Tlalpan Interpretation (QTI)

• Tlalpan Interpretation (QTI) is a framework that redefines wavefunction collapse as an emergent phase transition akin to spontaneous symmetry breaking in statistical physics.
• It introduces measurable order parameters—amplification fraction, record asymmetry, and retrocausal coherence time—to model the quantum-classical transition and test experimental predictions.
• By integrating retrocausal boundary conditions with time-symmetric microscopic dynamics, QTI offers a physically motivated explanation for irreversible quantum measurement outcomes.

The Tlalpan Interpretation (QTI) is a contemporary framework for quantum measurement, collapse, and quantum-classical transition. It integrates concepts from statistical physics—particularly phase transitions and critical phenomena—into the analysis of wavefunction collapse, reinterpreting it as an emergent process driven by amplification and record formation instead of as a primitive postulate. Distinctive in its incorporation of measurable order parameters and its treatment of time symmetry and retrocausal boundary conditions, QTI seeks to provide both a physically motivated and experimentally testable account of quantum measurement irreversibility.

1. Conceptual Foundations: Collapse as Spontaneous Symmetry Breaking

QTI posits that wavefunction collapse is a manifestation of spontaneous time-symmetry breaking, akin to phase transitions in condensed matter systems. Standard unitary quantum evolution governed by the Schrödinger equation,

$i \hbar \frac{\partial \Psi}{\partial t} = H \Psi,$

is invariant under time reversal, admitting both retarded (forward-in-time) and advanced (backward-in-time) solutions. Collapse arises when microscopic, time-symmetric quantum fluctuations are amplified into macroscopic, irreversible records, analogous to the emergence of long-range order in magnetization below the Curie temperature. The process is driven by crossing a critical threshold in a system-specific control parameter—termed the amplification fraction ($\chi$).

This perspective dispenses with the need for collapse as a primitive axiom. Instead, it locates the onset of irreversibility at the critical point where amplified records spontaneously pick a temporal direction, thereby granularizing smooth, time-symmetric trajectories into discrete histories.

2. Order Parameters and Experimental Accessibility

The interpretation introduces three main measurable quantities serving as order parameters for the quantum-to-classical transition:

Parameter	Formula/Definition	Physical Role
Amplification Fraction ($\chi$)	$\chi = N_{\text{measured}} / N_{\text{total}}$	Fraction of events amplified into records
Record Asymmetry ($O$)	$$O = \frac{1}{2}\left[D_{\text{KL}}(p_{\text{forward}}||p_{\text{backward}}) + D_{\text{KL}}(p_{\text{backward}}||p_{\text{forward}})\right]$$	Quantifies time-directional irreversibility
Retrocausal Coherence Time ($\tau_{\text{RC}}$)	Temporal scale for future boundary condition influences	Correlation length for retrocausality

The Kullback–Leibler divergences compare probability distributions of measurement records evolving forward and backward in time. $O=0$ signals time-symmetry; $O>0$ indicates irreversibility due to collapse. $\tau_{\text{RC}}$ measures the duration over which retrocausal effects are statistically relevant: it is finite for $\chi<\chi_c$, diverges at the critical point $\chi=\chi_c$, and vanishes for classical regimes ($\chi>\chi_c$).

Experimentally, these parameters allow direct tuning and observation of the quantum-classical transition, such as adjusting amplification in photon detection or analyzing interference versus record formation.

3. Time Symmetry, Retrocausality, and Boundary Conditions

QTI maintains the time symmetry of quantum evolution at the microscopic level but introduces retrocausal boundary constraints to account for quantum correlations and apparent nonlocality. In the regime below the critical amplification threshold, the system’s quantum state is sensitive not just to its past initial condition but also to future boundary conditions. This is formalized by the Aharonov–Bergmann–Lebowitz (ABL) statistical rule:

$$P(a_k \mid i, f) = \frac{|\langle f | P_k | i \rangle|^2}{\sum_j |\langle f | P_j | i \rangle|^2},$$

describing the probability of an intermediate outcome conditioned on both initial ($|i\rangle$) and postselected final ($|f\rangle$) states.

Amplification above the critical threshold ($\chi > \chi_c$) suppresses retrocausal influences, enforcing a forward-only arrow of time and classical behavior at the macroscopic level. Spatial locality is preserved: nonlocal correlations (such as in Bell-type experiments) are attributed to global boundary constraints rather than to action-at-a-distance.

