# Quantum Reference Frames and Single-Outcome Dynamics — A Compatibility Framework for Generative Presentism

Part 26 of 40 (1,521 words)



Which properties survive. Measured against the six parts of Proposition 13.28, the three

implementations compare as follows.



    (a) Completeness. Centre-time ordering: proved. Completion-time ordering: unchanged, with the

    same proof. Gapless pointers: holds for every finite configuration, with a separate proof

    (Proposition 13.31(a)–(b)), and needs no ordering rule.



    (b) Agreement with the causal-order dynamics. Centre-time ordering: proved in the flat local

    model. Completion-time ordering: unchanged for a uniform half-width; a separate proof would be

    needed if the half-width varied. Gapless pointers: holds on every admissible configuration of

    any globally hyperbolic background, with a separate proof (Proposition 13.31(d)), provided that

    the pointers are pre-chirped; without the pre-chirp it fails by the self-terms of Proposition

    13.31(b).



    (c) No signaling. Centre-time and completion-time ordering: proved for the covered operations.

    Gapless pointers: holds, with a separate proof, for every pointer or classical source whose

    region does not meet the causal past of the targets, on every configuration (Proposition

    13.31(e)); it is not established for arbitrary interventions. The second limit above does not

    arise for such operations, since no rule orders them.



    (d) Forward generation. Centre-time ordering: forward computability from present Cauchy data,

    not a mechanism. Completion-time ordering: strengthened to computability from the generated past

    (Proposition 13.29(c)), still without a mechanism. Gapless pointers: replaced, for finite

    configurations and given postulate (R), by forward generation through a local coupling, each

    collapse being the reading of a pointer whose coupling has ended (Proposition 13.31(g)); on

    spatially flat or open FLRW spacetimes, a forward evolution of the present state is not

    constructed.



    (e) Preferred-frame structure. Centre-time and completion-time ordering: proved. Gapless

    pointers: the energy–momentum injection survives unchanged, because the unread channel is the

    same (Proposition 13.31(c)); the cosmic-frame dependence of the outcome correlations that comes

    from the ordering rule fails: the law of Proposition 13.31(b) contains no ordering rule, and its

    correlations depend on the cosmic frame only through the smearings.



    (f) Infinite histories. Centre-time and completion-time ordering: proved when the past regions

    have finite four-volume, and open otherwise. Gapless pointers: a law of the pointer records

    exists and is unique on every FLRW spacetime of the class, including spatially infinite ones,

    with a separate proof (Lemma 13.30, Proposition 13.31(f)); it is a law of records, not a global

    present state containing infinitely many pointers, and it does not establish the generation of

    those records in an infinite volume.



What fails is the identification of the pointer law with the law of Candidate extension 13.27. On

non-admissible configurations the two differ, so the gapless-pointer construction is a different

candidate law, not a physical implementation of rule (iii). The gapless pointer, the natural local

realization of a Gaussian collapse, does not reproduce centre-time ordering: it yields a law with no

ordering rule.



The pointer realization has further costs. First, as explained above, it adds physical degrees of

freedom, one pointer at each Poisson centre prepared in a fixed state that depends on the smearing

through Γ_kk, together with postulate (R). Second, cosmological time still enters the law, through

the smearing law of Candidate extension 13.27(ii), which Proposition 13.24 makes necessary for

point-centred smearings; only the ordering rule is removed. Third, the coupling is a prescribed

function on spacetime, so the energy of Proposition 13.31(c) is supplied by the prescribed coupling,

and no dynamical account of the energy budget is given. Fourth, each pointer is a single degree of

freedom coupled throughout an extended region. It is a regulated probe, not a local probe field in

the sense of Fewster and Verch (2020), and the results depend on the free field and on the absence

of pointer dynamics. Fifth, the readings localize smeared field amplitudes, not matter (L2, D7). In

Bedingham’s (2011) model, a mediating relativistic field attaches a quantized degree of freedom to

each spacetime point; the pointers here attach one degree of freedom to each Poisson centre. The

pointer realization is recorded as a further candidate, alongside Candidate extension 13.27, and is

not adopted.



