10.1 Interpretive Routes
~~~~~~~~~~~~~~~~~~~~~~~~
(Q1) Decoherence-based readings: Macroscopic definiteness is approached without introducing an
observer-dependent ontology; CTGP interprets the realized quasiclassical history as the generated
one. Decoherence provides an account of why interference between macroscopically distinct states
becomes negligible due to entanglement with environmental degrees of freedom. Decoherence alone does
not select an outcome, however, so this route inherits the measurement problem rather than solving
it, and it secures CTGP’s unique factual past only by assumption. CTGP treats the realized
quasiclassical trajectory as generated stage by stage along n^μ.
(Q2) Objective collapse models (e.g., CSL): Collapse provides a physically real stochastic
actualization mechanism aligned with CTGP's ontological edge. σ can be treated as indexing collapse-
updated hypersurfaces. This route has the virtue of providing an explicit physical mechanism for
'selection' at each generation step.
dρ/dt = −(i/ħ)[H, ρ] − (λ_{CSL}/2) ∫ d³x [A(x), [A(x), ρ]]
Here A(x) is a smeared mass-density operator and λ_{CSL} sets the collapse strength; on this route,
collapse events realize the transition Σ_σ → Σ_{σ+Δσ}, making the stochastic dynamics coextensive
with the growth of M(σ).
(Q3) Epistemic readings: CTGP treats the wavefunction as informational while spacetime generation is
ontologically basic; local predictions remain unchanged. On this route, the quantum state encodes
epistemic facts about the actual generated structure, not additional ontological elements. Like
decoherence-based readings, this route does not itself select an outcome, so it secures CTGP’s
unique factual past only by assumption; collapse models and foliation-dependent hidden-variable
theories supply that uniqueness through their dynamics. Relational interpretations, which make facts
relative to observers, conflict with a unique factual past and are not among CTGP’s available
routes.
CTGP does not require a specific quantum interpretation, but it is most naturally aligned with
approaches that provide definite macroscopic outcomes at the present edge — collapse models and
foliation-dependent hidden-variable theories, such as relativistic Bohmian mechanics with a
covariantly fixed foliation, being the primary candidates. CTGP thus requires single-outcome
realism: at each stage, each measurement has exactly one realized macroscopic outcome. The standard
Everettian ontology, on which all branches are physically real, conflicts with this requirement,
although not with the cosmological foliation itself: an Everettian could accept the foliation and a
unique universal state on each level set while denying that each stage has a unique macroscopic
outcome. The claim is specific to CTGP; it is not the claim that no-collapse quantum theories are
incompatible with presentism in general.
Scope of quantum-compatibility claims. CTGP’s quantum-compatibility claims are conditional rather
than unconditional. Relativistic hypersurface-path independence is asserted only for admissible
local update generators whose spacelike-separated densities commute on a common invariant domain and
satisfy standard energy-bound and closability conditions (formalized in Proposition 17.16).
Likewise, continuum completely positive dynamics are claimed only as limits of UV-regularized local
semigroups under trace-norm convergence assumptions (Theorem 17.17). On the classical side, any
CTGP-induced correction terms are required to be perturbatively small relative to the
Einstein–matter principal part, so that ADM constraint violation remains O(ε) in Sobolev norm on
local existence intervals (Theorem 17.14). In strong-curvature regimes, CTGP treats smooth σ as an
emergent continuum representative of a more primitive causal growth ordering rather than as a
globally valid classical scalar (Proposition 17.18).
Corollary: CTGP entails a unique factual past. M(σ) contains exactly one realized causal history.
Any quantum interpretation incompatible with this consequence — including any that treats past
branches as ontologically real — falls outside CTGP’s scope regardless of its empirical status.
10.2 Pre-Classical Regime and Emergent Effective Laws
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
CTGP does not posit an absence of law at any stage of cosmic history, including the Planck epoch.
The earliest regime of the universe is governed by the minimal generative structure described in
Postulate 5: the σ-field constraint and its associated causal ordering. Classical spacetime — as a
smooth Lorentzian manifold — may not yet exist during this epoch. Light cones and metric structure
may be only approximate or emergent quantities, becoming valid only after sufficient decoherence and
coarse-graining. GR is therefore best interpreted as the low-energy effective limit of CTGP’s deeper
generative structure, not as a law that held unmodified from the initial singularity. This alignment
places CTGP within the broader class of quantum-gravity programs that treat classical spacetime as
emergent — including causal set theory, loop quantum gravity, and emergent spacetime approaches —
without committing CTGP to any one of them.
