COSMIC-TIME GENERATIVE PRESENTISM (CTGP)
A Generative Spacetime Ontology Compatible with General Relativity
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ABSTRACT
Cosmic-Time Generative Presentism (CTGP) proposes a dynamic ontology of spacetime in which reality
exists only at an advancing present boundary, generated through continuous causal-temporal
progression in which each present state emerges from the lawful evolution of immediately preceding
states. Earlier states no longer exist as independently real regions of spacetime; the specific
physical organizations constituting those earlier states cease to exist as present realities, while
their causal consequences continue propagating through later physical structures. Present systems
therefore inherit transformed physical continuities, causal records, and distributed consequences of
prior states, rather than preserving those earlier states themselves. Unlike static block-universe
interpretations of relativity, CTGP treats spacetime as a continuously generated structure emerging
through causal propagation governed by physical law. The framework preserves relativistic causal
structure while identifying cosmological time, which on large scales is the proper time of the
cosmic matter flow, as the natural parameter governing the progression of physical reality.
In this model, each present state of the universe arises as the causal continuation of prior states,
while the past remains accessible only through physical information encoded in present systems —
radiation fields, gravitational structures, and cosmological relics such as the cosmic microwave
background. In the emergent geometric regime, CTGP identifies the generative present with the level
sets of the cosmological time function: the maximal proper time elapsed since the initial
singularity. By a theorem of Andersson, Galloway, and Howard, these level sets are Cauchy surfaces
whenever cosmological time is regular, so the present remains globally well defined even where the
flow of matter develops caustics inside collapsed structure. The framework therefore applies insofar
as the actual universe is globally hyperbolic with regular cosmological time. Identifying these
level sets with the present is an interpretive posit rather than a theorem, and the present can be
located from its past alone, without reference to the future. The continuum generation parameter σ
is a monotone relabeling of cosmological time, which introduces no new field and can optionally be
expressed through a constrained action that leaves the Einstein equations unchanged.
The paper then determines which physical realizations of the generation parameter are consistent. A
natural hypothesis — that generation proceeds faster where matter is denser — fails: an exact
density-weighted law drives the generation flow out of alignment with matter within a light-crossing
time of any structure, and every stable soft completion forces a uniform generation rate inside
bound structures, suppressing any density-weighted cosmological effect below one part in 10⁴⁰. No
local density-dependent generation law in the classes analyzed survives these constraints: the
generation rate may vary with cosmic epoch but not across space, and CTGP predicts no intrinsic
cosmological axis. We further show that presentist and eternalist readings of identical physics are
observationally equivalent, so the ontology cannot be verified by measurement at fixed physics. It
remains empirically exposed: presentism requires the fundamental laws to be generable from the
present state, with no dependence on future boundary data and no global consistency conditions
requiring the whole history at once — a structural commitment that a confirmed chronology violation,
interventionist retrocausal dependence, or fundamental final-state condition would refute. 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. Current physics is
consistent with that commitment but does not establish it. Because it entails a unique factual past,
CTGP also requires single-outcome realism in quantum theory, which excludes standard Everettian
ontology. CTGP traces the causal, record-forming, and experiential arrows of time to the direction
of generation, relates the thermodynamic arrow to it without reducing it, answers the principal
objections — relativity of simultaneity, Lorentz invariance, diffeomorphism invariance, strong-
curvature foliation, point presentism, the absence of any intrinsic marker of the present, and
underdetermination — and constrains where physically instantiated processes associated with
experience may occur, without claiming to determine the nature of consciousness.
Keywords: presentism; generative presentism; philosophy of time; general relativity; cosmological
time function; foliation; causality; initial-value formulation; observational equivalence; cosmic
microwave background; decoherence; quantum foundations; qualia
READER’S GUIDE
Three layers of claim run through this paper and should be kept distinct when assessing it. Layer 1
is established physics that CTGP adopts without modification: the initial-value formulation of
general relativity, global hyperbolicity where applicable, cosmological proper time, relativistic
causal structure, conservation laws, and the observed matter-frame and CMB structure. Layer 2 is
CTGP’s ontological interpretation, which is the framework’s distinctive philosophical claim: only
the current generative state exists, the past possesses causal but not ontological persistence, and
the future is genuinely ungenerated. Layer 3 comprises physical hypotheses about how the generation
parameter is realized in the continuum: the form of the generation law, any coupling it has to
matter, and any observable consequences. Layer 1 is not at issue. Layer 2 is argued on grounds of
explanatory economy and carries one structural empirical commitment, that physical law be generable
from the present. Layer 3 is where physical hypotheses can fail, and §11 shows that one natural
family of them does. Objections directed at one layer should not be taken to bear on another.
