@Steve Agnew: "physical reality is made up of changes in matter action"
So, just to be clear, this notion of the "matter action universe" is your own personal metaphysics of science? While I have no time to delve into it please feel free to correct any of my probable misconceptions regarding the basic physics and mathematical formalism of my own proposed model. I am not a physicist, I am merely an itinerant philosopher.
SA: "The universe is a wavefunction, but is all that we can know about."
I thought that, strictly speaking, our actual observable universe is all that we can know as we are its observers. The wave function of the universe on the other hand, at least in the Everettian sense, is precisely what we can't know as we're already entangled in/as one of its relative state vectors--Wigner's friend has no possible perspective external to their relative entanglement in Ψ(U).
SA: "We cannot know about the multiverse..."
Not directly in a many worlds / relative state sense, where our actual observable universe is simply our experience of one branch of a constantly branching many worlds multiverse.
But what about inflationary bubble universes? They're just an extension of our own observable universe but accelerating away from our accelerating horizon--at least as far as I understand inflation. Tegmark makes an argument that the observed finetuning in our universe is evidence for that kind of what he calls Level I multiverse.
Then there's his Level IV multiverse that I read as the superposition of all possible universes, its wave function would describe the mathematical regularity of any and all states. One cross-section of this wave function would be our universe, another might describe a universe that evolves negative entropy over a reversed Planck second before annihilating itself. Obviously ours is easier to be alive in, observe, and know about, so we can't know/observe the whole multiverse in that sense.
However, this notion of a Level IV multiverse does change how we might think about and conceive of our observable universe as a subsystem of its wave function. I think its truth or falsity as a multiverse theory will probably rest on how effective it might be as a fundamental concept for any future metaphysics that actually succeeds in making some sense of a quantum mechanical worldview.
SA: "2. The matter action universe is discrete and not a continuum."
I was just referring to the way the Schrodinger equation is a continuous differential equation so wave functions evolve as continuums, mathematically at least, or as I might say their evolving potential is a continuum. Our actual, observable ('matter action' or otherwise) universe does appear to be fundamentally discrete though. Which is to say our observations of physical phenomena are discrete. Schrodinger himself was rather erudite on this apparently fundamental relation between the mathematical continuum and the discreteness of atomism / quanta.
MR: "3. The observable universe is to be modeled as a single 'world particle' in flux which is the instantaneous product of the intersection of the four fundamental force vectors."
SA: "The universe is made up of a finite number of particles."
Yes, or empirically observable physical stuff as I like to say. The 'world particle' would be the unitary flux of forces that at any moment in the evolution of the wave function of our universe gives rise to our fundamentally discrete observational experiences. Observations in this sense are higher order phenomena emergent on that Planck magnitude flux. So you can experience your observable universe of discrete particles where that discreteness emerges from the continuum of Ψ(U) of which the observer is a subsystem.
The 'world particle' is thus a model of our observable universe with an observer as its entangled centre.
SA: "4. It is not possible to measure anything outside of the universe."
Yes, more or less by definition if you mean trying to measure something not in our observable universe and thus by definition non-observable. The 'world particle' isn't something we might observe though as in this model it simply is the observable universe described as a unitary observational flux. I'm looking for a possible collaborator who might be able to mathematically model that flux of forces as an evolving set of entanglements.
SA: "5. Physics uses dimensions to fill in the blanks."
Hilbert Space is a multidimensional mathematical tool and as far as I know exceptionally useful for quantum calculation. As I understand it, Ψ(U) evolves in Hilbert Space following the Schrodinger equation. But here the 'world particles' dimensionality describes the total possible entanglements that might constitute it at any moment, and presumably by definition those entanglements would be defined by the wave function of its observable universe.
SA: "7. Entropy is a classical notion that helps physics cover up for what it does not yet know."
Yes, it's a measure of 'uncertainty' which as I understand it can also be used as a measure of randomness / regularity in data sets according to Shannon's notion; or as a measure of the overall energy density of a physical system, which also means its dis-orderliness according to the Boltzmann notion; whereas Von Neumann's entanglement entropy is a measure of the degree of entanglement in a system. And thus entropy in general can also be thought of as a measure of the complexity of any set, structure, or system ... more or less.
So then, I understand the 'world particles' degrees of freedom in Hilbert space as a function of its complexity in terms of its entanglement entropy. That entanglement would also define the scale of its observable universe: Would its holographic entanglement entropy define the boundary limit of that universe as a function of the surface area large enough to encompass it? This would be a spatial volume derived from HEE rather than from an external classical spacetime.
These are just some of the metaphysical 'picture' concepts I'm playing with based on a rather specific philosophical concept of the observer / observable universe. Please feel free to correct my language in your own terms!