1.1 Empirical Posture
~~~~~~~~~~~~~~~~~~~~~
CTGP is a thesis about what exists: the present, not the past or the future. Two readings of the
same physics that differ only in this respect make identical predictions for every measurement
(§12.1), so the framework does not claim that any instrument can detect the nonexistence of the
past. Its empirical exposure lies elsewhere: in the requirement that physical law be generable from
the present, which can be refuted (§12.2), and in the consistency of its continuum realization,
which the paper tests (§11).
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2. Philosophical Background: Locating CTGP Among Presentism, Eternalism, and the Growing Block
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2.1 The Standard Taxonomy
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Three major ontological positions on time are standardly distinguished in the philosophy of physics
literature. Eternalism (or the 'block universe' view) holds that past, present, and future are all
equally real; the universe is a completed four-dimensional manifold, and 'now' is merely an
indexical — like 'here' — with no special ontological status. Presentism holds that only the present
exists; past and future are not real. The growing block view, associated with C. D. Broad (Broad
1923) and developed in a relativistic setting by Ellis and Rothman (Ellis & Rothman 2010), holds
that past and present are real but the future is not: reality grows as new events are generated. A
fourth option, the moving spotlight view, keeps the whole block but lets presentness move through
it; Skow (Skow 2015) argues that it is the block universe’s strongest rival, although he ultimately
defends the block.
CTGP occupies a distinctive form of cosmologically grounded presentism, referred to throughout as
generative presentism. Unlike eternalism, CTGP denies the co-existence of past, present, and future.
Unlike growing-block theories, CTGP does not hold that past stages continue to exist; M(σ) is a
formal history, not an accumulating region of spacetime. Earlier states existed when present but no
longer exist. The present alone possesses ontological existence, while causal consequences of prior
states persist through records, memories, radiation fields, material structures, and other inherited
physical encodings. This is the framework's full position on the taxonomy, and it is not re-argued
below: §4.3 and §15.1 address only what CTGP inherits from prior growing-block models, not whether
it is one.
2.2 The Explanatory Challenge for the Block Universe
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The block universe faces a philosophical challenge that is not merely intuitive but structural. In a
truly static four-dimensional block, every event — including every purported moment of 'experiencing
the present' — is simply a fixed point in the manifold. The block does not evolve or generate; it
simply is. The verbs standardly used to describe temporal experience — 'moving through,' 'arriving
at,' 'leaving behind,' 'anticipating' — all presuppose change occurring over time. But change
occurring over time is precisely what the block universe denies at the ontological level.
One standard response is the worldline perspective: from any point along a worldline, past events
are causally connected and future events are not yet accessible. This gives a local asymmetry, but
it is a descriptive asymmetry, not an ontological one. The worldline runs through a pre-existing
structure; nothing is generated. The worldline perspective provides an account of why an observer
would represent things as temporally ordered, but it does not explain why there is any experience at
all — why the mathematical structure would be accompanied by, or would constitute, the felt
succession of 'nows.' Structure alone does not equal experience.
The point can be stated without assuming its conclusion. A complete description of a succession is
not necessarily a succession that is actually occurring. A four-dimensional block can contain every
state of a process and every relation among those states — that B follows A, that the organism at B
remembers A — and the eternalist rightly holds that this is what a temporally extended process is,
with no moving spotlight required. CTGP concedes all of that. What it disputes is that temporal
relations, however complete, amount to temporal becoming: a score is not a performance, and a
trajectory drawn on a spacetime diagram does not move through the diagram. CTGP therefore treats
succession as a primitive feature of reality rather than as a relation within a completed structure.
The present state is generated from its causal predecessor; the predecessor ceases to be the present
state; the successor does not yet exist. The disagreement is thus precise: whether a complete
temporal structure suffices for becoming, or whether becoming is an additional ontological feature
that the ontology must itself contain.
CTGP takes this challenge as a positive constraint on ontology: an adequate ontology of time must
not merely describe the temporal ordering of events but must sustain the conditions under which
genuine temporal becoming — and the experience grounded in it — is possible. The generative
presentist structure of CTGP is its response.