Comparison with a covariant alternative. Routes (iv) and (vi) of Remark 13.25 avoid a preferred

frame, and the two kinds of construction differ point by point. In frame, the candidate refers every

collapse to the cosmic rest frame, a structure CTGP already posits, whereas rGRWf refers each flash

to an earlier flash and Bedingham’s model works through an additional relativistic field. In scope,

the candidate is defined for a free field on a fixed background, on every domain of finite four-

volume and, when cosmological-time slabs have finite volume, on infinite histories (Proposition

13.28(f)), and in its gapless-pointer form, as a law of outcome records, on every FLRW spacetime of

the class (Proposition 13.31(f)), whereas rGRWf is defined for a fixed number of non-interacting

particles from given initial data. In generability, the candidate can be generated forward along

cosmological time in its free-field representation (Proposition 13.28(d)), and in its gapless-

pointer form, for finite configurations and given its reading postulate, through a local coupling

(Proposition 13.31(g)), whereas for rGRWf causal inheritance requires the earlier flash locations to

be physically instantiated in the present state, which is open (§13.12). In phenomenology, the

candidate predicts, as theoretical consequences of the free-field model, energy injected at rest in

the cosmic frame and, at the scales τ and ℓ, order effects for interfering interventions and cosmic-

frame-dependent correlations among collapse outcomes. The last two arise from the ordering rule and

are absent in the gapless-pointer form, whose outcome correlations depend on the cosmic frame only

through the smearings. None of these effects has yet been turned into an operational prediction for

an apparatus; any that become observable must respect the experimental bounds on collapse effects

(Bassi et al. 2013) and on preferred-frame effects (Kostelecký & Russell 2011), whereas a fully

covariant model predicts no such frame dependence. In localization, both leave open how matter,

rather than a field amplitude, is localized (L2, D7).



Adopting the candidate would change CTGP in one respect only: cosmological time would enter the

collapse law, and the generative foliation would become empirically accessible in principle. In the

gapless-pointer form it would enter only through the smearing law. That is a substantive commitment,

whose consequences become testable once its predicted preferred-frame effects are turned into

operational predictions. It is recorded here as a candidate, with its law, its variants, and its

predicted signatures stated, and it is not adopted.



13.12 Candidate Relativistic Realizations



Relativistic flash model. Tumulka’s relativistic GRW model (rGRWf) treats discrete spacetime flashes

as objectively realized events, with a Lorentz-invariant law for their joint distribution, for a

fixed number of non-interacting distinguishable particles (Tumulka 2006). Its law refers to

hyperboloids centred on each particle’s previous flash, which is one way of supplying the local

frame that, by Proposition 13.24, a point-centred law needs. It is the natural first test case. A

continuous generative present can contain a locally finite set of discrete flash events, so discrete

flashes do not imply discrete ontological time. The open questions are whether the flash law can be

represented as a generable process on CTGP’s cosmic-time hypersurfaces, with a physically

instantiated present state on each, and whether the construction extends to interacting fields,

particle creation, renormalization, and curved backgrounds. A realistic interacting relativistic

quantum field theory is a much harder target than a non-interacting model.



Spontaneous events. The detector networks of §13.6 are a measurement model: their events are

triggered by specified couplings. A spontaneous relativistic model would replace them by events

prescribed by the law itself, with a conditional intensity λ(x | S_Σ) defined from the present

state, together with the state update associated with each event. Such a law must be covariant

across admissible hypersurface descriptions, well defined on a regulated field state space, causally

admissible in the sense of (E3), normalized and free of pathological accumulation of events, and

generable from the physically instantiated present state. This is the relativistic objective-

collapse realization that CTGP contemplates. Section 13.7 constructs a regulated version, Gaussian

collapse of smeared fields on a fixed family of regions (Corollary 13.14), and §13.10 lets a

covariant Poisson law choose the locations (Theorem 13.21) and identifies the obstructions to a

fully covariant version (Propositions 13.22–13.24). A covariant version that localizes matter,

rather than linear field observables, remains open.



Bohmian dynamics. A second route keeps a definite configuration rather than collapsing the quantum

state: the present state is S_Σ = (Ψ_Σ, Q_Σ), with Q_Σ a particle or field configuration on the

hypersurface, and the dynamics is a guidance law. Such a theory already contains one actual

configuration and therefore one realized history. Relativistic Bohmian theories typically require a

distinguished foliation (Dürr, Goldstein, Münch-Berndl & Zanghì 1999), and the foliation may itself

be determined covariantly, for instance by the wave function (Dürr, Goldstein, Norsen, Struyve &

Zanghì 2014). CTGP’s cosmological-time foliation is a natural candidate. It must be shown that the

resulting predictions remain compatible with relativistic observations.



Success in either route would mean that at least one mathematically consistent single-outcome

relativistic quantum model can be equipped with CTGP’s ontology and its generability requirement

without unacceptable observational effects. It would not mean that every relativistic quantum field

theory or every interpretation is compatible with CTGP.