3.4 Alignment of Phenomenological and Physical Arrows
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
CTGP offers a single ontological account of three phenomena that are typically treated as
independent explananda: experiential temporal flow, the thermodynamic arrow of time, and the
directional structure of causal propagation. In standard physics, these are often traced to separate
origins — subjective flow to neuroscience or philosophy of mind, thermodynamic asymmetry to low-
entropy initial conditions, and causal directionality to the light-cone structure of relativity.
CTGP provides a single underlying account: all three arise from the continuously advancing
generative flow represented by M(σ), whose present boundary Σ_σ advances in one direction only along
the generation flow vector n^μ.
The following arrows all point in the same direction within CTGP, and their alignment is not
coincidental. The causal and memory-formation arrows point in the direction of generation by
construction; the thermodynamic and cosmological-expansion arrows are related to that direction but
not reduced to it, since each also depends on contingent features of our universe’s initial
conditions and matter content. The thermodynamic arrow — the increase of entropy from past to future
— runs in the direction in which stages are generated, since each new hypersurface is generated from
its predecessor and never the reverse. Generation supplies the orientation, not the gradient: as in
standard cosmology, the increase itself requires a low-entropy initial condition, which CTGP must
assume exactly as eternalism does. What the generative flow contributes is that this increase cannot
run counter to the direction in which stages are produced. The causal arrow — the asymmetry between
cause and effect, between light-cone past and future — is the direction of generation itself; where
an action formulation is used, it is represented formally by restricting the action’s domain to
M(σ), which excludes ungenerated future regions. The cosmological expansion arrow — the directional
growth of the universe under FLRW dynamics — provides the physical substrate for σ itself, whose
gradient, in FLRW, aligns with the matter-frame congruence. And the memory formation arrow — the
capacity of present systems to inherit and encode physical consequences of past events but not
future ones, some of which remain sufficiently organized to function as recoverable records — is
explained by the persistence of causal continuity within M(σ): information generated by earlier
states propagates forward through physical structure, while future hypersurfaces do not yet exist to
leave consequences in the present.
This alignment strengthens the overall explanatory power argument for CTGP. On CTGP’s assessment,
the block interpretation explains these arrows through distinct structures — a low-entropy boundary
condition, Lorentzian causal structure, and the architecture of cognition — rather than through a
single ontological mechanism by which their convergence would follow. CTGP traces their convergence
to a single underlying source: the one-directional succession of generated stages, ordered by
cosmological time and formally represented by M(σ). An ontology that provides an account of several
arrows of time through a single generative structure has, on this assessment, greater explanatory
economy than one that accounts for them separately; whether unification of this kind is an
explanatory virtue is part of the philosophical dispute. The economy at issue is explanatory
unification: one ontological mechanism underwriting arrows that otherwise require separate
explanations. It is not overall ontological parsimony. CTGP’s account of past truth carries its own
cost in primitive past-tensed properties (§5.2.1), and the two must be weighed against each other
rather than counted on the same side.
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4. Comparison with Block Universe and Growing-Block Models
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4.1 The Block Universe Position
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The block universe (eternalism) holds that the complete four-dimensional Lorentzian manifold is the
fundamental ontological structure. Every event — every point (x, t) in spacetime — is equally real,
regardless of whether it is in the past, present, or future relative to any observer. The GR field
equations and the associated mathematical formalism are naturally read on this view as describing an
already-complete structure, not generating one. The block universe has significant virtues: it is
mathematically parsimonious, it accommodates the relativity of simultaneity without requiring a
preferred foliation, and it avoids questions about the mechanism of temporal 'passage.'
Terminological note: CTGP is classed throughout as generative presentism rather than as a growing
block. It shares the growing block's commitment to directed generation but not its ontology —
earlier stages are represented within the formal history M(σ) as completed causal structure while
possessing no ontological existence, and this is a difference in what exists, not in what is drawn.
[FIGURE: Figure 1]
Figure 1. Ontological structure of the block universe (eternalism) and of CTGP (generative
presentism). In the block universe all slices exist equally and “now” is an indexical with no
special ontological status. In CTGP the double line marks the active present edge Σ_σ; single
lines mark earlier stages, which belong to the formal history M(σ) but no longer exist; the future
is ungenerated. The two readings agree on every observation (§12.1); they differ in what exists,
and presentism additionally requires the laws of nature to be generable from the present (§12.2).
4.2 The Livestream vs. Recording Distinction
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
CTGP's central claim against the block universe is best expressed through the recording-versus-
livestream distinction. A finished recording (DVD, film) encodes a complete temporal sequence; the
sequence is revealed as playback proceeds, but every frame is already determined before playback
begins. The block universe is structurally analogous: all events are determined; their 'unfolding'
for any observer is merely representational. A live production, by contrast, is actually being
created as it proceeds; the next scene is not pre-existing but is genuinely generated by the
performers, crew, and circumstances at the moment of production. CTGP claims the universe is more
like a live production than a finished recording.
This is not merely a metaphor. The formal claim is that the GR initial-value structure, read
generatively, produces Σ_{σ+Δσ} from Σ_σ by lawful dynamics without consulting any pre-existing
future state. The 'next slice' is not selected from an already-complete manifold but is genuinely
produced. CTGP's M(σ) formalism makes this precise: the domain formally represents the generated
history leading to the present state, not a restriction over a pre-existing complete block.
