The Empirical Distinguishability of Quantum Interpretations

1. 1 Introduction

Experiments distinguish probability laws for observable records. Interpretations of quantum theory supply more than such laws: they also describe what exists, how outcomes arise, and what probabilities mean. The empirical question is whether those differences produce distinct distributions of records under a common experimental specification. A difference between unobserved quantities may matter physically without supplying that distinction. Conversely, a change in dynamics may make a foundational proposal experimentally vulnerable even when it is conventionally called an interpretation.

These distinctions are established in the literature on quantum underdetermination (Acuña 2021; Acuña and Dieks 2014; Egg and Saatsi 2021). Pessoa’s account of the several relations between experiments and interpretations further explains why experimental influence cannot be reduced to selecting one ontology (Pessoa 2026). The difficulty addressed here is how to distinguish a genuine difference of recorded predictions from a difference in ontology, inaccessible variables, conditioning information, or incompletely constrained noise.

A related question is whether the surviving interpretations deserve equal confidence. Recent nanoparticle-interference measurements and XENONnT searches for spontaneous radiation constrain departures from standard quantum dynamics (Pedalino et al. 2026; Aprile et al. 2026). Their bearing on ontology requires a further argument. Section 8 distinguishes experimental discrimination, Bayesian comparison, and theoretical preference, including the conditional case for Everett and the scope of Bohmian field-theoretic and relativistic constructions.

Arrival times provide a demanding example. Das and Dürr derive spin-dependent Bohmian arrival-time distributions (Das and Dürr 2019). Goldstein, Tumulka, and Zanghì argue that these free-trajectory distributions cannot in general be the detection-time distributions of a single apparatus (Goldstein, Tumulka, and Zanghì 2024b, 2024a). In a preprint reply, Das and Aristarhov question the application of the measurement argument to realistic apparatuses and their effective wave functions (Das and Aristarhov 2023). A related proposal asks whether arrival-time information in a double-slit experiment can distinguish interpretations (Ayatollah Rafsanjani et al. 2023). The issue is experimentally substantive: does a detector record the first crossing calculated without that detector, or does its interaction produce a different distribution?

The general obstruction is already known. In particular, the spin-mixture identity and a total-variation lower bound on approximation by a POVM are established in the analysis of arrival versus detection times (Goldstein, Tumulka, and Zanghì 2024a). The first worked application calculates the free trajectories, their complete finite-time record laws, the sharp approximation radius, an explicit common detector, and a calibration-sensitive count test. The trapped geometry is chosen for exact solvability; it is not a reconstruction of the released-waveguide proposal of Das and Dürr. Its purpose is to isolate the inference that a difference in free arrivals establishes a difference in observed outcomes.

At one detector setting, the calculated click probability is approximately $0.370$, close to a free-arrival probability of $0.368$. The same detector must also give $0.370$ for a matched ensemble whose free-arrival probability is approximately $0.079$. The second preparation therefore changes the evidential assessment of the first agreement. This result supplies a concrete standard for claims about empirical discrimination: the proposed readout must work across the relevant preparations with the apparatus held fixed.

A second worked comparison places universal unitary evolution and genuine collapse in a coherent-memory experiment. It derives an exact confounding condition for ordinary and collapse-induced dephasing, then gives a robust separation and observation-time choice when independent calibration limits that confounding. The idea of using controlled reversal to probe modified dynamics has clear precedents (Arenz et al. 2015); the contribution here is the explicit comparison across common nuisance ranges. GRW matter-density and flash ontologies, relational quantum mechanics, and QBism then test how far the conclusions extend beyond the arrival-time dispute.

The baseline in the arrival calculation is quantum instrument theory, not a uniquely specified historical “Bohr model.” Likewise, state-update language alone does not specify a physical collapse law. The analysis compares nonrelativistic formulations with explicit probability rules and controls. Its exact comparisons concern that domain; the discussion separately considers how evidence and theoretical adequacy beyond it can affect the standing of an interpretation.

2. What Must Be Common in an Experimental Comparison?

2.1. Formulations, Records, and Hypotheses

Let M denote a physical formulation, including its dynamics, probability rule, and account of apparatus records. A protocol C specifies preparation, controls, detector operation, observation time, and the rule for retaining trials. The predicted law is

$$P_M(dz\mid C),z\in \mathcal{Z}.\left(1\right)$$

The record space $\mathcal{Z}$ must include failures to detect. Conditioning separately on successful detection can conceal differences in efficiency or introduce differences between otherwise comparable samples. For a specified domain $\mathcal{C}$, exact empirical equivalence means equality of (1) for every $C\in \mathcal{C}$. Agreement in one protocol establishes much less. Equality of a density operator at one time also need not imply equality under later interventions: for that stronger claim, the controlled dynamics and record instruments must agree.

A difference in an ontic variable ${\xi }_M$ is relevant to (1) only through the formulation’s physical account of how records are generated. Writing down a trajectory functional $\tau \left({\xi }_M\right)$ and assigning it the name of an experimental observable does not supply that account. This is particularly important for first entry into a region, since adding an apparatus can change the wave function and the trajectory. Weakly reconstructed velocity fields raise a related problem of what a measurement establishes about individual paths (Fankhauser and Dürr 2021).

Likelihood equality also has a precise scope. If two formulations assign the same law to the data from C, conditional on background evidence B, those data have Bayes factor one between them. Their posterior odds need not be equal: the odds conditional on B may already differ. Empirical equivalence in a restricted experiment therefore does not erase evidence from other domains or settle differences in theoretical adequacy (Laudan and Leplin 1991; Wallace 2023). Section 8.2 makes this distinction explicit and addresses the additional prior specification required when a hypothesis contains uncertain parameters.

2.2. A Paired Preparation with One Apparatus

Prepare a particle in a fixed spatial state $|\varphi \rangle$. In ensemble Z, choose spin $+z$ or $-z$ with equal probability; in ensemble X, choose $+x$ or $-x$ with equal probability. Their average input density operators coincide:

$${\overline{\rho }}_Z={\overline{\rho }}_X=|\varphi \rangle \langle \varphi |\otimes {\displaystyle \frac{I_2}{2}}.\left(2\right)$$

The apparatus is operated identically for both ensembles. Preparation labels can be retained for later analysis, but neither the detector nor its controls may use them. Its ready state and relevant environment must be the same and uncorrelated with the label. Trial order is randomized, the observation window is fixed in advance, and every launched trial contributes either a click record or a no-click record.

