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arXiv:0906.5205

Quantum Dynamics With Intrinsic Time Asymmetry and Indistinguishable Events

Peter William Bryant

Published Jun 29, 2009• 0 citations
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Abstract

The extrinsic quantum mechanical arrow of time is understood to be a consequence of the interaction between quantum systems and their environment. A choice of boundary conditions for the Schrödinger equation results in a different time asymmetry intrinsic to quantum mechanical dynamics and independent of environmental interactions. Correct application of the intrinsically asymmetric dynamics, however, leads unavoidably to predictions of the experimental signatures of the extrinsic arrow of time. We are led to a new, model-independent mechanism for quantum decoherence. We need not invoke a master equation or a phase-destroying, non-Hermitian Hamiltonian operator. As an application, we calculate predictive probabilities for the decoherence measured in Rabi oscillations experiments. We can also show that a previously puzzling experimental result, unexplained within the formalism of the quantum master equation, is in fact expected and is the measurable consequence of the indistinguishability of separate, uncontrolled interactions between systems and their environment.

DOI
10.48550/arxiv.0906.5205

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The extrinsic quantum mechanical arrow of time is understood to be a consequence of the interaction between quantum systems and their environment. A choice of boundary conditions for the Schrödinger equation results in a different time asymmetry intrinsic to quantum mechanical dynamics and independent of environmental interactions. Correct application of the intrinsically asymmetric dynamics, however, leads unavoidably to predictions of the experimental signatures of the extrinsic arrow of time. We are led to a new, model-independent mechanism for quantum decoherence. We need not invoke a master equation or a phase-destroying, non-Hermitian Hamiltonian operator. As an application, we calculate predictive probabilities for the decoherence measured in Rabi oscillations experiments. We can also show that a previously puzzling experimental result, unexplained within the formalism of the quantum master equation, is in fact expected and is the measurable consequence of the indistinguishability of separate, uncontrolled interactions between systems and their environment.
With a choice of boundary conditions for solutions of the Schrödinger equation, state vectors and density operators even for closed systems evolve asymmetrically in time. For open systems, standard quantum mechanics consequently predicts irreversibility and signatures of the extrinsic arrow of time. The result is a new framework for the treatment of decoherence, not based on a reduced dynamics or a master equation. As an application, using a general model we quantitatively match previously puzzling experimental results and can conclude that they are the measurable consequence of the indistinguishability of separate, uncontrolled interactions between systems and their environment.
Time asymmetry and irreversibility are signal features of our world. They are the reason of our aging and the basis for our belief that effects are preceded by causes. These features have many manifestations called arrows of time. In classical physics, some of these arrows are described by the increase of entropy or probability, and others by time‐asymmetric boundary conditions of time‐symmetric equations (e.g., Maxwell or Einstein). However, there is some controversy over whether probability or boundary conditions are more fundamental. For quantum systems, entropy increase is usually associated with the effects of an environment or measurement apparatus on a quantum system and is described by the von Neumann‐Liouville equation. But since the traditional (von Neumann) axioms of quantum mechanics do not allow time‐asymmetric boundary conditions for the dynamical differential equations (Schrödinger or Heisenberg), there is no quantum analogue of the radiation arrow of time. In this paper, we review consequences of a modification of a fundamental axiom of quantum mechanics. The new quantum theory is time asymmetric and accommodates an irreversible time evolution of isolated quantum systems.
Suppose a single qubit is repeatedly prepared and evolved under imperfectly-controlled conditions. A drunk model represents uncontrolled interactions on each experimental trial as random or stochastic terms in the qubits Hamiltonian operator. Time evolution of states is generated by a stochastic differential equation whose sample paths evolve according to the Schrödinger equation. For models with Gaussian white noise which is independent of the qubits state, the expectation value of the solution obeys a master equation which is identical to the high-temperature limit of the Bloch equation. Drunk models predict that experimental data can appear consistent with decoherence even if qubit states evolve by unitary transformations. Examples are shown in which reversible evolution appears to cause irreversible information loss. This paradox is resolved by distinguishing between the true state of a system and the estimated state inferred from an experimental dataset.
