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Implications of Time Dilation Decoherence for Operational Biophysics and for the Spectral Modulation of Catalytic Processes

Jonatan P. camargo

Published Feb 19, 2026• 0 citations
Publisher

Abstract

This work investigates the biophysical implications of a fundamental limit already established in the literature at the interface between quantum mechanics and relativity, namely, the decoherence induced by time dilation in composite systems, formally derived by Pikovski et al. This effect demonstrates that, even in the absence of an external environment, differences in proper time couple the internal and external degrees of freedom of quantum systems, leading to a loss of interferometric coherence as a direct consequence of the relativistic structure of spacetime. The present study does not introduce modifications to this formalism nor proposes new decoherence mechanisms; it starts explicitly from these results as a background physical constraint. Our objective is distinct: to analyze complex molecular systems operating persistently in non-equilibrium regimes — notably biological systems — in light of this universal limit. We propose that biochemical functionality should not be described solely by structural or energetic criteria, as in the classical spatial affinity paradigm (“lock-and-key”), but also by the system's ability to maintain temporal compatibility between its internal modes during finite operational intervals. We term this operational regime the Simultaneity Window, characterizing a dynamic condition of effective coherence sustained by a continuous flow of free energy. In this framework, processes involving the loss of functional viability can be modeled as the transition of the molecular system to the intrinsic decoherence regime predicted by relativistic-quantum theory, occurring when the variance of internal energy ($\Delta E$) exceeds the range compatible with the maintenance of this operational coherence. The notion introduced here does not alter the underlying physical mechanism but identifies a domain in which biochemical systems explore — and need to circumvent — such a limitation. Based on this operational interpretation, we introduce the concept of Chrono-Inhibitors: agents capable of modifying the internal spectral distribution of a target biological system, shifting it in a controlled manner into the effective decoherence regime without requiring direct structural modification. We operationally define a \emph{chrono-inhibitor} as any external perturbation capable of altering the internal spectral variance $\Delta E$ without directly modifying the system's average structure.

