The black hole information paradox presents us with the problem question "What is information in terms of physical theory?" Very similar problems arose prior to Einstein's statement of the equivalence of mass and energy in different forms. I have yet to do any significant research concerning the alternate theories presented prior to the consideration and acceptance of Relativity Theory, and yet I can't help but think that very similar difficulties arose with the consideration of these alternate theories, in that one would presume that they must have been inelegant by comparison.
Similarly, the idea that matter, energy, and information are all three equivalent would seem dificult to accept, but provides a very elegant solution to a number of problems, not the least of which is the black hole information paradox.
The Unitarity of Mass, Energy, and Information
For a black hole:
- Infalling Mass/Energy/Information is converted into the mass, charge and spin of the singularity, averaging the mass, charge, and spin of each unique particle infalling, which would seem to result in a loss of unique information without any further consideration of quantum states and temporal symmetries. This alone allows for the possibility of matter/information/energy equivalence.
- The energy of space/time is converted into the mass/energy of one half of a virtual particle pair, each such particle having a (random?) mass, charge, and spin. While no single particle's m/c/s is absolutely determined by the m/c/s of the singularity, the sum of all such particles is likely to be equivalent to the m/c/s of the singularity. Is the necessary information thus conserved, or do we need again to rely on the equivalence of M/E/I ?
- Infalling anti-matter reduces the mass of the singularity, increasing its temperature, and therefore increasing the rate of particle conversion in the form of Hawking radiation. This allows for black holes in the early Universe to have a decisive influence on the balance of matter and anti-matter, a question which still remains unresolved as well.
- The Conservation of Mass/Energy becomes the Conservation of Mass/Energy/Information.
- Gravity can be seen in part as a loss of the energy of space-time, shortening particle lifetime. (Resolved under current theory, or again unresolved? Can shorter particle lifetimes be interpreted as an increase in information density?)
- In a normal star, stellar fusion results in a loss of mass/energy and more complex elements, leaving us facing an increase in both complexity (information) and entropy. (The energy leaving a star may be extropic for us, but is entropic for the star.)
- Just as heat is a form of entropy, perhaps we should see complexity as a form of information. If so, any element more complex than Hydrogen must be seen as being more dense in information.