Any fixed quantum record instrument has an associated positive-operator-valued measure (POVM), $E\left(dz\right)$, and consequently

$$P_Z\left(dz\right)=tr\left[{\overline{\rho }}_{Z}E\left(dz\right)\right]=tr\left[{\overline{\rho }}_{X}E\left(dz\right)\right]=P_X\left(dz\right).\left(3\right)$$

This equality holds even for a spin-sensitive detector. Spin independence is therefore unnecessary for the central comparison. It will be imposed later only to make one detector model easy to solve. A fixed sequence of measurements, including feedback based on earlier outcomes, also defines a record instrument (Chiribella, D’Ariano, and Perinotti 2009). The requirement is that the same procedure act on the two preparations.

In equilibrium Bohmian mechanics, a full apparatus model gives the same record law through equivariance and the distribution of pointer configurations (Dürr, Goldstein, and Zanghì 1992, 2004; Beck and Lazarovici 2025). Equation (3) thus constrains that formulation as well as ordinary quantum measurement theory. An Everettian description supplied with the usual Born weights likewise assigns these records the same probabilities; justification of those weights is a further interpretive question (Greaves and Myrvold 2010). The comparison assumes the probability rules rather than deriving them anew.

The objection from realistic open apparatuses deserves a direct answer. Conditional wave functions can evolve nonlinearly and nonunitarily after conditioning on a record, as stressed in the arrival-time debate (Das and Aristarhov 2023). But a fixed initial environment, linear composite evolution, and a fixed record partition still give probabilities affine in the unconditioned input density operator. Enlarging the apparatus to include a bath does not by itself remove (3). A proposed exception must specify which assumption fails and calculate the resulting record law. Preparation-dependent environmental states, nonequilibrium configurations, or altered dynamics would change the comparison; naming one of these possibilities does not establish the proposed free-arrival readout.

3. An Exact Discrepancy Between Free Arrivals and Records

3.1. Trapped Spin Trajectories

Consider a spin-independent isotropic oscillator,

$$H_0={\displaystyle \frac{{\mathbf{p}}^2}{2m}}+{\displaystyle \frac{1}{2}}m{\omega }^2{\mathbf{r}}^2,\ell =\sqrt{{\displaystyle \frac{\hslash }{m\omega }}}.\left(4\right)$$

Its spatial ground state and a spinor of Bloch vector $\mathbf{s}$ give

$${\Psi }_{\mathbf{s}}(\mathbf{r},t)={\displaystyle \frac{e^{-{\mathbf{r}}^2/\left(2{\ell }^2\right)}}{{\pi }^{3/4}{\ell }^{3/2}}}{\chi }_{\mathbf{s}}{e}^{-3i\omega t/2}.\left(5\right)$$

Use the Pauli guidance current including its magnetization term,

$${\mathbf{v}}_{\mathbf{s}}={\displaystyle \frac{\hslash }{m}}{\displaystyle \frac{Im({\Psi }^{†}\nabla \Psi )}{{\Psi }^{†}\Psi }}+{\displaystyle \frac{\hslash }{2m}}{\displaystyle \frac{\nabla \times \left({\Psi }^{†}\sigma \Psi \right)}{{\Psi }^{†}\Psi }}=\omega \mathbf{s}\times \mathbf{r}.\left(6\right)$$

The current choice is part of the model. Its relation to the nonrelativistic limit of Dirac guidance is established work (Holland and Philippidis 2003); circulating trajectories for a stationary spinor are not a new observation. For $\mathbf{s}=\pm \widehat{\mathbf{z}}$ the trajectories rotate in the $xy$ plane. For $\mathbf{s}=\pm \widehat{\mathbf{x}}$, the coordinate x remains constant. Initial positions follow $|{\varphi }_0{|}^2$. The oscillator is an effective nonrelativistic model, with characteristic speed $\omega \ell$ small compared with c when $\hslash \omega \ll m{c}^2$.

Let $B_L=\{\mathbf{r}:x\ge L\}$, with $u=L/\ell >0$, and define the detector-free first-entry time

$${\tau }_0=inf\{t\ge 0:\mathbf{Q}\left(t\right)\in B_L\},T={\displaystyle \frac{2\pi }{\omega }}.\left(7\right)$$

The subscript emphasizes that no detector is present in this calculation. A particle initially in $B_L$ has ${\tau }_0=0$; one that has not entered by T receives record ⌀. Neither category is discarded. The Gaussian tails are retained rather than silently replaced by a source with compact support.

3.2. Complete First-Entry Laws

For either x orientation, only particles initially in $B_L$ ever enter. For either z orientation, every trajectory with cylindrical radius $R\ge L$ enters within one period. Integrating the ground-state density gives

$$p_X={Pr}_X({\tau }_0\le T)={\displaystyle \frac{1}{2}}erfc\left(u\right),p_Z={Pr}_Z({\tau }_0\le T)=e^{-u^2}.\left(8\right)$$

The complete time distribution can also be obtained. Write $\theta =\omega t$ and $r=R/\ell$. Conditional on $r\ge u$, the initial azimuth is uniform. The fraction of initial angles whose trajectories have entered by time t is

$$min\left\{1,{\displaystyle \frac{2arccos(u/r)+\theta }{2\pi }}\right\}.$$

Integration against $2r{e}^{-r^2}dr$ gives the cumulative distribution. Its continuous density per unit $\theta$ is

$$f_Z\left(\theta \right)=\left\{\begin{array}{cc}{e}^{-u^2}/\left(2\pi \right),\hfill & 0<\theta \le \pi ,\hfill \\ \left[e^{-u^2}-e^{-u^2/{cos}^2(\theta /2)}\right]/\left(2\pi \right),\hfill & \pi <\theta <2\pi ,\hfill \\ 0,\hfill & \mathrm{otherwise}.\hfill \end{array}\right.\left(9\right)$$

There is also an atom of mass $p_X$ at zero and a no-entry atom of mass $1-p_Z$. The X law has the same zero-time atom, no continuous part, and no-entry mass $1-p_X$. Reversing either spin changes the direction of rotation but not these laws. Equation (9) integrates to $p_Z-p_X$; multiplication by $\omega$ converts its density to physical time.

Write $Q_Z,Q_X$ for these complete hypothetical record laws. With total variation defined as $TV(P,Q)={sup}_A|P\left(A\right)-Q\left(A\right)|$, their distance is exactly

$$TV(Q_Z,Q_X)=\Delta \left(u\right)=e^{-u^2}-{\displaystyle \frac{1}{2}}erfc\left(u\right).\left(10\right)$$

The event ${\tau }_0\le T$ attains this distance. The two laws share their initial atom; the continuous mass gained by $Q_Z$ equals the no-entry mass lost. Thus the discrepancy does not arise solely from how particles initially beyond the plane are treated.