2.3 What CTGP Adds to Prior Becoming-Theories
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Existing theories of becoming in the literature — notably Ellis and Rothman's 'crystallizing block
universe' (Ellis & Rothman 2010), together with the presentist appeals to cosmic time defended by
Craig (Craig 2001) and Zimmerman (Zimmerman 2011) — establish the basic architecture but leave open
several questions that CTGP addresses explicitly. First, they do not provide a physically grounded
growth parameter defined without coordinates for realistic, inhomogeneous spacetimes: cosmic-time
presentists usually take the present from the homogeneous slices of idealized Friedmann models or
from the rest frame of the cosmic background radiation. CTGP identifies the growth parameter with
cosmological time, a geometric invariant fixed by the causal and metric structure of the spacetime
(§6.1). Second, they do not engage the phenomenology of conscious experience as a constraint on the
ontology; CTGP treats the present edge Σ_σ as a natural locus for the ongoing physical processes
associated with experience and develops the implications for philosophy of mind. Third, they do not
articulate the physically instantiated criterion that distinguishes ontological generation from
computational simulation. CTGP fills all three gaps. In the emergent regime, σ is fixed by the
causal and metric structure already present in general relativity and introduces no new propagating
degrees of freedom in the configuration λ = 0 adopted in §6.9.
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3. Phenomenology of Temporal Experience
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3.1 The Phenomenological Constraint
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Any adequate theory of time must satisfy what we call the phenomenological constraint: it must
explain, rather than explain away, the felt asymmetry between past and future — the sense that one
is moving through time from a fixed past into an open future, that the present is where things are
'happening,' and that the past is closed while the future is not. This is not merely an intuitive or
folk-psychological datum; it is a structural feature of experience that any reductive or eliminative
account must engage.
CTGP argues that the block universe does not meet this constraint in the sense sought here — not
because it gives the wrong answer, but because its ontology supplies no becoming for the
phenomenology to track. On the block view, all events are equally real and equally fixed. The
subjective sense of temporal flow becomes at best an illusion — a feature of how observers represent
their situation from inside the block — and at worst an inexplicable brute fact about certain
classes of mathematical structures. The eternalist can reply that thermodynamics, memory formation,
and the architecture of cognition explain why observers have this phenomenology; CTGP’s counter is
that such mechanisms explain why an observer has the experience of passage, not whether passage is
ontologically real. That is the philosophical disagreement at issue.
3.2 Flow, Asymmetry, and the Generated Present
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
CTGP's generative ontology provides the required apparatus. Reality advances as a continuously
flowing generative process: the generation flow vector n^μ propagates the present boundary Σ_σ
forward along a smooth, timelike field rather than advancing it frame-by-frame. The differential
notation Σ_σ → Σ_{σ+dσ} represents an infinitesimal increment of this continuous flow, not a
discrete jump between fixed stages. This flow is asymmetric by design: M(σ) formally represents the
generated history of the universe up to the present flow parameter σ, while only the present state
possesses ontological existence, and Σ_σ is the advancing edge at which new structure continuously
emerges. M(σ) should accordingly be read as a formal representation of causal ancestry and
generative ordering, not as a collection of simultaneously existing historical states; the symbol
organizes the lawful sequence of generation, it does not store the generated stages as co-present
entities. The experienced sense of temporal flow corresponds to this actual, continuously unfolding
generative process — not a sequence of discrete snapshots, but a river whose front perpetually
advances.
Crucially, this is not a mere relabeling of the block universe in generative vocabulary. The formal
structure of M(σ) differs from the block in that future hypersurfaces are not part of the domain at
any stage σ — they do not exist to be described, even in principle. The open future is not a gap in
our knowledge of a pre-existing structure; it is an ontological absence. This is the precise sense
in which CTGP sustains an 'open future': the future is genuinely ungenerated, not merely unknown.
3.3 Multiple Registers of the Argument
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The phenomenological case for CTGP can be made in at least three registers. At the intuitive level,
temporal experience has a directionality — a before-and-after — that is not symmetrically available
in both directions. The past is experienced as fixed and determinate; the future is experienced as
open and indeterminate. This asymmetry is not accounted for by the block universe, where all
directions in the manifold are equally determinate. At the analogical level, the distinction between
a finished DVD (block universe) and a live production (CTGP) captures the ontological point: the DVD
encodes a complete structure that is merely revealed as playback proceeds, while a live performance
is actually created as it unfolds. At the formal level, CTGP’s M(σ) structure makes the asymmetry
mathematically precise: the present is ontologically real, the past is historically real but no
longer existent, and the future is excluded from realization.