Quantum decoherence is conventionally understood as an environment-induced loss of phase coherence, described operationally through reduced density matrices and effective noise models. While this framework successfully captures how decoherence occurs, it leaves open the deeper physical question of why quantum phase coherence is generically fragile and lacks intrinsic protection. In this work, we propose a reinterpretation of decoherence within the Temporal Theory of the Universe (TTU), where time is treated as a physical field rather than an external parameter. We argue that decoherence can be understood as a manifestation of temporal-field inhomogeneity: a breakdown of global phase synchronization caused by spatial and temporal gradients of the underlying time field. Within this perspective, environmental noise and non-Markovian effects emerge as effective descriptions of deeper temporal misalignment rather than fundamental sources of randomness. We demonstrate how temporal-field inhomogeneity naturally induces phase damping in the reduced density matrix, leading to decoherence without invoking irreversible information loss. The framework remains fully compatible with standard quantum mechanics at the operational level, while offering a novel physical substrate for coherence, noise, and temporal memory effects. Finally, we outline several experimentally discriminable consequences of this interpretation, positioning it as a falsifiable and conceptually economical extension of existing decoherence theory. Keywords: quantum decoherence; temporal field; foundations of quantum mechanics; open quantum systems; phase coherence; density matrix; Lindblad master equation; non-Markovian dynamics; time as a physical field; quantum foundations. 1.Introduction 1.1.The decoherence problem as a foundational issue in quantum theory 1.2.Standard environmental and information-theoretic interpretations 1.3.Motivation for an alternative physical substrate 1.4.Scope and limits of the present work (interpretational, not engineering) 2. Decoherence in Standard Quantum Theory 2.1 Density matrix formulation and phase damping 2.2 Environment-induced decoherence and pointer states 2.3 Markovian vs non-Markovian regimes 2.4 Conceptual gap: why phase coherence is generically fragile Key point: standard theory describes how decoherence happens, but not why phase coherence lacks physical protection. 3. Temporal Field Framework (TTU Perspective) 3.1 Time as a physical field τ(x) rather than a parameter 3.2 Local temporal gradients and phase evolution 3.3 Global time-phase coherence as a physical condition 3.4 Relation to hyper-time / meta-time extensions (conceptual overview) 4. Reinterpreting Decoherence as Temporal-Field Misalignment 4.1 Phase evolution in inhomogeneous temporal backgrounds 4.2 Decoherence as loss of global time-phase synchronization 4.3 Effective noise as manifestation of temporal-field fluctuations 4.4 Comparison with environmental noise models Central thesis: Decoherence reflects not fundamental randomness, but breakdown of coherent phase evolution due to temporal-field inhomogeneity. 5. Relation to Known Quantum Phenomena 5.1 Non-Markovian dynamics as temporal memory effects 5.2 1/f noise and slow temporal drift 5.3 Temporal entanglement and time-correlated errors 5.4 Distinction from collapse models and hidden variables 6. Conceptual Advantages of the Temporal-Field Interpretation 6.1.Physical substrate for phase coherence 6.2.Natural explanation of environment sensitivity 6.3.Unified language for decoherence, noise, and drift 6.4.Compatibility with standard quantum formalism 7. Testable Consequences and Falsifiable Signatures 7.1.Test 1 — Temporal Gradient Sensitivity 7.2.Test 2 — Non-Markovian Residual Structure 7.3.Test 3 — Global Synchronization Effects 8. Limitations and Open Questions 8.1.No claim of immediate technological implementation 8.2.No replacement of quantum error correction 8.3.Relation to gravity and cosmology remains theoretical 8.4.Need for independent experimental discrimination 9. Discussion 9.1.Positioning relative to mainstream decoherence theory 9.2.Relation to other time-based approaches 9.3.Why temporal ontology matters for quantum foundations 10. Conclusion 10.1.Summary of reinterpretation 10.2.Why this framework is explanatory rather than speculative 10.3. Outlook for foundational and experimental research Reference Appendix A: Dimensional and Conceptual Consistency Check
A model quantum cosmology is used to illustrate how arrows of time emerge in a universe governed by a time-neutral dynamical theory constrained by time asymmetric initial and final boundary conditions represented by initial and final density matrices. In a quantum universe universe arrows of time are described by the probabilities of appropriately coarse grained sets of histories of quantities like entropy that grow or decay. We show that the requirement of that these sets of histories decohere implies two things: (1) A time asymmetry between initial and final conditions that is a basis for arrows ot time. (2) How a final state of indifference that is represented by a final density matrix proportional to the unit density matrix is consistent with causality, and allows a finer-grained description of the model universe in terms of decoherent histories than any other final state.
The states (Schrödinger picture) and observables (Heisenberg picture) in the standard quantum theory evolve symmetrically in time, given by the unitary group with time extending over − ∞ < t < + ∞ . This time evolution is a mathematical consequence of the Hilbert space boundary condition for the dynamical differential equations. However, this unitary group evolution violates causality. Moreover, it does not solve an old puzzle of Wigner: How does one describe excited states of atoms which decay exponentially, and how is their lifetime τ related to the Lorentzian width Γ? These question can be answered if one replaces the Hilbert space boundary condition by new, Hardy space boundary conditions. These Hardy space boundary conditions allow for a distinction between states (prepared by a preparation apparatus) and observables (detected by a registration apparatus). The new Hardy space quantum theory is time asymmetric, i.e, the time evolution is given by the semigroup with t 0 ≤ t < + ∞ , which predicts a finite "beginning of time" t 0 , where t 0 is the ensemble of time at which each individual system has been prepared. The Hardy space axiom also leads to the new prediction: the width Γ and the lifetime τ are exactly related by τ = ℏ/Γ .