Dear Marc,
Thank you for your wonderfully written note! Glad to meet you.
In regards to the identification of the (primal) arrow of time with 1st person experienced randomness, you may want to read the post I just wrote in reply to Jim Hoover, just immediately above, as it goes a bit more into this concept.
Essentially, on the scale of the very simple (which is also usually at the very microscopic limit of a domain), the notion of 'perceived randomness' is an inherently asymmetric relation between two otherwise symmetrically modeled 'possible world tracks' through some sort of phase-space described by that model. Symmetric models (mathematics in total) does not admit of the 'information generative' aspect of asymmetry -- that must come from 'outside' the model, and is effectively the very essence of what distinguishes the model from the real. If you think about it, you will see that it cannot be otherwise.
Therefore, the specificity of the randomness, _relative_ to an observer, is the asymmetry outside of the model that binds the notion of "here and now", in a specific possible universe -- and that is the basis for the being of locality _for_ that observer. It is in this way that the possible becomes the actual, in an 'oriented' way (asymmetric) -- ie, distinguishing 1st person (known) from 3rd person (unknown) by the introduction of "that which is unknowable". Ie, that the known, unknown, and unknowable, are ultimately distinct, inseparable, and non-interchangeable.
Not sure if that explanation (along with my above notes to Jim) helps make this clearer (let me know if not).
In regards to your question, I was initially meaning 'what must be true (equations) which would apply to any world'. However, the notion of 'universe' is generally given as a totalizing function (all that exists) and therefore, if that construct is to be believed as applicable/useful, then it may also be the case that the specific gauge constants for 'this' physical universe 'should also' be somehow derivable.
Personally, I think that this is a red-herring. Conceptually speaking, the use of totalizing functions is fraught with peril. Among physicists, I have not yet seen that implemented in a way I could consider proper, and as a result, I suspect that many of the big questions being asked are therefore misleading in the extreme. As such, I have taken it as my research question to determine what could be validly constructed without the use of totalizing operators of any sort, and have thus far, not found it to be a limit at all. It is surprising what can be done with the much simpler ingredients of just the immanent modality.
However, returning to the question at hand, I would regard that the primary metric basis would be a specification of the limits of maximum bandwidth between objective and subjective. In other words, it is to ask: what is the maximum of information flow associated with the "here and now", as classically defined? To some extent, this can only be computed on a volumetric basis, in a relation to surface area.
If we look 'from the inside out', my work with the Axioms, modalities, etc, does no have near enough information specifying complexity to provide the direct definition of the bit values associated with established physical constants. In that sense, my theories are far too simple.
Yet if we look 'from the outside in', assuming a universe with an absolute, a-priori defined structure of platonic lawfulness, then in that assumption itself, the constants basically become 'baked in'. Even under the most conservative methods of estimation, finding the gauge constants can hardly be helped.
For example, we can consider that the extreme bandwidth limit is set by the total differential scale delta between the domain limits, from smallest and the largest, and compute that as the 1st worst case metric product limit. The Planck length is 1.6 x 10^-35 m (microscopic limit) and the speed of light accessible universe history is on the order of 3 x 10^8 m/s by 14.5 Giga-years, giving an absolute max universal data flow constant of somewhere considerably south of approximately 10^60 bits per second.
We can refine the finite bandwidth max access control limit further (much lower) by establishing a relation between information and energy, and therefore of the degree of 'distortion' in the field of relation of available signaling access between the subjective and objective. If the information density is too high, its energy understood as mass causes it to form a black hole, thus disappearing it from being 'actually accessible'.
However, the "actual" bandwidth limits associated with the "here and now" is very probably a *lot* lower still, for any 'reasonable' meaning of the terms -- ie, something mesoscopic that we can actually relate to in terms of meters and seconds. For example, for a typical human nervous system, it is approximately 10^18, when integrating over all available sensory modalities, before any reprocessing.
Yet, when we look at the very best of what is available in terms of the level of relational specification from the totality of current physics, Standard Model, etc, we get a max of 10^12 under ideal conditions. 10^8 is far more typical. As such, there is a *lot* of room for free particularization -- at least 6 orders of magnitude in complexity.
As such, I do not think that it is actually "reasonable" -- ie a demonstration of something important -- to get the physics constants from a 3rd person 'universe assumption' (because it must assume what it is attempting to prove), or from a purely 1st person perspective (insofar as pure idealism can assume/define anything under the strong anthropomorphic argument). Something else is needed.
The constants of physics are an aspect expression of the total model complexity, and that is in itself but a small fraction of the total coherency of the immanent transfer bandwidth. My speculation is that the 'coherency fraction' is exactly half of the available, and that therefore, we still have something like one order of complexity remaining to develop in our theories of physics before hitting hard limits of the observable.
Forrest
