论文标题
反复可读的状态,自发崩溃和量子/经典边界
Repeatedly readable state, spontaneous collapse, and quantum/classical boundary
论文作者
论文摘要
我们提出了一个模型来识别量子/经典边界。该模型引入了状态叠加的自发崩溃:$ \ frac {d} {dt}ρ_{ij} = - \ frac {i} {i} {\ hbar} [h,ρ] _ {ij} _ {ij} -p_} -p_} - ρ_{ij} {ij}/τ_{与其他崩溃模型不同,折叠比例$τ_{ij} $此处不包含通用参数,而是由两个状态$ |指定的。我\ rangle $和$ | j \ rangle $:如果每个状态在原则上是{\ em},则可以反复读取(通常是通过QND测量),则$τ_{ij} $是{\ em潜在的}所需的时间来区分这两个状态,并且崩溃发生自发{\ em em vishice {\ em notical Moniture}任何实际的实际监控。否则,$τ_{ij} = \ infty $,这意味着不会崩溃和永恒的叠加。如果一个状态不可重复阅读,或者在特定情况下可能无法区分两个状态(例如,在Rabi振荡中),则会发生这种情况。详细分析表明,对于“被困的schr {Ö} dinger的猫”,$ | {\ rm的叠加} \ rangle $和$ | {\ rm and} \ rangle $如果$ e d \ gg4π\ hbar c $,则允许,如果$ e d \ le4π\ hbar c $,其中$ d $是陷阱分离,而$ e $是$ e $,则可以用$ m v^2 $估计。该模型还限制了“自由schr {Ö} dinger的猫”,以显示双缝干扰,如果$pθd\ ge 8 \ hbar $,其中$ p = mv $,$θ$是两个轨迹所跨越的角度,而$ d $是缝隙分离。相反,该模型对无质量光子的一致长度没有限制,因此米歇尔森干涉仪的臂可以任意长。我们提出的自发崩溃可能会发生在一个孤立的系统中,并与与环境相互作用引起的脱碳相似。
We propose a model to identify the quantum/classical boundary. The model introduces a spontaneous collapse of state superposition: $\frac{d}{dt} ρ_{ij} =-\frac{i}{\hbar}[H,ρ]_{ij}-ρ_{ij}/τ_{ij}$. Different from other collapse models, the collapsing scale $τ_{ij}$ here does not contain a universal parameter, but is specified by the two states $| i\rangle $ and $ | j\rangle$: If each state is {\em in principle} repeatedly readable (typically by a QND measurement), then $τ_{ij}$ is the {\em potentially} needed measuring time to discriminate the two states, and the collapse occurs spontaneously {\em without} any actual monitoring. Otherwise, $τ_{ij}=\infty$, 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 Schr{ö}dinger's cat", the superposition of $|{\rm here} \rangle$ and $| {\rm there} \rangle $ is forbidden if $E D \gg 4π\hbar c$, and allowed if $E D \le 4π\hbar c$, where $D$ is the trap separation and $ E$ is the energy gap, which can be estimated with $ M v^2$. The model also constrains a "free Schr{ö}dinger's cat" to display double-slit interference if $pθD\ge 8\hbar$, where $p= Mv$, $θ$ is the angle spanned by the two trajectories, and $D$ is the slit separation. 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 environment.