4.3 What CTGP Inherits from Growing-Block Models, and Where It Departs
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Ellis and Rothman (2010)'s 'crystallizing block universe' provides the closest prior art. They argue
that spacetime crystallizes from an uncertain quantum future into a determinate past, using quantum
indeterminacy as the mechanism for genuine becoming. CTGP shares with growing-block theories a
commitment to objective temporal becoming but differs in several respects. First, CTGP does not
require quantum indeterminacy as the engine of becoming; the generation parameter σ is defined by
cosmological time, a classical geometric invariant, and is compatible with multiple quantum
interpretations. Second, CTGP provides an explicit formal treatment of σ-reparameterization of ADM
evolution, which grounds the growth parameter in the variational structure of the Einstein–matter
system without requiring quantum indeterminacy as the mechanism of generation, while remaining
compatible with objective-collapse, consistent-histories, and epistemic interpretations alike.
The moving spotlight view occupies a different position: the present moves through a complete four-
dimensional manifold. Skow (Skow 2015) argues that it is the strongest rival to the block universe,
although he ultimately defends the block. CTGP rejects the moving spotlight framing because it
presupposes the block and adds a moving 'now' to it — a double ontology that CTGP finds unmotivated.
CTGP's ontological economy is greater: there is no pre-existing block; there is only the continually
generated present state together with its inherited causal structure, formally represented by M(σ).
4.4 The Mathematical Formalism Is Interpretation-Neutral
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
An important clarification: the four-dimensional mathematical formalism of GR is neutral between the
block universe and growing-block interpretations. The field equations G_{μν} = 8πG T_{μν} do not, by
themselves, determine whether the solution represents a pre-existing structure or a generated one.
CTGP's claim is interpretive, not that the mathematics is wrong. What CTGP adds is a principled
reason — grounded in the initial-value structure and the phenomenological constraint — to prefer the
generative reading over the static one.
4.5 Ontological Underdetermination and Explanatory Preference
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The observation that GR is interpretation-neutral (§4.4) raises the question of how to adjudicate
between ontologies that are empirically equivalent at the level of local predictions. Physics
routinely faces this situation: quantum mechanics is compatible with Everettian, Bohmian, and
collapse interpretations of the same Schrödinger equation; statistical mechanics admits both
Boltzmann and Gibbs readings of the Liouville equation; and GR admits both block and growing-
spacetime readings of the Einstein equation. Empirical equivalence does not imply ontological
parity. The standard philosophical move is to apply explanatory criteria: among empirically
equivalent ontologies, preference should be given to the one that provides an account of an
additional observed phenomenon without introducing new physical laws (see, e.g., Maudlin 2012;
Rickles 2016).
CTGP formalizes this as the Phenomenological Completeness Principle: among empirically equivalent
ontologies, preference should be given to the one that provides an account of additional observed
phenomena without introducing new physical laws. The block universe and CTGP make identical local
predictions. They differ in how they treat one datum: the phenomenology of temporal experience — the
felt asymmetry between past and future, the sense of genuinely unfolding succession. The block
universe typically explains this datum at the level of observer cognition and information processing
rather than at the level of fundamental spacetime ontology. CTGP differs by treating the asymmetry
of temporal experience as reflecting an objective asymmetry in the ontological structure of reality
itself. CTGP provides an account of it: temporal experience is grounded in the continuously
advancing generative flow at Σ_σ — the smooth propagation of the present boundary along n^μ, not a
discrete sequence of frames. CTGP therefore functions not as a competing physical model but as an
interpretive completion of relativistic spacetime — an explanatory expansion that accounts at the
ontological level for a datum the block universe explains through other structures, while remaining
consistent with all existing physics.
The Phenomenological Completeness Principle, stated more formally, runs as follows. Given two
empirically equivalent formalisms, the one whose fundamental ontology provides a causal-explanatory
structure for an additional, well-attested phenomenon is to be preferred, provided it does so
without introducing new physical laws or contradicting existing ones. On CTGP’s assessment, it
satisfies this criterion: it grounds the phenomenological arrow of time in the ontological arrow of
generation, which an action formulation can represent formally by restricting its domain (§9.1). On
this view, the felt direction of temporal experience is not an illusion generated by observer
psychology; it is the immediate experiential correlate of the asymmetric structure of generation,
which M(σ) represents formally — a profile that always includes the past and never the future. The
block universe generally interprets the same phenomenology as arising from the information-
processing structure of observers embedded within a static spacetime manifold. A static four-
dimensional block has no interior direction; every internal relation between events is given all at
once. CTGP’s succession of stages runs in one direction only, and the felt direction of experience
tracks that succession. Block-universe theorists explain the arrows through distinct structures: a
low-entropy boundary condition for the thermodynamic arrow, Lorentzian causal structure for the
causal arrow, and the architecture of cognition for temporal experience. On CTGP’s assessment, this
leaves their correlation without a single ontological source, whereas CTGP derives them from one.
Whether a unified account is preferable to a distributed one is the philosophical question at issue,
not a result either side can prove. The two ontologies are also economical in different respects:
presentism posits fewer existing things, eternalism less structure, since it needs neither a
distinguished foliation nor primitive succession. Which economy should weigh more is itself part of
the dispute.
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5. The Core Postulates of CTGP
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