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Let's say we have a perfectly flat cylinder. It stands on a perfectly flat table. We make it spin for one minute on the table with no more pressure than the weight of the cylinder itself. We can agree that the spot where the cylinder sits (with some extra area) will have its temperature rise compared to the rest of the table. Now we remove all the equipment from the room and let someone enters it with all the tools he can dream of.

Is it possible for that individual to know the rotation (clockwise or anti-clockwise)?

  1. If yes, how? (we can hypothesize tools that don't exist yet)
  2. If no, isn't it an example of information loss (comparable to a evaporating black hole from Hawkins radiation)

It's seems to me that it wouldn't be possible to determine the direction of rotation. For example, if instead of a rotation we did a translation from right to left on a path compared to a left to right one, we could see a temperature gradient from either side of the path, showing the direction taken. But in the context of a rotating cylinder, I don't see any kind of difference except maybe from the cinetic moment (sorry I'm speak french a little lost in english), where the clockwise rotation whould probably induce more heat compare to an anti-clockwise rotation. But without that knowledge, we probably would only be able to say "a clockwise rotation of a $x + \epsilon$ grams" versus "a anti-clockwise rotation of $x - \epsilon$ grams".

Another example completely different is the AND gate in logical circuitry. I only can be sure of the value of its input in the situation where the AND gate return 1, but having a 0 in a 2 inputs AND gate gives me 3 possibility. Maybe there is a difference between information loss and reversability?

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  • $\begingroup$ there is actually some information hidden in the "inherent state", because all we can ever observe is a random single outcome based on the absolute value of a projection from this "inherent state". By clever manipulation, we might be able to coax this hidden state information out into an observable that tells us something. How much of the history is actually stored is beyond me. $\endgroup$
    – James
    Commented Dec 5, 2022 at 5:38
  • $\begingroup$ there is a spooky description too by Plato: "Plato describes a group of people who have lived chained to the wall of a cave all their lives, facing a blank wall. The people watch shadows projected on the wall from objects passing in front of a fire behind them and give names to these shadows. The shadows are the prisoners' reality, but are not accurate representations of the real world. The shadows represent the fragment of reality that we can normally perceive through our senses, while the objects under the sun represent the true forms of objects that we can only perceive through reason." $\endgroup$
    – James
    Commented Dec 5, 2022 at 5:51
  • $\begingroup$ It depends - on the material, time, temperature, etc. There is a rather well-known experiment on mixing and unmixing the chocolate mousse, but I could google up only this (not very clear): physics.bgu.ac.il/EVENTS/FETE_2017/OlegK.pdf (from page 5 on) $\endgroup$
    – Roger V.
    Commented Dec 5, 2022 at 14:55

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In principle, though obviously not in practice, I could measure the position and velocity of every air molecule in the room. Then I could calculate their trajectories back in time and I would find there was a rotational motion corresponding to the air displaced by the rotating object. Then I would know the direction of rotation.

You could say "make the room a vacuum", and then I'd have to measure the vibrational motions of all the atoms in table and track them backwards. You could say "make the table frictionless" and then I'd have to analyse whatever mechanism you used to make the cylinder rotate.

The point is that in classical mechanics the information is still there and in principle it could be used to reconstruct the motion of the cylinder.

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