Outline of Relation of Quantum Mechanics and Information Theory

[From a outline in an October, 2004 email to one of the members of the Ultranet@topica.com email list. Connections to the ideas and terminology of Christopher Langan's "Cognitive-Theoretic Model of the Universe (CTMU) have been edited out for clarity, as have some mathematical speculations.]

1. Quantum Mechanics requires information theory
   
   1. Theories, measurements are just information
      1. Distinguishable states must differ by >=1 bit
         1. No outside agency besides the 2 minimally differing states can do the distinguishing between themselves.
            1. Otherwise the theory would have to explain how the 3rd thing distinguishes not only the 2 original entities from each other but also how it distinguishes itself from the other two as well.
            2. This requisite ability to distinguish is logically part of every distinguishable entity.
            3. This logical nature, this ability to distinguish information, is not just the basis for consciousness but a basic form of consciousness itself.
         2. Every system starts with a pattern reducible to some number of bits and must in any frame of reference be seen through interaction to have the same or greater number of bits as time goes on. (Thermodynamics.)
      2. The distinguishing of one thing from another creates another entity in the relation between them which is a new embedded subspace within the two which in turn will self-embed itself.
      3. The increasing dimensions of the binary information vectors' phase space are expanding into an implicit unfilled possibility space which is dynamically infinite in extent.
         1. The informational expansion into the larger possibility space may show why branches are more frequent than rejoins at the quantum level and thus why time seems to run from a big bang through increasingly entropic (information-containing or perceiving) developments.