It seems to me that both the “Twin Earth” experiment and the question of “which physical process can be legitimately interpreted as a computational process” can be easily solved if you view them as questions of degree rather than binary:
1) Having an identical twin on another Earth is the same as being uncertain about where you are. If I am uncertain whether water is H2O or XYZ, then my idea of “water” refers to a probabilistic mixture of H2O and XYZ.
2) The degree to which a physical process represents a computational process depends on the simplicity of the program that prints out the latter given the former.
It seems to me that both the “Twin Earth” experiment and the question of “which physical process can be legitimately interpreted as a computational process” can be easily solved if you view them as questions of degree rather than binary:
1) Having an identical twin on another Earth is the same as being uncertain about where you are. If I am uncertain whether water is H2O or XYZ, then my idea of “water” refers to a probabilistic mixture of H2O and XYZ.
2) The degree to which a physical process represents a computational process depends on the simplicity of the program that prints out the latter given the former.