At $u=1$, $p_Z=0.367879$, $p_X=0.078650$, and $\Delta =0.289230$. Differentiation yields

$${\Delta }^{\prime }\left(u\right)=e^{-u^2}\left({\displaystyle \frac{1}{\sqrt{\pi }}}-2u\right),u_{*}={\displaystyle \frac{1}{2\sqrt{\pi }}},\Delta \left(u_{*}\right)\simeq 0.578539.\left(11\right)$$

This is the geometry that maximizes the mathematical discrepancy in the specified model. It need not maximize experimental feasibility: moving the plane changes the initially occupied region and the demands on state and detector calibration.

3.3. A Sharp Obstruction to a Common Readout

Let $P_{\mathbf{s}}^E$ be the actual law of a common POVM for each of the four pure-spin preparations, and let $Q_{\mathbf{s}}$ be its detector-free target law. Equation (3) implies that their two averaged actual laws have a common value P. Convexity and the triangle inequality give

$$\underset{\mathbf{s}\in \{\pm \widehat{\mathbf{z}},\pm \widehat{\mathbf{x}}\}}{max}TV(P_{\mathbf{s}}^E,Q_{\mathbf{s}})\ge {\displaystyle \frac{\Delta \left(u\right)}{2}}.\left(12\right)$$

For completeness, if all four errors were at most r, averaging each pair would put P within r of both $Q_Z$ and $Q_X$. Equation (10) would then imply $\Delta \le 2r$. Equality is achievable in the unrestricted POVM class: the state-independent measure

$$E\left(dz\right)=\frac{1}{2}[Q_Z\left(dz\right)+Q_X\left(dz\right)]I\left(13\right)$$

has error $\Delta /2$ for all four states. This device is simply a randomized record generator. Its existence proves sharpness of the approximation radius; it does not make it a measurement of the individual first-entry time, nor show that an absorbing detector attains the radius.

Equation (12) instantiates the established arrival-time approximation obstruction (Goldstein, Tumulka, and Zanghì 2024a). The exact value for the present complete record law is $0.144615$ at $u=1$. Even an arbitrarily complicated common detector therefore cannot approach all four free laws with smaller worst-case total-variation error within quantum instrument theory. Improving temporal resolution alone cannot repair this failure.

4. One Explicit Detector for Both Ensembles

4.1. A Normalized First-Click Instrument

To compare records directly, switch on a spin-independent detector in $B_L$ at $t=0$. Use the ideal Markov detection-rate operator

$$\Gamma =\kappa \Theta (x-L),K_t=exp\left[\left(-{\displaystyle \frac{i{H}_0}{\hslash }}-{\displaystyle \frac{\Gamma }{2}}\right)t\right],\kappa >0.\left(14\right)$$

The exponential contains the sum of the noncommuting generators. The no-click evolution $K_t$ determines the first-click and no-click effects,

$$E\left(dt\right)=K_t^{†}\Gamma K_{t}dt,E(⌀)=K_T^{†}{K}_T.\left(15\right)$$

They are positive and normalized because

$$-{\displaystyle \frac{d}{dt}}\left(K_t^{†}{K}_t\right)=K_t^{†}\Gamma K_t,{\int }_0^{T}E\left(dt\right)+E(⌀)=I.\left(16\right)$$

The spin factor is $I_2$ throughout. A jump into a recorded sink supplies one realization; the lost no-click norm is counted as detection probability. Effective non-Hermitian descriptions of monitored quantum dynamics are well established (Dubey, Bernardin, and Dhar 2021). Here (14)–(16) define the detector approximation explicitly. They do not postulate fundamental collapse, nor identify absorption in an effective wave equation with an unperturbed Bohmian crossing.

For the initial spatial ground state, the cumulative click probability is

$$G\left(t\right)=1-\parallel K_t{\varphi }_0{\parallel }^2.\left(17\right)$$

It is the same for both ensembles and all four spin orientations. At finite $\kappa$, $G\left(0\right)=0$ and $G^{\prime }\left(0\right)=\kappa p_X$: the detector has a finite initial click rate, whereas the free law has an atom at zero. The more consequential disagreement persists over the full observation window.

4.2. Calculation and Physical Consequence

Separability reduces (17) to evolution in the x oscillator. In units $\hslash =m=\omega =1$, expand in its normalized Hermite functions $h_n$. With $N_b$ retained basis states, the generator has matrix elements

$$A_{mn}=-i(n+\frac{1}{2}){\delta }_{mn}-{\displaystyle \frac{k}{2}}{D}_{mn},D_{mn}={\int }_u^{\infty }{h}_m\left(q\right)h_n\left(q\right)dq,k={\displaystyle \frac{\kappa }{\omega }}.\left(18\right)$$

Starting from the ground-state vector $e_0$, the computed endpoint is $G\left(T\right)=1-\parallel e^{2\pi A}{e}_0{\parallel }^2$. Table 1 reports the result. The last column measures basis sensitivity, not a rigorous bound on the continuum truncation error. Numerical details and executable checks are provided in the Appendix and accompanying calculation files.

At $k=1$, the endpoint nearly agrees with the Z free-arrival probability. Taken alone, that agreement could seem to validate the free-arrival readout. The paired X preparation defeats the inference: the detector still gives $0.370007$, while the target becomes $0.078650$. Changing the detector strength also changes the common law. In this calculation, increasing k from 4 to 16 decreases the endpoint click probability. Stronger absorption therefore cannot simply be equated with a more faithful reading of the undisturbed path.

This detector is a controlled theoretical example. A specific implementation would require a physical derivation of the rate operator, switch-on behavior, spatial resolution, and relevant unwanted couplings. Those details can change Table 1, but any common instrument still obeys (3). The empirical relevance of first-detection distributions is already demonstrated elsewhere: Ryan and colleagues measured first-passage distributions of trapped-ion energy using stroboscopic projective measurements (Ryan et al. 2026). Their experiment concerns energy thresholds and a different monitoring protocol; it does not measure the spatial free-entry variable used here.

Figure 1. (a) Free first-entry cumulative distributions and common-detector click probabilities at $u=1$. Each detector curve applies to both ensembles. The free laws include their initial zero-time atom; the detector curves begin at zero. (b) Exact total-variation discrepancy and sharp common-law approximation radius as the plane position varies. Detector curves use 256 oscillator basis states; the free curves are analytic.

Figure 1. (a) Free first-entry cumulative distributions and common-detector click probabilities at $u=1$. Each detector curve applies to both ensembles. The free laws include their initial zero-time atom; the detector curves begin at zero. (b) Exact total-variation discrepancy and sharp common-law approximation radius as the plane position varies. Detector curves use 256 oscillator basis states; the free curves are analytic.

