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Suppose that one could "flip" a coin, and that it settled onto a platform. For simplicity, let the coin processed with the nonzero angular momentum on $y$ axis only. To further simplify the question, suppose that the platform was in vacuum, and the "falling" of the coin onto the platform was created by some "fictional force", that act with a potential of $1/r$.

It's obvious that the process were all unitary (reversible) since it's "classical". However, once the coin settled onto the platform with the dissipation of the (kinetic) energy, it's evidential that one could not determine the states for which it came from.

Thus, one had a "measurement" for which the entire process was unitary. This seemed to be some what counter intuitive to the usual non relativistic quantum mechanics, as a measurement was somewhat "magical". How was a "measurement" being "unitary"? How could one ever settle with a coin flip?

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    $\begingroup$ How come dissipation of energy results in unitary evolution? $\endgroup$
    – Ruslan
    Jul 1 '20 at 4:38
  • $\begingroup$ @Ruslan I meant kinetic energy, one could assume the coin and the platform was in thermal isolation so that the total energy $E_{sub}$ in each of the sub system was both conserved. (edited) $\endgroup$ Jul 1 '20 at 5:00
  • $\begingroup$ @Ruslan - That comment makes a good answer. $\endgroup$ Jul 1 '20 at 8:50
  • $\begingroup$ @AndersSandberg well, I wasn't sure that's what this question was about, so was expecting some requests for clarification. But OK, let's see how it's taken if posted as an answer. $\endgroup$
    – Ruslan
    Jul 1 '20 at 9:44
  • $\begingroup$ @Ruslan (I just realized that the thermal conversion was not allowed... so suppose that the system had no temperature increase.) This seemed to be reduced into a schrodinger's cat question, where the measurement did not happen at the point of contact or with the interaction of the platform, rather when a measurement was seen. But at the same time, if a person looked at the coin when its in the "air", a measurement was made, it's "classical" result was thus determined. So it's unitary, but the result was already measured, or not settled until seen. (at least from copenhagen convention) $\endgroup$ Jul 2 '20 at 4:12
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If the energy (and all associated momenta, phases of vibrations) remains in the system, then simple reversal of time will bring back all the vibrations induced by the landing so that they will at some point concentrate in one punch to make the coin jump back. These vibrations all contain the information about the flip. In other words, what you are proposing doesn't have "true" dissipation of energy (all that could be called that is exactly accounted for by the model).

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