海南师范大学学报（自然科学版）2026，Vol.39Issue(1)：1-12,12.DOI:10.12051/j.issn.1674-4942.2026.01.001
重复可读态、自发塌缩和量子/经典界限
Repeatedly Readable State,Spontaneous Collapse,and Quantum/Classical Boundary
摘要
Abstract
This paper proposes a model to determine the quantum/classical boundary.The model introduces a spontaneous collapse of state superposition:d/dtpij=-i/ℏ[H,ρ]ij −ρij/τij.Different from other collapse models,the collapsing scaleτij here does not contain a universal parameter,but is specified by the two states|i>and|j>.If each state is in principle repeatedly readable[typically by a quantum non-demolition(QND)measurement],then τij is the needed measuring time to discriminate the two states,and the collapse occurs spontaneously without any actual monitoring.Otherwise,τij=∞,which means no collapse and everlasting superposition.This happens if one state is not repeatedly readable,or if the two states cannot possibly be discriminated in a particular circumstance(for example,in the Rabi oscillation).Detailed analysis shows that for a"trapped Schrödinger's cat",the superposition of|here>and|there>is forbidden if ED ≫ 4πℏc,and allowed if ED≤4πℏc,where D is the trap separation and E is the energy gap,which can be estimated with Mv2.For example,if D ～ 10 µm and v ～ 102 m/s,then the quantum/classical boundary is at M ～ 2×103 GeV/c2.The model also constrains a"free Schrödinger's cat"to display double-slit interference if pθd≥8ℏ,where p=Mv,θ is the angle spanned by the two trajectories,and d is the slit width.For typical values v ～ 103 m/s,θ ～ 10−5 rad,and d ～ 10 µm,the quantum/classical boundary is at M ～ 5 GeV/c2,which,impressively,is just marginal for the performed experiments with Helium.In contrast,this model sets no limit on the coherent length of massless photon,thus the arm of a Michelson interferometer can be arbitrarily long.The spontaneous collapse which we propose can occur for an isolated system,and parallels the decoherence induced by interaction with the environment.关键词
量子测量问题/自发塌缩模型/量子/经典界限/重复可读性Key words
quantum measurement problem/spontaneous collapse model/quantum/classical boundary/repeatable read-ability分类
数理科学引用本文复制引用
彭小富,罗宇航,朱江,华邦辉,陈雪楠,连丹丹,陈子维,陈相松..重复可读态、自发塌缩和量子/经典界限[J].海南师范大学学报（自然科学版）,2026,39(1):1-12,12.基金项目
国家自然科学基金项目(11535005) （11535005）