5. A Test That Includes Finite Samples and Calibration

5.1. The Hypotheses That the Counts Can Distinguish

Coarsen each complete record to $Y=1$ for a click by T and $Y=0$ otherwise. Let $p_Z^{\mathrm{rec}}$ and $p_X^{\mathrm{rec}}$ be the corresponding record probabilities and $D=p_Z^{\mathrm{rec}}-p_X^{\mathrm{rec}}$. The common-instrument prediction is $D=0$. The proposed rule equating recorded first detection with detector-free first entry predicts $D=\Delta \left(u\right)$.

Thus the proposed experiment distinguishes an observation rule from the common-instrument prediction. It does not separate equilibrium Bohmian mechanics from ordinary quantum theory, since both satisfy the latter. A nonzero contrast exceeding justified uncertainties would call at least one assumption of the common comparison into question. It would not by itself identify which interpretation or new dynamics supplied the correct replacement.

Preparation and detector mismatches can be bounded operationally. If

$${ϵ}_p=\frac{1}{2}{\parallel {\overline{\rho }}_Z-{\overline{\rho }}_X\parallel }_1,{ϵ}_d=\underset{\rho }{sup}TV({\mathcal{M}}_Z\left(\rho \right),{\mathcal{M}}_X\left(\rho \right)),\left(19\right)$$

where ${\mathcal{M}}_Z,{\mathcal{M}}_X$ are the actual record channels, then contractivity and the triangle inequality give

$$TV(P_Z,P_X)\le {ϵ}_p+{ϵ}_d,\left|D\right|\le ϵ=min\{1,{ϵ}_p+{ϵ}_d\}.\left(20\right)$$

Relevant source–environment correlations must either be included in the input state or covered by the instrument uncertainty. Spin tomography alone does not bound uncontrolled spatial differences or information about the preparation reaching the detector. Nor do a few matching calibration statistics automatically give an upper bound on trace distance. Such a bound needs a justified preparation model, adequate state characterization, or a direct bound on the particular record contrast. The uncertainty budget must state what it covers.

For a conservative comparison, suppose the common-instrument family obeys $D\le ϵ$ and a specified free-arrival readout family obeys $D\ge \Delta -ϵ$. The latter allowance requires its own control of geometry and preparation errors; it does not follow from the quantum-channel bound alone. The common symbol $ϵ$ denotes a bound on the contrast error for each hypothesis family. If the available error bound is instead b for each arm separately, the corresponding contrast allowance is $2b$.

5.2. A Uniform Sufficient Sample Size

Take n independent trials from each ensemble and let $\widehat{D}={\widehat{p}}_Z-{\widehat{p}}_X$. Hoeffding’s inequality for the $2n$ bounded, signed Bernoulli contributions gives

$$Pr(\widehat{D}-D\ge t)\le e^{-n{t}^2},Pr(D-\widehat{D}\ge t)\le e^{-n{t}^2}.\left(21\right)$$

This bound does not require equal variances (Hoeffding 1963). Reject the common-instrument family when

$$\widehat{D}>ϵ+\sqrt{{\displaystyle \frac{log(1/\alpha )}{n}}}.\left(22\right)$$

The false-positive probability is at most $\alpha$. If $\Delta >2ϵ$, a sufficient condition for power at least $1-\beta$ throughout the stipulated free-arrival family is

$$n\ge ⌈{\displaystyle \frac{{\left[\sqrt{log(1/\alpha )}+\sqrt{log(1/\beta )}\right]}^2}{{[\Delta \left(u\right)-2ϵ]}^2}}⌉.\left(23\right)$$

Equation (23) is a conservative guarantee, not an optimal sample-size claim. It follows by making the smallest separation of the families, $\Delta -2ϵ$, exceed the sum of the two concentration margins. If $\Delta \le 2ϵ$, the contrast ranges overlap: increasing n cannot give uniform discrimination of these composite families from this statistic alone.

As an illustrative design, set $u=1$, $ϵ=0.02$, $\alpha =0.04$, and $\beta =0.20$. Then (23) gives $n=152$ per ensemble, or 304 science trials, and (22) has threshold $\widehat{D}>0.165523$. No calibration cost is included in that count. If an independent calibration procedure supplies the required bounds with failure probability at most $\gamma =0.01$, the overall false-positive probability is at most $0.05$ by a union bound. Unconditional power is at least $1-\beta -\gamma =0.79$ when the calibration guarantee also covers the stated alternative. The numerical value $0.02$ is an assumed achievable error budget, not a reported detector performance.

Table 2 shows how geometry changes this sufficient count. The rapid increase at larger u results from a shrinking separation after subtracting the same uncertainty budget. A design with more scientific trials but unchanged systematic uncertainty eventually ceases to help. Calibration and geometry are therefore part of the discrimination problem rather than corrections applied after it.

6. Universal Unitary Evolution and Genuine Collapse

6.1. A Common Memory and a Common Interference Measurement

The arrival-time comparison tests a proposed relation between trajectories and records. A second comparison concerns a physical loss of coherence. Everettian quantum mechanics retains unitary evolution for the measured system and its memory (Everett 1957). A specified objective-collapse model can suppress coherence between their branches. These alternatives can disagree about a later interference experiment, provided that the relevant coherence remains accessible. A state update made on learning an outcome is not, by itself, the additional physical process required for this comparison.

Let $|0_L\rangle =|0\rangle |M_0\rangle$ and $|1_L\rangle =|1\rangle |M_1\rangle$ be orthogonal states of a system and a controllable memory. After an ideal premeasurement, take the joint state with an uncontrolled environment to be $\left(\right|0_L\rangle |e_0\rangle +|1_L\rangle |e_1\rangle )/\sqrt{2}$. The reduced states assigned by unitary evolution and by a model that additionally attenuates branch coherence by $r\in [0,1]$ are

$${\rho }_U={\displaystyle \frac{1}{2}}\left(\begin{array}{cc}1& \chi \\ {\chi }^{*}& 1\end{array}\right),{\rho }_C={\displaystyle \frac{1}{2}}\left(\begin{array}{cc}1& r\chi \\ r{\chi }^{*}& 1\end{array}\right),\chi =\langle e_1|e_0\rangle .\left(24\right)$$

Both predict equal probabilities for reading $0_L$ or $1_L$. If joint interference measurements on the system and memory are available, diagonalizing their difference gives

$$\frac{1}{2}{\parallel {\rho }_U-{\rho }_C\parallel }_1={\displaystyle \frac{(1-r)\left|\chi \right|}{2}},P_{\mathrm{success}}^{\mathrm{opt}}={\displaystyle \frac{1}{2}}+{\displaystyle \frac{(1-r)\left|\chi \right|}{4}}.\left(25\right)$$

The second expression is the equal-prior, single-copy discrimination probability for known states (Helstrom 1976). The optimal measurement resolves the relative phase of the two logical branches. Restricting the available effects to the diagonal algebra instead gives zero distinguishability, even when the full trace distance is nonzero. If an inaccessible environment carries a perfectly distinguishing record, $\chi =0$ and the reduced states coincide. This dependence on retained path information is familiar from interference theory (Englert 1996). Its application to records in Wigner’s-friend scenarios has been developed explicitly by Baumann (Baumann 2023).