4. Phase Transition Phenomenology and Scaling Laws

Collapse, in QTI, exhibits the critical scaling characteristic of phase transitions:

• Order parameter for irreversibility (Record Asymmetry): $O \sim (\chi - \chi_c)^{\beta}$
• Interference visibility: $V \sim |\chi - \chi_c|^{\nu}$
• Retrocausal coherence time: $\tau_{\text{RC}} \sim |\chi - \chi_c|^{-\gamma}$

$\beta, \nu, \gamma$ are critical exponents theoretically universal and independent of underlying system details. At $\chi < \chi_c$, interference persists and retrocausal effects are pronounced; at $\chi = \chi_c$, a sharp transition occurs abolishing interference and retrocausality; and for $\chi > \chi_c$, the system is classical, irreversibly recording outcomes.

This analogy with symmetry breaking in statistical mechanics supplies a physical narrative for collapse: it is neither mystical nor instantaneous but a collective, threshold-driven process.

5. Testable Predictions and Experimental Manifestations

QTI yields distinct experimental predictions:

• Threshold-like disappearance of interference: Interference fringes in e.g. one-photon double-slit experiments persist for $\chi < \chi_c$ but abruptly vanish as amplification exceeds the critical value.
• Enhanced decay of time reversal fidelity in chaotic cavities: The Loschmidt echo,

$$F_{TR}(t) = |\langle \Psi(0) | U^\dagger(t) U(t) | \Psi(0) \rangle|^2,$$

decays anomalously rapidly in chaotic systems, consistent with faster approach to irreversibility due to intrinsic amplification—even absent environmental decoherence.

• Distinct interference patterns in time-symmetric diffraction: In a time-symmetric extension of Moshinsky’s diffraction experiment (shutter opens and closes), QTI predicts the appearance of new fringes for $\chi < \chi_c$, described by

$$\psi(x, t) = \psi_{\text{ret}}(x, t) + \alpha(\kappa)\, \psi_{\text{adv}}(x, t; \tau),$$

where $\alpha(\kappa) \rightarrow 1$ below threshold and $\alpha(\kappa) \rightarrow 0$ above.

These sharp transitions contrast with the gradual decoherence expected from standard interpretations, allowing discrimination in experiment.

6. Theoretical and Foundational Implications

Acceptance of QTI’s predictions has significant consequences:

• Collapse would be explicable as a physical phase transition involving amplification and record creation, not as a primitive rule.
• The quantum-classical transition gains a rigorous, testable structure grounded in statistical physics.
• Bell-type quantum correlations are ascribed to retrocausal boundary conditions rather than spatial nonlocality.
• The removal of the "collapse postulate" offers a unified account reconciling microscopic time symmetry with macroscopic irreversibility.

More broadly, QTI may inform foundational debates—such as the interpretation of measurement, causality, and the observer’s role—by providing operational definitions for quantum records and the quantum-classical boundary.

7. Relation to Other Interpretative Frameworks

QTI, by its explicit extension of minimal quantum theory via new postulates (measurable order parameters, retrocausal conditions, and amplification-induced symmetry breaking), satisfies the requirements for a genuine interpretation of quantum mechanics as laid out in (Muller, 2014). It moves beyond hermeneutic reinterpretation and semantic reformulation, instead providing a logically stronger theory with new vocabulary and experimental criteria.

This approach stands in marked contrast with modal, Everettian, and Bohmian interpretations, which extend or modify the Hilbert-space formalism and postulates in pursuit of physical reality but do not typically reframe collapse itself as an emergent thermodynamic phenomenon linked to critical transitions.

Summary

The Tlalpan Interpretation (QTI) establishes collapse as a collective, critical phase transition characterized quantitatively by amplification, record asymmetry, and retrocausal coherence time. Its central tenet—spontaneous time-symmetry breaking driven by the formation of persistent, irreversible records—offers a physically motivated and experimentally distinguishable framework for the quantum-classical interface, linking quantum measurement to the universal language of critical phenomena in statistical physics. QTI aligns with rigorous criteria for interpretational adequacy in quantum mechanics, introduces new testable mechanisms for collapse, and preserves local, time-symmetric microscopic dynamics subject to global boundary constraints.