Introduction

In the context of Bohm’s version of the EPR (Einstein-Podolsky-Rosen) experiment, two entangled electrons are prepared in a singlet state, meaning their total spin is zero. When these electrons move in opposite directions, their spins are correlated in such a way that if one electron is found to have spin-up in a certain direction, the other will have spin-down in that same direction.

Introducing Scattering Before Detection

If the electrons undergo scattering before reaching the detectors, the scenario becomes more complex. Scattering can be viewed as an interaction between the electrons and other particles or fields, which may cause several effects:

  1. Decoherence:
    • Scattering can cause decoherence, which means the quantum entanglement between the electrons could be reduced or even lost. Decoherence happens because the environment (particles or fields causing scattering) interacts with the electrons and “measures” their state in a certain sense. As a result, the electrons may no longer be in a pure entangled state but rather in a mixed state.
  2. Spin Alteration:
    • Depending on the nature of the scattering process, the spin of the electrons might change. For instance, if the scattering involves a magnetic field or a spin-dependent force, the spins could be altered before they reach the detector. The final measured spin at the detectors might then be different from what would be expected if no scattering had occurred.

Outcome at the Detectors

  • If Decoherence Occurs:
    • The correlation between the spins of the two electrons may be weakened or lost. The results at the detectors would no longer show perfect anti-correlation (as expected from a singlet state). Instead, the outcomes might resemble those of independent, unentangled particles, showing only classical correlations if any.
  • If Spin is Altered:
    • The spin measurement results would depend on how the spins were altered by the scattering process. For instance, if the scattering flips the spin of one electron, the detectors might register results that suggest different spin correlations than originally prepared.
  • No Significant Effect:
    • If the scattering process is weak or doesn’t significantly interact with the electron’s spin state, the spins at the detectors may still show the original anti-correlation expected from the entangled state.