The following table formalizes the domain of validity for each ontological level and its associated
formal machinery within CTGP. The column “Formal Domain” specifies where each description applies;
the column “Status” specifies the ontological category per Postulate 5.
Level | Description | Status (per | Formal domain
| | Postulate 5) |
-----------------+--------------------------+-------------------+---------------------------------
σ-generation law | Primitive generative | Fundamental | All regimes (pre-geometric and
| ordering parameter | | emergent)
Causal ordering | Partial order on | Fundamental- | All regimes; light-cone
| generative stages | emergent hybrid | representation valid only post-
| | | emergence
General | Effective classical | Effective (α(ρ) → | Emergent geometric regime only
Relativity (GR) | spacetime dynamics | 1) | (ρ ≪ ρ_P)
QFT | Relativistic quantum | Effective | Emergent geometric regime only
| field dynamics | |
Thermodynamics | Statistical regularities | Emergent | After sufficient decoherence and
| from coarse-graining | | coarse-graining
The asymmetry in the “Formal Domain” column is the central structural claim of §10.2: σ-ordering is
present and active at all stages, while every other level of law acquires its formal machinery only
after the conditions for that level have been realized. GR is therefore never retroactively applied
to the pre-geometric regime, and the σ-constraint is never suspended in the emergent regime. This
table instantiates Postulate 5 mathematically: σ is the only structure whose domain of validity is
unrestricted.
10.3 Pre-Geometric Ontology
~~~~~~~~~~~~~~~~~~~~~~~~~~~
CTGP posits that the deepest layer of reality consists not of spacetime geometry but of lawful
generative ordering, of which classical spacetime geometry is an effective continuum approximation.
The principles that govern this relationship are stated below and in §10.4.
Emergent Metric Principle: The Lorentzian metric g_{μν} is not fundamental but emerges as an
effective low-energy description of underlying generative and causal relations. Diffeomorphism
invariance is correspondingly an emergent symmetry of the continuum limit rather than a primitive
feature of pre-geometric reality. The continuum action of CTGP (§9.1), which contains √(−g) d⁴x,
should therefore be interpreted as an effective low-energy action valid after the emergence of
classical geometry, not as a fundamental statement about pre-geometric structure.
Causal Reconstruction Principle: Effective spacetime geometry is reconstructed from underlying
causal relations and generative ordering. This principle connects naturally to the
Hawking–King–McCarthy and Malament reconstruction results already cited in §6.2, which establish
that causal ordering determines conformal metric structure. CTGP’s pre-geometric ontology
strengthens these results from a mathematical convenience into an ontological commitment: geometry
is not prior to causality but is derived from it. The generative ordering therefore takes
ontological precedence: generative ordering → causal structure → emergent metric, not the reverse.
Fundamental Ontological Hierarchy: The following chain specifies the direction of ontological
priority in CTGP. Each arrow denotes “grounds” or “gives rise to”, never the reverse:
σ (primitive generative ordering) → causal partial order → conformal geometry → full Lorentzian metric → GR dynamics (effective) → QFT (effective) → thermodynamic regularities (emergent)
Each step in this chain has associated formal conditions for when the transition becomes valid. The
step from causal partial order to conformal geometry corresponds to the large-N limit of causal-set
theory. The step from conformal geometry to full metric requires specifying a volume element (in
causal-set theory, this is supplied by the counting measure). The step from full metric to GR
dynamics requires the α(ρ) suppression factor of §9.2 to reach the value α → 1, which occurs as
ρ/ρ_P → 0. No step in this chain runs in the reverse direction within CTGP; the hierarchy is
strictly one-directional. This provides the formal grounding for the claim that GR cannot be
“applied at the Planck epoch”: GR appears only at the end of the chain, where all prior steps have
been completed.
Effective Law Emergence Principle: Stable regularities emerge when the generated present acquires
sufficient physical structure to support reproducible signal propagation and dynamical constraints.
This links directly to the signal-based epistemological dimension of CTGP: the observability of
physical laws is itself signal-dependent. Effective laws become epistemically accessible only when
the universe supports the propagation and persistence of the signals required to reveal those
regularities. Physical structure and epistemic accessibility therefore co-emerge at the same
threshold.