Hi Jonathan,
You say, "I've seen quite a few attempts to explain the direction of time, where the given cause turns out to be a process, needing another flow of time underneath it. I don't know about your idea that the direction of time arises from the self-interaction of the gravitational field"
I just posted a variant of the following on Phil Gibbs page:
At one point Phil suggests that "quantization as a sum over histories is more fundamental than particles or field or even time and space." What is history without time or path without space? He then asks if there is a fundamental law which is not derived from anything deeper? Well, if we assume that a law governs something, there must exist at least one thing. Since I cannot conceive of this one (and only) thing being a particle, I assume it's a field, or at least a continuum. Phil then says that such law must be as it is because it could not be any other way, and asks "Why would those answers be incomprehensible to us?"
Conscious experience is our contact with the universe; Phil says "information is everywhere" crossing the universe. I prefer "energy is everywhere" crossing the universe. When energy triggers a change in structure (absorb the photon, switch a logic gate, ...) the structure is 'in'-formed and becomes a record (~bits of information). It has no meaning absent a codebook or context: "one if by land, two if by sea." Thus it's hard for me to find meaning in the statement: "the information in a wave function is conserved." Most wave functions describe situations in which energy is conserved, so in that sense "information" might be conserved. He notes we're dealing with idealizations. If information implies energy and change of structure, where is the energy of the wavefunction and what does it change? Phil notes that such "informative" 'records' are more real than the 'past'; "Our reality is what we experience."
Phil then sets up the problem, noting that recursion can take us places independent of the starting point:
"... we must define this recursion... in algebraic terms and see how the physics of space, time, and particles can emerge..."
He notes this iteration will be algebraic without a Lagrangian, and conjectures that the holographic principle may argue for 'complete symmetry'. I believe one can formulate the holographic principle in terms of energy, with no mention of information. Would this imply such symmetry?
Phil suggests a "free algebra" generated from a vector space V and says that "if it requires information to specify how it works then a theory can't be fundamental"; concluding by expecting to find symmetry in a pre-geometric meta-law that transcends space-time, taking a purely algebraic form, beyond which point it will be emergent.
Jonathan, based on Phil's formulation of the problem, I suggest how this might work?
I don't believe a 'lattice' can satisfy his requirements for 'fundamentalness', so I assume a continuum, f. "Pre-geometric" must mean there is only one such, else we would have two different things and can subtract f1 from f2 and begin geometric correlations between continuums (kind of like Einstein's inertial reference frames). So if there is only one continuum, f, it can only interact with itself, as there is nothing else to interact with! This provides a basic principle for the pre-geometric, primordial law, based on algebra only:
The Principle of Self-interaction is that any operator O acting on the continuum f must be equivalent to the continuum f acting on itself, represented as
Of = ff.
This iteration is fundamental, not derived from anything deeper, and is infinitely recursive. One can solve this for characteristic features of the continuum, and the operator spectrum might determine the feature spectrum. Let one operator be the essential derivative d/dq and the second operator be the generalized derivative 'Del' = d/dp. [it's hard to find symbols that don't bring something to mind, so I've already biased you.]
As it turns out we have two unique solutions corresponding to these two operators. For O = d/dq we find that f = 1/(-q) solves the algebraic equation, Of = ff, and for O = d/dp we find that f = 1/p solves Of = ff. We assume geometric algebra (Clifford/Hestenes) is our context. Therefore we need only interpret q and p. These may of course be anything we can get away with that agrees with our experience, but I believe the most fundamental (or at least the most useful) fundamental interpretation's are q = time t and p = spatial vector r.
Jonathan, please note that there is only one solution to the self-interaction equation of the form 1/t, and that is 1/(-t). That is, if t is time, then only one 'direction' of time solves the self-interaction equation!
Thus our Self-interaction Principle leads to a unidirectional time and a general 3D space. One feature of the continuum is the frequency f ~ 1/t and another feature is a 1/r spatial dependence, with appropriate gradient, ~1/r.r . All of this is easy to prove (except the identification of q with time and p with space) once one adds a 'connector' c ~ r/t then ccf is an acceleration and f is a frequency. The dimensions thus associated with f and f are those of the gravito-magnetic field: G ~ cc/r, C ~ -1/t --- acceleration and frequency. When one brings rotation into the picture the self-interaction equation generates a quantum solution, and the minus sign associated with the frequency yields a fundamental left-handedness such as that characterizing neutrinos and amino acids.
The equations that govern these fields are in my essay's equation (1). A result of iteration is figure on page 12. Of course there's much more of interest than will fit into a comment. For example, the Self-interaction Principle leads to Newton's law, Einstein's equations, and the Klein-Gordon equation, for starters, when augmented by E = mcc. I do believe "we arrive at a final level where everything is possible and the whole theory is described with zero information."
My very best regards,
Edwin Eugene Klingman