Harwit's argument against yet undiscovered "radically new" phenomena
I am guessing you know the textbook by Martin Harwit,
Astrophysical Concepts, 4th edition, Springer, 2006, but have you read his book
Cosmic Discovery: The Search, Scope, And Heritage Of Astronomy? One of the interesting "information theoretic" arguments he gave applies a statistical analysis which had previously been applied to guess the remaining oil reserves from the changing rate of discovery of new oil fields to conclude that the number of completely unexpected phenomena such as quasars is in fact finite and has, Harwit asserted, probably been exhausted, a prediction which has been borne out in the quarter century since the book was published. (I forget whether he took gravitational radiation into account, but this would only postpone the inevitable, according to this line of argument.) This claim set off a firestorm of invective from fellow astronomers, curiously unaccompanied by mathematical argument
If we dare, perhaps in another thread we can revisit the issue of whether or not it is reasonable to expect further "heroic ages" in
any currently known field of science. The argument is rather general, a bit like counting spheres packed into a keyspace, and it would be interesting to try to abstract away the elements of quantum theory, if possible.