Is Entropic Disorder Due to an Observer's Information Scheme or a State Property?

Entropy is often said to be linked to “disorder”, i.e. higher entropy means more disorder. We try to investigate what disorder means. We consider a simple example of 26 encyclopedia books and argue that order is linked to an observer’s information scheme or map and is not an intrinsic state of the system. In other words, it is relative to the observer’s information in this particular example. We further consider the information required for a map or information scheme as data not necessarily linked to entropy which requires probabilities in Shannon’s picture (and also Boltzmann’s). For example, an ordering of the books may represent disorder and entropy to a person with one information map or scheme, but complete order to another observer with a different map or information scheme. In one case, there are probabilities and entropy and in the other case, no probabilities and zero entropy.

    We also consider the case of photons passing through a two-slit apparatus. If one does not follow each photon in time, or is interested in the relative numbers of photons at different screen positions, then there is entropy. If one only measures that N photons hit the screen, regardless of where and when, then there is no probability and entropy.. If one has a set of N photons sent in one at a time, these are correlated (described by one information scheme or map which states that all photons have p momentum pointing in the y direction). After scattering, the information scheme or map for identical photons is different, (it is based on the interference pattern), but this simply means that one changes maps or information schemes. There is no probability unless one can resolve time such that one tries to predict what each photon does or deals with relative numbers of photons at different screen positions. Thus, entropy seems to be linked with resolution in a measurement.