Equation (25) is therefore not an experiment that selects Everett over every single-outcome interpretation. Equilibrium Bohmian mechanics also predicts the unitary interference law for the same complete apparatus. The result tests physical coherence and the proposed dynamics of its loss. The experimental constraints reviewed in Section 8.1 have the same interpretive limitation: support for the shared dynamics does not accrue exclusively to one ontology.

6.2. What an Echo Removes and What It Leaves Confounded

An explicit protocol clarifies the ordinary-noise alternative. Prepare $|{+}_L\rangle =\left(\right|0_L\rangle +|1_L\rangle )/\sqrt{2}$ and use a logical echo that swaps both system and memory branches halfway through storage, followed by a final swap restoring the original labeling. In the storage intervals, suppose

$$\dot{\rho }=-{\displaystyle \frac{i\delta }{2}}[Z_L,\rho ]+{\displaystyle \frac{\gamma +\lambda }{2}}(Z_L\rho Z_L-\rho ).\left(26\right)$$

Here $\delta$ is a detuning constant within each trial, $\gamma \ge 0$ is an ordinary Markov dephasing rate, and $\lambda \ge 0$ is the additional effective collapse rate for the selected branch geometry. The latter is not automatically the elementary GRW or continuous-spontaneous-localization parameter; a physical implementation must derive its relation to masses, separation, and localization length. The unitary hypothesis has $\lambda =0$, with ordinary dephasing understood as reduced dynamics arising from an unobserved environment. The rival has $\lambda \ge {\lambda }_{*}>0$.

For Gaussian detuning of mean zero and variance ${\sigma }_{\delta }^2$, the normalized off-diagonal coherence is

$$c_{\mathrm{free}}\left(t\right)=e^{-{\sigma }_{\delta }^2{t}^2/2}{e}^{-(\gamma +\lambda )t},c_{\mathrm{echo}}\left(t\right)=e^{-(\gamma +\lambda )t}.\left(27\right)$$

The echo expression holds for every constant detuning, before averaging over its distribution. It follows from $X_L{Z}_L{X}_L=-Z_L$: the Hamiltonian phases cancel, while the dissipator is invariant under changing $Z_L$ to $-Z_L$. Pulse duration, pulse errors, and time-dependent detuning are omitted from this identity and must be bounded in applying it.

This calculation also supplies an exact identifiability obstruction. Two decompositions $(\gamma ,\lambda )$ and $({\gamma }^{\prime },{\lambda }^{\prime })$ with equal sums define the same generator, hence the same controlled channels and record laws when the preparation and instruments are fixed. Adaptive measurements and additional logical pulses cannot recover the decomposition from those identical channels. If $\gamma \in [{\gamma }_{-},{\gamma }_{+}]$ is allowed under both hypotheses and ${\lambda }_{*}\le {\gamma }_{+}-{\gamma }_{-}$, choose ${\gamma }_U={\gamma }_{-}+{\lambda }_{*}$ and ${\gamma }_C={\gamma }_{-}$. The two hypothesis families then intersect exactly. No test within this model can distinguish them uniformly.

The restriction to the common Markov model is essential. Faster controls that resolve bath memory or additional access to the environment can invalidate that model and change the comparison. Proposals to distinguish ordinary decoherence from modified dynamics by dynamical decoupling already exist (Arenz et al. 2015). The present finite-control example identifies the residual nuisance direction and quantifies what an independent noise bound must accomplish. A failed echo alone is insufficient evidence for collapse.

6.3. A Robust Separation and Its Best Observation Time

After the echo, measure $X_L$. To retain every trial, assign the score $Y=1$ to the positive result, $Y=0$ to the negative result, and $Y=1/2$ to a flagged failure to read the memory. Under a balanced readout model, preparation contrast and outcome-independent efficiency combine into $\nu \in [{\nu }_{-},{\nu }_{+}]$, with $0<{\nu }_{-}\le {\nu }_{+}\le 1$. Let a residual imbalance or other bounded model error change the mean score by $b_M$, with $|b_M|\le b$. The recorded mean is

$${\mu }_M\left(t\right)={\displaystyle \frac{1+\nu e^{-(\gamma +\lambda )t}}{2}}+b_M.\left(28\right)$$

This specifies the observation model rather than conditioning on successful readout. Branch-dependent losses require their own bound within b or an enlarged model. Calibration must also justify the phase of the interference measurement. The quantities ${\nu }_{\pm }$, ${\gamma }_{\pm }$, and b are common allowed ranges, not favorable values chosen separately after inspecting the science data.

For the unitary family $\lambda =0$ and the collapse family $\lambda \ge {\lambda }_{*}$, their nearest mean-score endpoints are

$$L_U\left(t\right)={\displaystyle \frac{1+{\nu }_{-}{e}^{-{\gamma }_{+}t}}{2}}-b,U_C\left(t\right)={\displaystyle \frac{1+{\nu }_{+}{e}^{-({\gamma }_{-}+{\lambda }_{*})t}}{2}}+b.\left(29\right)$$

Thus a sufficient separation, and the exact separation of these interval families when their endpoints lie in $[0,1]$, is

$$g\left(t\right)=L_U\left(t\right)-U_C\left(t\right)={\displaystyle \frac{{\nu }_{-}{e}^{-at}-{\nu }_{+}{e}^{-ct}}{2}}-2b,a={\gamma }_{+},c={\gamma }_{-}+{\lambda }_{*}.\left(30\right)$$

If $c\le a$, then $g\left(t\right)\le 0$ at every time. If $c>a>0$ and the calibration bounds are constant over the time range considered, differentiation gives the unique maximum at

$$t_{*}={\displaystyle \frac{log\left(c{\nu }_{+}/\left(a{\nu }_{-}\right)\right)}{c-a}}.\left(31\right)$$

A positive maximum establishes robust separation for this score. A finite allowed time window requires maximizing over that window; time-dependent error bounds require using their actual dependence in (30). Equation (31) optimizes the gap, and therefore the following sufficient sample bound for equal trial cost. It does not optimize total laboratory time when longer storage makes trials more costly.

