I have figured out that:

  1. When photons leak out from a container, the entropy of the photon collection increases, because each photon has a different escape time.
  2. Photons that have leaked out from a container can be collected into a container of the same size, if that container is in a gravity well deep enough.
  3. When photons fall some distance in a gravity field, each photon's energy becomes multiplied by some factor, which does not change the entropy.
  4. After aforementioned container has been winched up from the gravity well, the entropy of the photons inside must be increased compared to the entropy of the photons inside the first leaky container.

So I suspect that lifting some radiation increases its entropy. Am I on a right track here?


I have a suggestion how the entropy increases when a cube-shaped mirror walled container of radiation is lifted: A photon moving into just right direction does not touch the floor or the ceiling of the container during the lifting process. The lifting agent does not do any work on that photon. Work done on a photon ranges from zero to X joules, which increases entropy. When gravity does work on photons, every photon's energy increases by K percents, which does not increase entropy.

Clarification to point 2: Observer in the gravity well sees the radiation to leak out rapidly. The short time implies small entropy increase. Observer outside the gravity well sees that radiation slows down when the radiation enters the gravity well. The line of photons contracts when photons at the front are slowing down.

Oh yes, optically dense material has the same effect as gravity well. And also if a photon catcher device moves rapidly towards the photons, then photons go in rapidly and come out slowly, which allows an arbitrarily large photon gas cloud to be caught into a small volume container, in this process temperature of radiation increases without entropy of radiation increasing.

  • $\begingroup$ But wouldn't the temperature of the photon gas increase as it falls in the gravity field, thus increasing the entropy during step 3? $\endgroup$ – Mark Beadles Jan 13 '12 at 13:19
  • $\begingroup$ Also see this related question on gravity vs entropy and this thought experiment on John Baez' site. In particular, wouldnt' some of the photons escape the gravitational well in 2? $\endgroup$ – Mark Beadles Jan 13 '12 at 13:28
  • $\begingroup$ No photons escape, because they are caught in a box, the box has a open door, that is closed at the right moment. I got the idea from this: physics.stackexchange.com/questions/15251/… $\endgroup$ – kartsa Jan 13 '12 at 19:07
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    $\begingroup$ first the law of increasing entropy holds for closed systems. A box manipulated up and down is not a closed system. secondly have a look at the statistical mechanics definition of entropy en.wikipedia.org/wiki/Entropy to see that entropy is proportional to the logarithm of the number of microstates and increases in closed systems. This should show you that all the up down manipulations you introduce in your thought experiment increase the entropy of you and box and earth, which is the closed system. $\endgroup$ – anna v Jan 14 '12 at 5:54
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    $\begingroup$ @MarkBeadles: I see, if the radiation containers were anything but the perfect mirrors using kind, then we could say that radiation gravitationally collapses into a container. Well the containers are mirror lined containers. That's an important fact, I forgot to say. $\endgroup$ – kartsa Jan 14 '12 at 23:55

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