Formation and lifetime of objective classical records
For a specified system–environment dynamics and fragment-access model, bound the formation time, redundancy, disturbance and lifetime of independently accessible classical records, using an explicit objectivity criterion.
Problem statement
For a specified system–environment dynamics and fragment-access model, bound the formation time, redundancy, disturbance and lifetime of independently accessible classical records, using an explicit objectivity criterion.
Lean 4
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Background
Why does the macroscopic world look classical — with definite, stable, publicly agreed facts — if the underlying dynamics is unitary and superposition-generating? The task is to derive, quantitatively, the emergence of a preferred (pointer) basis, the stability of records, and the effectively Boolean logic of everyday events.
What is known: Decoherence theory (Zurek, Joos–Zeh) explains a great deal: environmental monitoring rapidly suppresses interference between pointer states and selects a robust pointer basis via the predictability sieve, on extremely short timescales. Quantum Darwinism (Zurek) adds that classical objectivity arises because information about pointer states is redundantly imprinted on many environment fragments, so many observers independently access the same facts; this redundancy has been quantified (mutual-information plateaus) and observed in models and experiments. Consistent/decoherent histories (Griffiths, Gell-Mann–Hartle) formalize when families of coarse-grained histories obey classical probability.
A mutual-information plateau by itself need not establish that independent observers can read the same classical record without disturbance. Strong quantum Darwinism and spectrum-broadcast structure give more discriminating criteria; Le–Olaya-Castro establish an equivalence under the additional strong-independence condition.
The open dynamical task is quantitative formation, stability and degradation of such records in specified interacting environments and at finite fragment access, including approximate rather than exact objectivity. Outcome selection is the distinct interpretational task in F1 and is not part of this entry's success criterion. Related: F1, F4, F6.
Progress & source assessment
Source catalogue review: 4 September 2026. Improved indicates partial progress, including qualified preprint claims.
- [1]Zurek, 'Decoherence, einselection, and the quantum origins of the classical', Rev. Mod. Phys. 75, 715 (2003) link
- [2]Zurek, 'Quantum Darwinism', Nat. Phys. 5, 181 (2009) link
- [3]Le & Olaya-Castro, 'Strong Quantum Darwinism and Strong Independence are Equivalent to Spectrum Broadcast Structure', PRL 122, 010403 (2019) link
Recorded progress
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