The paper is organized in four parts. Part I (Interpretive Framework, §§1–5) sets out the
philosophical case: the motivation, the position of CTGP among presentism, eternalism, and the
growing block, the phenomenological constraint, the comparison with block-universe and growing-block
models, and the five core postulates. Part II (Formal Framework, §§6–10) develops the mathematics:
the generative present as the level sets of cosmological time, the generation parameter and its
admissible forms, general relativity as initial-value generation, the ADM decomposition, the action
principle and cosmological foliation, and compatibility with quantum theory and with a pre-geometric
ontology. Part III (Physical Realization and Empirical Standing, §§11–12) determines which
generation laws are dynamically admissible and states precisely what observation can and cannot
establish about the ontology. Part IV (Evaluation, §§13–17) addresses objections, treats
cosmological observables as causal records, situates CTGP relative to causal set theory and growing-
block models, and collects the formal results. Appendices A–E contain ADM derivations, causal-
structure theorems, a vulnerability assessment, the extension of CTGP to conscious experience, and a
worked example (Supernova 1987A).
Readers primarily interested in the physics case may proceed directly to §6, §9, §11, and §12. The
discussion of conscious experience is confined to Appendix D and is not presupposed by any argument
in the main text.
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PART I. Interpretive Framework
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1. Introduction
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CTGP begins from two distinct sources of friction. The first is the well-known tension between (i)
the mathematical convenience of four-dimensional spacetime descriptions and (ii) the phenomenology
of temporal passage and the asymmetry between past and future. The second, and less often
foregrounded, is the explanatory gap between block universe ontology and the very existence of
dynamic experience: if the universe is simply a completed four-dimensional structure, it is unclear
how or why any part of that structure would constitute or generate the felt succession of 'nows'
that characterizes conscious experience.
CTGP’s core claim is not that relativity is false, but that the ontology suggested by a static
‘block’ is not forced by the formalism. GR’s initial-value structure is entirely compatible with a
generative reading: evolution equations are not merely descriptive of a pre-existing block, but
lawlike rules governing a continuously advancing generative flow, whose state at any moment admits
hypersurface descriptions in the emergent-geometric limit. More precisely, minimal generative laws
govern the continuous propagation of the present boundary Σ_σ along the generation flow vector n^μ,
while effective low-energy laws (GR, QFT) govern the detailed dynamics realized upon generated
hypersurfaces.
References to the “σ field” denote the effective continuum representation of the primitive
generative ordering parameter σ (§10.4).
The generative reading of general relativity advanced here does not conflict with quantum mechanics
or current approaches to quantum gravity. Relativistic quantum field theory preserves relativistic
causal structure at all experimentally tested scales, while decoherence explains the emergence of
classical behavior without requiring fundamental retrocausality or the abandonment of causal
ordering. Several interpretations of quantum mechanics remain compatible with a causally ordered
ontology (§10.1), and among quantum-gravity approaches, causal set theory is a natural companion
(§15.2).
CTGP articulates this reading precisely and suggests that it satisfies all local relativistic
constraints while sustaining an open-future ontology.
The framework therefore pursues three interlocking goals: (a) preserving local relativistic
constraints, (b) articulating a global ontology in which only the present physical state exists,
while causal consequences of prior states continue propagating through transformed matter-energy
configurations, inherited structure, and causal records within later states — without implying that
such records exhaust all truths about the past, and without implying that physical existence
vanishes except for surviving traces, since CTGP locates non-persistence specifically at the level
of the earlier state’s organization rather than at the level of physical continuity itself — and the
future remains ungenerated, and (c) grounding the phenomenology of temporal experience — including
conscious qualia — in the generative structure of the present hypersurface. These goals are
addressed in order: the philosophical case first, the mathematics second, and the implications for
mind and experience third.
CTGP constrains where and when outcomes become ontologically definite — at the advancing present
boundary — without requiring a further selector beyond lawful physical dynamics; conscious agency,
where present, contributes as an emergent causal process within those dynamics rather than as an
extra-physical source of outcome selection.
CTGP introduces no modification to Einstein’s equations and is empirically equivalent to GR at the
level of local dynamics. A note on CTGP’s fundamental ontological character: CTGP is a fundamentally
continuous framework. Its core mathematical structures — the timelike gradient ∇_μσ, the generation
flow vector n^μ, smooth scalar-field representations, continuous propagation equations, smooth
Cauchy foliation, and ADM evolution — are all continuously defined. Causal-set models and other
discrete approaches to quantum gravity are compatible with CTGP as possible discrete realizations of
its generative-ordering principles, but they are not its ontological foundation. CTGP’s fundamental
picture is a continuously advancing generative flow, not a sequence of discrete frames.