9.4.2 Why There Is Always a Present
Stated without formalism, CTGP’s core claim is one that ordinary experience already assumes: there
is a way things currently are. Not a privileged coordinate system, not a universal clock reading,
not a synchronization procedure — simply that reality has a current state, which is succeeded by
another. On this framework that assumption is correct and is what Σ_σ formalizes. It is worth noting
which side of this dispute is the revisionary one. The block universe does not merely add a claim to
ordinary understanding; it denies one, holding that “the way things currently are” picks out nothing
ontologically distinguished. CTGP’s burden is to show that the formalism can carry the ordinary
assumption, not to motivate the assumption itself.
The present also need not be postulated as an additional structure laid over spacetime. On this
framework it is constituted. At any generative stage, every physical state in the universe is
undergoing the transition from what it is to what it becomes next. This is CTGP’s ontological
premise and is not established by general relativity, which describes evolution without asserting
that later states are brought into existence; what follows here is what that premise yields, not a
derivation of it. Take the totality of those transitions — one per state, across the whole universe
— and that totality is the cosmic present. Σ_σ is not a surface selected from among many and then
declared privileged; it is the collection of everything currently being generated. Once the
generative ontology is adopted, the universe-wide present is therefore not an additional structure
appended to the physical dynamics; it is constituted by the totality of physically ongoing state
transitions. The posit is the generative ontology itself, not a privileged surface added on top of
it. A system undergoing no change is included on the same terms, its transition being to the same
state (§9.4.1).
Two things must be kept apart here, because the constitutive account establishes less than it may
appear to. It establishes that there is a present: the totality of transitions is well defined
whether or not any observer selects a slicing. It does not by itself establish either that those
transitions glue into a single spacelike hypersurface or that the resulting slicing is unique. The
first is secured elsewhere in the formalism. The Hamiltonian and momentum constraints are precisely
the conditions under which a local generative step is consistent with the steps taken in
neighbouring regions, so the transitions cohere into a surface rather than fragmenting into
unrelated local advances (§6.7; Appendix A.1). The second is not secured by the transitions at all.
ADM evolution admits many-fingered time: different choices of lapse and shift foliate the same
spacetime differently while describing identical physics. What selects one foliation among these is
cosmological time (§6.1), the maximal proper time elapsed since the initial singularity. The
constitutive argument therefore answers why there is a cosmic present; cosmological time answers
which one it is. Presenting either as discharging both burdens would overstate the case.
The scope of the claim should nevertheless be stated precisely, because it is easy to overstate.
CTGP does not hold that every mathematical solution of the Einstein field equations possesses a
unique globally privileged present. That would be false: Gödel’s rotating dust solution, Taub-NUT,
and the region of the Kerr interior beyond the Cauchy horizon admit no global Cauchy foliation, and
no time function of the required kind exists on them. The solution space of GR is a space of
mathematical objects, most of which are not realized. What CTGP holds is that physically realized
spacetime — the actual history that is generated — possesses such a present, and that the solutions
lacking one are for that reason not candidate histories.
The direction of the argument matters. Under the Causal Reconstruction Principle (§10.3), causal
ordering is primitive and metric geometry is reconstructed from it; generation is therefore prior to
spacetime structure rather than a feature added to a spacetime already given. A solution with closed
timelike curves is not a generated history whose foliation happens to fail. It is a geometry that no
sequence of generative stages could produce, since producing it would require an event to be among
the conditions of its own production. The restriction to globally hyperbolic spacetimes is thus not
a boundary drawn around the theory to protect it; it is what the theory says about which geometries
can be real. A confirmed observation of closed timelike curves, or of any phenomenon requiring a
Cauchy-horizon-crossing region to be physically realized, would falsify the framework (§13).
This also disposes of a question sometimes raised as though it bore on the matter: whether current
physics exhibits any non-abstract existence that is absolutely unchanged from one instant to the
next, and whether such absolute stasis has been shown impossible. Neither has been established, and
neither needs to be. An absence of known examples together with an absence of a proof of
impossibility is evidentially neutral and supports nothing. Under CTGP the question does not arise
in the first place, for the reason given in §9.4.1: persisting is being generated. An unchanging
configuration is one in which successive stages produce the same state, not one standing outside the
succession. Absolute stasis is not a rival to the generative present; it is not a describable
condition within it.
9.5 Foliation in Strong-Curvature Regimes
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The FLRW foliation is well-defined in the cosmologically relevant regime of large-scale homogeneity
and isotropy. However, a global Cauchy foliation is not guaranteed in all spacetimes. Pathological
topologies, strong anisotropy, closed timelike curves (CTCs), and black hole interiors may each
undermine the existence of a smooth global foliation. CTGP addresses these cases via a three-option
framework:
Option (1): Restrict CTGP's domain of application to cosmological-scale regions where the FLRW
approximation holds and a global Cauchy foliation exists. This is the conservative stance and is the
primary intended domain of the framework. On cosmological scales, this restriction is well-motivated
by the empirical fact of CMB isotropy.
