QUANTUM REFERENCE FRAMES AND SINGLE-OUTCOME DYNAMICS
A Compatibility Framework for Generative Presentism
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ABSTRACT
Quantum reference frames (QRFs) permit different quantum systems to serve as reference frames,
raising a foundational question for single-outcome theories: how can frame-dependent descriptions
represent one objectively realized history? Cosmic-Time Generative Presentism (CTGP) holds that only
the present exists, that physical reality is generated through successive stages, and that truths
about the determinate past are grounded in primitive past-tensed properties of the present world. We
develop a mathematical compatibility framework connecting these commitments to QRF covariance,
stochastic quantum instruments, and relativistic measurement theory.
We first construct an explicit QRF-covariant, single-outcome quantum model using relational GRW-type
events and a Lucretian truth profile. We establish a frame-independent determinacy criterion,
characterize when different frame descriptions identify the same complete physical state and
realized history, and prove covariance of the generative law and its history probabilities. We
distinguish physical-state identity, historical identity, and observational indistinguishability,
and show that the present quantum state need not determine the complete past. The construction
demonstrates the joint mathematical consistency of these commitments without deriving their
ontological interpretation or establishing physical adequacy.
We then formulate a compatibility program for relativistic quantum field theory, quantum clocks, and
quantum gravity. For specified causally local instruments, we establish conditions for foliation-
independent outcome histories and operational no-signaling. Free-field detector and Gaussian-
collapse constructions identify both sufficient conditions for causal admissibility and obstructions
to extending them to arbitrary local operations and to covariantly located collapses. We calculate
the energy–momentum cost of Gaussian collapse and examine, without adopting it, a cosmological-time-
guided candidate that defines normalized finite-volume dynamics but introduces preferred-frame
structure.
To distinguish formal collapse prescriptions from physical implementations, we compare centre-time
ordering, completion-time ordering, and a local field–pointer coupling. The pointer construction
yields foliation-independent statistics, reproduces ordered-collapse predictions for causally
orderable configurations with suitably prepared pointers, and defines a consistent law of outcome
records even in spatially infinite universes. Interfering collapse regions, however, produce
different joint outcome laws, showing that this local coupling does not in general reproduce a
prescribed collapse ordering. Definite pointer readings require an explicit single-outcome
postulate, and infinite-volume generation of the physical state remains open. We also give clock-
neutral descriptions of late-record instruments for two ideal clocks and exhibit interference
between alternative clock-dependent interaction orders.
These results establish a concrete mathematical compatibility framework, not a completed
relativistic theory or an empirical confirmation of CTGP. They separate frame-dependent descriptions
from the identity of realized events, identify which features of single-outcome dynamics survive
changes of reference frame and foliation, and isolate the additional physical requirements for
relativistic collapse, temporal quantum reference frames, and quantum gravity.
Keywords: presentism; generative presentism; Lucretianism; quantum reference frames; perspective-
neutral framework; objective collapse; GRW; flash ontology; quantum instruments; quantum jump
processes; single-outcome realism; determinacy; truth preservation; non-supervenience; relativistic
quantum field theory; foliation independence; particle detectors; measurement models; Gaussian
collapse; impossible measurements; no-signaling; Poisson point processes; collapse energy; temporal
quantum reference frames; quantum clocks; clock-neutral instruments; quantum gravity; cosmological
time; preferred frames; philosophy of time
READER’S GUIDE
Three layers of claim run through this preprint and should be kept distinct. Layer 1 is established
mathematics adopted without modification: the perspective-neutral framework for quantum reference
frames with a finite symmetry group, quantum instruments (Kraus operators) for stochastic single-
outcome dynamics, and piecewise-deterministic quantum jump processes in continuous time. Layer 2
consists of the definitions proposed here: the complete ontological state, the space of admissible
histories, the determinacy criterion, the cross-frame identification criterion, and the validity
condition for frame-relative laws. Layer 3 is the concrete model of Part III, which shows that the
Layer 2 definitions are jointly satisfiable by an explicit dynamics. Part V adds a further kind of
material, a research program, whose items are labeled by status: proved theorems and propositions,
definitions offered as proposals, and conjectures or targets that remain open.
Three kinds of result should likewise be kept apart. An existence result says that at least one
model in a specified class satisfies a given set of commitments. A general compatibility result
would say that every physically admissible QRF theory can accommodate those commitments. A physical
adequacy result would say that the model reproduces the relevant features of established quantum
physics and relativity. This preprint establishes an existence result. It does not establish the
other two, and §17 states precisely why not.
