Dear Yutaka,
First, my apologies for being so slow in following up on reading your essay. I've been away from FQXi entirely for about the last week, actually.
I quite like both of your essays, as well as your interesting questions about black hole information loss at my essay thread.
Your 2013 essay 2013 essay on an "operational" derivation of physical laws strikes me as very compatible with multiple essays this year, including Flavio Del Santo's excellent essay on quantum-induced temporal uncertainty. Your description of "operational" as formalizing into information theory struck me as compatible in particular with the theme that what is in play in classical physics is really far more of an information game than is generally recognized.
In a sense, in my essay this year I just take that kind of thinking to its logical extreme: Classical physics is the physics of information, an unending game of bits making real what had previously only been quantum and ahistorical. In some ways, unfortunately I think, the focus in the last couple of decades on quantum bits, on undecided bits, has obscured the incredible power of real bits to lock down the fabric of reality. Even mass in this perspective boils down to a broken pair of quantities, locked by historical state data from recombining. Without the intransigence of classical bits, even a quantity as fundamental as mass-energy itself would have no enduring existence. Having two time vectors -- having a dual pair of universes hurtling away from each other -- provides that first huge it-from-bit event of making the existence of mass-energy, biased from the start towards matter rather than antimatter (that's the other universe), into the fundamental paradox of every pair that comes after it in our universe.
Your current essay on quantum random number generation was impressive to me because I think in that idea you exactly nailed what I would call a perfect bit creation: An exact, one-bit capture of our universe discarding half (!) of all possible future events, even if the bit created is for now merely local and seems no great deal. And your random-number quantum computer idea perfectly matches the physical detection model for an electron passing through two slits: If balanced (and if losses are factored out), then the electron will be detected going thought one or the other slit exactly half the time, with each such decision adding one more bit, one more historical path, to our classical universe.
Incidentally, I cannot help but notice that your one-bit quantum random number generator also fits nicely with the title of my own poor essay: You are achieving indeterminacy based on the absolutism of the underlying pair cancellation constraints. In a dark-function model of quantum mechanics -- I guess I should say "my" dark-function model? I know of no refs -- the superb irony is that quantum uncertainty is actually just a particularly massive and universe-spanning (via entanglement) version of a pseudo number generator, one that derives new bit results based on conservation rules applied simultaneously to a near-infinity of shattered entanglements with the other already-existing bits, the fabric, of the classical universe.
But because the bits that define the classical universe are always both finite in number and entangled in unbelievably complex ways with the thermal matter of the universe, that same nominally "pseudo" random process can also become indefinitely "picky" about how to preserve, say, a spin here and another spin there. That is the uncertainty your are invoking in your one-bit quantum random number generator: A large but finite number of bits, used to generate the next new bit in some new observed event. However, at the same this bit generation process will depend on massively parallel applications of quantum-level absolute conservation rules that are so strict that a bit on the other side of the universe can strongly affect an outcome here, in a fashion that appears analog-smooth rather than digital-precise.
Anyone looking at such a bit generation process from the viewpoint of classical physics will, pretty much by definition, never have sufficient bit resources, even in the entire classical universe, to calculate what the quantum-conservation outcome will be. We cannot see the creation of bits precisely because we are the bits, pieces of a finite-granularity universe that literally lacks enough data to resolve its own classical details. Yet that same "finite granularity" is both variable and multi-scale bits, enabling the simulation of infinite smoothness whenever anyone "looks" for such smoothness, e.g. HAWC Consortium gammas that recently soundly disproved string theory. This is in sharp contrast to some naive and energetically infinitely-costly fixed-size cell structure of space, which would break everything.
So again: Out of the resolute, absolute determination of the underlying broken virtual pair quantum word to resolve, eventually, back to true null, the much cruder layer of historical bits slathered on top of it, what we call the classical universe, can never achieve anything more than results that are forever beyond our ability even to see, let alone to calculate: the perfect random number generator, even if ironically it uses the universe itself as its starting seed.
I should also note however that this does not mean that the classical roots of quantum uncertainty in the dark-function interpretation are completely invisible. Quite the contrary: The dark function interpretation of quantum mechanics, which relies on the Humpty-Dumpty theory of observers (hdtoo, or just hd2), should make possible controlled local quantum experiments in which the quantum collapse is not totally random. So dark functions and hd2 observers are more than just another non-testable quantum interpretation: If dark functions and hd2 are real, they predict that there should exist experiments that disprove absolute quantum randomness, if the set up is done right.)
Finally, regarding black holes: Dark functions don't allow singularities anymore than they allow many-worlds... not to mention that point about dark functions also unraveling some of the key assumptions of top-end quantum computing. So a black hole would simply become a special type of information geometry.
From reading 't Hooft's papers in recent years, I am pretty convinced that he knows blinkin' well that he has undercut the entire concept of an interior in a black hole with them, and thus has implicitly force the whole (hole?) black hole concept back its earlier days of the frozen horizon where nothing penetrates because classical time stops. (Hint: But not dark-mirror time! Momentum space has its own version of change, one that scrambles ours badly.) But 't Hooft is above all a polite man, and I think that he is (appropriately if you ask me) trying to be respectful of all of the amazing analytical and mathematical work so many folks have done before.
My only poor addition there, other than to complain a bit that you have to be careful about assuming the existence of antipodes in 2D spaces (waves work differently in even and odd spaces), is simply to point out that what 't Hooft came up with -- momentum waves across the surface of the impenetrable black hole -- sounds an awful lot like momentum space as seen in mirrors. So if infalling black hole particles become "mostly" 2D momentum waves, it just starts getting difficult not to call the result a giant ball of 2D momentum space. All the information stays right there at the impenetrable top, just in scrambled "dark mirror" form.
("Impenetrable surface" for a black hole?!? Sure. Hey, how else could the silly things evaporate? I mean, seriously... is the event horizon supposed to drop a fishing line down to the singularity and ask it pretty-please to return the mass-energy it stole? And again, 't Hooft in his analysis of SK coordinates in his new model actually does address the issue of whether the matter ever really reaches the singularity, but again rather quietly and politely.)
So basically, I think 't Hooft has already rewritten the black hole classics. He just hasn't received enough attention for it yet. You know how it is: It's so tough these days for these newbies with only one Nobel Prize to get folks attention for their ideas... :)