DOI
10.5281/zenodo.18689965

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This work investigates the biophysical implications of a fundamental limit already established in the literature at the interface between quantum mechanics and relativity, namely, the decoherence induced by time dilation in composite systems, formally derived by Pikovski et al. This effect demonstrates that, even in the absence of an external environment, differences in proper time couple the internal and external degrees of freedom of quantum systems, leading to a loss of interferometric coherence as a direct consequence of the relativistic structure of spacetime. The present study does not introduce modifications to this formalism nor proposes new decoherence mechanisms; it starts explicitly from these results as a background physical constraint. Our objective is distinct: to analyze complex molecular systems operating persistently in non-equilibrium regimes — notably biological systems — in light of this universal limit. We propose that biochemical functionality should not be described solely by structural or energetic criteria, as in the classical spatial affinity paradigm (“lock-and-key”), but also by the system's ability to maintain temporal compatibility between its internal modes during finite operational intervals. We term this operational regime the Simultaneity Window, characterizing a dynamic condition of effective coherence sustained by a continuous flow of free energy. In this framework, processes involving the loss of functional viability can be modeled as the transition of the molecular system to the intrinsic decoherence regime predicted by relativistic-quantum theory, occurring when the variance of internal energy (ΔE\Delta EΔE) exceeds the range compatible with the maintenance of this operational coherence. The notion introduced here does not alter the underlying physical mechanism but identifies a domain in which biochemical systems explore — and need to circumvent — such a limitation. Based on this operational interpretation, we introduce the concept of Chrono-Inhibitors: agents capable of modifying the internal spectral distribution of a target biological system, shifting it in a controlled manner into the effective decoherence regime without requiring direct structural modification. We operationally define a \emph{chrono-inhibitor} as any external perturbation capable of altering the internal spectral variance ΔE\Delta EΔE without directly modifying the system's average structure.
This work presents an exploratory conceptual analysis of the possible biophysical implications of fundamental coherence limits arising from gravitational time dilation. The objective is to investigate, at a phenomenological level, whether complex biological processes can operate in regimes sensitive to decoherence mechanisms already predicted by relativistic quantum theory. The study builds upon results established by Pikovski et al. regarding time dilation-induced decoherence, utilizing them exclusively as a background physical limit. No modification or extension of this formalism is proposed. The contribution of the present work consists of examining how such limits might be operationally relevant in the description of non-equilibrium molecular systems, particularly in enzymatic contexts and intracellular dynamics. In this context, we introduce the notion of spectral modulation of the internal energy variance (ΔE\Delta EΔE) as an effective parameter to experimentally test the functional sensitivity of biological systems to these physical limits. The hypothesis is formulated in a falsifiable manner, with suggestions for verification based on time-resolved spectroscopic and structural techniques. The manuscript has an exploratory and interdisciplinary character, situated at the interface between fundamental physics, biophysics, and molecular chemistry, and intends to serve as a starting point for further theoretical and experimental investigations, without claiming the existence of macroscopic quantum coherence in living systems.
Recent models have demonstrated that quantum superpositions undergo inevitable decoherence due to gravitational time dilation, even in the absence of external classical environments. In this work, we show that such results can be naturally misinterpreted within the context of General Relativity as a Quantum Theory (GRQT) as a consequence of the geometric spectral stability of spacetime. Without modifying the known dynamic formalism, we interpret the decoherence time as an operational coherence limit imposed by the spectral discretization of geometry. The approach remains conservative, introduces neither new fields nor collapse mechanisms, and suggests experimental regimes where the effect can be tested.
Abstract We investigate the emergence of an operational temporal limit for coherent recombination in globally unitary quantum dynamics. Using numerical interferometric simulations, we introduce an operational notion of temporal compatibility defined through the decay of interferometric visibility, without invoking wavefunction collapse, classical noise, or external dissipation. Through systematic numerical simulations of a minimal unitary model with a finite internal sector, explicitly formulated in interferometric terms, we show that temporal compatibility exhibits qualitatively distinct dynamical regimes. In systems with low spectral density, coherence losses are transient and compatibility remains recoverable through spontaneous revivals. By contrast, when temporal incompatibility is distributed across an internal sector with sufficiently dense spectral structure, the visibility decays without relevant revivals, and a well-defined compatibility timescale, Δτcompat, becomes operationally accessible. We demonstrate that this emergent timescale is statistically robust, invariant under changes in microscopic clock dynamics, and controlled by collective spectral properties rather than by subsystem-specific parameters. In the post-compatibility regime, Δτcompat obeys a simple scaling law governed by an effective collective parameter combining coupling strength and spectral dispersion. These results provide a concrete mechanism for the emergence of operational irreversibility within globally unitary systems and establish temporal compatibility as a meaningful dynamical notion. More broadly, they support interpretations in which effective temporal horizons arise from internal dynamical structure rather than from fundamental state reduction or observer-dependent processes.
We present a unified metric framework describing the loss of spatial interference visibility in relativistic quantum superposition states driven by path-dependent proper-time mismatch. By condensing special-relativistic kinematic time dilation and general-relativistic gravitational redshift into a single, dimensionless differential proper-time rate parameter, ∆τ̇ ≡ |∆Φ/c² − v∆v/c²|, we trace the evolution of spatial trajectories coupled to an internal clock ensemble. Using the reduced density matrix formalism and tracing over internal degrees of freedom, we show that a continuous internal energy dispersion ∆E generates path-discriminating phase information. Evaluating the Fourier transform of a Gaussian spectrum yields an exact, closed-form expression for the spatial coherence envelope decay, defining the characteristic coherence timescale τG = ℏ/(∆E · ∆τ̇). We delineate the physical boundary of this framework: elementary point particles lacking internal energy variance (∆E = 0) experience a deterministic relative phase shift while retaining full quantum contrast, whereas composite systems (∆E > 0) undergo spatial decoherence through relativistically induced path distinguishability. Finally, we demonstrate that expanding the rest-mass phase factor exp(−imc²τ/ℏ) in the weak-field, low-velocity limit naturally yields the time-dependent Schrödinger equation, confirming full compatibility with standard non-relativistic quantum mechanics.
In this work, we study the emergence of relativistic effects in a composite quantum clock within the Page-Wootters relational formulation of quantum mechanics. We consider a system with internal and center-of-mass degrees of freedom and analyze the conditioned evolution of the center-of-mass relative to the internal system treated as an internal clock. We show that the internal sector exhibits an effective time dilation. Retaining the full mass-energy structure of the composite particle, a back-reaction of the internal energy on the center-of-mass sector appears through an operator-valued normalization factor. As a direct consequence of the back-reaction, the conditioned center-of-mass dynamics is governed by a Schroodinger equation that is non-local in the clock time, with an effective temporal non-locality of the order of the Compton time of the composite system. Applying the formalism to a center-of-mass momentum superposition, we find that the interferometric visibility acquires a correction that is quadratic in the internal energy, and therefore depends on the absolute distribution of clock energies rather than only on the energy gaps that control the standard time-dilation dephasing. Although this correction is parametrically small, it is a generic feature of relativistic composite clocks and can, in principle, be isolated through a differential visibility measurement comparing clocks with equal transition frequency but different mean internal energies.
The possibility of distinct physical systems remaining dynamically compatible over time is often implicitly assumed in various areas of physics, from interferometric descriptions to clock comparisons and the analysis of composite systems. In this work, we show that such continuous compatibility is not a generic property but encounters a structural limitation that stems directly from the variational formulation of dynamics. Starting from only minimal hypotheses—the existence of an accumulative action, monotonic proper parametrizations, and operational dependence on action differences via factors eiS/ℏe^{iS/\hbar}eiS/ℏ—we demonstrate that dynamically independent systems cannot maintain functional coincidence of their actions over open intervals, except under fine-tuning. Consequently, moments of compatibility form a necessarily discrete set, and any coherent coupling is effective only within a time scale determined by the difference between the rates of action accumulation. The result does not depend on a specific microscopic model, nor on dissipative, statistical, or environmental mechanisms, being consistent with classical mechanics, relativity, and quantum field theory. It is shown, in particular, that effects such as the loss of interferometric visibility associated with time dilation can be understood as physical realizations of a more general constraint: the structural incompatibility between evolutions parameterized by distinct actions. Thus, the so-called ``compatibility window'' does not constitute a new dynamic principle, but an inevitable consequence of the variational architecture common to established physical theories.