For n independent science trials at the chosen time, reject the unitary family when $\overline{Y}<L_U-\sqrt{log(1/\alpha )/\left(2n\right)}$. Hoeffding’s bound applies to the scores in $[0,1]$, including the failure score. Size at most $\alpha$ and power at least $1-\beta$ against the stated collapse family follow if

$$n\ge ⌈{\displaystyle \frac{{[\sqrt{log(1/\alpha )}+\sqrt{log(1/\beta )}]}^2}{2g{\left(t\right)}^2}}⌉,g\left(t\right)>0.\left(32\right)$$

For illustration, choose a time unit $t_0$, $\nu \in [0.88,0.92]$, $\gamma t_0\in [0.01,0.03]$, ${\lambda }_{*}{t}_0=0.08$, and $b=0.005$. Then $t_{*}/t_0=19.0511$, $L_U=0.743450$, $U_C=0.587817$, and $g\left(t_{*}\right)=0.155634$. With $\alpha =0.04$ and $\beta =0.20$, (32) gives 194 science trials and rejection threshold $\overline{Y}<0.652367$. If independent calibration bounds fail with probability at most $0.01$, the overall false-positive probability is at most $0.05$. Calibration trials must be added to the science count; the bounds on $\gamma$ must come from independent physical characterization, since estimating the same echo decay measures only $\gamma +\lambda$. These dimensionless numbers illustrate the calculation and assert no demonstrated apparatus performance.

Figure 2. Robust coherent-memory comparison. The lower edge of the unitary mean-score interval and the upper edge of the collapse interval use the illustrative calibration ranges stated in Section 6.3. Their vertical separation is the gap available to the bounded-score test. The selected time maximizes that gap when the bounds and cost per trial are time independent.

Figure 2. Robust coherent-memory comparison. The lower edge of the unitary mean-score interval and the upper edge of the collapse interval use the illustrative calibration ranges stated in Section 6.3. Their vertical separation is the gap available to the bounded-score test. The selected time maximizes that gap when the bounds and cost per trial are time independent.

6.4. Separating a Collapse Kernel from a Specified Spatial Background

For spatial superpositions, a second control can constrain the effective rate itself. Objective-collapse models modify the evolution and are already studied using statistical estimation and testing (Ghirardi, Rimini, and Weber 1986; Bassi et al. 2013; Marchese et al. 2021; Schrinski, Nimmrichter, and Hornberger 2020). Consider a phenomenological coherence-decay rate at path separations d and $2d$,

$$y\left(d\right)=\eta d^2+{\lambda }_0\left(1-e^{-d^2/\left(4r_c^2\right)}\right)+e\left(d\right).\left(33\right)$$

Here $\eta$ is an unknown quadratic background, ${\lambda }_0$ a localization-rate coefficient, $r_c$ a fixed localization length, and e a residual term. This kernel is an illustrative localization model, not a universal extended-body formula. With $x=d^2/\left(4r_c^2\right)$,

$$C=4y\left(d\right)-y\left(2d\right)={\lambda }_{0}K\left(x\right)+u,K\left(x\right)=3-4e^{-x}+e^{-4x},u=4e\left(d\right)-e\left(2d\right).\left(34\right)$$

The nuisance coefficient cancels, while $K\left(0\right)=0$ and $K^{\prime }\left(x\right)=4(e^{-x}-e^{-4x})>0$ for $x>0$. If the measured contrast has Gaussian error with known standard deviation ${\sigma }_C$ and $\left|u\right|\le B$, a threshold test of ${\lambda }_0=0$ against ${\lambda }_0\ge {\lambda }_{0*}>0$ has size at most $\alpha$ and power at least $1-\beta$ when

$${\lambda }_{0*}K\left(x\right)\ge 2B+[z_{1-\alpha }+z_{1-\beta }]{\sigma }_C.\left(35\right)$$

The variance must include covariance between the component estimates, and B must cover nonquadratic ordinary processes. A spatial control is useful precisely when the background and candidate collapse term respond differently to it. If both have the same dependence over the measured range, the identifiability problem returns. Neither this contrast nor the echo by itself establishes a collapse ontology. Existing spontaneous-radiation searches constrain concrete collapse models through a different observable; their scope and inferential limits are considered in Section 8.1.

7. Different Ontologies and Different Perspectives

7.1. GRW Matter Density and GRW Flashes

GRWm and GRWf provide a comparison independent of the usual opposition between trajectories and orthodox measurement theory. They use the same GRW stochastic wave-function law but posit different matter in space-time: a continuous matter-density field in GRWm and discrete events, or flashes, in GRWf. Their empirical equivalence for ordinary macroscopic records is developed by Allori and colleagues and in the GRW measurement formalism (Allori et al. 2008, 2014; Goldstein, Tumulka, and Zanghì 2012). Identifying a collapse rate would therefore not, on that basis alone, identify which of these ontologies is correct.

The record mapping remains indispensable. To make its role explicit, couple the two descriptions to the same stochastic history h, and let $R_m\left(h\right)$ and $R_f\left(h\right)$ denote their calibrated apparatus records. If the records disagree only on a set with probability at most ${ϵ}_{\mathrm{PO}}$, then for every record event A,

$$|P_m\left(A\right)-P_f\left(A\right)|\le Pr(R_m\ne R_f)\le {ϵ}_{\mathrm{PO}},TV(P_m,P_f)\le {ϵ}_{\mathrm{PO}}.\left(36\right)$$

This elementary coupling bound makes the empirical-equivalence claim conditional on the physically relevant readouts. If the maps agree almost surely, the record laws agree exactly. For n independent repetitions, the bound is at most $1-{(1-{ϵ}_{\mathrm{PO}})}^n$. A shared master equation alone does not prove that the two primitive ontologies display the same outcome; that is why their calibration functions must be examined. Equation (36) does not supply a numerical mismatch bound for realistic GRW apparatuses. It states what a proposed refinement of the macroscopic equivalence argument would have to control.

7.2. Relational Quantum Mechanics and QBism

Relational quantum mechanics makes physical accounts relative to interacting systems (Rovelli 1996). QBism treats a quantum state as an agent’s probability assignment for the consequences of that agent’s actions (Fuchs, Mermin, and Schack 2014). Their disagreement about the significance of a state is substantial, but their names alone do not specify different frequencies for a shared apparatus. An empirical comparison must fix whose accessible records are being predicted, the conditioning information, and how the predictions will be compared. Recent work on Wigner’s-friend scenarios makes the importance of these choices explicit (Del Santo, Manzano, and Brukner 2025).

