11.5 No Intrinsic Cosmological Axis
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Three directions on the sky must be distinguished. The kinematic dipole n̂_{kin}, near Galactic (l,
b) ≈ (264°, 48°), records the motion of the Solar System relative to the CMB rest frame at about 370
km s⁻¹. The axis n̂_{mod} of the observed large-angle hemispherical power modulation, with amplitude
A ≈ 0.07, lies near (l, b) ≈ (220°, −20°) (Hoftuft et al. 2009; Planck Collaboration 2020), roughly
70–80° from n̂_{kin}. A third direction, n̂_σ, would be the spatial projection of ∇_μσ on the
present hypersurface, if such a projection existed.
On a homogeneous background it does not: ∇_μσ̄ = (σ̄̇, 0, 0, 0), so the spatial projection vanishes
and n̂_σ is undefined. An intrinsic axis would require a long-wavelength gradient mode of σ, which
by Proposition 11.2 is a tilt of the generation foliation relative to matter. For admissible
generation laws such a tilt decays as 1/a, leaving no intrinsic axis at late times; for density-
weighted laws it grows by a factor of order 10²⁶ and is either fine-tuned or runaway. Superhorizon
modes invoked to generate hemispherical asymmetry are further constrained by the low multipoles they
induce through the Grishchuk–Zel’dovich effect (Erickcek, Carroll, and Kamionkowski 2008).
CTGP therefore predicts no intrinsic cosmological axis and offers no explanation of the observed
large-angle anomalies, which remain questions for standard cosmology. This is a consequence of the
framework rather than an omission: the generative present is a geometric structure, and geometry
alone does not single out a spatial direction in a homogeneous, isotropic universe.
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12. Empirical Standing of the Ontology
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This section states precisely what observation can and cannot establish about CTGP’s ontology. The
results are general: they apply to any presentist reading of physics, not only to CTGP.
12.1 Observational Equivalence
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Proposition 12.1 (Observational equivalence of presentist and eternalist readings). Let P
(presentist) and E (eternalist) be two ontological readings of the same physical content 𝒦 = (M,
g_{μν}, matter fields, dynamical laws, probability measure μ over admissible histories). Call a
quantity *observable* if it is a function of the physical records present to an observer at the
stage where the observation occurs — for the presentist, the records on the present surface Σ_σ.
Then every observable has the same probability distribution under P and under E, and no experiment
can discriminate between them.
Proof. An observation is a physical process, and its outcome is a function of the records present at
the stage where it occurs. Both readings assign the same admissible histories and the same measure
μ, and hence the same distribution of present records at every stage, so each observable has the
same distribution — the pushforward of μ — under both. □
Remark (what is observed). Every observation available to an observer is an observation of present
records. A fossil, a memory, a photograph, a detector event, or a photon arriving from SN1987A
carries information about an earlier state, but information about another time is not the existence
of that time: under CTGP the earlier state has ceased to exist, and a present observer cannot
observe it as a presently existing state — not as a limitation of instruments but because, under
CTGP, a presently existing past state is not there to be observed; the notion of observing one is
incoherent within the ontology. The same holds for the future, which a present observer can predict
or represent but cannot observe, because it has not been generated. This does not break the
equivalence; it is the reason the equivalence holds. Eternalism does not permit observation of
another time either: its earlier events exist, but not at the observer’s location, and an observer
interacts only with the records present there. Neither ontology allows an observer to observe
another time as present. They differ only over whether the unobserved earlier events exist, and
present records — the same under both — cannot decide that. A theory that did allow observation of
another time as present would be different physics, with different records, and would fall under
§§12.2–12.3 rather than under this proposition.
Remark (indeterminism). The result does not depend on determinism. For stochastic laws, E represents
the realized history as one member of the ensemble, weighted by μ; P represents it as generated
stage by stage with the same transition probabilities. The observable statistics coincide.