Interpretation enters at identifiable points, and those points are flagged in the text. The theorems
are mathematical consequences of the definitions. The claims that the perspective-neutral state and
the truth profile represent what exists, and that each orbit of frame descriptions represents one
realized present with one history, are interpretive theses (Ontological Reading 4.3 and Thesis
5.10). They are what CTGP adds to the mathematics, and they are argued for rather than derived. The
spaces of histories and the probability measures over future trajectories used throughout are
mathematical representations of possibilities; they do not assert that past or future stages exist
(§4.5).
Part I (§§1–2) states the problem and the background. Part II (§§3–5) develops the general formalism
for any finite symmetry group. Part III (§§6–10) builds the concrete model in discrete-stage and
continuous-time form and checks CTGP’s further requirements. Part IV (§11) identifies what CTGP adds
beyond QRF covariance. Part V (§§12–16) sets out the compatibility program for relativistic quantum
field theory, temporal quantum reference frames, and quantum gravity. Part VI (§§17–19) states the
scope of the results and the open problems, and maps the results back to the original questions.
Appendix A collects the frame-relative forms used in the model. Appendix B contains the verification
script for the model and the finite theorems, with its output and the information needed to
reproduce it, and Appendix C contains separate scripts for the results of §§13.8–13.11 and §14.5.
Nothing here modifies the CTGP postulates, and nothing here is an empirical result. The aim is to
replace schematic statements about CTGP and quantum theory with definitions precise enough to be
proved or refuted.
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PART I. The Problem
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1. Introduction
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CTGP claims that the present stage of the universe is all that exists, that it is generated from the
preceding stage by physical law, and that truths about the past are grounded Lucretian-style in the
present world’s primitive past-tensed properties: the present world has the property *having been,
at stage σ′, such that φ* (CTGP – explained, §5.2.1 and Definition 17.20). Because it entails a
unique factual past, CTGP requires single-outcome realism in quantum theory, which excludes the
standard Everettian ontology, and it rejects relational interpretations on which facts are relative
to observers (CTGP – explained, §10.1).
Quantum reference frames put pressure on this combination. In the QRF literature (Giacomini, Castro-
Ruiz & Brukner 2019; Vanrietvelde, Höhn, Giacomini & Castro-Ruiz 2020; de la Hamette & Galley 2020),
there is no external classical reference frame: a physical system is described relative to another
quantum system. A system in a definite position relative to one frame can be in a superposition, and
entangled, relative to another. Three questions then arise for CTGP. Is determinacy frame-relative?
If two frames describe the present differently, what makes them descriptions of one present and one
history? And where do the Lucretian past-tensed properties sit relative to a quantum state that has
many frame-relative descriptions?
A prior analysis of these questions proposed the schematic representation
Ω_σ = (S_σ, L_σ), S_{σ′} ∼ K(S_{σ′} | S_σ), L_{σ′} = L_σ ∪ ΔL_{σ→σ′},
in which S_σ is the present physical state governing successor-state generation, L_σ is the present
world’s Lucretian past-tensed truth profile, K is a stochastic generative law, and ΔL_{σ→σ′}
represents the truths newly acquired about what occurred during the transition. It drew a key
distinction: CTGP’s unique factual history must be grounded in the chosen single-outcome quantum
ontology, and L represents truths about the history actually generated rather than serving as an
independent mechanism that determines which history occurs. It identified four tasks:
(T1) Which propositions are determinate under the chosen quantum ontology.
(T2) How corresponding physical facts are identified across quantum reference frames.
(T3) Whether valid QRF transformations preserve the truth of those corresponding propositions.
(T4) How Lucretian past-tensed properties relate to the physical quantum state without
introducing unjustified dynamical assumptions.
It added a fifth requirement: a QRF-compatible single-outcome model must also satisfy CTGP’s
requirements of definite generative ordering and generability (T5). It also posed the question at
the heart of T2: how can one establish that two frame descriptions refer to the same realized
history, rather than simply assuming that they do?
This preprint addresses all five tasks by construction. It specifies a class of QRF-covariant,
single-outcome stochastic quantum dynamics, shows that every member of the class admits a CTGP
interpretation, and proves what that interpretation implies. The strategy has three parts. First,
the underlying present state lives in the perspective-neutral (gauge-invariant) Hilbert space of the
QRF framework, and frame descriptions are obtained from it by unitary reduction maps. Second, the
single-outcome dynamics is a stochastic quantum instrument whose operators are invariant under the
symmetry group, so that each outcome is a frame-independent event; this is a relational version of
the flash ontology of the Ghirardi–Rimini–Weber (GRW) collapse model (Ghirardi, Rimini & Weber 1986;
Bell 1987; Tumulka 2006). Third, the truth profile L is defined as the past-tensing of the realized
states and events, so that it is generated by the dynamics rather than feeding into it, and the
space of admissible profiles is specified exactly.