We propose a dynamical model for state symmetrization of two identical particles produced in spacelike-separated events by independent sources. We adopt the hypothesis that the pair of non-interacting particles can initially be described by a tensor product state since they are in principle distinguishable due to their spacelike separation. As the particles approach each other, a quantum jump takes place upon particle collision, which erases their distinguishability and projects the two-particle state onto an appropriately (anti-)symmetrized state. The probability density of the collision times can be estimated quasi-classically using the Wigner functions of the particles’ wavepackets, or derived from fully quantum mechanical considerations using an appropriately adapted time-of-arrival operator. Moreover, the state symmetrization can be formally regarded as a consequence of the spontaneous measurement of the collision time. We show that symmetric measurements performed on identical particles can in principle discriminate between the product and symmetrized states. Our model and its conclusions can be tested experimentally.

我们提出了一个动力学模型，用于由独立来源在空间分​​离事件中产生的两个相同粒子的状态对称。我们采用这样的假设：成对的非相互作用粒子最初可以用张量积状态来描述，因为它们由于空间上的分离而在原则上是可区分的。随着粒子彼此接近，粒子碰撞时会发生量子跃迁，这会消除它们的可区分性，并将两个粒子的状态投射到适当的（反）对称状态上。可以使用粒子波包的Wigner函数近似经典地估计碰撞时间的概率密度，或者使用适当的到达时间算符从完全量子力学考虑中得出碰撞时间的概率密度。而且，状态对称化可以被正式认为是自发测量碰撞时间的结果。我们表明，对相同粒子执行的对称测量原则上可以区分乘积状态和对称状态。我们的模型及其结论可以通过实验进行检验。