The memory model supplies a simple check. Copy the branch label into an external orthogonal register R that remains outside the interference operation. The state is then $\left(\right|0_L\rangle |0_R\rangle +|1_L\rangle |1_R\rangle )/\sqrt{2}$. If a final observer measures the logical system in a basis containing $|w\rangle$ and also reads R, the joint law is

$$P(i,w)={\displaystyle \frac{1}{2}}|\langle w|i_L\rangle {|}^2,P(w\mid i)={\left|\langle w|i_L\rangle \right|}^2.\left(37\right)$$

The unitary description and the nonselective collapse description yield the same accessible joint law in this protocol. Summing over i removes the interference term even if nobody reads the external register. Conversely, coherently erasing every copy of the branch label changes the experiment and makes the interference comparison of Section 6 possible. The difference between a conditional prediction and its marginal must not be counted as evidence between interpretations.

Equation (37) is a calculation for a specified shared-record experiment, not a proof that every version of relational quantum mechanics and QBism agrees in every conceivable setting. Relational accounts must explain how perspectives are compared; the cross-perspective proposal of Adlam and Rovelli addresses the case in which the relevant physical record has survived (Adlam and Rovelli 2023). QBist agents need not begin with identical assignments, but a difference arising from different prior information is not a fixed rival dynamical law. To turn either position into a discriminator, one must state incompatible predictions for the same agent or comparison record under matched information and interventions.

Local-friendliness inequalities provide a further, conditional route. Bong and colleagues derive constraints from a conjunction involving absolute observed events, locality, and freedom of settings, and investigate quantum violations (Bong et al. 2020). Rejecting that conjunction can restrict interpretations or their assumptions. It does not single out Everett, relational quantum mechanics, or QBism without an account of which premise each formulation retains and what constitutes an observed event in the implemented experiment. In particular, coherent control of a microscopic memory should not silently be promoted to a demonstration about conscious observers.

Table 3. What the additional comparisons establish. Each judgment refers to the formulations and experimental domain specified in the text. Section 8 considers their bearing on comparative evidential support.

[b]Comparison	[b]Common experiment	[b]Evidential reach
Equilibrium Bohmian mechanics and quantum instrument theory	Matched spin ensembles and one detector	Shared record law; a differing free-arrival readout is tested separately.
Universal unitary evolution and genuine collapse	Coherent-memory echo and identical readout	A positive gap in (30) permits a uniform test; noise can otherwise mask collapse.
GRWm and GRWf	Macroscopic records from the same collapse process	A collapse signal need not distinguish the underlying matter ontology.
Relational quantum mechanics and QBism	One specified comparison record and matched conditioning	Different state meanings alone supply no frequency difference; the shared-record example obeys (37).
Local-friendliness assumptions and quantum predictions	A specified extended Wigner’s-friend protocol	A conjunction of assumptions is tested; an interpretation is not uniquely selected.

Table 3. What the additional comparisons establish. Each judgment refers to the formulations and experimental domain specified in the text. Section 8 considers their bearing on comparative evidential support.

[b]Comparison	[b]Common experiment	[b]Evidential reach
Equilibrium Bohmian mechanics and quantum instrument theory	Matched spin ensembles and one detector	Shared record law; a differing free-arrival readout is tested separately.
Universal unitary evolution and genuine collapse	Coherent-memory echo and identical readout	A positive gap in (30) permits a uniform test; noise can otherwise mask collapse.
GRWm and GRWf	Macroscopic records from the same collapse process	A collapse signal need not distinguish the underlying matter ontology.
Relational quantum mechanics and QBism	One specified comparison record and matched conditioning	Different state meanings alone supply no frequency difference; the shared-record example obeys (37).
Local-friendliness assumptions and quantum predictions	A specified extended Wigner’s-friend protocol	A conjunction of assumptions is tested; an interpretation is not uniquely selected.

8. Discussion: Unequal Evidence Without a Unique Ontology

The calculations distinguish several reasons why an interpretation can remain undecided. A trajectory variable may have been substituted for a detector record; an ordinary noise process may imitate the proposed collapse term; distinct ontologies may produce the same accessible records; or observers may be conditioning on different information. These failures require different remedies. None entails that all formulations deserve equal confidence. Conversely, a calculable difference in a proposed experiment is not itself observed evidence against either rival. The numerical examples above establish conditional comparisons, not experimental preferences.

8.1. What Recent Experiments Disfavor

Two experiments published in 2026 make the distinction concrete. Pedalino and colleagues observed interference of sodium nanoparticles containing more than 7,000 atoms and masses above 170,000 Da (Pedalino et al. 2026). Their observations extend the tested domain of spatial quantum superposition and constrain modifications that would suppress coherence in that regime. They do not test the coherent-memory apparatus specified in Section 6, and their successful description by standard quantum mechanics supplies no unique evidence for Everettian branching.

The XENONnT collaboration used low-energy electronic-recoil data to search for radiation predicted by Markovian continuous-spontaneous-localization and Diósi–Penrose models (Aprile et al. 2026). The analysis strengthened earlier constraints by up to two orders of magnitude for CSL and a factor of five for DP, and excluded values within originally proposed CSL parameter ranges. These results apply to the specified temporal noise and radiation models. They cannot be extended without calculation to every colored-noise, dissipative, or otherwise modified collapse proposal, or treated as a blanket exclusion of the original GRW jump process.

The defensible direction of evidential change is consequently toward standard quantum dynamics relative to the particular modifications that predicted signals the experiments constrain. Surviving collapse parameters require separate assessment. Among interpretations that assign the same ordinary quantum probabilities to these experiments, the observations provide shared confirmation rather than an exclusive advantage. The absence of a unique winner therefore coexists with substantial experimental progress: some physical possibilities have become less tenable even though several accounts of the surviving dynamics remain open.

8.2. Likelihood Equality and Posterior Confidence

Let D denote recorded data from a common protocol and B the background evidence available before those data. For two specified formulations with nonzero prior probabilities, Bayes’ rule gives

$${\displaystyle \frac{P(M_1\mid D,B)}{P(M_2\mid D,B)}}={\displaystyle \frac{P(D\mid M_1,B)}{P(D\mid M_2,B)}}{\displaystyle \frac{P(M_1\mid B)}{P(M_2\mid B)}}.\left(38\right)$$

Equal likelihoods make the Bayes factor one. The data then leave the relative odds unchanged, but need not leave either model’s probability unchanged relative to other rivals. Nor must the odds conditional on B have been equal. Evidence from other domains and reasoned judgments about explanatory adequacy can already distinguish the formulations. This is compatible with their exact record-law equality in the present comparison (Laudan and Leplin 1991; Egg and Saatsi 2021).

