Dear Karen
Apologies in advance for the enormity of my reply.
It is fabulous to receive feedback from a person with strong cross-disciplinary experience. I would like to take up a couple of your comments to provide greater clarity relating to the basis of my arguments.
First and foremost, I did not choose the Planck time because of empirical measurements or existing theory. Rather, I aligned the Planck time to that which arises naturally from the primitive universal model developed in my previous essay, 'How to build a universe from Wheeler's immaterial source, in nine pages or less,' at https://fqxi.org/community/forum/topic/1904 . That there is a minimum increment and that it is necessarily constant follows from the action of the necessary principle that builds the Harmony Set, which I claim is a proper model of the actual universe. That our measurements happen to align to the Harmony Set should be expected because the argument that develops the model can only be the case, speaking as an endpoint sceptic (see essay), thereby forced to accept endpoint rationalism. That is, the heuristic arguments to which you refer are, strictly speaking, irrelevant to my argument. Moreover, the nature of the Harmony Set implies directly that the foundational structure of what we interpret as space and time is in a sense quantised.
I think it is worth noting that the method has produced an ontically causal model of the universe, where present theories are only nominally causal. This hasn't been done by anyone anywhere before. Also this is a background independent theory, which is what everyone is looking for, as I recall.
Hence, a minimum time, which I propose aligns to the Planck time follows necessarily from the action of the General Principle of Equivalence. My model is developed from an endpoint sceptic and endpoint rationalist stance, which is explained (perhaps overly concisely) in that essay. The endpoint sceptic turns his or her back on the world of empiricism for a time. From that stance, I built a model. You will be well aware that this is not supposed to be possible, based on the arguments of Hume and Kant in particular, but their arguments are incomplete and my development punches Quine on the nose as well (never did like Quine).
The following is in no way meant to be a negative criticism of your comments. I include it only to respond to the issues put by you, which are good and valid aspects to raise. That said, this may seem a little hard...
I am well aware of our current best theories. You refer to them as 'established' and well-confirmed (Popper would say, 'not yet falsified' and several centuries of revisionist physics supports that). Lee Smolin would look askance at this ('The Trouble with Physics' is a long and somewhat rambling, but perspicacious read). As for 'established', having a good correlation between the universe today that describes around 4% of what there is, is hardly well-confirmed. Empiricists are so revisionist. String theory? Really? I know you aren't defending string theory, surely - it seems to encompass 10^500 possible theories at least. That's around 10^388 theories per bit in the universe, if the Bekenstein Hawking calculations are anything like correct, which my model corrects by the way, and without any tweaking or jiggery pokery - why might that be? Unlike our best current theories that flap around the edges of proposals that might perhaps tentatively maybe explain the nature of dark energy, my work implies directly the source of evolution of space, and questions the existence of dark energy. I say this knowing that there are many areas for further investigation, especially relating to topologies that produce a 3-space. But empirical physics has had hundreds of years to develop, and my model seems to explain several previously intractable problems of physics. Stephen Hawking want's to know what breathes fire into the equations we have. I am answering that from the ground up. It would be nice if someone might draw some of this to his attention. Oh, what he might do with my piffling efforts.
The aim of my work is fundamentally different from other works, such as the papers you mention (I have followed Huggett's work since around 2001 and used it in a thesis). Other works seek to pick a proper description of the universe. My work aims to EXPLAIN why there is something rather than nothing (done that - first essay) and why it comes to be as it is (first steps - second essay - seems to explain why the universe went bang). Not too shabby I hope.
Lastly (phew), you and many others are unconvinced of the physicality and fundamentality of information. Again, the nature of the physical and of information is not derived from an empiricist perspective. It comes from an endpoint rationalist approach. It is the responsibility of the investigator to see how the physical aligns to the informational structures of the Harmony Set, not the other way around, because endpoint rationalism, if carried out rigorously (see my first essay for how this is approached) is epistemologically superior to that of empiricism.
Again, as with my derivation based on information, the information is just that which differentiates one thing from another - my first essay. Then my whole plan comes into focus as being the expression of the General Principle of Equivalence. The foundation of human understanding is an innate idea of equivalence and difference (see my essay for rigour). The principle of equivalence is just this idea expressed in words. The problem of bundling is just the dichotomy that seems to be the case if the principle is true, but this leads to a unique origin and minimal simple (explaining why there can never be just nothing, there was always something). The General Principle of Equivalence, being both global and necessary, is then necessarily a model of an actual condition of the world. As such, we have spanned the epistemological to ontological divide (PhD please) and coincidentally defeated Kant (didn't like his negative attitude anyway) and identified Hume's ask for a law or whatever that could in some way guarantee uniformity of outcomes (I forget his exact words).
How can a thoroughgoing philosopher takes sides between the physical and the mental? How can one take the empirical to be in some way more trustworthy than the rational? Are not Descartes's arguments about dreams and evil genius's correct? They absolutely are. Should we not set aside the negative empiricist and when the rational conflicts with the empirical, rather, be thinking (as with the problem of bundling - Hume, Armstrong, Lewis) 'these seeming inconsistencies cannot be truly inconsistent (for example Zeno's arrow paradox, Parmenides' denial of change) rather they must be trying to tell us our analysis is incomplete.' My work (first essay) shows how the universe holds together (PhD please) and how change occurs (PhD please) and why time has a positive arrow independent of entropy (another one please) and why there should be quantisation (one more please).
My work may seem Spartan, but, while physics has had hundreds of years of development, the endpoint rationalist, me, has had but a few years. It would be nice if more people of your capacity would help with the mathematics. For example, what does it mean that the rate of rise of the central peak of the Harmony Set converges on ln2? It might have converged on any number, yet it comes out to be ln2? That's odd isn't it, given it was developed without any reference to known values. Actually the set is pervade with no end of seeming coincidences. So much more to do.
