Einstein’s Greatest Legacy: Thought Experiments, Backreaction, July 25, 2020:

Einstein’s greatest legacy is not General Relativity, it’s not the photoelectric effect, and it’s not slices of his brain. It’s a word: Gedankenexperiment – that’s German for “thought experiment”.

Today, thought experiments are common in theoretical physics. We use them to examine the consequences of a theory beyond what is measureable with existing technology, but still measureable in principle. Thought experiments are useful to push a theory to its limits, and doing so can reveal inconsistencies in the theory or new effects. There are only two rules for thought experiments: (A) relevant is only what is measureable and (B) do not fool yourself. This is not as easy as it sounds.

The maybe first thought experiment came from James Maxwell and is known today as Maxwell’s demon. Maxwell used his thought experiment to find out whether one can beat the second law of thermodynamics and build a perpetual motion machine, from which an infinite amount of energy could be extracted.

Yes, we know that this is not possible, but Maxwell said, suppose you have two boxes of gas, one of high temperature and one of low temperature. If you bring them into contact with each other, the temperatures will reach equilibrium at a common temperature somewhere in the middle. In that process of reaching the equilibrium temperature, the system becomes more mixed up and entropy increases. And while that happens – while the gas mixes up – you can extract energy from the system. It “does work” as physicists say. But once the temperatures have equalized and are the same throughout the gas, you can no longer extract energy from the system. Entropy has become maximal and that’s the end of the story.

Maxwell’s demon now is a little omniscient being that sits at the connection between the two boxes where there is a little door. Each time a fast atom comes from the left, the demon lets it through. But if there’s a fast atom coming from the right, the demon closes the door. This way the number of fast atoms on the one side will increase, which means that the temperature on that side goes up again and the entropy of the whole system goes down.

It seems like thermodynamics is broken, because we all know that entropy cannot decrease, right? So what gives? Well, the demon needs to have information about the motion of the atoms, otherwise it does not know when to open the door. This means, essentially, the demon is itself a reservoir of low entropy. If you combine demon and gas the second law holds and all is well. The interesting thing about Maxwell’s demon is that it tells us entropy is somehow the opposite of information, you can use information to decrease entropy. Indeed, a miniature version of Maxwell’s demon has meanwhile been experimentally realized.

But let us come back to Einstein. Einstein’s best known thought experiment is that he imagined what would happen in an elevator that’s being pulled up. Einstein argued that there is no measurement that you can do inside the elevator to find out whether the elevator is in rest in a gravitational field or is being pulled up with constant acceleration. This became Einstein’s “equivalence principle”, according to which the effects of gravitation in a small region of space-time are the same as the effects of acceleration in the absence of gravity. If you converted this principle into mathematical equations, it becomes the basis of General Relativity.

There is more at the link.