Hi John -- Thanks for posting this... though I'm not sure there's really anything new here with respect to quantum theory.
But I want to take issue with this definition of information in terms of copying, specifically in connection with quantum physics.
This definition makes sense with respect to one class of information systems, where the meaning of the information is specified outside the system. The article gives the example of information in a timetable:
The “meaning” of a timetable consists primarily in the fact that, having it, we can catch a train... Of course, we must understand the symbolism contained in the timetable. We need to translate the numbers and letters included in it into the appropriate moment and place of departure. This is an important issue, but as a matter of fact, purely technical in nature.
Likewise when we’re dealing with computer technology, the meaning of all the symbols at each level of the programing language and the meaning of the data stream are predefined outside the system itself. In that case we can set aside the need to interpret the data as a “purely technical” issue irrelevant to information theory.
For many purposes in physics we can adopt this kind of approach. Apart from quantum theory, we can treat information about physical systems as a matter of given fact, because we assume there’s always a wider physical context in which that information is observable.
But when it comes to the physical universe itself, we’re clearly dealing with another class of information system, where there is
no “outside” system where information can be defined.
All information in this system must in fact be defined and “interpreted” by this system itself, in terms of other information available within the same system. That is, the mass of a particle only has meaning because of the way the particle moves, and its stat of motion only has meaning because of the way it affects some other physical system, etc. etc.
This is a very strong constraint. In this kind of “self-defining” system, it doesn’t make sense to treat information as inherently determinate – i.e. as given data that can just be copied without regard to its “meaning”. In this case there exists information about a system only to the extent it makes a specific difference to information in some other system, that makes a specific difference to some other system.
It’s worth noting that in nature, data is almost never merely copied from one system to another – as we copy information between computers. Every physical interaction involves a conversion (“interpretation”) of information from one kind of information context to a different kind – as when the energy of a photon is absorbed by an electron jumping to a higher energy-level within an atom. So copying per se is not a fundamental information-process in nature. It only applies in situations where we can take the observable “meaning” of the information for granted.