Option (2): Use local foliation patches with gluing rules. In regions where the global foliation
breaks down, define Σ_σ patchwise over overlapping open sets, with consistency conditions on patch
boundaries. This extends CTGP's applicability at the cost of introducing gluing ambiguities that
must be handled by additional physical data (e.g., the stress-energy distribution at the boundary).
Option (3): Treat black hole interiors and CTC-permitting solutions as requiring separate analysis
or as lying outside CTGP's intended domain. The interior of a black hole beyond the Cauchy horizon
may be physically inaccessible and dynamically isolated from the exterior universe; CTGP's
generative structure applies to the exterior region, and the interior is flagged as a domain
requiring separate treatment in any future extension.
CTC-permitting solutions are handled under Option (1) by restricting to globally hyperbolic sectors:
CTGP treats CTC-permitting solutions as physical idealizations absent from our universe's actual
global structure.
Each option can be substantiated by existing results in GR. For Option (1), the empirical and
theoretical case is strong: global hyperbolicity is a standard causal assumption of relativistic
cosmology (Hawking and Ellis 1973); strong cosmic censorship, the still-unproven conjecture that
generic physically reasonable spacetimes admit no extension beyond their maximal globally hyperbolic
development, would make it a consequence of the dynamics rather than an assumption; and nothing in
the observed large-scale structure of our universe indicates its failure; CMB isotropy to one part
in 10^5 confirms the FLRW approximation at cosmological scales to high precision. CTGP’s restriction
to this domain is therefore a principled constraint, not a limitation, in the same sense that
thermodynamics restricts its domain to systems with well-defined state variables. For Option (2),
dual foliation methods developed in mathematical GR suggest that overlapping foliation patches can
be glued consistently wherever the constraint data on the overlaps can be reconciled; patch
inconsistencies are therefore diagnosable and resolvable by standard constraint-solving methods
(Theorem 17.15). For Option (3), the relevant physical fact is that the spacetimes known to require
it — Kerr interiors, Taub-NUT, and Gödel universes — are not consistent with our observed
cosmological boundary conditions. Kerr interiors are idealized; real astrophysical black holes
formed by collapse develop apparent horizons whose exterior evolution remains well-posed and
globally hyperbolic. CTGP’s generative structure continues without interruption in the exterior. The
instability of the Cauchy horizon to perturbations (mass inflation) further suggests that the Kerr
interior beyond the inner horizon is physically unrealized. These three anchors ground the three-
option framework in established GR results.
9.6 Emergent but Law-Selecting Structures
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
CTGP belongs to a broader class of physical frameworks in which large-scale emergent structures
activate effective physical constraints. This framing positions CTGP within emergent-law physics
rather than metaphysics.
The key idea is that certain large-scale physical structures — while not themselves fundamental —
nonetheless select which effective laws govern the system. Consider the following canonical
examples:
Emergent structure | Effective law selected
---------------------------------+-------------------------------
Fluid phase | Navier–Stokes equations
Superconductivity (Cooper pairs) | London equations
Cosmic fluid (FLRW) | FLRW foliation and cosmic time
In each case, a lower-level theory (classical mechanics, quantum electrodynamics, general
relativity) is formally foliation-neutral or medium-neutral. But the actual physical configuration —
the fluid phase, the superconducting condensate, the cosmic matter distribution — selects an
effective structure that constrains physical law at the relevant scale.
CTGP applies the same logic to the cosmological foliation. The matter distribution of the universe
may produce, through its large-scale dynamics:
• the CMB rest frame as the dynamically selected preferred frame;
• the σ ordering as the physically realized temporal ordering;
• the cosmological time slicing as the constraint-preserving foliation for the initial-value
problem.
These structures are emergent in the technical sense: they are not present in the Einstein equations
as written, but they arise from the physical solution. Once emerged, however, they are law-
selecting: they determine which temporal framework is operative and which temporal ordering is
physically operative.
This framing recasts the central CTGP claim from a metaphysical thesis about the nature of time into
a physical thesis about how the universe's matter content generates its own temporal structure.
Physicists who would be skeptical of the former are often already committed to the latter in other
contexts. CTGP asks only for consistency: if emergent structures can select effective dynamics in
fluids, superconductors, and condensed matter systems, then the cosmological matter distribution can
select an effective temporal structure for the universe as a whole.
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10. Quantum Compatibility and Pre-Geometric Ontology
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CTGP is compatible with multiple quantum interpretations so long as they preserve (i) relativistic
causal structure and (ii) the open-future ontology at the global level. The layered structure of
causality that makes this possible is stated in the Layered Causality Principle (§10.4).