Information domains

Schrödinger's cat redux

Consider a variation of the famous thought experiment. A device is constructed consisting of a random event generator, and an indicator. When the generator produces an event the indicator changes state and latches the event. This device is placed in a container which can be sealed. As in the original we have an observer (A) who is unable to observe what is happening inside the container.

Graphing the state of the indicator from observer A's point of view we have: This is identical to the original experiment. Note that we are assuming the indicator has been triggered at some point. The boundary cases in which the indicator is triggered instantaneously and never are left as an exercise for the reader.

Now let us add a second observer (B) who is able to observe what is happening inside the container. Let both observers (A & B) observe simultaneously. However, no communication is allowed between A & B. Graphing the indicator state for this situation we have:

From this we can note that while the state remains indeterminate to A there is in fact no time at which it is undefined inside the container, i.e. from the cat's point of view.

Now let us rerun the experiment. In this run however we will periodically allow B to communicate the state of the indicator to A. Thus we have:

Here there are two facts of note. First is that as we increase the frequency and/or duration of the communication between A & B the state graph for A  becomes closer and closer to that of B. Second is that once the indicator has been triggered, and this fact has been communicated to A, the two state graphs are identical, even though A still cannot observe the interior of the container. This is a result of knowledge A possesses about the functioning of the mechanism. Namely that the indicator is of a latching type. If we remove this information from A the graph becomes symmetrical about the transition.

The above makes clear that the problem of indeterminacy is the result of A lacking information, not  an inherent condition of the system. In effect what has been done is to isolate the information domain of A from that of the container (and B). Put another way we can say that information occupies domains, and that if the connection between domains is limited or broken then the state of one domain becomes indeterminate from the other.


The origin of the idea.

I did not in fact arrive at the idea of information domains from the above described route.

Sometime ago I had a part time job doing IT for a machine shop. When a machine shop gets a job they are provided with a drawing of the parts to be made. This drawing is used to write a script for the CNC machine tools to run which produces the part. Typically the process will involve multiple scripts running on one or more machine tools. As part of my job I was tasked with developing a system to store these scripts for future retrieval.

It occurred to me that the drawings, the collection of scripts, and the physical finished part were all representations of the same information, just in different domains, the paper domain, the digital domain, and the physical domain. While each representation provided some information the others did not, e.g. the scripts listed the cutting tools used, there was a core set of information which was transferred from domain to domain. First by the programmer who wrote the scripts, and then by the machine tools which removed material from a blank to reveal the finished part. From this point of view the programmer and the machine tools served as translators between information domains, converting the core set of information from it's representation in one domain to a different yet equivalent representation in another. It was not the information which changed, just it's encoding.