Remark (scope). The proposition assumes that every observation, including an observer’s reports
about experience, is a physical record. First-person temporal phenomenology is not observable in
this sense; it enters CTGP as an explanatory datum through the Phenomenological Completeness
Principle (§4.5), not as experimental evidence.
Corollary. With the physics held fixed, the ontology cannot be verified by measurement. Empirical
bearing on it must come either from constraints the ontology places on which physics is possible
(§12.2) or from physical content added to 𝒦, which bears directly on that content and only
indirectly on the ontology.
12.2 The Generability Constraint
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Observational equivalence holds for fixed physical content. The two ontologies do not, however, make
the same demands on what that content can be. If only the present exists, each new state must be
producible from the current one alone: the fundamental dynamics must admit a generative initial-
value formulation relative to the existing present, with no dependence on future boundary data and
no global consistency conditions that require the whole history at once. Eternalism carries no such
requirement. A block universe can contain initial-value laws, but it can equally contain laws with
future boundary conditions, final-state constraints, or self-consistency conditions on closed causal
loops.
Let G denote the proposition that the fundamental laws are generable in this sense. Because
generability is part of what CTGP means by presentism, a confirmed failure of G would directly
contradict the ontology, whereas eternalism merely permits generable laws. Finding that our best
theories admit generative initial-value formulations is therefore evidence the ontology could have
failed and did not.
The criterion stated precisely. Generability requires a state S_σ on each level set and a law fixing
the transition probabilities P(S_{σ′} | S_σ) for σ′ > σ — a point mass in the deterministic case —
without reference to data on later level sets. Future dependence counts against generability only if
no empirically equivalent formulation of this kind exists. Enlarging the state space is legitimate
only if the added variables are physically instantiated on Σ_σ and have dynamics of their own, not
if they are defined by reference to later data; without that restriction, any history could be made
generable by encoding its future in the present state. Global formulations do not count against
generability when they are equivalent to a well-posed initial-value problem: general relativity can
be derived from an action over spacetime, but its classical content is captured by the Cauchy
problem of §7.
No particular probability is assigned here to generable laws on the eternalist view; the point is
only that presentism is exposed to this evidence where eternalism is not.
This does not conflict with Proposition 12.1: the discrimination occurs across candidate physical
theories, not within a fixed one.
The evidence. The successful physical theories considered here admit well-posed initial-value
formulations: general relativity on globally hyperbolic spacetimes and relativistic field theories
with hyperbolic equations of motion. No confirmed fundamental dynamics has required future-dependent
input, and physics has survived increasingly stringent tests without it. The accurate summary is
that the empirical physics examined so far has not revealed a confirmed violation of the
generability requirement.
The limits of the evidence. Three qualifications apply. First, the support is shared: the growing
block entails generability as well, so the evidence favors dynamic ontologies as a class over
eternalism, not CTGP over the growing block. Second, an eternalist may regard generable, locally
predictive dynamics as independently natural for reasons unrelated to temporal ontology — one
example is the argument that observers can arise only where the field equations are hyperbolic and
the world is predictable (Tegmark 1997). To the extent that such reasons hold, the evidence has
correspondingly little force. Third, the evidence is theory-relative: it bears on which laws nature
has, and so on the ontology only through the constraint the ontology imposes on laws. The evidence
is therefore consistent with the requirement, but its evidential force is limited: current physics
does not establish generability.
Future tests. The constraint is exposed to physics still to come. A fundamental final-state
condition in quantum gravity, such as the black-hole final-state proposal (Horowitz and Maldacena
2004; for its difficulties, see Gottesman and Preskill 2004), would be incompatible with CTGP’s
generability requirement and would therefore provide strong evidence against its presentist
ontology; resolution of black-hole evaporation through ordinary initial-value dynamics would be a
further survived risk. A unique final state that simply results from deterministic evolution does
not count; only a final condition that must be imposed as an independent input to fix earlier
evolution would. A requirement that quantum gravity involve indefinite causal order at the level of
spacetime itself would similarly bear on CTGP’s definite primitive ordering (§6.4).