A composite model requires a further specification. If $\vartheta$ denotes its physical and nuisance parameters, its marginal likelihood under a proper parameter prior is

$$P(D\mid M,B)=\int P(D\mid \vartheta ,M,B){\pi }_M(d\vartheta \mid B).\left(39\right)$$

Equality of the sets of attainable record laws does not ensure equality of (39): the priors may weight those laws differently. Equality does follow when the two priors induce the same distribution over the common record laws. The frequentist bounds in Sections 5 and 6 avoid such a prior by giving uniform error guarantees over stated uncertainty sets. They do not assign posterior probabilities to interpretations. Likewise, an experimental exclusion region is not a posterior probability that collapse is false. A Bayesian comparison of a collapse family with standard dynamics must specify the parameter prior, account for any mass placed near experimentally indistinguishable limits, and examine the resulting sensitivity.

8.3. How Far a Preference Among Interpretations Can Be Defended

Theoretical scope matters as well as performance in a restricted test. Wallace argues that the success of interacting quantum field theory undermines a general claim of evidential parity between unmodified quantum mechanics and its Bohmian or collapse rivals (Wallace 2023). A formulation cannot claim the entire evidential success of another merely because it reproduces a nonrelativistic sector. This is a substantive argument about the reach of an existing theory, not an additional result of the arrival-time calculation.

There are, however, Bohmian constructions for regularized quantum field theories with particle creation and annihilation (Dürr et al. 2004). Relativistic proposals also explore whether the required space-time foliation can be determined covariantly by the wave function (Dürr et al. 2014). Their existence precludes dismissing Bohmian mechanics simply as unable to address either phenomenon. The disputed questions concern how fully these constructions reproduce realistic interacting field theory, how macroscopic records arise, and what additional structure they require. A fair comparison must examine that scope explicitly rather than assume either universal equivalence or an impossibility theorem.

On criteria that give greatest weight to a universal dynamical law and economy of additional physical postulates, Everett has a defensible conditional advantage over formulations that supplement or modify that dynamics. It applies unitary evolution to the system and apparatus together, with decoherence accounting for the suppression of accessible interference between branches. The resulting branch structure is an interpretive commitment, however, and relating it to experienced outcomes and Born probabilities remains essential to the case for the interpretation (Everett 1957; Greaves and Myrvold 2010). Its merits under those criteria do not constitute a unique experimental signature. In particular, repeated confirmation of a probability law shared with equilibrium Bohmian mechanics does not, by itself, alter their relative odds.

Bohmian mechanics supplies definite configurations as an explicit account of actual outcomes while the wave function retains its dynamical role. Giving greater weight to that account can support a preference for it, provided the quantum-equilibrium rule and the formulation’s physical scope are also defended (Dürr, Goldstein, and Zanghì 1992, 2004). That judgment accepts additional ontology in exchange for a particular explanation of definiteness. The trajectory calculation here establishes neither a failure of its equilibrium predictions nor evidence that its unobserved paths are individually measured.

Bohr-inspired operational accounts, relational quantum mechanics, and QBism also inherit empirical support where they retain the successful record laws. Their distinctive explanatory claims require separate evaluation. “Copenhagen” does not denote one sufficiently precise universal dynamical model to which a single likelihood can be assigned. Relational and QBist descriptions differ in what a state and an outcome signify, but Section 7.2 gives no basis for ranking those meanings by unmatched conditional probabilities. Thus there is a qualified preference available on stated theoretical criteria, and a genuine experimental preference against specified departures from standard dynamics, without an established overall probability ranking of the surviving interpretations.

8.4. What Can Be Identified Despite the Remaining Ambiguity

Let ${\mathcal{M}}_{\mathrm{adm}}$ contain the formulations compatible with the experiment, its uncertainty bounds, and background evidence. For a claim represented by $g\left(M\right)$, define

$$\mathcal{G}=\{g\left(M\right):M\in {\mathcal{M}}_{\mathrm{adm}}\}.\left(40\right)$$

A singleton identifies that claim within the candidate class even if several ontologies survive. This elementary use of partial identification (Manski 2003) complements accounts of quantum knowledge grounded in commitments shared by surviving theories (Egg 2021; Fraser and Vickers 2025). The candidate class must itself be defended. A collapse test may constrain the dynamical rate without identifying primitive ontology; a shared-record test may constrain the observation rule without deciding whether a state is ontic, relational, or personal. Scientific progress can therefore consist in identifying a physical claim that survives the remaining interpretive disagreement, as well as in eliminating a rival.

9. Conclusions

The degree to which interpretations of quantum theory are empirically distinguishable depends on their complete predictions for accessible records. The paired-arrival calculation demonstrates a large difference between unobserved trajectory statistics alongside exact equality of the common-detector laws. The coherent-memory calculation shows a different possibility: genuine collapse and a specified unitary account can be distinguished, but only when ordinary noise and readout uncertainty leave a positive separation. Within the common Markov model, an equal total dephasing rate defeats every allowed control strategy aimed solely at separating its ordinary and collapse contributions.

These results extend beyond an opposition between Bohmian and orthodox descriptions. GRWm and GRWf illustrate how agreement of records can survive a change in ontology even after collapse dynamics has been detected. Relational and QBist accounts require a common specification of conditioning and comparison records before differing state assignments become rival empirical predictions. Local-friendliness tests constrain assumption packages without automatically identifying one interpretation.

Recent interference and radiation searches make the evidential position uneven: specified collapse dynamics are constrained while the successful quantum predictions continue to receive support. That support is shared wherever rival interpretations assign the same record laws. A preference for Everett on grounds of universal unitary dynamics, or for Bohmian mechanics on grounds of definite configurations, requires those criteria to be stated and the formulations’ wider adequacy to be examined. Neither preference is an experimental verdict supplied by the comparisons here.

The scientific task is to identify where complete formulations disagree about a realizable record, determine whether that disagreement survives the allowed uncertainties, and distinguish the resulting evidence from assumptions used to rank the remaining accounts. This permits a substantive assessment of unequal support without claiming that current observations select a unique quantum ontology.

Ethics Approval and Consent to Participate: Not applicable. This theoretical and computational study involved no human participants, human research data, or animals.

   Code Availability: The Python scripts, dependency versions, and instructions needed to reproduce the calculations and figures are included in the accompanying version 4.0 package.

Use of Artificial Intelligence: OpenAI ChatGPT was used for literature discovery and organization, development and checking of mathematical arguments, generation of computational code, numerical verification, and drafting and editing of the manuscript. Its role extended beyond language correction. The derivations, assumptions, and executable calculations are provided for scrutiny. The author retains responsibility for evaluating AI-assisted material and for the accuracy, interpretation, and final submission of the work.