Weinstein (2008) argued from the Popescu-Short-Winter typicality theorem and the unitary invariance of the maximally mixed state that generic subsystems of a typical global pure state of the universe remain near maximally mixed at all times, so decoherence and einselection can explain only the persistence of distinctively classical behavior for subsystems in highly atypical (low-entropy, decoherence-prone) states, not its emergence. The paper leaves open what additional physical input beyond unitary quantum dynamics and the local system-environment interaction Hamiltonian accounts for the distinctively classical behavior of macroscopic subsystems: either the actual quantum state of the universe is a highly non-generic special initial condition whose nature and origin must be characterized, or some further dynamical or cosmological principle must make the required subsystem states generic. The question is treated as unresolved across the decoherence, quantum-Darwinist, typicality, Past Hypothesis, and quantum-cosmology literature through 2026.

Background

Decoherence is the process by which a quantum system that interacts with an environment (e.g. a dust particle coupling to air molecules and photons) loses phase coherence between components of its state superposed in a basis selected by the interaction; the selected basis is called the preferred basis, and the environmentally driven selection of stable, effectively classical pointer states is called einselection (environment-induced superselection). Standard open-system models of decoherence presuppose that the system begins in a special, unentangled, low-entropy state, and then show that einselection makes its subsequent distinctively classical behavior persist. Throughout this task, the target property is this distinctively classical behavior of a macroscopic subsystem - behavior in which the subsystem occupies a stable, effectively localized, low-entropy pointer-basis state exhibiting approximately classical correlations - and it is to be distinguished from the generic, unremarkable quasiclassicality that subsystems of a typical environment retain even in the absence of dynamical decoherence (Weinstein, arXiv:0906.4544, ref 2). Weinstein (arXiv:0807.3376) asks whether this presupposition can itself be dispensed with. His technical engine is the Popescu-Short-Winter (PSW) typicality theorem (Nature Physics 2, 754 (2006)), which states that for a composite system, the reduced density matrix of a small subsystem is almost always very close to the maximally mixed state (the state of maximal entropy), with high probability over the choice of the global pure state. Weinstein combines this with the fact that the maximally mixed state of the total system is invariant under unitary evolution (the quantum analogue of Liouville's theorem for phase-space distributions in classical statistical mechanics): if the global state were generic, subsystems would stay near maximally mixed at all times, never developing the low-entropy, effectively localized states whose stability einselection is supposed to explain. Hence distinctively classical behavior of macroscopic subsystems requires the universe's initial quantum state to be highly atypical - a low-entropy condition of the same general kind as the Past Hypothesis, the proposal (Albert, Time and Chance, 2000) that the thermodynamic arrow of time is explained by a special low-entropy early condition of the universe. In the decoherent-histories approach to quantum cosmology, where a quantum universe is described by probability assignments to entire coarse-grained histories rather than to states at one time, Hartle (arXiv:0806.3776; Foundations of Physics 41, 982 (2011)) has spelled out what the initial state must supply for a quasiclassical realm - an ensemble of decohering histories that exhibit approximately classical correlation - including low total entropy, locally low entropy for a homogeneous arrow of time, and an effectively classical spacetime geometry. The residual question sits at the junction of decoherence theory, the foundations of statistical mechanics, and quantum cosmology: is the needed special initial condition a primitive fact (a boundary condition or law), a consequence of a theory of the universe's quantum state such as the no-boundary proposal (the Hartle-Hawking idea that the universe's quantum state is fixed by a path integral over compact geometries with no initial boundary), or replaceable by some as-yet-unidentified principle that makes classicality generic?

Problem Statement

What additional physical input, beyond unitary quantum dynamics and the local system-environment interaction Hamiltonian, is required to account for the distinctively classical behavior of macroscopic subsystems? An answer must do one of the following. (1) Identify and characterize the highly non-generic initial condition of the universe's quantum state on which einselection-based accounts of classicality depend: specify which of its properties (e.g. low total entropy, locally low entropy, decoherence of quasiclassical histories) account for the distinctively classical behavior of macroscopic subsystems, and establish that condition's origin and physical status - primitive boundary condition, fundamental law, or consequence of a theory of the universe's quantum state such as a no-boundary-type proposal. (2) Identify and establish an alternative dynamical or cosmological principle (for example one tied to the thermodynamic arrow of time) that makes the required low-entropy, decoherence-prone subsystem states generic rather than special. (3) Refute the underlying necessity argument by showing that the PSW-typicality-plus-unitary-invariance reasoning does not in fact entail that generic initial states fail to yield distinctively classical macroscopic subsystems. Weinstein's original formulation leaves all three routes open; the problem is solved when one of them is carried through in full.

References

  1. Steven Weinstein, Decoherence and the (non)emergence of classicality (2008), arXiv:0807.3376, DOI 10.48550/arXiv.0807.3376, https://arxiv.org/abs/0807.3376
  2. Steven Weinstein, Decoherence without decoherence (2009), arXiv:0906.4544, DOI 10.48550/arXiv.0906.4544, https://arxiv.org/abs/0906.4544
  3. James B. Hartle, The Quasiclassical Realms of This Quantum Universe, Foundations of Physics 41 (2011), DOI 10.1007/s10701-010-9460-0, arXiv:0806.3776, https://arxiv.org/abs/0806.3776
  4. Sandu Popescu, Anthony J. Short, Andreas Winter, Entanglement and the foundations of statistical mechanics, Nature Physics 2 (2006), DOI 10.1038/nphys444, https://doi.org/10.1038/nphys444
  5. S. Goldstein, J. L. Lebowitz, R. Tumulka, N. Zanghì, Long-time behavior of macroscopic quantum systems, The European Physical Journal H 35 (2010), DOI 10.1140/epjh/e2010-00007-7, https://doi.org/10.1140/epjh/e2010-00007-7
  6. Wojciech Hubert Zurek, Quantum Darwinism, Nature Physics 5 (2009), DOI 10.1038/nphys1202, https://doi.org/10.1038/nphys1202
  7. David Z. Albert, Time and Chance, Harvard University Press (2000), DOI 10.4159/9780674020139, https://doi.org/10.4159/9780674020139
  8. John Earman, The 'Past Hypothesis': Not even false, Studies in History and Philosophy of Modern Physics 37 (2006), DOI 10.1016/j.shpsb.2006.03.002, https://doi.org/10.1016/j.shpsb.2006.03.002
  9. David Wallace, The Nature of the Past Hypothesis, in The Philosophy of Cosmology, Cambridge University Press (2017), DOI 10.1017/9781316535783.025, https://doi.org/10.1017/9781316535783.025
  10. Eddy Keming Chen, The Past Hypothesis and the Nature of Physical Laws, in The Probability Map of the Universe, Harvard University Press (2023), DOI 10.4159/9780674287716-008, https://doi.org/10.4159/9780674287716-008
  11. Sean M. Carroll, Jennifer Chen, Spontaneous Inflation and the Origin of the Arrow of Time (2004), arXiv:hep-th/0410270, DOI 10.48550/arXiv.hep-th/0410270, https://arxiv.org/abs/hep-th/0410270